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Age structure changes and extraordinary lifespan in wild medfly populations
Version of Record online: 18 MAR 2008
© 2008 The Authors. Journal compilation © Blackwell Publishing Ltd/Anatomical Society of Great Britain and Ireland 2008
Volume 7, Issue 3, pages 426–437, June 2008
How to Cite
Carey, J. R., Papadopoulos, N. T., Müller, H.-G., Katsoyannos, B. I., Kouloussis, N. A., Wang, J.-L., Wachter, K., Yu, W. and Liedo, P. (2008), Age structure changes and extraordinary lifespan in wild medfly populations. Aging Cell, 7: 426–437. doi: 10.1111/j.1474-9726.2008.00390.x
- Issue online: 18 MAR 2008
- Version of Record online: 18 MAR 2008
- Accepted for publication 6 March 2008
- age structure;
- captive cohort;
- Ceratitis capitata;
- deconvolution model;
- field demography;
- life tables
- Top of page
- Experimental procedures
- Supporting Information
The main purpose of this study was to test the hypotheses that major changes in age structure occur in wild populations of the Mediterranean fruit fly (medfly) and that a substantial fraction of individuals survive to middle age and beyond (> 3–4 weeks). We thus brought reference life tables and deconvolution models to bear on medfly mortality data gathered from a 3-year study of field-captured individuals that were monitored in the laboratory. The average time-to-death of captured females differed between sampling dates by 23.9, 22.7, and 37.0 days in the 2003, 2004, and 2005 field seasons, respectively. These shifts in average times-to-death provided evidence of changes in population age structure. Estimates indicated that middle-aged medflies (> 30 days) were common in the population. A surprise in the study was the extraordinary longevity observed in field-captured medflies. For example, 19 captured females but no reference females survived in the laboratory for 140 days or more, and 6 captured but no reference males survived in the laboratory for 170 days or more. This paper advances the study of aging in the wild by introducing a new method for estimating age structure in insect populations, demonstrating that major changes in age structure occur in field populations of insects, showing that middle-aged individuals are common in the wild, and revealing the extraordinary lifespans of wild-caught individuals due to their early life experience in the field.
- Top of page
- Experimental procedures
- Supporting Information
In the 50 years since the distinguished ecologist LaMont Cole (1957) noted that problems involving age distribution in the field are ‘... among the most important and least elementary matters with which demographers have to deal’, it is remarkable that still so little is known about the age dynamics and lifespan potential of individuals in wild populations. There are at least two reasons for this paucity of information on population age structure and lifespan in the wild. The first reason is that technologies for estimating the age of individuals are woefully inadequate, particularly when used to estimate the ages of older members in a population. For example, the confidence limits for age estimates that are based on follicular relics in females (Tyndale-Biscoe, 1984), the accumulation of pteridines in insect eye capsules (Mail et al., 1983; Lehane, 1985; Lehane et al., 1986), transcriptional profiling (Cook et al., 2006, 2007), or the progressive layering of hydrocarbons in insect cuticles (Desena et al., 1999; Gerade et al., 2004) are often quite large even for young and middle-aged insects.
The second reason involves the constraints on the traditional approaches for tracking individuals in the field including mark–recapture techniques (Amstrup et al., 2005) and biotelemetry methods (Cooke et al., 2004). For example, several avian ecologists (Anderson et al., 1981; Lakhani & Newton, 1983) noted that one of the main models used to estimate age-specific survival rates from recovery data of birds ringed as young is ‘... misleading, untrustworthy and gives a false sense of precision’ (Anderson et al., 1985, p. 97). These ecologists believe that the use of this model may account for the conclusions forwarded by earlier researchers that avian mortality is age independent (Botkin & Miller, 1974). These conclusions are now in doubt (Wooler et al., 1992; Ricklefs, 2000). Similarly, research on water voles (Arvicola terrestris) revealed a male-skewed recruitment sex ratio due to the attachment of radio-collars to females (Moorhouse & MacDonald, 2005).
