Month: February 2025

Gate voltages and DC currents are applied, and amplified voltages recorded, with a home built data acquisition system based on AD5760 and AD7734 chips.In crystalline solids, orbital magnetization arises from the Berry curvature of the bands and intrinsic angular momentum of the Bloch electron wave packet. Although the orbital magnetization often contributes—at times substantially—to the net magnetization of ferromagnets, all knownν = An corresponds to the number of electrons per unit cell area A with n the carrier density.In an intrinsic orbital magnet in which all moments arise from conduction electrons, the magnetization depends strongly on the density. Additional density dependence arises from the fact that contributions to the orbital magnetization from both wave-packet angular momentum and Berry curvature need not be uniformly distributed within the Brillouin zone[84]. Transport observations of aquantum anomalous Hall effect measure only the total Berry curvature of a completely filled band. At partial band filling, however, extrinsic contributions from scattering complicate the relationship between transport and band properties. In contrast, measuring m provides direct information about the density-dependent occupation of the Bloch states in momentum space.Although crystalline defects on the atomic scale are unlikely in tBLG thanks to the high quality of the constituent graphene and hBN layers, the thermodynamic instability of magic angle twisted bilayer graphene makes it highly susceptible to inhomogeneity at scales larger than the moir´e period, hydroponic nft as shown in prior spatially resolved studies. For example, the twist angle between the layers as well as their registry to the underlying hBN substrate may all vary spatially, providing potential pinning sites.

Moir´e disorder may thus be analogous to crystalline disorder in conventional ferromagnets, which gives rise to Barkhausen noise as it was originally described. A subtler issue raised by our data is the density dependence of magnetic pinning; as shown in Fig. 5.3, Bc does not simply track 1/m across the entire density range, in particular failing to collapse with the rise in m in the Chern magnet gap. This suggests nontrivial dependence of either the pinning potential or the magnetocrystalline anisotropy energy on the realized many body state. Understanding the pinning dynamics is critical for stabilizing magnetism in tBLG and the growing class of related orbital magnets, which includes both moir´e systems as well as more traditional crystalline systems such as rhombohedral graphite. In order to understand the microscopic mechanism behind magnetic grain boundaries in the Chern magnet phase in tBLG/hBN, we used nanoSQUID magnetometry to map the local moir´e superlattice unit cell area, and thus the local twist angle, in this device, using techniques discussed in the literature. This technique involves applying a large magnetic field to the tBLG/hBN device and then using the chiral edge state magnetization of the Landau levels produced by the gap between the moir´e band and the dispersive bands to extract the electron density at which full filling of the moir´e superlattice band occurs . The strength of this Landau level’s magnetization can be mapped in real space , and the density at which maximum magnetization occurs can be processed into a local twist angle as a function of position .

It was noted in that the moir´e superlattice twist angle distribution in tBLG is characterized by slow long length scale variations interspersed with thin wrinkles, across which the local twist angle changes rapidly. These are also present in the sample imaged here . The magnetic grain boundaries we extracted by observing the domain dynamics of the Chern magnet appear to correspond to a subset of these moir´e superlattice wrinkles. It may thus be the case that these wrinkles serve a function in moir´e superlattice magnetism analogous to that of crystalline grain boundaries in more traditional transition metal magnets, pinning magnetic domain walls to structural disorder and producing Barkhausen noise in measurements of macroscopic properties.There is another way to make a moir´e superlattice. Two different 2D crystals with different lattice constants will form a moir´e superlattice without a relative twist angle; these systems are known as heterobilayers . These systems do not have ‘magic angles’ in the same sense that tBLG and tMBG do, and as a result there is no meaningful sense in which they are flat band systems, but interactions are so strong that they form interaction-driven phases at commensurate filling of the moir´e superlattice anyway. Indeed, many of the interaction-driven insulators these systems support survive to temperatures well above 100 K. The most important way in which heterobilayers differ from homobilayers, however, is in their insensitivity to twist angle disorder. In the small angle regime, the moir´e unit cell area of a heterobilayer is almost completely independent of twist angle, as illustrated in 5.17E-F.

A new intrinsic Chern magnet was discovered in one of these systems, a heterobilayer moir´e superlattice formed through alignment of MoTe2 and WSe2 monolayers. The researchers who discovered this phase measured a well-quantized QAH effect in electronic transport in several devices, demonstrating much better repeatability than was observed in tBLG. The unit cell area as a function of twist angle is plotted for three moir´e superlattices that support Chern insulators in 5.17G, with the magic angle regime highlighted for the homobilayers, demonstrating greatly diminished sensitivity of unit cell area to local twist angle in the heterobilayer AB-MoTe2/WSe2. MoTe2/WSe2 does have its own sources of disorder, but it is now clear that the insensitivity of this system to twist angle disorder has solved the replication issue for Chern magnets in moir´e superlattices. Dozens of MoTe2/WSe2 devices showing well-quantized QAH effects have now been fabricated, and these devices are all considerably larger and more uniform than the singular tBLG device that was shown to support a QAH effect, and was discussed in the previous chapters. The existence of reliable, high-yield fabrication processes for repeatably realizing uniform intrinsic Chern magnets is an important development, and this has opened the door to a wide variety of devices and measurements that would not have been feasible in tBLG/hBN.The basic physics of this electronic phase differs markedly from the systems we have so far discussed, and we will start our discussion of MoTe2/WSe2 by comparing and contrasting it with graphene moir´e superlattices. In tBLG/hBN and its cousins, valley and spin degeneracy and the absence of significant spin-orbit coupling combine to make the moir´e subbands fourfold degenerate. When inversion symmetry is broken the resulting valley subbands can have finite Chern numbers, so that when the system forms a valley ferromagnet a Chern magnet naturally appears. Spin order may be present but is not necessary to realize the Chern magnet; it need not have any meaningful relationship with the valley order, since spin-orbit coupling is absent. MoTe2/WSe2 has strong spin-orbit coupling, and as a result, the spin order is locked to the valley degree of freedom. This manifests most obviously as a reduction of the degeneracy of the moir´e subbands; these are twofold degenerate in MoTe2/WSe2 and all other TMD-based moir´e superlattices. The closest imaginable analog of the tBLG/hBN Chern magnet in this system is one in which interactions favor the formation of a valley-polarized ferromagnet, hydroponic channel at which point the finite Chern number of the valley subbands would produce a Chern magnet. There is now substantial evidence that this system instead forms a valley coherent state stabilized by its spin order, which would require a new mechanism for generating the Berry curvature necessary to produce a Chern magnet. In general I think it is fair to say that the details of the microscopic mechanism responsible for producing the Chern magnet in this system are not yet well understood. In light of the differences between these two systems, there was no particular reason to expect the same phenomena in MoTe2/WSe2 as in tBLG/hBN. As will shortly be explained, current-switching of the magnetic order was indeed found in MoTe2/WSe2. The fact that we find current-switching of magnetic order in both the tBLG/hBN Chern magnet and the AB-MoTe2/WSe2 Chern magnet is interesting. It may suggest that the phenomenon is a simple consequence of the presence of a finite Chern number; i.e., that it is a consequence of a local torque exerted by the spin/valley Hall effect,which is itself a simple consequence of the spin Hall effect and finite Berry curvature.

These ideas will be discussed in the following sections.In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a nonmagnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin-orbit torque. Here, we demonstrate a spin-orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moir´e superlattice site. We observe hysteretic switching of the resistivity as a function of applied current. Magnetic imaging reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns with spin accumulation measured near the high Berry curvature Hubbard band edges. This suggests that intrinsic spin or valley Hall torques drive the observed current-driven magnetic switching in both MoTe2/WSe2 and other moir´e materials. The switching current density is significantly less than those reported in other platforms, suggesting moir´e heterostructures are a suitable platform for efficient control of magnetic order. To support a magnetic Chern insulator and thus exhibit a quantized anomalous Hall effect, a two dimensional electron system must host both spontaneously broken time-reversal symmetry and bands with finite Chern numbers. This makes Chern magnets ideal substrates upon which to engineer low-current magnetic switches, because the same Berry curvature responsible for the finite Chern number also produces spin or valley Hall effects that may be used to effect magnetic switching. Recently, moir´e heterostructures emerged as a versatile platform for realizing intrinsic Chern magnets. In these systems, two layers with mismatched lattices are combined, producing a long-wavelength moir´e pattern that reconstructs the single particle band structure within a reduced superlattice Brillouin zone. In certain cases, moir´e heterostructures host superlattice minibands with narrow bandwidth, placing them in a strongly interacting regime whereCoulomb repulsion may lead to one or more broken symmetries. In several such systems, the underlying bands have finite Chern numbers, setting the stage for the appearance of anomalous Hall effects when combined with time-reversal symmetry breaking. Notably, in twisted bilayer graphene low current magnetic switching has been observed, though consensus does not exist on the underlying mechanism.We emphasize that in both twisted bilayer graphene and our current MoTe2/WSe2 heterostructure, magnetic switching arises in regimes for which doping, elevated temperature, or disorder ensure that electrical current flows in the sample bulk. Ultra-low current switching of magnetic order has also been observed in twisted bilayer graphene. In that system, where spin orbit coupling is negligible, nearly identical mechanisms may arise mediated by orbital, rather than spin, Hall effects. The bulk nature of the spin Hall torque mechanism means that similar phenomena should manifest not only in the growing class of intrinsic Chern magnets, but in all metals combining strong Berry curvature and broken time-reversal symmetry, including crystalline graphite multilayers. Research into charge-to-spin current transduction has identified a set of specific issues restricting the efficiency of spin torque switching of magnetic order. Spin current is not necessarily conserved, and as a result a wide variety of spin current sinks exist within typical spin torque devices. Extensive evidence indicates that in many spin torque systems a significant fraction of the spin current is destroyed or reflected at the spin-orbit material/magnet boundary. In addition, the transition metals used as magnetic bits in traditional spin-orbit torque devices are electrically quite conductive, and can thus shunt current around the spin-orbit material, preventing it from generating spin current. These issues are entirely circumvented here through the use of a material that combines a spin Hall effect with magnetism, and as a result of these effects this spin Hall torque device has better current-switching efficiency than any known spin torque device.We do not know the precise origin of these holes, but there are a few possibilities that we can discuss. Bubbles are some of the most common defects in stacks of two dimensional crystals, and they can form between any two layers of a stack.

Many magnetometers are sensitive to magnetic flux, not field, so very high magnetic field sensitivities are achievable by simply sampling a large region, but of course that is not a useful option when imaging microscopic magnetic systems. Suffice to say that nanoSQUID sensors, which had been invented in 2010 and integrated into a scanning probe microscope by their inventors by 2012, combine high spatial resolution with very high magnetic field sensitivity. This combination of performance metrics was and remains unique in its ability to probe the minute magnetic fields associated with gate-tunable electronic phenomena at the length scales demanded by the size of the devices. Gate-tunable phenomena in exfoliated heterostructures and nanoSQUID microscopy were uniquely well-matched to each other, and although at the time I started my graduate research only a small handful of gate-tunable magnetic phenomena had so far been discovered in exfoliated two dimensional crystals, nanoSQUID microscopy seemed like the perfect tool for investigating them.So what exactly is nanoSQUID microscopy? We can start by discussing Superconducting Quantum Interference Devices, or SQUIDs. In summary, SQUIDs are electronic devices with properties that strongly depend on the magnetic field to which they are exposed, which makes them useful as magnetometers. I won’t delve into the details of how and why SQUIDs work here, growing lettuce hydroponically but I will explain briefly how SQUIDs are made, since that will be necessary for understanding how nanoSQUID imaging differs from other SQUID-based imaging technologies.

A SQUID is a pair of superconducting wires in parallel, each with a thin barrier in series . The electronic transport properties of this device depend strongly on the magnetic flux through the region between the wires, i.e. inside the hole in the center of the device in Fig. 1.3. To be a little bit more precise, superconductors transport current without dissipation, so long as the current density stays below a sharp threshold. When this threshold is exceeded, the superconductor reverts to dissipative transport, like a normal metal. Above this critical current, in the so-called ‘voltage state,’ electronic transport is dissipative and highly sensitive to B. Any non-superconductor can function as a barrier, including insulators, metals, and superconducting regions thinner than the coherence length.This makes SQUIDs excellent magnetic field sensors, with the caveat that they do not sample the magnetic field at a point, but averaged over a region A. Making a SQUID is as easy as depositing a superconducting material onto a surface in the correct shape, and it can be done using many of the same techniques used to produce other microscopic electronic devices, like photolithography and thermal evaporation. This is sufficient for many applications, but it presents some issues for producing sensors for scanning probe microscopy. Scanning probe microscopy is a technique through which any sensor can be used to generate images; we simply move the sensor to every point in a grid, perform a measurement, and use those measurements to populate the pixels of a two dimensional array . This can of course be done with a SQUID, and many researchers have used SQUIDs fabricatedthis way to great effect. But the spatial resolution of a scanning SQUID magnetometry microscope is set by the size of the SQUID, and there are limits to how small SQUIDs can be fabricated using photolithography.

