Individual-level daily egg laying data for three fruit fly species were used for the analysis for the two tephritid fruit fly species including the Mediterranean fruit fly , commonly known as the Medfly , the Mexican fruit fly , commonly known as the Mexfly , and the vinegar fly, Drosophila melanogaster . Husbandry details for each species are described in the above-cited papers. In brief rearing conditions were 25-27° C and 50-75% RH, and 12:12 L:D for the two tephritid species and 10:14 L:D for D. melanogaster. Whereas the two tephritid species were fed a 3:1 sugar-yeast hydrolysate diet, D. melanogaster females were fed a standard agar-gelled Drosophila food medium. Eggs were collected from mesh at one end of the individual cages for the tephritid females and from the food medium for D. melanogaster . These species were chosen primarily for the availability of databases on individual-level lifetime egg laying. However, they were also chosen because they allowed for three levels of comparison to test the robustness of our discoveries—between two dipteran families , between two tephritid genera , and among three different species.Reproductive data were excluded for the first 10 days of adult life for each of the species, a period during which all individuals matured and developed their first eggs. The remaining data for each fly were then parsed into 1-of-2 segment categories: Terminal segment consisting of the sequence of daily reproduction from 11 days before death to and including the day of death. There were 873, 1,071 and 425 terminal segments derived from individual female Medflies, raspberry containers size the Mexflies and D. melanogaster, respectively; and Midlife segments of the same length. The midlife segments were created from contiguous 11-day series of individual flies that started after maturation and ended 11 days before the fly died.
This selection criteria thus excluded individual flies that lived less than 32 days . This segmentation process was repeated until the number of remaining days to the terminalsegment was less than 11. The remaining days were ignored. The 11-day egg-laying sequences were chosen primarily because the results of preliminary investigations revealed that 11-days was the shortest period of egg laying that contained patterns that yielded consistently high performance metrics across all three species. This period was also chosen because longer egg-laying periods would have substantially reduced the number of segments in each of the databases. We computed two metrics from all of the 11-day egg laying sequences for all three species and the terminal and mid-life segments: 1) Total eggs . This metric was chosen based on the observation that most flies laid fewer eggs at the end of life; and egg-laying ratio . This metric was based on the observation that the relative rate of egg laying in most flies decreased at the end of life. This metric was computed as the ratio of the number of eggs produced from 11 to 6 days prior to death to the number of eggs produced from days 5 to 0 prior to death. This ratio specified both a direction and a magnitude of change as an individual fly approached death. Egg ratio was assigned a value of ER=0 if no eggs were laid in either time interval and a value of ER=5.0 if eggs were laid in the first 6 days but none in the last 5 days—a pattern that suggests rapid egg-laying decline to zero but that results in a zero in the denominator . This value was chosen because it was at the mid-range of the highest ER-values when eggs were laid in both first and last segments. This ER value was high enough to serve as a major change metric between the first and last egg-laying subsegments but not so high to be the overriding drivers of the statistical outcomes.Fig. 1 shows the egg laying patterns of selected individual medfly females at 10 different life table deciles.
With the exception of female #5, the egg laying patterns during the terminal segments were consistent with the hypothesis that rate of egg laying near the end of each of their lives was both low and decreasing . However, the egg-laying patterns that characterize the end of female’s life are also sometimes observed at times when they are not approaching death. Indeed, there are also a number of 11-day midlife sequences of some flies that are indistinguishable from these same patterns in the terminal phases. For example, egg laying rates decrease in fly #5 from days 20 to 30 and in fly #8 from days 30 to 40 days. Although these decreasing egg-laying patterns usually predict impending death, both of these flies another 11 days beyond these ages. Similar egg-laying trends are also evident during the midlife of fly #9. Fly #10 produced very few eggs for a 40-day period from ages 20 through 60 days. Thus this visual inspection of egg laying in 10 different individuals reveals the statistical challenge of classifying egg-laying sequences as either terminal or mid-life.Although computing all three of these parameters is straightforward in both chronological or thanatological age, the values for and interpretations of GRR and T differ between the two age categories. Consider the following hypothetical case for clarifying the differences. Suppose that in chronological time, the age-specific egg laying in four female fruit flies was identical for the ages each were alive with reproductive peaks at 50 eggs/day on day 20. However, they each die at different ages 20 days apart—i.e., at ages 20, 40, 60 and 80 days. When their reproductive schedules are considered in thanatological ages, which is to say, relative to their age of death rather than their age of birth , then their reproductive peaks are in thanatological time correspond to ages 0, 20, 40 and 60 days . Although R0 remains the same since every female still produces the same lifetime number of eggs, the values of both GRR and T will in the vast majority of cases be different because the timing of reproduction is relative to age of death rather than to age of birth .