Several important and widely cited investigations concerned with aging in wild populations do not attempt to estimate field survival or population age structure but instead make life table comparisons in the laboratory between biotypes in one-of-two ways. The first involves comparisons between two or more field-collected biotypes such as between guppy biotypes collected from streams that differ in predation levels (Reznick et al., 1996, 2001), between grasshopper biotypes collected from regions of the Sierra Nevada that differ in altitude (Tatar et al., 1997), and between rotifer species collected from the wild that differ in preferred habitats (Kirk, 1997). The second type of comparison is between biotypes that differ in degrees of laboratory selection such as between laboratory-adapted and wild-type lines of Drosophila melanogaster (Sgro & Partridge, 2000; Linnen et al., 2001) or between laboratory vs. wild-derived mice (Miller et al., 2000, 2002).
With several important exceptions including studies of a radio-collared marsupial (Austad, 1993), a dipteran species that exhibits extremely high fidelity to mating sites (Bonduriansky & Brassil, 2002, 2005), and fruit-feeding butterflies that restrict their movement to well-circumscribed territories (Molleman et al., 2006), the majority of investigations on aging rate in the wild are based on large vertebrates, modest numbers, and life table and lifespan data that are either derived from cross-sectional data (Deevey, 1947; Caughley, 1977; Promislow, 1991) or augmented with longevity information for captive animals (Carey & Judge, 2000; Kohler et al., 2006). For studies in which the sample sizes are large and the data collection in the field is longitudinal, the long lifespans of species studied necessitate the construction of costly databases assembled over several decades (Clutton-Brock et al., 1982; Charmantier et al., 2006; Nussey et al., 2007).
In light of the technological, logistical, and conceptual constraints on studying aging in field populations, the paucity of published research on longevity and aging in the wild, and the need for data used in hypothesis-testing that is gathered from evolutionarily relevant (field) environments, we initiated a field study on the medfly to answer four questions: What is the age distribution in medfly populations through a field season? Does this distribution include individuals at middle and advanced ages? Is there evidence for changes in population age structure? Does the early life experience of free-living flies extend their longevity in the laboratory relative to flies that only experience laboratory conditions when young?
The approach we use in this research is based on four concepts. First, that the frailty of an individual of unknown age that is captured in the wild will be reflected in its remaining longevity. Thus, the postcapture lifespan of individuals that are young and robust when captured will, on average, be greater than that for individuals that are older and more frail. Second, that the postcapture mortality rates of these captured individuals reflects the frailty distribution and, in turn, the physiological age distribution in the population from which they were obtained. Third, that either a relative or an absolute increase in the estimated physiological age of the captured individuals between two sampling periods is an indication of a change in population age structure (Preston et al., 2001; Uhlenberg, 2005) that occurs due to a change in: (i) the proportion of older individuals in a population as indicated either by an change in the mean (or median) age of a population; or (ii) the proportion of individuals over a fixed older age (e.g. 65 years in humans; 40 days in medflies). Fourth, that baseline life tables and deconvolution models (Müller et al., 2004, 2007) can be brought to bear on mortality data derived from field-trapped medfly adults of unknown age that were maintained in the laboratory to estimate population age structure and, in turn, of changes in population age structure in the wild (see Experimental procedures for additional details).
- Top of page
- Experimental procedures
- Supporting Information
The average times-to-death for the 2653 females and 1435 males captured during the 3-year field study were 52.5 and 59.6 days, respectively. These values were less than their respective life expectancies at eclosion (x = 0) in the reference cohorts suggesting that the age of the medfly in the wild was greater than newly eclosed. The presence of younger flies of both sexes in the wild (Fig. 1) is evident from the 8% of field-caught females and 12% of males that survived for 100 days or more in the laboratory (i.e. assuming that only extremely young flies could survive to this age). The presence of older and/or more frail flies (both sexes) in the wild is indicated by the high mortality (10–12%) of captured flies during the first 20 days postcapture. Such high mortality is only found in the reference life table for flies that are already old. In the reference table, mortality during the first 20 days after eclosion was only around 1% per day.