It is also challenging to fashion these SQUIDs into probes that can be safely brought close to a surface for scanning; photolithography produces SQUIDs on large, flat silicon substrates, and these must subsequently be cut out and ground down into a sharp cantilever with the SQUID on the apex in order to get the SQUID close enough to a surface for microscopy. In summary, the ideal SQUID sensor for microscopy would be one that was smaller than could be achieved using traditional photolithography and located precisely on the apex of a sharp needle to facilitate scanning. As is so often the case when developing new technologies, we have to make the best of the tools other clever people have already developed. In the case of nanoSQUID microscopy, the inventors of the technique took advantage of a lot of legwork done by biologists. Long ago, glass blowers found that hollow glass tubes could be heated close to their melting point and drawn out into long cones without crushing their hollow interiors. Chemists used this fact to make pipettes for manipulating small volumes of liquid, and biologists later used the techniques they developed to fashion microscopic hypodermic needles that could be used to inject chemicals into and monitor the chemical environment inside individual cells in a process called patch-clamping. A rich array of tools exist for producing these structures, called micropipettes, for chemists and biologists. Eli Zeldov noticed that these structures already had the perfect geometry to serve as substrates for tiny SQUIDs. By depositing superconducting materials onto these substrates from a few different directions, one can produce superconducting contacts and a tiny torus of superconductor on the apex of the micropipette. The same group of researchers successfully integrated these sensors into a scanning probe microscope at cryogenic temperatures.

The sizes of these SQUIDs are limited only by how small a micropipette can be made, and since the invention of the technique SQUIDs as small as 30 nm have been realized. We call these sensors nanoSQUIDs, or nanoSQUID-on-tip sensors. A few representative examples of nanoSQUID sensors are shown in Fig. 1.4. A characterization of the electronic transport properties of such a sensor, and in particular the sensor’s response to an applied magnetic field, is shown in Fig. 1.5. NanoSQUID microscopes share many of the core competencies of more traditional, planar scan-ning SQUID microscopes. They dissipate little power, and the measurements they generate are quantitative and can be easily calibrated by measuring the period of the SQUID’s electronic response to an applied magnetic field. Measuring a magnetic field with a SQUID does not require optical access; many other magnetic field measurement techniques do. Together, these facts mean that scanning SQUIDs are often the best tools available for probing extremely low temperature phenomena. NanoSQUID sensors also have many advantages over planar SQUIDs. The most obvious, of course, has already been discussed, and that is their higher spatial resolution. A less obvious advantage- indeed, an advantage that became clear only after the first nanoSQUID sensors were fabricated and tested- is the geometry of the thin superconducting contacts, which under normal circumstances are aligned with the axis of the applied magnetic field. Large magnetic fields tend to destroy superconducting phases, so superconducting devices are all limited by the maximum magnetic fields at which they can operate. This so-called critical field HC is not an intensive property; there is a large-size limit that can be measured and tabulated for different materials, but the critical field of an individual piece of superconductor is a strong function of geometry. A thin superconducting film in the plane of an applied magnetic field can accommodate much higher magnetic field magnitudes than can be accomodated by a large piece of the same superconductor. The bulk limit for lead at low temperature is about 80 mT; we routinely make lead nanoSQUIDs that can survive magnetic fields of 1 T, and we have on occasion made nanoSQUIDs that can survive magnetic fields above 2 T. It turns out that many of the most useful magnetic imaging techniques are limited to low field operation. This thesis will focus primarily on low field phenomena, but there are also many magnetic phenomena that require high magnetic fields to appear, including the quantum Hall effect and a variety of magnetic phase transitions. The nanoSQUID technique is useful for studying these as well.It remains true that superconducting materials with higher bulk critical fields tend to produce nanoSQUIDs with higher critical fields, growing hydroponically so we must choose the material with which we fabricate nanoSQUID sensors carefully for each application. Characterizations of nanoSQUIDs fabricated from both lead and indium are shown in Fig. 1.6. In the bulk limit, indium has a critical field of HC = 0.03 T. A characterization of electronic transport through an indium nanoSQUID is presented in Fig. 1.6A. Periodic oscillations in the critical current are visible; in this regime, thenanoSQUID is useful as a sensor of local magnetic field. Above about 0.2 T, superconductivity begins to rapidly degrade in the nanoSQUID sensor, destroying the sensitivity of the sensor and rendering it useless as a sensor of magnetic field. This limits this particular nanoSQUID to operation in the regime −0.2T < B < 0.2T. This is fairly general to indium nanoSQUIDs; their precise critical fields vary, but are generally considerably below those of lead nanoSQUID sensors. As with any sensor, measurements with nanoSQUIDs are contaminated with noise, and the dependence of that noise on SQUID bias and magnetic field can be characterized.

A characterization of the noise spectrum of the indium nanoSQUID shown in Fig. 1.6A is shown in Fig. 1.6B. In nanoSQUID sensors, local maxima in critical current are often associated with high noise and thus low magnetic field sensitivity . This produces ‘blind spots’ in magnetic field for nanoSQUID sensors. These blind spots often in practice include B = 0, making true zero-field operation challenging for nanoSQUID sensors. Technologies exist for circumventing this issue, but in practice we mostly work around it. The low magnetic field DC response of a lead nanoSQUID is shown in Fig. 1.6C. A higher magnetic field characterization is shown in Fig. 1.6D, illustrating the collapse of superconductivity in this nanoSQUID at a considerably higher magnetic field of about 0.75 T. The inventor of the technique has been active in developing ways to deposit other materials onto micropipettes for use as nanoSQUID sensors, and has succeeded in producing aluminum, niobium, tin, and alloyed molybdenum/rhenium nanoSQUIDs, in addition of course to indium and lead nanoSQUIDs. The MoRe nanoSQUIDs in particular are capable of operating in extremely large ambient magnetic fields, up to about 5T [6]. The magnetic field noise floor of nanoSQUID sensors seems to vary for different materials as well. We do not have a strong model explaining why this is the case, but it is empirically true that indium and lead nanoSQUIDs have particularly low noise floors. Plots illustrating the dependence on magnetic field of the magnetic field sensitivity of a lead nanoSQUID sensor 80 nm in diamater are shown in Fig. 1.7. NanoSQUID sensors have some unique disadvantages as well. Like planar SQUIDs, nanoSQUIDs require superconductivity to function, which limits them to fairly low operating temperatures. In planar SQUIDs it is often possible to keep the SQUID itself cold while scanning over a much hotter sample, but nanoSQUID sensors are extremely poorly thermalized to their scan heads, which meansthat they generally are thermalized either to the surface over which they are scanning or to the black body spectrum of the vessel in which they are contained . This gives nanoSQUID sensors some interesting capabilities, namely that under the right conditions they can function as extremely sensitive scanning probe thermometers, but it also comes with some drawbacks. NanoSQUIDs composed of superconductors with critical temperatures below 4.2 K, the boiling point of helium-4 at atmospheric pressure, must thus have actively cooled thermal radiation shields to operate in very high vacuum, and of course imaging of hot samples is completely out of the question for these sensors. A variety of exciting opportunities exist for the application of sensitive magnetic imaging techniques to biological systems, and this is not a realistic option for nanoSQUID sensors. NanoSQUIDs are quite fragile and can be easily destroyed by vibrations, necessitating vibration isolation systems, and the superconducting film on the apex of the micropipette is quite thin, typically between 15 and 20 nm, so superconducting materials that oxidize in air will be quickly degraded. Thankfully indium and lead do not oxidize rapidly, but they do oxidize at a finite rate, so nanoSQUIDs composed of these materials only last for a few days when left in air. Storage in high vacuum can improve their lifespan, but generally not indefinitely. In summary, scanning probe microscopes fitted with nanoSQUID sensors can function as magnetometry microscopes with 30-250 nm resolution. Their high sensitivities allow them to detect the minute magnetic fields emitted by electronic phases composed entirely of electrons forced into a two dimensional heterostructure with an electrostatic gate. We will discuss some of the properties of two dimensional heterostructures next.

A glance at figure 12 suggests that there are two generalized groups of ant predators on the berry borer: the big ants and the small ants . So we can think of it as a two-predator, one-prey system. But there is an obvious indirect effect because the bigger ants negatively affect the ability of the smaller ants to be predators, as was discussed above. Depending on nest densities, it would seem that because the smaller ants prey on all three life stages of the borer and throughout the year for those that forage in infected berries on the ground, they might, in the end, be more efficient predators than the larger ants. Furthermore, the larger ants have an indirect trait-mediated effect on the smaller ants, reducing their effectiveness. One might argue that it is the existence of the smaller ants that potentially regulates the borers over the long run. Unpublished evidence even supports the idea that the berry borer actually seeks areas that are under protection from the ants, supporting the speculation of Gonthier and colleagues that the berry borer gains protection from smaller predators by preferring to attack berries under the protection of larger ants. This basic speculation was put to an unintended test in 2012. Because of a major outbreak of the coffee rust disease , the coffee landscape where we work was heavily sprayed with a combination of calcium carbonate and copper sulfate, a permitted activity for organic agriculture. In figure 13, round plant pot we show the distribution of P. synanthropica as a heat map based on how many tuna fish baits placed in coffee bushes had swarms of P. synanthropica after about 30 minutes.

It is clear that in a single year, a population of thousands of nests of P. synanthropica simply disappeared. Surveys in subsequent years indicated that the smaller ants in the system began to recuperate from the reduced state they had been in, apparently because of the indirect effects of P. synanthropica . Those small ants that attack the borer within the seed, both on the tree and on the ground, especially increased over the next few years. In figure 14, we show the distribution of several of the species in a 50 × 50 meter subplot within the 45-hectare plot. Note how, during the years 2009–2012, the distribution of P. synanthropica remained relatively constant, perhaps slowly increasing in its area of dominance, at the expense of P. protensa on the ground and S. picea arboreally. Then, after the collapse of P. synanthropica between 2012 and 2013, both of those smaller species began to move into the area previously dominated by P. synanthropica. If the above speculations about how the ant community affects the borer are true, we might expect that the elimination of one of the borer’s predators would result in better overall control of the berry borer. In surveys of the berry borer in 2005 and then repeated in approximately the same area in 2018, the attack rate of the borer went from an average of about 15% of berries infected with borers to less than 1%. Insect populations are notoriously variable and respond to many cues in the environment by increasing and decreasing population numbers, frequently in unpredictable ways. Therefore, although this dramatic decline in borer numbers cannot bedirectly linked to the change in the ant community structure, it is nevertheless worth noting that the underlying narrative of how that community functions as a system of biological control concords perfectly with the changes observed.In the early 1980s, a specter haunted the coffee growing regions of Central America.

The infamous coffee rust disease had arrived in Brazil, and its eventual spread all the way to Mexico was expected, causing extreme worry among farmers and technical advisors. This worry was certainly justified on the basis of the history of the coffee rust disease in Asia . Great Britain’s expansion in what was then called Ceylon was qualitatively distinct from many of its previous imperial adventures. Planting what was effectively a monoculture of coffee, along with a great deal of infrastructure for the time, it was a remarkable centrally planned agricultural development plan. However, the plan effectively created ideal conditions for any disease that could get a foothold, with its virtually shadeless monoculture and networks of roads and railroads that could help distribute the fungal spores widely. When the disease arrived, it took hold and spread throughout the entire island, eventually causing a complete loss of coffee production . However, the rust scare of the 1980s Mesoamerica turned out to be a bit of a false alarm, at least until 2012. Before that year, the rust was always an irksome constraint on production, but the complete devastation that had been feared when it was discovered in the early 1980s never came to pass; it was a problem, to be sure, but not one to get overly agitated about. But then, without much warning, there was an explosion of coffee rust in the 2012–2013 cycle. Countries in the zone declared emergencies as one of their main sources of income seemed to be threatened with severe disruption. Local governments throughout the affected area provided emergency support to coffee producers and both the United Kingdom and the United States came up with significant international aid, specifically for what rapidly came to be called the most devastating emergency in the history of coffee production throughout the region . There are two ecological questions associated with this episode. First, why did the disease not become rampant for approximately 30 years after its introduction, and, second, what caused the very sudden explosion? Although the answers to either of these questions remain enigmatic, using tools from complexity science provides us with some ideas.