Whereas day 20 was the average age of peak reproduction in chronological time for the hypothetical example, it is day 30 in thanatological time [i.e., /4].A 2×2 contingency table that classifies prediction is shown in Fig. 2 where the numbers along the major diagonal represent the correct decisions made, and the numbers in the other diagonal represent the errors . If the instance is positive and the instance is a positive, it is counted as a true positive. However, if it is classified as a negative it is a false negative. If the instance is negative and the instance is a negative, it is counted as a true negative. However, if it is classified as a positive it is a false positive. This contingency table forms the basis for a number of common metrics given below.Event-history reproductive charts plotted in both chronological and thanatological time for all three fruit fly species are presented in Fig. 3. Several aspects of these graphs merit comment. First, the chronological plots of egg laying patterns for all species reveal the familiar progression starting at eclosion from the pre-reproductive, raspberry plant container maturation period, followed by a periods of high reproduction with relatively high levels of intra-individual and inter-species variability. This period, in turn, is followed by a period of tapering off, the length of which depends largely on an individual’s lifespan. The low levels of egg laying are evident at older ages in all species but is most striking in the oldest D. melanogaster. Second, the event-history plots in thanatological time reveal visually the repositioning of reproduction that occurs when the schedule is normalized with respect death rather than birth . This shift is especially evident in diagonal band of high reproduction that tracks to the left of the cohort survival the curve. In these cases the most advanced ages in thanatological time correspond the very youngest and thus most fecund ages in chronological time. Third, patterns of egg laying near death as seen in all three species and for both time frames differ between short-lived and long-lived individuals. This is outcome of the differences in the underlying “causes” of death at young and old ages. Increasing frailty due to old age is the most likely “cause” of death in the longest lived individuals. This accounts for the progressive decrease in egg production at older ages. However, increasing frailty due to aging is an unlikely “cause” of death for flies that die young and at ages when they are at or near their peak in egg production. Thus no single egg laying pattern or combination of patterns will likely ever apply to all flies regardless of age or cause of death.Comparisons of the average reproductive rates and timing for all three species plotted with respect to both chronological and thanatological ages are given in the different panels shown in Fig. 4. Because the number of eggs laid by the average female in her lifetime is the same regardless of whether the eggs are summed from birth to death or from death to birth, net reproductive rates, R0, will be the same regardless of whether it is considered in chronological or thanatological time. But as noted in Methods section, this not the case for gross reproductive rate computations.
For example, the 50% greater value of GRR for thanatological age relative to the value of this metric for chronological age in D. melanogaster is the result of a subset of extremely long-lived individuals who both matured early and produced many eggs at young ages. When re-plotted these young ages in chronological time represent the “old” ages in thanatological time. Thus individuals who are both long-lived and highly fecund at young chronological ages represent a large fraction of the small number at the tail end of the “death” cohort. Differences in the values of the mean age of parenthood, T, across species for chronological versus thanatological ages revealed that it was 8 days closer to birth than to death in D. melanogaster, but slightly over 4 days closer to death than to birth in the Mexfly and nearly equidistant from birth and death in the Medfly .The means and frequency distributions of the two independent variables we use in the regression model for each of the fly species are shown in the series of plots contained in Fig. 5. These graphs anticipate the outcome of the modelling results by revealing the differences between the metrics in the midlife segments relative to the terminal segments. There were striking differences in the metrics for each of the two categories of segments in D. melanogaster with nearly 5-fold fewer eggs and 3-fold greater average egg ratio in the terminal segments. The signs of the differences in the mean and overall distributions for the two tephritid species were similar but the magnitudes of the differences were much less. We thus anticipate more favorable performance metrics for distinguishing between terminal and mid-life egg laying patterns in D. melanogaster than in the two tephritid species.The logistic regression model yields three general results. First, the model’s overall performance supports the concept that the egg-laying patterns of total eggs and egg ratio as individual flies approached death are, in the majority of cases, distinctly different from those patterns over an 11-day sequence in middle of their lives. This wasevident in the performance metric of fraction correct —i.e., the FC-value for all species exceeded 0.64 using all data and exceeded 0.73 using only the segments in which flies laid 25 eggs or greater . Second, with a minor difference for several of the D. melanogaster metrics, the performance of the regression model was more favorable when applied to the censored data than with use of the uncensored data. The reason for the differences was because there were 11-day egg-laying sequences in which few or no eggs were produced or that egg laying was declining in midlife. These are the patterns for the independent variables that were associated with and thus predictive of the terminal segments. These midlife patterns occurred more in in the two tephritid species than in D. melanogaster and thus helps explain the higher performance levels for the regression model in this species. Third, the performance metrics for D. melanogaster were extraordinarily high relative to those for the two tephritids as well as absolute.