Population age changes
The differences between the mean ages of deaths in flies captured during the different sampling periods exhibited both within- and between-season trends (Figs 2, 3; Table 1) with average times-to-death of captured females at different dates differing by 23.9 days in 2003 (35.5 vs. 59.4 days), by 22.7 days in 2004 (38.8 vs. 61.5 days), and by 37.0 days in 2005 (30.5 vs. 67.5 days). Likewise, the differences in postcapture life expectancies for males captured at different dates in 2005 ranged from 20 to 30 days over the season. Assuming these shifts are proxies for relative shifts in the population age structure of the wild medflies, the results imply that the mean age in the wild medfly populations varied by a minimum of 3–4 weeks over the 3-year sampling period. Statistical tests revealed that differences in mean postcapture lifetimes due to both sex and month of capture were highly significant (p < 10−3; see Supplementary Table S2.1). These tests detect differences among samples rather than trends. The visual evidence for trends is largely confined to the year 2005 for which the sample sizes are more than three times as large as for the other years and correspondingly more persuasive. The significant differences among cohorts support the hypothesis that there were significant changes in age distribution in wild medfly populations over each of the three seasons, with a suggestion of younger populations later in the season.
|n||Mean (days)||SD||Maximum (days)||n||Mean (days)||SD||Maximum (days)|
High remaining lifespans
Remaining lifespans were extraordinarily high during selected periods, particularly during the fall when life expectancies were 52.9 and 62.1 days for the respective 1671 females and the 910 males captured each fall (i.e. September, October, and November). The frequency of captured female medflies that lived to 100 days or more in the laboratory ranged from less than 1-in-10 individuals trapped in June and July in the 2004 and 2005 field seasons to a remarkable 1-in-4 flies trapped in August and September during these same years. Nearly as surprising is the observation that 22% of all males captured in 2003 lived 100 days or more. A total of 19 captured females but no reference females survived in the laboratory for 140 days or more, and 6 captured but no reference males survived in the laboratory for 170 days or more.
The mean remaining lifetimes by sex for reference and captive cohorts at advanced ages are presented in Table 2. Note that differences between both sexes and cohort types were statistically significant for all ages despite the smaller reference sample size (Tables S2.1–S2.2 in Supplementary material). For example, female life expectancy at 80 days postcapture equaled 24.1 days for wild-caught flies, compared to 16.0 days for 80-day-old reference flies. We found that the differences are caused to a large extent by distributional differences in remaining lifetime after 80 days, where many more deaths occur in the reference than in the captures flies. The captured cohorts have a somewhat longer right tail (Table S2.2 in Supplementary material).
|Days||Male cohorts||Female cohorts||p-value*|
|Reference||Captive||Reference||Captive||Male–female comparisons||Reference–captive comparisons|
Wild age structure
Monthly changes in the actual age distributions of wild medflies were estimated using a deconvolution model (Müller et al., 2004, 2007) with three assumptions. First, that relative changes in the patterns of death between cohorts of medflies captured during two or more sampling periods reflects relative changes in their respective population age distributions (Ryder, 1975). Second, in conjunction with the use of age-specific mortality derived from reference life tables, that changes in these postcapture death patterns can be used to estimate the actual age structure in the field if both laboratory-reared and wild-caught adult medflies experience the same mortality risk in the laboratory (for perspective, see Carey et al., 1998; Mair et al., 2005). Third, if we further assume that wild medflies of all ages are captured in proportion to their abundance, then the estimated age distribution of wild-caught flies can also be used to infer the actual age structure in the field.
The overall age trends (Fig. 4) are consistent with the ecological argument that the availability of ovipositional hosts is the primary driver of medfly populations on Chios Island (Papadopoulos et al., 2001). We pool samples from the 3 years of data because of the small sample sizes for 2003 and 2004, which do not support separate analysis. The larger samples from 2005 drive the main patterns of older early populations and younger later populations seen in Fig. 4. Thus, spring medfly populations tend to be older because of the shortage of suitable hosts earlier in the season, and late summer and fall medfly populations tend to be younger because of the abundance of good hosts later in the season. Estimates of the medfly age compositions over the 6-month period from June through November indicate that: (i) during June and July nearly half the individuals were 30 days or older; (ii) during the remaining 4 months (i.e. August through November) from 70% to 90% of medflies were aged less than 30 days; and (iii) throughout the season individuals in all age classes up to 60 days were present in substantial numbers. Our finding that there are wild medfly populations that consist of individuals over 30 days old during a substantial part of the field season is consistent with the hypothesis that medflies survive long enough in their natural environment to mature. The percentage of the 505 medfly females in the reference cohort that were mature at 1, 2, and 3 weeks was 2.8%, 43.8%, and 77.2%, respectively, with an average maturation time of 16.3 days.