The relevant biology of the rust disease is well known. A windblown spore adheres to the undersurface of a leaf and encounters a small amount of moisture, causing germination directly into a stoma. The mycelia grow intercellularly and produce haustoria, which penetrate into the plant cell and absorb nutrients, effectively killing the cell. As the fungus grows within the leaf tissue it eventually forms uridia that contain new spores, exiting the leaf from other stomata, causing the characteristic yellow spots on the undersurface of the leaves . The transmission dynamics of the disease are dual , with some close plant-to-plant dispersion of spores , especially when plants are close enough to touch one another, along with propagule rain from the general spore load that exists in the atmosphere, especially in areas of high concentration of coffee production, when that coffee is attacked by the rust. From the perspective of an individual coffee plant, there are two sources of rust spores: its local neighbors and the general accumulation of spores in its region—that is, from the overall spore load in the atmosphere. But it is also the case that this coffee plant and all others over a very large region contribute to the spores in the overall spore rain from the atmosphere. Coffee plants generally both receive spores from the general spore pool and contribute to that pool. Given this narrative, it is easy to imagine a situation in which a generally traditional shade coffee landscape would receive a particular rate of spore rain each year and would contribute a bit to the general pool, but because the shade trees act as windbreaks, much of the spore load is never delivered to the coffee plants. One could imagine an equilibrium in which the rust disease would be endemic but not severe, partly because the wind-borne spores have limited access to the coffee trees, round garden pot meaning that the increment of spore load in the general atmosphere would be limited. Focusing on the large landscape level, if the abundance of spores in the atmosphere is low, it is likely that the incidence of the disease will also be low. But each epidemic will increase the spore density in the atmosphere. The probability that a given farm will become epidemic is a function of both the spore density in the atmosphere and the dispersion rate from the atmosphere to the farm. Changing focus to the local level, the rate of spread of spores from coffee bush to coffee bush on an average individual farm will partially determine whether the rust within that farm will become epidemic. From the point of view of an individual coffee bush, the danger of being infected by a spore comes from two sources: the atmosphere and neighboring infected plants—a regional source and a local source. Imagine that a forested ecosystem is gradually deforested of both shade trees in the coffee farms and the trees in the natural forest around them, and ask what proportion of the farms could be susceptible to an epidemic of coffee rust? According to a simple model that incorporates both regional and local dispersal , the initial deforestation will generate an increase in the number of farms experiencing an epidemic. That increase is likely to be slow and steady at first, but there will be a specific point at which a critical transition will occur and a large number of farms will suddenly become highly infected.

This will happen in the complete absence of any other environmental driver, such as climate change or a new more virulent strain of the disease. Indeed, one study in Costa Rica showed that the incidence of rust disease was correlated with the amount of sun coffee and pasture in the surrounding landscape. It could very well be that the sudden outbreak of coffee rust in 2012 is an example of the inevitability of surprise arising from the formality of a critical transition that we have come to associate with highly nonlinear complex systems . A cartoon version of this theoretical process is presented in figure 16. An important component of the rust disease system, not yet completely understood, is the existence of several natural enemies of the rust . Providing an example of the sorts of ecological complexity of popular literature, the fungal disease of the first pest we discussed, the green coffee scale , is caused by the same species of fungus that, when given the chance, attacks the coffee rust fungus. That same white halo fungus that attacks the green coffee scale, now acts as a mycoparasite . Because this natural enemy is also a natural enemy of the green coffee scale, the connection to the Azteca ant became obvious early on ; Azteca creates conditions under which the scale insect becomes highly concentrated locally, which attracts the infestation of the white halo fungus and creates local hot spots of spores that disperse locally and attack the rust. Correlative evidence for this hypothesis, prior to the 2012 epidemic of rust, comes from multiple sources . Indeed, there has been considerable discussion at international conferences on the potential of L. lecanii as a spray for the rust disease. Our work suggests that partial control of the rust may naturally occur through this and other agents , although the epidemic throughout Mesoamerica in the 2012–2013 growing season shows the potential for the disease to escape such control, if, in fact, it did exist before that. It is quite a remarkable qualitative impression one gets when examining the rust and its control comparatively. It is endemic but rarely epidemic in Puerto Rico but has maintained a relatively severe status in much of Mesoamerica since 2012 . Examining coffee leaves in Mexico easily reveals the presence of L. lecanii but only after considerable searching effort, whereas in Puerto Rico, it is almost inevitable that, if one encounters the rust on a leaf, it is almost certain that one encounters L. lecanii also. What seems epidemic in Puerto Rico is the L. lecanii that seems to keep the rust under control. In addition to the white halo fungus, the larval form of a small fly, Mycodiplosis hamaelae, preys on the spores directly on the coffee leaf but probably also acts as a dispersal agent, at least locally . The coffee leaf rust continues to plague Latin American coffee farmers.

Despite varied reports, Lee et al. also demonstrated a linear positive relationship between norisoporenoids in the grape berry and concentrations in wine, with the berry concentration was always greater than that of the resultant wines. It may be possible that carotenoid degradation due to excessive temperatures in C0 treatments was negligible or less than the biosynthesis of C-13 norisoprenoids, resulting in similar concentrations as D4 and D5 shade film treatments. Therefore, the results of this study demonstrated that partial solar radiation exclusion with reductions in UVA, UVB and NIR radiation does not hinder norisoprenoid content in wines. Additionally, the concentrations of bdamascenone across all treatments in both years exceeded the odor active threshold for this compound, indicating that significant differences in b-damascenone concentrations between C0 and treatments may be perceivable in resultant wines.In a typical year, debates surrounding the state’s budget are among the most controversial matters addressed by Colorado state lawmakers. Because the current legislature is closely divided along party lines, many expected the budget to take center stage once again in the 2018 legislative session. Funding for transportation and education have been especially salient issues in recent months. Before the current session began, the Denver Post outlined some of the major items on the General Assembly’s agenda. Among the most pressing issues facing lawmakers were transportation funding, large plastic planting pots the opioid crisis, energy development, and the financial stability of the Public Employees’ Retirement Association , in addition to matters surrounding sexual harassment in the legislature .

For the fourth consecutive year, divided party control exists in the General Assembly with Democrats holding a 10-seat advantage in the state House, while a slim Republican majority exists in the Senate with 18 Republicans, 16 Democrats, and one unaffiliated senator. At times the partisan differences between the chambers have been substantial. In prior legislative sessions, the issue of guns has been among the most controversial topics addressed by legislators as evidenced by the successful recall elections of two Democratic lawmakers over their votes on gun control bills in 2013 . During the current session, the Republican controlled Senate passed legislation in a party-line vote to allow Coloradans to conceal carry a firearm without a permit . With no Senate Democrats supporting the measure, the bill was dead on arrival in the House where Democrats hold the majority. A bill to ban bump stocks was recently defeated by Republicans in the State, Veterans, and Military Affairs Committee following a party-line vote. While political parties in Colorado remain bitterly divided on the issue of guns, other previously controversial measures witnessed unexpected compromise during this session such as increased funding for the program to provide driver’s licenses for undocumented residents. Beginning in August 2014, an estimated 120,000 undocumented residents could begin applying for driver’s licenses. Although the state issued 32,325 licenses through the program, it was troubled by a lack of staff and funding since demand outpaced the number of appointments offered by the state . Many expected further problems as the licenses first issued were due for renewal, and the program originally required all individuals to procure or renew their licenses in person. However, a bill recently passed in the Republican-controlled Senate provides additional funding to the program and allows existing licenses to be renewed online, among other changes .

Following successful passage in the House, Governor Hickenlooper signed the bill in May. The passage of this bill into law demonstrates the possibility for bipartisan compromise in a divided General Assembly on controversial issues as well as debates surrounding spending priorities. The emergence of the #MeToo movement also appears to have brought the parties together in an effort to change the prevailing culture in the legislature. The most publicized controversy of the legislative session was the emotionally charged debate surrounding the expulsion of a Democratic legislator following multiple sexual harassment allegations. Representative Steve Lebsock was the subject of multiple allegations of sexual harassment. Three formal complaints were made against him, including one from fellow Representative Faith Winter . Following an independent investigation, which found credible evidence that he had engaged in harassment and retaliation, and a full day of emotional speeches on the House floor, the chamber voted 52 to 9 to expel Lebsock from the legislature. The outcome was far from certain prior to the historic vote, as the expulsion resolution required a two-thirds majority vote in order to remove the incumbent representative. Many who supported removing Lebsock cited a need to change the culture in the state legislature. As a result of the vote, Lebsock became the first state representative to be expelled in more than 100 years. In a strange twist, Lebsock submitted the paperwork to change his party affiliation from Democrat to Republican minutes before the expulsion vote. According to state law, this handed the House vacancy to the state’s Republican Party to fill instead of the Democrats who previously held the seat. This act was clearly intended to spite fellow Democrats who abandoned their support of Lebsock once the extent of his harassing behavior became apparent. A spokesperson for the Colorado GOP initially floated the idea of not filling the seat within 30 days, which would allow the Democratic governor the opportunity to appoint a successor.

However, the party ultimately decided to appoint a Republican to temporarily hold the seat, which many expected to be regained by the Democrats in the next election cycle. This did not alter the majority party in the chamber since Democrats hold an eight-seat majority after Lebsock’s expulsion. Lebsock was not the only state legislator rebuked for inappropriate behavior, as an independent investigation found credible evidence that Senator Randy Baumgardner sexually harassed a legislative aide in 2016. Senator Baumgardner resigned a key committee chair position while maintaining his innocence in advance of an expulsion vote in the Senate. While the vote to expel Lebsock was supported by representatives of both parties, the parties appeared more divided in the Senate with regard to the allegations against Baumgardner. Republican leadership ordered Baumgardner to undergo sensitivity training, while Democrats have called for more severe sanctions including expulsion. In early April, Baumgardner survived an expulsion vote with 17 voting in favor and 17 voting opposed. While this fell short of the two thirds majority necessary to remove a lawmaker, potential expulsions from the Senate threatened larger reverberations on policy and the budget as the Republicans held a narrow one-seat majority until Senator Cheri Jahn changed her party affiliation from Democrat to unaffiliated in December 2017. On the legislative front, the second session of the 71st General Assembly convened on January 10, 2018 after a special session called by Governor John Hickenlooper in October 2017 failed to produce any accomplishments. Hickenlooper previously called a special session in 2012 to debate a civil unions bill, which ultimately failed to pass. The 2017 special session similarly adjourned amid partisan gridlock. The governor called this special session to address what was described as a bill drafting error contained in a major reform that passed at the end of the General Assembly’s regular session in 2017. Senate Bill 17-267 imposed many substantial reforms . Among the most notable of these was the repeal of the existing hospital provider fee structure and the creation of the Colorado Healthcare Affordability and Sustainability Enterprise as a government enterprise fund to collect healthcare sustainability and affordability fees. Importantly, black plastic planting pots this change made it so hospital provider fees do not count as state revenue for the purposes of the Taxpayer’s Bill of Rights . The bill drafting error concerned a modification to the taxes levied on recreational marijuana sales. When Colorado voters approved Amendment 64 to legalize recreational marijuana use in 2012, the amendment included the following language governing the General Assembly’s authority to levy taxes on retail marijuana sales, “The General Assembly shall enact an excise tax to be levied upon marijuana sold or otherwise transferred by a marijuana cultivation facility to a marijuana product manufacturing facility or to a retail marijuana store at a rate not to exceed fifteen percent prior to January 1, 2017 and at a rate to be determined by the General Assembly thereafter, and shall direct the department to establish procedures for the collection of all taxes levied.” Senate Bill 17-267 collapsed the existing 2.9 percent sales tax on retail marijuana sales and the 10 percent special tax into a single 15 percent state tax. The drafting error occurred because legislators intended to only remove the statewide sales tax, while an exemption allowed municipal governments to impose their own sales taxes on marijuana sales where permitted. The bill, however, failed to include a similar exemption for special districts such as the Denver metro area’s Regional Transportation District and the Scientific and Cultural Facilities District , among several others.

