On the analysis and interpretation of late-life fecundity in Drosophila melanogaster

Highlights

• I examine patterns of age-specific fecundity in Drosophila melanogaster.

• The central question is whether fecundity levels reach a plateau in old age.

• At the cohort level fecundity plateaus are explained by population heterogeneity.

• At the individual level plateaus arise from random environmental variance.

• There is currently no evidence that plateaus are heritable or adaptive.

Abstract

Late-life plateaus have been described in both cohort and individual trajectories of fecundity in Drosophila melanogaster females. Here I examine life history data recently analyzed by Le Bourg and Moreau (2014) and show that non-linearity in the cohort trajectory of fecundity is largely explained by heterogeneity in the duration of reproductive life spans. A model specifying linear post-peak decline of fecundity in individual flies provides a better fit to the data than one that combines linear decline with late-life fecundity plateaus. Using repeated measures analysis of variance, I show that age-dependent trends in individual fecundity are mostly linear, while among the most longevous individuals up to 20% of the variation in trends is non-linear. Plateaus in individual trajectories might be explained by evolutionary processes or by random environmental variation. The dominant role of environmental variation is supported by several observations, including the high variability of late-life fecundity, the occurrence of occasional individual plateaus in inbred lines, and the observation of plateaus in only a fraction of the population. Plateau and non-plateau flies identified by Le Bourg and Moreau (2014) have, on average, the same total fecundity and the same fecundity trajectories. The available evidence suggests that the environmental variance for late-life fecundity is sufficiently large to produce occasional individual trajectories that resemble plateaus but are not heritable.

Introduction

Late-life plateaus in age-specific mortality are well documented in Drosophila and other invertebrates (Economos, 1979, Economos, 1982, Carey et al., 1992, Curtsinger et al., 1992, Curtsinger et al., 2006, Pletcher and Curtsinger, 1998, Vaupel et al., 1998, Drapeau et al., 2000, Wu et al., 2006). Mortality plateaus are widely thought to be explained by heterogeneity in mortality rates (Beard, 1959, Beard, 1971, Vaupel et al., 1979, Vaupel and Carey, 1993, Steinsaltz and Wachter, 2006, Gavrilov and Gavrilova, 2011, Wrigley-Field, 2014), though there are unresolved questions about the magnitude of variation required (Service, 2000, Pletcher and Curtsinger, 2000, Drapeau et al., 2000, Mueller et al., 2003, Rose et al., 2005). An alternative explanation is that late-life deceleration of mortality trajectories reflects age-dependent changes in individual organisms. This idea was termed “personal aging” by Khazaeli et al. (1998), to distinguish it from heterogeneity models driven by age-related changes in population composition. The basic idea of the personal aging model is that risk of mortality may moderate late in life because certain causes of mortality diminish or completely cease. For instance, older individuals might be less active or no longer engaged in reproduction, thereby reducing demands on somatic maintenance. The two classes of explanation are distinct because the heterogeneity theory involves changes in population composition over time, while personal aging concerns age-dependent changes in individuals. While heterogeneity is the more widely accepted explanation, there are no definitive results demonstrating that it is the sole or primary factor governing late-life survival in experimental organisms. The two explanations are not mutually exclusive.

Rauser et al., 2003, Rauser et al., 2005a, Rauser et al., 2005b, Rauser et al., 2006 proposed that, like mortality, population trajectories of age-specific fecundity reach plateau levels in old age. By analogy with mortality, fecundity plateaus could be explained by personal aging, by population heterogeneity, or by a combination of those factors. Rauser et al. (2005a) tested and rejected a heterogeneity model involving trade-offs between survival and reproduction, and concluded that the plateaus observed in experimental populations reflected changes in the physiology of old flies. Subsequent reports considered implications of these results in the context of cessation of aging and immortality (Rose et al., 2005, Mueller et al., 2007, Mueller et al., 2009, Mueller et al., 2011).

Other studies have not supported the hypothesis that late-life fecundity in Drosophila typically reaches a plateau. Novoseltsev et al. (2005) found evidence for three stages in the life history of adult Drosophila: maturation, followed by a period of high, relatively constant fecundity in the prime of life, and then a long period of senescent decline with no clear break point marking the start of a late-life plateau. Klepsatel et al. (2013) suggested a four-stage model: maturation to a peak in daily fecundity, followed by linear and then exponential decline, and then a post-ovipository period. The best fitting model was not consistent with late-life fecundity plateaus.

Curtsinger (2013) reanalyzed the data of Rauser et al. (2005a) and found that the late-life curvature in the population fecundity trajectory can be explained by variation in reproductive life spans (RLS) of individual flies. RLS is defined as the period from emergence until the oldest age at which at least one egg was laid. Variation in RLS causes non-linearities in cohort trajectories of average fecundity, including plateaus, even when the trajectories of individual flies are strictly linear. This occurs because the declining population trajectory curves upward at older ages as individuals with shorter RLS lay their last eggs, while individuals with longer RLS continue ovipositing. The phenomenon is analogous to the creation of mortality plateaus by mixing sub-populations with different log-linear mortalities (Vaupel et al., 1979, Vaupel and Carey, 1993, Wrigley-Field, 2014). Heterogeneity in RLS explains the shape of post-peak fecundity trajectories in a variety of Drosophila populations, including inbred lines, lab-adapted outbred populations, and recently collected wild stocks (Curtsinger, 2013, Khazaeli and Curtsinger, 2014).

Recently Le Bourg and Moreau (2014; henceforth LBM) suggested that late-life plateaus occur frequently in the fecundity trajectories of individual flies. Here I reanalyze the data treated by LBM and argue that, at the population level, plateaus in their data are largely explained by heterogeneity in RLS, while at the individual level plateaus are non-heritable manifestations of environmental variance. I also discuss the limitations of quadratic regression and the advantages of repeated measures analysis of variance for treating these data, and consider evolutionary implications of the analyses.