The logic of demographic selection (Vaupel et al., 1979; Vaupel & Carey, 1993) underlies the argument that the variance in the age composition of a group of mixed-aged individuals will progressively decrease as the individuals that were old at the beginning of the observation period die off and the individuals that were young at the beginning of the period continue to survive. It follows that the mortality trajectories for a group of individuals of mixed ages (i.e. wild-caught) and for a newborn cohort will converge if the individuals within each these cohorts are subject to the same age-specific rates. This is because the higher attrition of older individuals relative to the younger ones reduces age heterogeneity in the mixed-age (wild-caught) cohort with the passage of time. Thus, only the very youngest individuals present in the original captive cohort are also present (i.e. survive) at the most advanced ages postcapture. Because these individuals would be the demographic contemporaries of those constituting the radix of the reference cohort, the trajectories of the reference and captive cohort mortality rates will be different shortly after postcapture but will converge at advanced ages if age-specific mortality rates are identical in each cohort. Although the trajectories of the hazard rates (Müller et al., 1997) observed at young postcaptive ages for the group of wild-caught medflies are consistent with this logical prediction, they are inconsistent with this prediction at older postcaptive ages in that the trajectories cross rather than continue on similar paths (Fig. 5). And the crossing (Carey et al., 1995) is much more pronounced in female than in male medflies.
By disaggregating the capture data by month, we discovered that the effect of lower old age hazard is tied to seasonal flies with strong effects (in decreasing order) for females in August, September, and October cohorts and higher old age mortality for June (highest of all relative to reference), July, and November cohorts (Fig. 6). Lower old age mortality for males occurred (in decreasing order) for October, September, and August cohorts and higher old age mortality for males occurred in July and November cohorts. Thus, longevity potential of medflies appears to have a strong seasonal component (Tables S2.1–S2.2 Supplementary material).
- Top of page
- Experimental procedures
- Supporting Information
The results of this study involving the captive lifespans of over 4000 wild-caught medflies provide evidence in support of three important hypotheses: (i) that changes in population age structure occurs in wild medfly populations of both sexes; (ii) that middle-aged and moderately old medflies are common throughout much of the field season in central Greece; and (iii) that the lifespans of a fraction of once-wild flies would exceed the lifespans of any never-wild flies. Evidence in support of the first hypothesis was based primarily on the 20- to 40-day differences in postcapture survival times of field-caught medflies, while evidence in support of the second hypothesis was based on estimates from the deconvolution model derived by Müller et al. (2004, 2007). We elaborate in detail on evidence supporting the third hypothesis.
Because we assumed initially that the stress and wear-and-tear experienced by flies in the wild would reduce rather than extend their potential postcapture lifespans, the extraordinarily long lifespan of the medflies captured as adults in the wild was the most surprising findings of this study. The high survival rates for ‘fresh collections’ (field-collected) of D. melanogaster adults relative to the survival of laboratory-selected colonies was attributed in one study to genetic adaptation of the flies to laboratory conditions (Sgro & Partridge, 2000). However, our results raise the possibility that the higher survival of field-caught fruit flies is due to their experience (conditioning?) in the wild. This finding is important because it points to mechanisms that are either suppressing longevity in the captive environment or enhancing longevity in the wild. Genetic differences could not account for the exceptional longevity observed in captured medflies relative to reference medflies because the reference cohorts were derived from pupae collected from field-infested hosts over many different months during both the 2003 and 2005 seasons. Age bias of field captures cannot account for the increased frequency of survival to extreme ages since the reference cohorts were initiated entirely with newly eclosed medflies (i.e. the youngest flies captured from the wild could not be younger than newly eclosed).
The higher frequency of long-lived individuals in the group of captured medflies can be accounted for by invoking demographic selection arguments (Vaupel et al., 1979; Vaupel & Carey, 1993) – medflies in the wild that are more frail are probably less likely to be captured due to their reduced foraging ability or because they die sooner in the field than in the laboratory. Selection arguments might in principle account for these differences, but extended analysis (see Experimental procedures) indicates that selection is not likely to be strong enough to account on its own for the larger maximum lifespans found among the once-wild flies. For such an explanation to hold valid, two claims would have to be true. First, death at young ages in the wild would have to be substantially correlated with reduced late-life survival potential. Early death could not be largely random, nor could it be tied primarily to traits associated with early acting kinds of risks. Second, the raw amount of young mortality in the wild would have to be large enough to cull a substantial fraction of the weaker members of the population. Enough of the population would have to be removed to account for the special late survival of the remainder.