This omission meant that these districts could no longer continue collecting tax revenue on marijuana sales as they had before Senate Bill 17-267 went into effect. While the SCFD supports scores of organizations and programs including the Denver Zoo, Denver Art Museum, and Denver Museum of Nature & Science, the funding losses incurred by RTD were arguably more likely to affect Colorado residents. The RTD special district encompasses 2,342 square miles across eight counties. The district includes nearly three million residents in its service area. Ridership statistics from the past three years show that annual ridership on RTD commuter rail, light rail, and bus services exceeded 100 million trips . Analysts projected that the bill drafting error would cost RTD nearly $600,000 per month. SCFD monthly losses were estimated at about $56,000. The special session to correct the bill drafting error was opposed by many Republicans. Some argued that modifying the existing tax structure would require a vote of state residents consistent with TABOR’s requirements. The session ended after two measures to correct the error were rejected in the Senate after passage in the House with mostly Democratic support. Following an unsuccessful special session, Governor John Hickenlooper enters the final year of his second term as governor. Term limits prevent him from running again, although there are several indications that he is preparing to launch a bid for the presidency in 2020. A November 1 letter to the General Assembly’s Joint Budget Committee provided details on the key aspects of the governor’s budget request. The budget proposal for the 2018–2019 fiscal year proposed a total funds budget of $30.5 billion, which is an increase of 3.7 percent from the prior year. The General Fund spending budget of $11.5 billion represents a 2.6 percent increase. After legislators considered nearly 200 amendments to the long bill, the state budget totals enacted into law were close to the numbers proposed by the governor. The state’s final General Fund budget was $11.42 billion with $30.63 billion in total fund spending . The letter to the JBC stated that the governor’s budget request “reflects the dynamic factors that are occurring in Colorado’s economy, constitutional and statutory requirements, and demand for services from State government” . It further noted that the “passage of S.B. 17-267 has materially and positively changed the State’s financial outlook compared with one year ago, when the request had to close a $500 million funding gap in the General Fund. We believe the request reflects the priorities that Colorado citizens expect and accordingly the request addresses important needs in K-12 and higher education as well as certain essential criminal justice system needs” . In percentage terms, spending on K-12 education represents the largest share of the general fund request at 36 percent, while the spending allotment for higher education budget is 9 percent. Nearly every state department was slated to receive increased funding relative to the prior fiscal year with just two exceptions. The budget approved by the General Assembly ultimately increased funding for every state department except for Labor and Employment. The three sections that follow discuss the state’s demographics, revenue, and spending. While a growing population provides a larger tax base, affordable housing and transportation problems have also accompanied this rapid population growth. The most recent census estimated that the state’s population was approximately 5 million residents. The 2017 update places the number of Colorado residents at slightly greater than 5.6 million . This figure represents an increase of 11.5 percent since 2010 and a 1.2 percent increase since 2016. Of the 223,260 individuals who moved to Colorado in 2016, the Census estimates that 14 percent immigrated from abroad.

In Zone 2, we measured higher cyanidins and di-hydroxylatedanthocyanins on 24 August , and that was the only date Zone 2 had higher concentrations in any of these derivatives. The temporal relationships between TSS and berry skin anthocyanins were investigated in both years . In both years, skin anthocyanins increased with the accumulation of TSS at first. In 2016, berry anthocyanins of Zone 1 had a significant decline in skin anthocyanins after 25◦Bx TSS, resulting a lower concentration when compared to Zone 2 . Conversely, the second season consistently showed greater anthocyanin concentration in Zone 1 than Zone 2 . However, Zone 1 showed a more rapid decline after around 25◦Bx TSS, and the skin anthocyanins were similar in values with Zone 2.Wine-free anthocyanins and proanthocyanidins were assessed in both years. For anthocyanins, Zone 2 had higher concentrations of all derivatives in 2016, including tri-, di- hydroxylated, and total anthocyanins . All the compounds were more than two times greater than Zone 1. However, there was no difference observed in any of these compounds in 2017. The overall concentrations of all these compounds were greater in 2017 than 2016. For proanthocyanidins, similar results were observed . In 2016, all the extension and terminal subunits were higher in Zone 2 than Zone 1. The amount of total proanthocyanidins were also higher in Zone 2. In 2017, however, there was no difference observed in any of these subunits or total proanthocyanidins. Again, plastic pot plant containers the second season showed greater concentrations in all of these compounds compared to the first season. Neither year showed difference in mDP between the two zones.

In our previous work, we were unable to deduce a significant relationship between site topography variables such as absolute elevation and berry chemistry . Bramley et al. showed that soil bulk EC was directly related to soil clay content, which was contradictory to our findings. We attributed this discrepancy to the relatively stable soil texture throughout the season or even several seasons. On the other hand, the effect of soil water content might be the major factor to influence plant development during the season. The soil texture and soil bulk EC sensing analysis conducted in this study were able to explain the variability in plant water status that the site topography could not. Soil texture and soil bulk EC can be related to spatial differences in soil water availability . Specifically, soil texture is a determinant of soil water holding capacity, hence affecting the amount of water available to the plants. In our study, the western section of the vineyard had greater loam proportion, where the grapevines were experiencing more severe water deficits . The eastern section had more sandy soil in both deep and shallow soil, where the grapevines were under less severe water deficits. Our findings are corroborated with previous work, where clay soil would lead to less plant available water, although clay soil had higher water holding capacity than sandy soil . Furthermore, Cabernet Sauvignon grapevines grown in clay soil would result in lower gs and An compared to grapevines grown in soils that had higher proportion of sandy soils . There was evident variability in soil bulk EC in this study. Previous studies reported that when soil bulk EC was proximally sensed, it was closely related to soil water content . Our findings are corroborated by previous works , where higher soil bulk EC values corresponded to higher soil water content. Previous studies suggested that the relationship between soil water content and soil bulk EC was soil-specific, and needed to include soil chemical and physical properties to explain variability and plant water status .

Due to the limited amount of water put into wine grape vineyards, soil water content would be the major factor affecting soil electrical properties rather than the residual salinity after water evaporation from soil. The significant relationship between soil bulk EC and 9 stem in this study agreed with previous studies, indicating the possibility of soil bulk EC sensing being used to assess plant water status . Moreover, in our study, the spatial variability in grapevine physiology reflected the variability in soil bulk EC very well when assessed by proximal sensing. Due to the relationship of soil bulk EC on the amount of available water to plants reported in previous research , this approach had been utilized to identify the variability in the plant physiology based on the soil sensing technologies and apply targeted management strategies , and our study provided more evidence toward the feasibility of it.The variability we measured proximally in soil characteristics was reflected in plant water status and leaf gas exchange in our study. Previous research had reported that variable soil characteristics in space would cause spatial variations in plant water status . Although the precipitation amounts were vastly different between the two dormant seasons, the uniformly scheduled irrigation did not ameliorate the natural spatial variability in plant water status induced by soil properties. On the contrary, the separations in plant water status and leaf gas exchange were already significant even before the irrigation ceased after veraison. This proved that the spatial variability in the soil dominated the accessibility of the available soil water toward the plant, and made the spatial variability expressed in the grapevine. Our results in the second year corroborated those of the first year, showing that the separation in both plant water status and leaf gas exchange between the two zones were consistent. Leaf gas exchange was closely related to plant water status, and this relationship was shown in previous research . The relationships between leaf gas exchange and plant water status were evident in our study, where a higher 9 stem would promote a greater stomatal conductance to increase carbon assimilation capacity and decrease intrinsic water use efficiency.

In our study, the lowest 9 stem we observed were around harvest with 9 stem of -1.6 MPa and gs of around 50 mmol H2O m−2 ·s −1 , which were not severe enough to impair berry ripening although the photosynthetic activities were still affected. Overall, the gs and AN reached the maximum values at veraison and declined with decreasing plant water status and leaf age toward the end of the season. This further affirmed that the continuous water deficits during the growing season, especially being more pronounced after irrigation was ended after veraison, would reduce stomatal conductance. The water deficits would act as passive hydraulic signals or active hormonal signals with the upregulation in abscisic acid synthesis to limit plant photosynthetic activities, hence lower gs and AN values .According to the previous research, components of yield may be affected by plant water status, where higher water deficits would result in reductions of yield, berry skin weight, and berry weight . In our study, we observed constant separation in plant water status after veraison. However, there was no difference shown in cluster number, yield, berry number, large plastic gardening pots or pruning weight. The only difference measured in yield components was that berry skin weight was higher in Zone 1 in the second season. Early season water deficit irrigation had higher probability to decrease yield than later season water deficit irrigation . However, a season-long water deficit irrigation would have the lowest yield even despite the season-long water deficit irrigation regime applying double amount of water than the other regimes . Some other studies did not have the same results, as early water deficit irrigation did not show significant influences on yield compared to late water deficit irrigation . Another possible explanation was that Zone 1 had greater water amount held in the soil due to the higher clay content. The clay soil with higher water-holding capacity had a better water status at the early season compared to Zone 2, even though the sandy soil in Zone 2 would benefit the plant growth with irrigation when the season progressed . The later season water deficit was exacerbated in Zone 1 due to its higher clay content, causing Zone 1 lost the benefits from the high water status in the early season, and eventually had similar yield components with Zone 2 at harvest. In our work, we did not see any evidence of Ravaz index being affected by spatial variability of plant water status. These results were corroborated by Terry and Kurtural when grapevine cultivar ‘Syrah’ was exposed to post-veraison water deficits in comparable severity of -1.4 MPa .Water deficits affect advancement of grape berry maturity, they promote TSS accumulation and TA degradation in grape berries . Two factors contributed to these differences between the two zones. First, a greater water deficit advanced the berry maturation, leading to a higher TSS and lower TA . Second, berry dehydration may have occurred and the TSS concentration increased in the berries. In our study, smaller berries were observed in Zone 1, which can confirm the berry dehydration could have led to higher TSS in Zone 1. As for berry TA, one study showed that grape organic acids biodegradation would be faster with more solar radiation and higher temperature .

Although the acid degradation was not related to water deficits, like mentioned above, water deficits would limit the grapevines’ ability to regulate temperature . Thus, waterdeficits could promote the organic acid degradation and this effect was observed in this study.Mild water deficits increased the flavonoid content and concentration of red-skinned grape berry due to the upregulation in flavonoid synthesis and the advancement of berry dehydration during growing season . A positive relationship was noticed between soil bulk EC and total skin anthocyanins in 2017 at both depths of soil bulk EC measurements. A more prolonged severe water deficit would lead to deleterious stomatal and temperature regulation and eventually resulted in flavonoid degradation, specifically anthocyanins . This was a plausible explanation for the non-significant relationship between soil bulk EC and total skin anthocyanins in 2016, wherein harvest took place at higher soluble solids and Zone 1 berry skin anthocyanins were presumably in decline. Furthermore, the berry weights were higher in Zone 2, which was similar to the observations in our previous work , indicating there was less berry dehydration. Thus, the higher anthocyanins in Zone 2 was mainly due to the upregulation in anthocyanins other than anthocyanins degradation. These effects were also observed in the wines of 2016, where Zone 2 had higher anthocyanin concentrations. However, in the second season, the differences in berry skin anthocyanins at harvest did not carry over into the wines. We contributed this to the more advanced berry maturity levels at harvest in the first season, the skin cell walls could have become more porous during ripening and increased the extractability of flavonoid compounds . With relatively greater amounts of flavonoids extracted, there was a higher chance to pass on the separations of anthocyanins from the berries to the wines. Grape berry skin proanthocyanidins are less sensitive toward water deficits than anthocyanins . Nevertheless, their biosynthesis and concentration may be modified by water deficits . In 2016, wine total proanthocyanidins and all the subunits were greater in Zone 2. These differences were not observed in the second season. We attributed this lack of consistency in proanthocyanidin disparities between the two zones to the more advanced maturity of the berries were harvested in 2016 than in 2017. We suggest that similar to skin anthocyanins, the more advanced berry maturity in 2016 could have promoted the proanthocyanidin extractability in the skin tissues , which may augment the separations in the concentration of all the subunits between the two zones.The global COVID-19 pandemic affected nearly every aspect of modern society and caused millions of hospitalizations and deaths across the globe. By the end of 2021, the state of Colorado alone reported nearly one million positive COVID-19 cases that resulted in more than 10,000 deaths . The economic shocks from the pandemic produced a recession that disproportionately affected certain economic sectors and the lives and livelihoods of all Coloradans. The state’s unemployment rate ballooned to 12.1 percent in April 2020 after ending the prior year at 2.6 percent . Federal and state governments adopted numerous public health measures seeking to contain the spread of the virus. Congress and state legislatures across the country also enacted economic stimulus bills aimed at mitigating the pandemic’s economic damage.

PCR reaction aliquots were loaded on an E-Gel pre-cast agarose gel 0.8% to determine the optimalcycle number. Second-strand cDNA was synthesized and amplified using the Kapa HiFi PCR kit with the 59 PCR primer IIA following the manufacturer’s instructions. Large-scale PCR was performed using the number of cycles determined during the optimization step . Barcoded double-stranded cDNAs were pooled at equal amounts and used for size selection. Size selection was carried out with a BluePippin and 1-2 kbp, 2-3 kbp, 3-6 kbp, and 5-10 kbp fractions were collected. After size selection, each fraction was PCR-enriched prior to SMRTbell template library preparation. cDNA SMRTbell libraries were prepared using 1-3 mg of PCR enriched size-selected samples, followed by DNA damage repair and SMRTbell ligation using the SMRTbell Template Prep Kit 1.0 . A second size selection was performed on the 3-6 kbp and 5-10 kbp fractions to remove short contaminating SMRTbell templates. A total of 8 SMRT cells were sequenced on a PacBio Sequel system . Demultiplexing, filtering, quality control, clustering and polishing of the Iso-Seq sequencing data were performed using SMRT Link ver. 4.0.0 . Iso-Seq read error rates were estimated using the identity of the best alignment on the diploid Cabernet Sauvignon genomic assembly . Alignment was performed with GMAP ver. 2015-09-29 using the parameters “-K 20000 -B 4 -f 2”. Coding sequences were identified using Transdecoder as implemented in the PASA ver. 2.1.0 .Previous analyses of gene content in a limited number of grape cultivars showed that up to 10% of grape isoforms were not shared between genotypes.

Some of these “dispensable” genes were associated with cultivar-specific characteristics . To identify protein-coding transcripts characteristic of Cabernet Sauvignon , square plastic plant pots we looked for homologous sequences among the ISNT transcripts in the PN40024 genome and in the transcriptomes of Corvina , Tannat , and Nebbiolo . Approximately five percent of the ISNT did not have a homologous copy in any of the four datasets . These putative Cabernet Sauvignon private isoforms were involved in various biological processes of berry development and ripening like phenylpropanoid/flavonoid biosynthesis, sugar accumulation and transport, water transport , and cell wall metabolism and loosening.To evaluate the non-redundant Iso-Seq transcriptome’s completeness and usefulness as a reference for RNA-seq analysis, the protein-coding genes in the Cabernet Sauvignon genome were predicted as described in Figure S3. First, the repetitive regions of the genome were masked using a custom-made library of Cabernet Sauvignon MITE, LTR, and TRIM information. Overall, 51% of the assembly consisted of repetitive elements , with 412,994 repetitive elements on the primary assembly and 274,123 on the haplotigs , LTRs were the most abundant class, covering over 335 Mb of the genomic sequences, with Gypsy and Copia families accounting for 201 Mb and 104 Mb, respectively. Next, MAKER-P identified putative protein-coding loci, combining the results of six ab initio predictors trained ad hoc with publicly available experimental evidences. Ab initio predictors were trained using a custom set of 4,000 randomly selected gene models out of the 5,636 high-quality, nonredundant, and highly conserved gene models of the PN40024 V1 transcriptome . Experimental evidence from public databases was incorporated and used to validate the predicted models.

The final MAKER-P prediction included 38,227 high-quality gene models on the primary contigs and 26,789 on the associated haplotigs. Using the covariance models from the Rfam database, 5,780 non-overlapping putative long non-coding RNAs belonging to 275 different families were annotated . Gene models were further improved using the information from all Iso-Seq full-length datasets , RNA-seq, and the publicly available grapevine transcriptome assemblies. This final refinement improved the annotation of the UTRs and added isoform information. PCIRs helped identify 155 new loci not detected by MAKER-P, update the structure of 10,801 gene models, and add 2,712 alternative transcripts. C-FLNC reads introduced 830 additional missing loci and added 3,738 alternative transcripts to the annotation. Together, 14,388 gene models were updated. FLNC reads introduced 14 new loci and 20,493 alternative transcripts, bringing the number of updated model structures to 24,945. Predicted genes without similarity to known proteins in the RefSeq database and without any functional domains identified by InterProScan were removed. The final predicted transcriptome included 55,887 transcripts on 36,689 loci on primary contigs and 40,444 transcripts on 25,479 loci on haplotigs . GO terms were assigned to 80,752 transcripts based on homology with protein domains in RefSeq and InterPro databases .For 2,995 of the 25,479 protein-coding gene loci identified on the haplotigs, we could not find a corresponding homologin the primary contigs, likely reflecting the diversity in gene content between parental genomes, as in Corvina , Tannat , and Nebbiolo . We could not find homologous genes in PN40024, Corvina, Tannat, and Nebbiolo for 1,714 protein-coding gene loci . Those genes included likely members of the phenylpropanoid/flavonoid biosynthesis pathway: four phenylalanine ammonia-lyase, three chalcone synthases, a chalcone isomerase, a dihydroflavonol-4-reductase, a flavanone 3-hydroxylase, a flavonoid 39,59- hydroxylase, a leucoanthocyanidin dioxygenase, and an anthocyanin acyltransferase.

Other private Cabernet Sauvignon genes were associated with terpenoid biosynthesis, including six valencene synthases that may play a role in grapevine flower aroma, three vinorine synthases , and a -geranyllinalool synthase. The incorporation of Iso-Seq data in the gene prediction pipeline also allowed the structural annotation of alternative transcripts. Twenty five percent of the 62,168 annotated gene loci had two or more alternative isoforms, an average of 1.55 6 1.29 alternative transcripts per locus, confirming previous reports in PN40024 . Intron retention was the most abundant type, accounting for over 44% , similar to what was observed for rice , Arabidopsis and maize . Alternative acceptor sites , alternative donor sites , and exon skipping were the other most abundant types of alternative splicing found in the Cabernet Sauvignon genome; a full description of the selected splicing events is reported in File S12.The final step of the analysis was to evaluate the effectiveness of the reconstructed ISNT as reference for RNA-seq analysis of berry development compared to the gene space predicted on the Cabernet Sauvignon genome. Comparisons between the predicted transcripts and the reconstructed ISNT as references for RNA-seq are summarized in Table 1. Only about three percent more RNA-seq reads mapped on the Cabernet Sauvignon predicted transcriptome than on the ISNT , suggesting that Iso-Seq reconstructed most of the transcripts detectable by RNA-seq at a coverage of 26 M reads/ sample. Approximately 75% of the ISNT and
expressed was detected as $ 1 in at least one stage . In both datasets, the number of expressed genes was slightly higher at pre-véraison stage than at later developmental stages, consistent with previous observations of ripening Cabernet Sauvignon berries . For both datasets, Pearson’s correlation matrix and Principal Component Analysis showed a clear distinction between pre-véraison stage and the three ripening stages, square pot plastic as well as a stronger correlation between post-véraison and full-ripe berry transcriptomes , confirming the well-known transcriptional reprogramming associated with the onset of ripening and suggesting that similar global transcriptomic dynamics of berry development can be obtained using either Iso-Seq or the whole genome as reference. We then applied a sequence clustering approach to define associations between ISNT isoforms and gene loci to directly compare the expression values of each gene in the two transcriptomes. Based on reciprocal overlap of the alignment, we were able to associate 25,306 ISNT transcripts with 26,873 gene loci in the Cabernet Sauvignon genome . Gene expression levels measured on the two transcriptomes were well-correlated . Differential gene expression analysis identified 14,477 ISNT transcripts and 18,600 Cabernet Sauvignon genes significantly differentially expressed at least once during berry development . More genes were differentially regulated between pre-véraison and véraison than during ripening for both transcriptomes, as previously observed . Ninety one percent of the differentially expressed ISNT isoforms were also differentially expressed when RNA-seq data were mapped on genomic loci. Similar relative amounts of Biological Process GO terms among differentially expressed genes were observed between the two transcriptomes . Interestingly, 302 Cabernet Sauvignon private isoforms were differentially expressed during berry development, square pot plastic including transcripts encoding a polyol transporter, an inositol transporter, and five aquaporins.

Full-length cDNA sequencing with SMRT technology can be used to rapidly reconstruct the grape berry transcriptome, enabling the identification of cultivar-specific isoforms, refinement of the CabernetSauvignon genome annotation, and the creation of a reference for transcriptome-wide expression profiling. In contrast to transcriptome reconstruction using short-read sequencing that requires de novo assembly, Iso-Seq delivers full-length transcripts that eliminate the introduction of assembly errors and artifacts like chimeric transcripts and incomplete fragments due to PolyA capture . The incorporation of high-coverage short-read sequencing is still necessary to benefit from the complete transcript sequencing enable by Iso-Seq. Although Iso-Seq provides much longer reads than second-generation sequencing platforms and as a result is excellent in resolving transcript structure, its sequencing error rate is high and throughput is still relatively low . Here we show that combining Iso-Seq with Illumina sequencing at high coverage enables expression profiling and sequence error correction of IsoSeq reads, particularly those derived from low-expression genes. The clustering analysis of the SMRT link pipeline discarded 18.5% of the FLNC reads, likely caused by low sequence accuracy. To overcome this technical issue, we applied a hybrid error correction pipeline consisting in performing the error correction of the unclustered FLNC reads, followed by an additional clustering step of both to resolve redundancies. Error correction with Illumina reads recovered a significant amount of Iso-Seq reads that would have otherwise been removed by the standard Iso-Seq pipeline, highlighting the importance of integrating multiple sequencing technologies with complementary features . Transcriptome reconstruction has been widely used to develop references for genome-wide expression profiling in the absence of an annotated genome assembly . Though a genome reference is available for grape, transcriptome reconstruction overcomes the limitations of a cultivar-specific reference that lacks the gene content of other cultivars. Although cultivar-specific genes appear nonessential for berry development, those private genes could contribute to cultivar characteristics. For example, the wine grape Tannat accumulates unusually high levels of polyphenols in the berry; its cultivarspecific genes account for more than 80% of the expression of phenolic and polyphenolic compound biosynthetic enzymes . De novo transcriptome assembly from short RNA-seq reads has been used to explore the gene content diversity in Tannat , Corvina , and Nebbiolo . Iso-Seq identified 1,501 Cabernet Sauvignon transcripts expressed during berry development that were found in neither the genome of PN40024 nor the transcriptomes of Tannat, Nebbiolo and Corvina. Some private Cabernet Sauvignon transcripts have functions potentially associated with traits characteristic of Cabernet Sauvignon grapes and wines like their color and sugar content. These transcripts included three sugar transporter-coding genes, which could be involved in the accumulation of glucose and fructose during berry ripening , and a chalcone synthase, a flavanone 3-hydroxylase, and a flavonoid 39-hydroxylase, all involved in the flavonoid pathway. Chalcone synthases catalyze the firstcommitted step of the flavonoid biosynthesis pathway , which produces different classes of metabolites in grape berry, including flavonols , flavan-3-ols and proanthocyanidins , and anthocyanins . In addition, products of the flavonoid 39-hydroxylase can lead to the synthesis of cyanidin-3-glucoside, a red anthocyanin . The analysis of the gene space in the genome assembly showed that private Cabernet Sauvignon genes identified using Iso-Seq are only a fraction of the private Cabernet Sauvignon transcriptome. As in other transcriptome reconstruction methods, Iso-Seq can only identify transcripts that are expressed in the organs and developmentalstages used for RNA sequencing. Obtaining the full set of private transcripts without genome assembly would require sequencing additional organs and developmental stages. In addition, it is challenging to differentiate isoforms derived from close paralogous genes, alleles of the same gene, and alternative splicing variants, in any transcriptome obtained by RNA sequencing ; this potentially leads to an overestimation of the genes in the final transcriptome reference. This study could not resolve isoform redundancy in the final transcriptome for about 37% of the gene loci in the Cabernet Sauvignon genome. This is a limitation of Iso-Seq as well as of all transcriptome references that cannot be overcome without a complete genome assembly. In this study, we tested whether the transcriptome reconstructed using Iso-Seq can be used for expression profiling. Only an approximately 3% difference in read alignment between ISNT and the genome reference was observed, implying that at high coverage, ISNT detects almost all genes expressed during berry development.

The 33%L-100%F had the fewest berries per cluster compared to all other treatment combinations.Canopy area was affected by defoliation, but not with fruit removal or its interaction with defoliation during the experimental years . There was a strong linear trend, as expected with defoliation; where removing 66% of canopy area resulted in a 65% decrease of it in 2017 ; and a 58% in 2018 . The carryover effects of source-sink adjustments on the canopy area in 2019 were evident. The strong linear decrease in 33%L continued to this year, as the grapevines did not recover from the removal of 66% of their leaf area, regardless of fruit removal in previous years. In 2017, both defoliation and fruit removal affected leaf area to fruit ratio; however, the interaction amongst them was not significant . There was a strong linear trend where leaf area to fruit ratio decreased by 47% when66% of the canopy area was removed . Conversely, we measured a strong linear trend where leaf area to fruit ratio increased by 56% this time when 66% of the fruit was removed. In 2018, defoliation and fruit removal interacted to affect the leaf area to fruit ratio . Within the interaction, blueberry box there was a linear trend where leaf area to fruit ratio decreased linearly as the number of clusters retained increased. We measured the greatest leaf area to fruit ratio with 100%L-33%F as well as in 66%L-33%F. The 33%L-100F and 66%L-100F had similar leaf area to fruit ratio .