There are reasons that argue against both these claims. With regard to correlated risks, previous experiments have been conducted to detect demographic selectivity and have found no effects. For example, experiments involving approximately 400 000 medflies subject to periodic starvation at younger ages had no detectable effect on either the level or the pattern of mortality at older ages (Carey et al., 1999). Similarly, dietary restriction studies on D. melanogaster (Mair et al., 2003) demonstrated that 2 days after the application of dietary restriction at any age, previously fully fed flies were no more likely to die than flies of the same age that had been subjected to long-term dietary restriction. While neither of these experiments fully mimic stresses in the wild, they suggest that high correlations of the relevant kind are not a run-of-the-mill phenomenon. Furthermore, death in the wild is generally regarded as having a strong random exogenous background component of luck and accident.
With respect to the required raw amounts of mortality for demographic selectivity, we are able to perform a mathematical calculation. This calculation leads to the conclusion that extra hazards experienced by flies in the wild before ages of capture would have to deplete the population by an extra factor of more than 99%. The wild and reference populations are separated at the larval stage. Conceivably, substantial mortality could occur in the soil for wild pupae as contrasted with the vermiculite for pupae in the reference population. But it would be a striking surprise if such mortality were strongly selective for late-life fly longevity. Instead, one would expect that the main extra mortality contributing to demographic selection would have to be occurring in the wild between eclosion and ages of capture. Based on the average age in medfly populations (shown in Fig. 4) that were estimated from the convolution model, we think that a plausible figure for young medfly mortality in the wild is on the order of 3–5% per day, or from 25% to 40% of all flies dead at 10 days. These are far below the required 99%. If one tried to argue for much higher daily mortality, say 90% spread over 2 days, one would be hard-pressed to offer mechanisms that would make such mortality not only severe but highly selective. In the Experimental procedures we describe the mathematical calculation which leads to our 99% figure and which suggests that demographic selection would not easily account for the observed differences in mean remaining lifetimes between wild-caught and reference cohorts.
We thus offer two hypotheses for the greater lifespan extremes observed in captured flies. The first is that the early life experience of free-ranging adults may reduce their reproductive costs by inhibiting their ability to habituate in the captive environment. This cost reduction is borne out in our study inasmuch as the total number of eggs laid by field-captured medfly females was 134.1 eggs/female compared with the 413.8 eggs/female in the reference cohort (Papadopoulos and Carey, unpublished data). The second hypothesis is that there is a window in the early adulthood of medflies when the presence of certain amounts or kinds of bacteria in their diet is important and that wild flies have access to these bacteria but that reference flies in the laboratory do not. This hypothesis is based on the recent finding that adult Drosophila maintained in axenic environments in early life experienced reduced longevity in later life even when switched to non-axenic environments relative to those that were given access to bacteria throughout their lives (Brummel et al., 2004). Further research is needed to explore this explanation.
This was not the first study to use mortality patterns derived from individuals of unknown age to gain insights into the actuarial properties of wild populations. For example, one Drosophila study reported survival patterns of wild-caught adults of unknown age between two different species (Begon, 1976) and another estimated age-at-capture by using the difference between the duration-to-death (captive age) and the life expectancy of laboratory-reared individuals (Boesiger, 1968). Unlike our study, however, no attempt was made in either of these investigations to interpret the data in broader demographic contexts, to develop models for estimating population age structure, or to compare systematically differences in the oldest ages of wild-caught flies vs. flies reared from eclosion in the laboratory. The recent modeling study by Anderson et al. (2008) provides a possible alterative to the method described here. In this framework, longevity is expressed through the rate of loss of vitality, an abstract stochastic measure of survival capacity. However, the approach does not describe age itself but rather the probability distribution of vitality as a function of age and stressors and characterizes extreme longevity in terms of vitality.