There was no carry over effect of source-sink adjustments on leaf area to fruit ratio in 2019 , nor was there an effect of main effects carrying over to this year . We measured an interactive effect of fruit removal and year on Ravaz Index . During both experimental years,there was a strong trend of fruit removal on Ravaz Index . In 2017, removing 66% of fruit resulted in a 56% decrease of Ravaz Index. We saw a similar response in 2018 as well. There was no effect of defoliation within the experimental years. We also did not measure an interactive effect of defoliation and fruit removal on Ravaz Index either. There was no carryover effect of source-sink adjustments on Ravaz Index in 2019 ; and we did not measure a carry-over effect of main effects of Ravaz index either . Berry TSS was affected strongly by the defoliation treatments during the experimental years, and we did not measure an interactive effect of defoliation and fruit removal in 2017 or in 2018 . There was a linear increase in TSS as the severity of defoliation decreased in both experimental years . The effect of fruit removal on speed of ripening in 2017 was negligible. However, we also saw a strong effect of fruit removal on berry TSS where it declined linearly with the decrease in fruit removal severity in 2018 . This indicated a level of self-adjustment in previous grapevine season’s applied treatments. Conversely, under free-growth in 2019 when the grapevine was allowed to sprawl without any defoliation and fruit removal, we saw a reversal of the trends with defoliation . Although there were limited main and interactive effects, in the absence of fruit removal there was a linear decrease in TSS accumulation as the severity of defoliation treatments decreased, revealing the carry-over effect .

We measured a significant year and defoliation interactive effect on AN, and gs . There was never an interactive effect of fruit removal and year on any of the leaf gas exchange variables monitored. In regards to AN during the experimental years , there was a strong linear trend where AN and gs increased linearly with the increase in the severity of defoliation . In 2017, AN and gs increased by 10 and 13%, respectively, when 66% of leaves were defoliated. Defoliating 66% of leaves resulted in a 23% increase in AN, and a 30% increase in gs integrals in 2018. In either experimental year we did not see an effect of cluster thinning on leaf gas exchange integrals or an interaction of defoliation and fruit removal. The carryover effects to source sink adjustments in 2019 were inconsistent. We did not measure any significant effects of defoliation, fruit removal, or their interaction on AN, or gs . However, as mentioned above, the year effect on AN, and gs were significant. There was a quadratic response to years where AN and gs declined from 2017 to 2018 but then increased significantly in 2019.We destructively harvested the grapevines following the 2018 growing season and separated them into roots, trunk, and aerial organs. Trunk and cordon masses were not affected by the defoliation, fruit removal, or their interactive effects . Shoot and root masses were affected by the defoliation treatments. The shoot mass decreased by 1/3 with the 33%L treatment compared to the 100%L treatment . Root mass decreased by 1/4 with the 33%L treatment when compared to 100%L treatment . The total grapevine mass was also 20% lower in the 33%L treatment compared to 100%L treatment. Fruit removal did not affect plant biomass or biomass accumulation in plant organs, and there was no interaction of defoliation or fruit removal evident in our work. The starch accumulation in grapevine roots was affected by defoliation treatments and time of sampling . We did not measure an interactive effect of defoliation and fruit removal. The starch accumulation was affected at similar times during the experiment during each year. In 2018, the root starch content of 33%L was one-third of 100%L starting in mid-ripening until harvest .

The starch content of 33%L roots, however, equilibrated to the same content of 100%L by December 2018 when pruning was conducted. In 2019, when no treatments were applied to observe the carry over effects, we saw a reversal of this response. The starch content of root tissues of the 33%L treatments had ca. 20 and 40% more starch than 100%L in 2019 during mid-ripening through harvest. Crop level rather than defoliation affected the soluble sugars content in the roots . We did not measure the interactive effect of defoliation and fruit removal on soluble sugars at any time point during the experiment. In contrast to root starch accumulation , the soluble sugars were greater in the 33%F when compared to 100%F at treatment application in 2018. However, their content decreased to ½ of 100%F by December 2018 . In the follow-up year where grapevines grew without treatments, we saw transient differences in root soluble carbohydrates at mid-ripening where 100%F had greater content than 33%F. However, post-harvest in 2019, the soluble carbohydrate content in roots of 33%F was ca. 2× of 100%F prior to leaf fall. At pruning time, compared to the previous year; there was no difference.The day of bud break was not affected by defoliation treatments during the experimental years or the follow-up year of 2019 . However, bud break was 1 day later in 2019 in the 66%F and 100%F treatments compared to 33%F . The date of flowering was not affected by defoliation treatments in 2018 . However, it was 1 day later with 100%L in 2019. Likewise, we did not see a shift in flowering date with fruit removal in 2018, but a carry-over effect was evident with 33%F being 2 days earlier than 66%F and 100%F in 2019 . In 2017, blueberry package the treatments started having an impact few weeks after they were imposed. Veraison was delayed by defoliation treatments by ca. 5 days in 2017 and 2018 . Leaf senescence was consistently delayed the defoliation treatments . Extreme defoliation delayed leaf senescence by 9, 5, and 2 days in 2017, 2018, and 2019, respectively. Conversely, we saw a reversal of this trend where retaining more fruit delayed leaf senescence, albeit with a less strong effect than defoliation.At the moment when the treatments were imposed, the proportions between the numbers of leaves to clusters were extremely different amongst treatments. These differences were self-balanced largely by harvest. Changes in berry size explained a great part of this variation. Typically, berry size is managed by limiting the access of grapevine to water . However, in this case, defoliated plants had a most certain lower consumption of water, and therefore, better water status , but this was concomitant to a reduction in berry mass which ruled out the water status as cause. Another common way to manipulate berry size is a delay in cluster thinning that encourages a competition of fruits early in their development, making berries smaller . Mechanistic experiments revealed that berry growth and the import of sugars may not occur in absence of the one or the other , and therefore, defoliation may have induced lower berry size through a reduction a sugar allocation . Berries per cluster were also affected by the severity of defoliation. This was a complex result as number of flowers, percentage of fruit set, or spontaneous fruit abortion may determine the number of berries at harvest development. However, in the 1st year of treatments, berry abortion after pepper-corn stage was evident. This was in fact the case, and vines in 33%L treatment displayed berry abortion close to veraison which was associated to carbon starvation . Exogenous gibberellin applications are typically used in commercial table grape production to reduce cluster compactness through flower abscission . Endogenous gibberellin and auxin determine the number of berries set, therefore affecting the number of berries and thusly berry size . Although reductions in the number of berries per cluster were significant in the second season, berry abortion was not evident, which suggested this was an acclimation response to the treatments of the previous season. This was reported by previous studies where the number of inflorescence and flowers were reduced by defoliation during the previous season .

However, balancing leaf area to fruit mass is a very precise task that involves a great amount of hand-labor or investment in a large equipment park to conduct these practices mechanically . In this pursuit, trellis, vine spacing, canopy management, and irrigation have been proposed as indirect methods to optimize LA/FM . Thus, the concept of vine balance appears to work in a practical sense, as it is used to make cluster-thinning decisions and but not defoliation. Our data suggested that one unit of leaf area was not equivalent to one unit of fruit mass. The main factor that made leaf area outweigh the value of fruit mass is that fruit is only a fraction of the total amount of carbon assimilated by leaves throughout the year is translocated to fruit . Furthermore, leaves do not only assimilate carbon , and canopy size has deeper implications than fruit mass for root growth and the transduction of ripening signals. For instance, defoliation may suppress ABA signaling induced by water deficits , which would reduce berry ripening stimulation . In fact, ABA biosynthesis in leaves relies mostly on leaf induction rather than root signaling . There is a feedback mechanism between the production of auxin and cytokinin by leaves and roots, respectively; where auxins are biosynthesized by developing leaves and shoot tips and therefore stimulating root growth, and roots produce cytokinins that stimulate the growth of the aerial portions. Therefore, defoliation may not only reduce the amount of reduced carbon allocated to berries, but also to the ripening stimuli through endogenous plant growth regulators. Fruits are the fate of many growth regulators depending on the berry developmental stage , and thus, changes in crop load could potentially alter the balance between the amount stimuli and fates. Therefore, leaf area to fruit mass is typically correlated to berry must soluble solids as in the 2nd year of study . Although, it is possible to find situations in which crop level does not compensate for defoliation as in the 2nd year of study . In fact, it is rather unusual to find lack of effects on ripening when two thirds of the clusters are removed from such an early stage as the present study. Finding only a significant effect of fruit removal in total soluble solids in the 2nd year could also suggest cumulative effects of crop level.

Internal consistency reliability across the items was high . Higher scores reflect higher levels of cumulative risk. We treated cumulative risk as a strictly between-child or time-invariant variable, given the limed within-person variability in cumulative risk over time .Informed by prior studies , we adopted a variety of child and family covariates in an attempt to adjust for potential confounding factors that could bias our estimates. As we describe in detail in the online supporting material, our control covariates included infant gender , race , temperament, primary caregiver reading ability, age at birth, marital status, maternal education, maternal hours worked per week, and research site . These control covariates were measured when the target child was 2 months of age, with the exception of temperament, which was measured at 7 months. Within- and between-person variation in saliva collection times were also controlled in all models.As indicated in prior work , there is little evidence of selective attrition in the sample through early childhood. Missing data were modest. For the cortisol measures missingness ranged between 13% and 26%, the latter representing children’s cortisol levels at 24 months. There was no clear pattern to the missingness; missingnesss was not associated with maternal education, income, or partnered status. Missing data with regard to child care quantity ranged between 3% and 9%. Of those who had a spell of child care , growing bags missing data for estimated caregiver responsivity was 19%, and missing data for those reporting center-based versus non–center-based care ranged from 23% to 31%. To adjust for biases emerging due to missing data, we fitted all models using full information likelihood estimation .

FIML estimation helps to reduce biases to the extent to which missingness is missing at random —that is, conditionally random after adjusting for the observed variables included in the likelihood function . As a robustness check, we fitted an identical taxonomy of models in which only children with 10 or more hours of child care were included in the observed covariance matrix . As the findings were substantively identical and because zero hours represents a “real” value on the childcare hours distribution, we report findings based on the less restricted sample.To address our questions, we fitted a taxonomy of multilevel models . We present a simplified exemplar model in the equations given below for parsimony and ease of explication. Here, the model tests the extent to which the respective within person effects of child care hours, age, and a within-person interaction between child care hours and age varies as function of between-person cumulative risk. We, however, tested identical series of models for non-parental caregiver responsivity and type and peer exposure. In all models, we first tested the main effects of cumulative risk and the given child care predictor. We then added the respective two- and three-way interaction terms to the model in distinct steps. In a final step, we integrated all of the child care predictors into a final model to test their unique relations. Only interaction terms that survived Benjamini-Hochberg corrections were integrated into this final specification. Sometimes called a hybrid model , this multilevel specification is more efficient than typical child-fixed effect models common to the econometrics literature while still retaining the advantages of child-fixed effect models; specifically, the estimates for the Level-1 predictors are identical those obtained using a child-fixed effects specification, such that they account for all potential observed and unobserved time-invariant confounds.

The hybrid approach also affords the ability to simultaneously model between-person relations at Level 2. Importantly, for our purposes, they also allow one to estimate cross-level interactions; specifically, as shown by parameter γ31, we tested the three-way cross-level interaction addressing our questions: Does the within-person effect of child care exposure moderate the association between cumulative risk and cortisol, and does this interactive effect vary as a function of age? As displayed, the model for the residual variances includes only within-person, time-specific residual and a random intercept —implicitly constraining the within-person effects to be identical across children. This parsimonious specification is tested and relaxed, as appropriate.Child care quantity—As displayed in Column A of Table 2, preliminary main effect models indicated that, when considered in aggregate, within-child changes in child care hours were not associated with contemporaneous changes in children’s cortisol levels. However, as evidenced by the statistically significant three-way interaction in Column B , this null main effect was explained by the fact that direction of the within-person child care effect was conditional on level of cumulative environmental risk experienced by the child, as well as child age. We display these conditional relations in Panels A through C in Figure 1; the values of all other predictors in the model were held at their respective means. Irrespective of cumulative environmental risk, no within-person child care effects were evident at 7 or 15 months of age; none of the displayed simple slopes for child care hours differed statistically from zero. Instead, the interactive effect grew over time, becoming more pronounced and statistically significant by 24 months of age. For children from high-risk contexts, increases in child care exposure at 24 months were associated with contemporaneous decreases in children’s resting cortisol levels. In contrast, for children from low-risk contexts, increases in children’s child care exposure at 24 months were associated with contemporaneous increases in children’s resting cortisol levels Tests of model constraints indicated that the absolute magnitude of the simple slopes displayed in Panel C of Figure 1 were statistically identical . In absolute terms, these relations corresponded to absolute standardized simple slopes of approximately .

Albeit somewhat modest, it is worth noting that in relative terms these simple slopes are approximately two thirds the size of the standardized within-person effect for time of day —one of the most well-understood biological mechanisms underlying normative within-person variation in cortisol. Between-child differences in children’s average weekly child care hours were predictive of only children’s cortisol growth rates , and neither this relation nor the relation between average child care hours and children’s 7-month cortisol levels were moderated by children’s level of cumulative environmental risk. Children who attended greater hours in child care on average tended to show less negative declines in their cortisol levels over, irrespective level of cumulative environmental risk . We display this relation in Figure 2 for prototypical children experiencing low versus high levels of child care exposure per week on average across infancy and toddlerhood; all other predictors are held constant at their respective means. Whereas children attending 40 hours of child care per week were estimated to maintain their 7-month cortisol levels over time , those attending 10 hours a week were predicted to show a statistically significant decline their cortisol levels between 7 and 24 months of age . Note that this decline was rather modest, approximating a 0.02-SD decrease, per month. Child care type—There was no evidence of a within-person effect with respect to child care type ; that is, nursery grow bag time-specific shifts to center-based or non–center-based child care were not associated with contemporaneous changes in cortisol. There was, however, some evidence that the positive between–person relation between attending comparatively more center-based care between 7 and 24 months and children’s cortisol levels differed for children from higher versus lower levels of cumulative risk . This two-way interaction did not vary as a function of age—that is, it was not predictive of cortisol growth. There was, however, evidence that attending greater proportions of time in center-based child care was predictive of more rapid cortisol decreases over this period . In the former case of the interaction, it is also worth noting that the raw pvalue for this estimate, .01, dropped to marginal levels of statistical significance after adjusting family-wise false discovery rate. We nonetheless display the simple slopes derived from this interaction in Figure 3, with this caveat in mind.As shown in Figure 3, we found evidence that, for children experiencing low levels of environmental risk, those who attended comparatively greater proportions of their time in center-based child care tended to have higher cortisol levels . This is most clearly illustrated by considering the vertical distance between the dashed and non dashed gray trajectories at 7 months in Figure 3; it reflects the 7-month simple slope for those attending 100% of their time in child care in center-based care, compared to those who spent 100% of their time in non–center-based child care. This conditional relation is noteworthy, approximating a standardized association of .41. In contrast, child care type was unrelated to children’s 7-month cortisol levels, for children from high-risk contexts .

As indicated by the divergence of the dashed and non dashed black trajectories over time, there was a descriptive indication that, for those from high-risk contexts, attending predominantly non–center-based care was predictive of comparatively less rapid cortisol declines between 7 and 24 months. However, the conditional effect of child care type at 24 months only approached statistical significance . Considered another way, despite the descriptive differences in the estimated cortisol values plotted at 24 months of age in Figure 3, these values were statistically identical. non-parental caregiver responsivity—Within-person changes in caregiver responsivity between 7 and 24 months were not associated with contemporaneous changes in children’s cortisol levels, irrespective of child age or level of cumulative risk. Similarly null relations were evident with respect to between-person differences in children’s average levels of caregiver sensitivity across this period. Peer exposure—Within-child changes in peer exposure were not associated with changes in children’s cortisol levels over time. However, there was some indication that between-child differences in children’s average levels peer exposure were predictive of children’s overall cortisol levels. Specifically, on average, children who typically attended child care with greater numbers of peers tended to evince lower cortisol levels . This corresponded to a moderate standardized coefficient of approximately. Adjusting for false-discovery rate, this relation did not vary over time or as a function of children’s levels of cumulative risk.There is good evidence that children’s child care experiences affect HPA axis functioning . However, it is increasingly clear that these relations may be quite different for children growing up in high-risk environmental contexts. The aims of the present study were twofold. The first aim was to test the extent to which within- and between-child differences in children’s child care experiences—quantity, type, caregiver responsivity, and peer exposure —across infancy and toddlerhood were associated with children’s cortisol levels over this period. The second aim was to consider whether these relations differed for children experiencing higher levels cumulative contextual risk outside of child care.Our results provide some support for such interactive effects. As hypothesized, for children from low-risk contexts, within-child increases in weekly child care hours were associated with contemporaneous increases in children’s resting cortisol levels. The inverse was evident for children from high-risk contexts; increases in weekly child care hours were associated with contemporaneous cortisol decreases. The magnitude of this cross-level interaction strengthened over time, reaching statistical significant between the ages of 15 and 24 months. Interactive effects between cumulative risk and attending center-based care were also evident; however, they extended to only between-child differences in overall centerbased exposure between 7 and 24 months of age . Controlling for child care hours, caregiver responsivity, and peer exposure, children from low-risk families who spent greater proportions of their time in center-based child care tended to have higher cortisol levels than their peers who attended more non– center-based childcare. In contrast, for children from high-risk contexts attending center based care was unassociated with children’s cortisol levels. With respect to children’s exposure to peers in child care, there was evidence that children exposed to greater numbers of peers between 7 and 24 months tended to show comparatively lower cortisol levels. This relation did not vary as a function of cumulative risk or age. Within-person changes in peer exposure were unrelated to changes in cortisol, irrespective of age or level of cumulative risk.Prior work conducted with lower risk samples has shown that children’s cortisol levels tend to increase over the course of the day on days when they attend child care yet show normative diurnal declines on days in which they do not attend child care . Nontrivial differences between this prior literature and the present study make direct comparisons impossible.

Since birds do not eat coffee cherries, bio-control by birds would only occur during the brief dispersal period when CBB are vulnerable. There is a rich bird community during this period of time as both resident and migratory birds are present . Neotropical migrants are potentially more abundant on coffee farms than resident species that may prefer forest habitat due to higher prey abundances . Many migratory warbler species of the Setophaga genus that frequent coffee farms have been confirmed as CBB predators, as have resident bird species such as the rufous-capped warbler and common tody flycatcher   This positive density-dependent relationship between population growth and density is an Allee effect , and escape from predation is one mechanism for this phenomenon . In general, predator-driven Allee effects can occur when predators are the main driver of prey dynamics and when predators are generalists as are insectivorous Neotropical migrants . Additionally, predators can exert strong pressure when prey availability is not temporally or spatially limited—a potential limiting factor in the coffee system, since CBB are only available to birds during dispersal. The degree to which birds exert an Allee effect on CBB might depend on the starting population size of the pest. Variation in starting population size is likely dependent on how recently CBB have colonized in an area, timing of trapping , the size of the farm , and the extent to which farmers used control measures the previous year . We found that only under very low initial population sizes of CBB could birds be expected to suppress pest numbers by 50%. We note that earlier, nursery pots stronger CBB suppression by birds would lead to lower infestation numbers later in the coffee season, but this might require selective foraging by birds, depending on relative abundances of other prey species.

In conclusion, our models suggest that birds can control CBB under some circumstances, depending on the relative size of the starting CBB population and existing local bird density. To put this idea into practice it is important to remember that managing farms for bird habitat does not always result in pest reduction. Birds may not prey on the pest of interest or birds might cause pest numbers in increase by preying on insect predators that normally regulates the pest population . Aside from predators, pest species are also impacted by the agricultural environment directly . In fact, on coffee farms where bird densities are higher in shade, CBB infestations are also higher , possibly because CBB native range is in humid, shade forests of Africa . It is important that future modeling include such habitat-specific factors to understand Our research helps quantify the densities under which birds have the potential to control CBB populations. Putting these numbers into practice will require understanding how management practices affect both bird and CBB densities.Synsepalum Daniell and Englerophytum K. Krause are two closely related genera of the sub-family Chrysophylloideae in the family Sapotaceae. These two genera comprise 35 and 19 recognized species respectively and are predominantly distributed across West-Central tropical Africa. Both genera share the frequent presence of stipules, usually 5-merous flower with the irregular presence of small staminodes, similar seeds, and embryos. They are however considered to be different genera due to the consistent striate brochidodromous venation and strong fusion of the filaments into a staminal tube found in species of Englerophytum, whereas in species of Synsepalum leaf venation tends to be eucamptodromous and the filaments are free. In their study of the SynsepalumEnglerophytum complex, reported six lineages from combined data from nuclear DNA, chloroplast DNA and morphology analyzed using parsimony. The views of [2] are however different from the previously obtained results from in which the two genera formed a single heterogeneous clade where species of Synsepalum genus were grouped within species of Englerophytum. The differences between the two genera are a call for concernas the decision to either merge the two genera or separate them is yet to be reached.

Also, [5] in their multi-gene phylogeny study, found support for the monophyly of the Synsepalum–Englerophytum clade but did not sample either genus extensively, only very limited sampling of the two genera.Synsepalum has undergone several taxonomic changes throughout history as new species have been discovered. It is comprised of trees and shrubs native to tropical lowland areas of Africa. It was described in 1852 and currently consists of about 35 species, including the very popular miracle berry plant, S. dulcificum Daniell which is the type species on which the genus is based. Like the genus Diploon Cronquist, Synsepalum has glabrous staminodes and imbricate to valvate corolla lobes. A very common feature in the genus is their fused sepals, a character that gave the name to the genus. Synsepalum can also be characterized by its long spreading corolla lobes and large stipules. The current 35 recognized species in the genus are a combination of species from previously recognized smaller genera, including Afrosersalisia A.Chev., Pachystela Radlk, Vincentella Pierre, Synsepalum, and Tulestea Aubrév. & Pellegr. Previous generic classifications were considered unsatisfactory and therefore the genera were united under Synsepalum. The small genera were merged using overlapping characters to form the currently recognized genus. The combination of the following characters was used to describe Synsepalum: frequent occurrence of large stipules, eucamptodromous venation, 5-merous flowers, corolla nearly always rotate, cyathiform or shortly tubular with wide-spreading lobes, corolla lobe aestivation imbricate or induplicate valvate, stamens fixed at or near the top of the corolla tube, exserted with well-developed filaments. The seed is broad and not laterally compressed, with a broad adaxial scar that sometimes extends to cover most of the surface. The embryo has plano-convex cotyledons and endosperm is known to be generally absent in the genus. Due to the inconsistency in the characters of the small genera that were merged, species in the genus are often individually very distinct.

This has complicated the taxonomic revision of the genus and caused many synonyms to have emerged. With the emergence of molecular technique, the lumping of these genera to form the genus Synsepalum has been disputed by many authors as the conclusion was purely based on morphological characters.Englerophytum K. Krause was described as a genus, with Englerophytum stelechanthum as the type species. Five species were added to the genus, two of which were newly described while the other three were products of new combinations of species previously classified in different genera. As opposed to the views of [11], who advocated for the distinct status of the genera Englerophytum, Wildemaniodoxa Aubrév. & Pellegr. and Zeyherella Aubrév. & Pellegr, united the genera based on the fusion of their filaments and the number of floral parts. Although considered Synsepalum to be closely related to Englerophytum because of the frequent presence of stipules, usually 5-merous flowers, irregular presence of small staminodes, and similar structure of seeds and embryo, he considered Synsepalum distinct genus from Englerophytum.The Sapotaceae classification of was purely morphological as that was the standard used then in reaching taxonomic conclusions. Nuclear DNA and plastid trnH-psbA were used by to estimate phylogeny within the Synsepalum–Englerophytum clade. Their results do not support the classification by Pennington, and the species of the two focal genera of this study that they analyzed were resolved in a polytomy of six clades: two comprising the species of Englerophytum and four of Synsepalum. However, plastic planters their result cannot be considered final due to incomplete sampling, as only 11 out of the 35 accepted species of Synsepalum and 8 out of the 19 species of Englerophytum were used for the study. They also recommended that more work is required before a comprehensive taxonomic conclusion about the clade can be reached. Aside from the work of [2], there are no published reports on phylogenetic relationships within the Synsepalum-Englerophytum clade. In their studies of the SynsepalumEnglerophytum complex, reported that four of the six lineages comprised Synsepalum species, and three out of the four lineages of Synsepalum corresponded to the smaller genera of the earlier generic classification by [9]. There are, however, some concerns with the lineages reported. Some of the lineages had just a single species, which was not the type species of the small, segregated genus . More species need to be investigated to better understand the phylogenetic relationships among species currently classified in Synsepalum and Englerophytum and to determine the number, names, and circumscriptions of genera that should be recognized in a phylogenetically based classification.In general, plant phylogenetic studies provide a framework for understanding the fundamental processes of evolution and help in organizing the diverse plants of the earth in a way that will make sense to all. In the genus Synsepalum, although the presence of stipules and 5-merous flowers has been suggested as diagnostic characters for the genus, the presence of stipules is not consistent. They are missing in some species, these may represent secondary losses, however. Phylogenetic analyses based on molecular data should make it possible to evaluate relationships among species in the group and compare them with the ancient generic concept. Moreover, not much has been done in resolving the divergent views of researchers on the merging of the small genera by Pennington to form Synsepalum sensu lato. This research proffers a solution to taxonomic problems in the Synsepalum–Eglerophytum complex.