The approach we used to estimate age structure or to characterize changes in population age structure in this study has three potentially important sources of bias. The first source is from differences in age-specific mortality between wild-caught and laboratory-reared medflies. If same-aged mortality is higher in wild-caught relative to reference flies, the deconvolution model will overestimate the average age in the wild population. However, if mortality is lower in wild-caught vs. reference flies, the model will underestimate average age in the wild population. The magnitude of the errors in age estimates are conditional on the extent to which age-specific mortality differs between the once-wild and the reference cohorts (see the results of sensitivity analyses in Appendix S2 of the Supplementary material). The second source of potential bias is in the age and/or frailty composition of field captures. If trapping methods are biased towards capturing certain age classes over other age classes, the estimates of age structure will be valid only for the subgroups of flies captured but not for the wild population as a whole. However, there was no indication of major age bias in trapped medflies in this study (see Appendix S1 of the Supplementary material). A third source of potential bias applies to estimates of changes in population age structure. Whereas we attributed changes in the average ages of death for flies captured at different times in the season to shifts in population age structure, an alternative explanation is that the average ages of death were due to differences in adult fitness resulting from the nutritional characteristics of the larval hosts in which they developed (Carey, 1984). However, laboratory studies of host effects on adult medfly longevity (Krainacker, 1986; Krainacker et al., 1987) suggest that change in larval host quality would account for age shifts in the neighborhood of 3–5 days, with a maximum of 10 days under extreme conditions (i.e. single favorable or unfavorable host available). These potential shifts are far less than the 20- 40-day differences in the average times-to-death that were observed in the captive medflies in the current study.
Although caveats certainly apply to the current results, they also apply to the results of virtually all other studies designed to estimate individual or population age in insects. For example, the transcriptional profiling method of aging applied to the mosquito Aedes aegypti (i.e. based on genes that display age-dependent expression) is not only costly and time-consuming, but generates age estimates that fall only within ±5 days of the actual age and only to around 3 weeks (Cook et al., 2006). Moreover, it is yet to be determined how robust the calibration models used in the transcriptional profiling method are across season or regions or whether the results can be replicated. Many similar issues arise with the use of cuticular hydrocarbons (Gerade et al., 2004), pteridine concentrations (Lehane & Mail, 1985), and follicular relics (Tyndale-Biscoe, 1984; Lehane et al., 1986) for estimating the age of insects in the field. Data obtained from insect mark–recapture studies used to estimate survival are often fraught with problems that violate many of the most basic assumptions of this method (e.g. independence of recapture probability, closed populations). These problems not only include the inability to distinguish between emigration and death, but also issues associated with large variation in capture probabilities due to changes in weather (e.g. persistent cold front, long rainy period), in insect behavior (e.g. dispersal tendencies when young, trap ‘happy’ or ‘shy’ individuals), in ambient food availability (i.e. competing attractants), or in trap densities (i.e. opportunities for capture). Thus, the sophistication of the analytical methods applied to mark–recapture data (e.g. White & Burnham, 1999) cannot offset errors introduced due to the violation of the basic assumptions of the models.
We believe that the results of the current study are important for at least two reasons. First, the uncertainty of the causal mechanism(s) for the longevity-extension effect observed in wild-caught medflies points to a more general void in our understanding of longevity – not only are different factors that affect the aging rate in wild populations unknown, but the importance of factors that are known to affect aging (e.g. dietary restriction) in model systems are also poorly understood in virtually all wild populations (Austad & Kristan, 2003). Related to this point is that the interpretation of data that reflect fruit fly survival in the field rather than in the laboratory will require new thinking about the importance of aging in the larger context of ecology and evolution of the species (Kirkwood, 1992).
Second, the analytical and empirical techniques introduced here provide a new ecological tool for the demographic analysis of aging in wild populations by linking the theoretical, analytical, field, and laboratory components into a single fabric of demographic interconnectedness. This new approach may prove useful in a variety of contexts ranging from analysis of medically important insect populations (Styer et al., 2006) and ecological mark–recapture studies (Juanes & Smith, 1995; Hagler & Jackson, 2001; Amstrup et al., 2005) to field studies concerned with tests of evolutionary theory (Abrams, 1993), and development of new concepts in gerontology (Hayflick, 2002).