It is generally believed that fresh materials from the field are more reliable for DNA extraction but due to the outbreak of the Covid-19 pandemic, getting to the field to sample materials was not an option to be explored for this study. Thus, materials for both Synsepalum and Engleropytum were mostly accessed from herbarium material. Materials were obtained as loans through the University of California Davis Herbarium . Samples were collected from Missouri Botanical Gardens , New York Botanical Gardens , Harvard University Herbarium and The Conservatory and Botanical Garden of the city of Geneva . A few other samples were collected in silica gel from people who grow them in their gardens. Leaf material sufficient for use in extracting DNA was removed from the herbarium samples.To avoid the destructive removal of leaf samples, leaves already placed in the fragmented packet in the herbarium sheets were first used. Where there were no leaves in the fragment packet, a single leaf was removed and used for the experiment. A total of 103 leaf samples were used for this study, comprising 43 from different herbaria in the United States , 56 from Switzerland and France , and four were fresh samples, see Supplementary Materials, Table S1.The amplified fragments for both regions were controlled for their quality by electrophoresis. 1.8 g of powdered agarose gel was added to 100 mL of 1X TAE buffer. The mixture was shaken vigorously to ensure the agarose gel was completely immersed in the 1X TAE buffer. After heating, 1 µL of Sybrsafe DNA gel stain is added to the beaker containing the agarose gel, which is placed in a bath containing water for a few seconds until the beaker is cool enough to be handled with the hand using hand gloves. The gel solution was poured into a tray fitted with combs and allowed to stay for 20 min until it solidified. After solidification, the comb is removed, and the wells are loaded with PCR. The chamber containing the loaded DNA is connected to power at 76 KVA and allowed to run for 1 h. The gel is then visualized under UV light. Wells that produce bands are considered successful. The bands are excised using a razor blade. DNA was extracted from the bands and purified by application of a QIA quick PCR purification kit from Qiagen .To obtain DNA sequences, extracted purified DNA from the gel was sent to the UC Davis sequencing center. For each direction of the primer, six micro-liters were used. Raw data from the facility were opened on Sequencher 5.4.6 which was used to assemble contigs and edit the sequences. The first nucleotides of each end of the sequences were trimmed until readable bases were obtained. After trimming up the sequences, BLAST searches were performed to ensure the results obtained were that of Sapotaceae. In cases of contamination, blast results give different plant families and in some cases insects. Whenever contamination was observed the experiment was repeated to be sure the right species was used for the research. Alignment was done using muscle in MEGA X. For the GenBank codes of sequences used in our phylogenetic analyses, see Supplementary Materials, Table S2.The evolutionary history was inferred using the Bayesian Inference and Maximum Likelihood methods.

Analogous to exchanging charges between Gaussian surfaces, changing the topological invariant necessarily requires two sets of Brillouin zone wave functions or equivalently, two bands to touch and exchange quanta of the invariant. Thus, the system becomes gapless as it is tuned across a topological phase transition. Table 1.1 contains a list of analogies between Gauss’s law in electrostatics and topological phenomena in non-interacting band structures. An important consequence of the gaplessness of band structures as they are tuned across a topological phase transition is the existence of protected gapless states on the surface of a topological insulator or superconductor. If a topological insulator or superconductor is placed next to a topologically trivial one, including vacuum, the phases on the two sides of the interface are topologically distinct. Thus, gapless states exist at the interface and survive in the presence of weak perturbations as long as certain basic symmetries of the system are preserved by the perturbations. The number of such protected surface states is intimately tied to the value of the bulk topological invariant. These surface states are very important from a practical point of view as well as they are more easily accessible to many experimental probes than the bulk states and hence, help in identifying the topology of the bulk bands without requiring the bulk bands to be probed directly. Moreover, the surface states fully determine the low energy physics in the presence of a bulk gap and hence, are the only ones relevant for transport. And finally, black flower buckets the surface states of many topological phases display various unusual phenomena that ordinary quasiparticle states do not.

As mentioned earlier, the precise form of the topological invariant in terms of the Bloch functions depends on the symmetry properties of the system of interest. Table 1.2 lists the classes of non-interacting Hamiltonians classified using their symmetry properties, and the sets of topologically distinct gapped phases each class of Hamiltonians may have in one, two and three spatial dimensions. The only physical symmetries used in the classification process are time-reversal symmetry and particle-hole symmetry , since these are the only ones generic to random, disordered systems. Thus, crystal symmetries, which are in general absent in disordered systems, are not considered. The sublattice symmetry in Table 1.2 is defined as the product of TRS and PHS. The ten classes are obtained as follows: both time-reversal and particle-hole conjugation are anti-unitary operations and hence, can either be absent, or be present and square to either +1 or −1. This gives 9 classes of Hamiltonians. The tenth class, AIII is one where both TRS and PHS are broken but their product, the SLS, is preserved.The second way in which topology appears in band Hamiltonians is in the form of topological defects in momentum space. These defects occur at points where the band structure becomes gapless and are analogous to real space topological defects such as domain walls, vortices and hedgehogs, where an order parameter has a non-trivial winding around the defect and vanishes at the defect. Like real space topological defects, topological defects in momentum space can be combined by moving them in momentum space while keeping their total topological quantum number conserved. On a finite system, band structure singularities result in peculiar surface states. Whereas gapped topological phases carry dispersing surface states, gapless topological phases host dispersionless or flat bands on their surface. The flatness of these bands is protected by the topological nature of the bulk band structure and cannot be removed as long as the topological objects in the bulk band structure survive.

One crucial manner in which the topological nature of gapless band structures is different from that of gapped ones is that the former is not immune arbitrary disorder. Since the topological entities occur in momentum space, it is vital that momentum be a good quantum number. Thus, perturbations that break translational symmetry can potentially gap out the topological defects. We now briefly review two common instances of band structure singularities and their associated flat surface bands.The Fermi surface of a Weyl semimetal on a slab consists of unusual states known as Fermi arcs. The Fermi arcs are like a two dimensional Fermi surface, except that the two dimensional Fermi surface is broken into two parts and one part is localized on the top surface while the other is localized on the bottom surface. On each surface, the Fermi arc connects the projection of the bulk Weyl nodes onto the surface, as shown in Figure 1.2.2. A simple way to understand the presence of Fermi arcs is by recalling that the Weyl points are sources of Chern flux. Each two dimensional slice in momentum space perpendicular to the line joining the Weyl nodes can be thought of as a Chern insulator, and the Chern numbers of two slices on either side of a Weyl node differ by one. Thus, if the slices in the region far away from the Weyl nodes have Chern number 0, the Chern number of the slices between the Weyl nodes must be 1 and so on. The Fermi arcs, then, are simply the edge states of the Chern insulators. In summary, there are two broad ways in which topology manifests itself in the spectra of non-interacting band Hamiltonians. For gapped Hamiltonians, a topological phase exists when the Bloch wave functions of the occupied bands form non-trivial topological textures across the Brillouin zone. The exact class of textures that is stable against perturbations depends on the symmetries and the dimensionality of the system. Gapless Hamiltonians, on the other hand, can be characterized by topological invariants by focusing only on the states near the gapless region. The latter manifestation of topology in band structures is, in some sense, less stable than the former because it requires translational invariance and is thus notoblivious to disorder. Both classes of topological phases are associated with unconventional states on the surface of a finite system – dispersing Dirac, Weyl or Majorana modes for gapped phases and flat bands for gapless phases.

In the next chapter, the physics of a famous gapped topological phase – the strong topological insulator – will be briefly introduced and reviewed. Some novel phenomena associated with this phase as well as some material realizations will be mentioned.In the last half of a decade, the buzzword that has perhaps stolen the greatest amount of limelight in condensed matter physics is topological insulators. Two examples of insulators with non-trivial band topology, hence topological insulators according to the definition, were touched upon in the previous chapter. This section does a brief review of the phase that is colloquially called the topological insulator and is the one that has actually captured most of the attention. This is the three-dimensional insulator with time-reversal symmetry – class AII according to Table 1.2 – which has a non-trivial Z2 topological invariant. Henceforth, unless otherwise mentioned, the term ‘topological insulator’ will be used to refer to this particular realization of an insulating topological phase. It is closely related to the quantum spin Hall state; thus, the latter is often also termed the ‘two-dimensional topological insulator’.Having reviewed the main ideas in band structure topology and the basics of topological insulators, we now investigate other possible gapped phases of band Hamiltonians in three dimensions. A convenient starting point is a three Dirac dispersion, french flower bucket since it is proximate to a variety of orders, which when established, lead to an energy gap. In the context of graphene, charge density wave and valence bond solid order as well as antiferromagnetism are known to induce a gap, and lead to an insulating state. Several years back Haldane pointed out that the integer quantum Hall state could be realized starting from the graphene semimetal, in the absence of external magnetic fields. A valuable outcome of this Dirac proximity approach, was the discovery of an entirely new phase of matter, the Z2 Quantum Spin Hall insulator, obtained in theory by perturbing the graphene Dirac dispersion. By analogy, here we study three dimensional Dirac fermions, and their proximate gapped phases, on a cubic lattice. In three dimensions, Dirac points naturally occur in some heavy materials like bismuth and antimony, with strong spin orbit interactions. A three dimensional version of the quantum spin Hall state – the Z2 topological insulator , can be realized by appropriately perturbing such a state, as demonstrated in [38], in a toy model on the diamond lattice. According to recent experiments, this phase is believed to be realized by several Bibased materials including Bi0.9Sb0.1, Bi2Se3 and Bi2Te3. Both the Z2 quantum spin Hall and the Z2 topological insulator phases require time-reversal symmetry to be preserved. The Z2 index represents the fact that only an odd number of edge or surface Dirac nodes are stable in these phases. In contrast, in this chapter we study a toy model on the cubic lattice, with π flux through the faces, which realizes three dimensional Dirac fermions, and identify the proximate states.

To begin with, we consider insulating phases of spin polarized electrons. In addition to conventional insulators, e.g., with charge or bond order, we also find an additional novel topological insulator phase within this model, the chiral Topological Insulator . This provides a concrete realization of this phase, which was recently predicted on the basis of a general topological classification of three dimensional insulators in different symmetry classes. This phase is distinct from the spin-orbit Z2 topological insulators in two main respects. First, it is realized in the absence of time-reversal symmetry. Instead, it relies on another discrete symmetry called the chiral symmetry. Second, these insulators also host protected Dirac nodes at their surface, but any integer number of Dirac nodes is stable on its surface. Thus, it has a Z rather than Z2 character. In an insulator, chiral symmetry restricts us to Hamiltonians with only hopping terms between opposite sublattices. Clearly, this is not a physical symmetry, and hence such insulators are less robust than topological insulators protected by time reversal symmetry. However our results will be relevant if such symmetry breaking terms are weak, or in engineered band structures in lattice cold atom systems . With spin, an interesting gapped state that can be reached from the Dirac limit is the singlet topological superconductor , also first discussed in [119]. This state also possesses protected Dirac surface states. The stability of these states is guaranteed, as long as time reversal symmetry and SU spin symmetry, both physical symmetries, are preserved. The Dirac limit allows for an easy calculation of the charge response of the cTI , and provides an intuitive picture of these phases. For example, the cTI can be understood as arising from a quasi 2D limit of layered Dirac semi-metals, with a particular pattern of node pairings, leading to a bulk gap, but protected surface states. It is hoped that this intuition will help in the search for realistic examples of these phases. Additionally, this picture helps in understanding Z2 topological insulators protected by TRS whose bulk Dirac nodes are at time-reversal-invariant momenta , such as Bi2Se3, Bi2Te3 and Sb2Se3. Finally, we utilize the Dirac starting point to derive relations between different gapped phases. We show that there is a duality between Neel and VBS phases: point defects of the Neel order are found to carry quantum numbers of the VBS state and vice versa. This is done by studying the midgap states induced by these defects, and the results agree with spin model calculations that are appropriate deep in the insulating limit. Thus, the Dirac approach is a convenient way to capture universal properties of the gapped phases in its vicinity. These results are also derived following a technique applied to the one and two dimensional cases, by integrating out the Dirac fermions and deriving an effective action for a set of orders. In particular we focus on the Berry’s phase term which, when present, implies non-trivial quantum interference between them. Such sets of ‘quantum competing’ orders can be readily identified within this formalism. We show that in addition to Neel and VBS orders, interestingly, Neel order and the singlet topological superconductor also share such a relation.