It is remarkable that a half century after Cole's musings about demographic research in the field (1957), the evidence for both actuarial and changes in age structure in wild populations is still scarce. In light of the paucity of literature containing the results of aging studies conducted in evolutionarily relevant environments and of Medawar's (1981) argument that the origin and evolution of aging is one of the most important unsolved problem in biology, we believe the methods presented in this paper have the potential to open up new areas of aging research (Partridge et al., 2005) through the use of field studies on insects. Our approach offers a logical framework, a new methodology, and testable hypotheses for revealing age patterns and lifespan potential in wild insect populations.
- Top of page
- Experimental procedures
- Supporting Information
Two different types of life tables were brought to bear on the analysis of age patterns in wild medfly populations. Reference life tables were constructed to obtain age- and sex-specific mortality rates for medfly adults of known age that emerged from field-infested hosts and maintained in the laboratory. Approximately one-third of medfly pupae were obtained from infested figs (Ficus carica) and two-thirds from infested mandarin oranges (Citrus aurantium) in Chios Island over three sampling periods: (i) September 2003 (135 females, 125 males); (ii) December 2004 (144 females, 133 males); and July/August 2005 (226 females, 209 males). Newly eclosed adults were placed individually in transparent plastic cages (0.4 L capacity), provided with adult food (4 : 1 ratio sugar + yeast hydrolysate), water and an oviposition device (females only). Stress-related mortality (e.g. transport, transfer) was extremely low (< 1% mortality during first 48 h postcapture). Survival of both sexes was monitored daily and the number of eggs laid by individual females was recorded for individuals captured during the 2003–2004 field seasons (although not reported in this paper). Laboratory conditions were maintained at 25 ± 2 °C, 65 ± 5% relative humidity, and 14 : 10 L: D photoperiod.
Captive life tables were constructed from the postcapture survival of free-ranging adults of unknown age that were trapped in the field and maintained in the laboratory through death. Thus, adult medflies of both sexes were trapped on the Greek island of Chios during the 2003–2005 field seasons using 30 McPhail traps (McPhail, 1939) baited with food attractants in 10 trapping locations (three traps per location) in two citrus orchards 2 km apart. The flies captured within a 1-day period were air-shipped for same-day arrival to the University of Thessaloniki, where they were transferred to the laboratory and maintained under the identical conditions as were individual medflies used to generate data for the reference life table.
Survival patterns of medflies in the captive life table were interpreted by comparing them with patterns observed in the reference life tables. Thus, captive life tables constructed using wild-caught medflies and that exhibited similar survival patterns and expectations of life to the reference life table in which life expectancy in females and males was 65.8 and 75.6 days, respectively, implied that the field population from which they were trapped was composed primarily of newly eclosed individuals. It follows that survival schedules of wild-caught flies that departed from this baseline survival schedule indicated flies that were older and/or more frail.
Age structure estimation
The general concept for estimating age structure in wild populations is that the age composition of captured flies can be coupled to their death rates in the laboratory. The convolution equation for this population age structure is:
where fA and fR are the probability density functions of age-at-death in the laboratory-raised reference cohort and of age-at-capture from the wild, respectively, and F̄R is the survival function of the wild-caught flies in the captive cohort. If each individual in the wild population has the same chance of being sampled, irrespective of its age, then fA also corresponds to the density of the age distribution in the wild. The convolution equation is a consequence of the assumption that the force of mortality acting on an individual depends solely on the individual's age and on whether the individual is in the wild or in the laboratory. From life tables of the reference cohort and the captive cohort one can estimate fC, FR , and fR, and then obtains the target density fA by deconvolution. The details are described in the paper by Müller et al. (2007).
Sensitivity analysis of age structure estimates
The results of sensitivity analysis of a ±20% perturbation of the medfly female hazard function derived from the reference life table shown in Fig. 7 reveals differences between the actual age distribution of the population and the distribution estimated using the deconvolution model. When the captive population's mortality in the laboratory is 20% lower than the mortality in the reference life table at each age, the estimates are skewed to younger ages relative to the actual because the lower mortality corresponds to younger ages. When the captive population's mortality in the laboratory is 20% higher than the mortality in the reference life table at each age, the estimates are skewed to older ages relative to the actual because the lower mortality corresponds to older ages.
A summary of analyses across a range of perturbations from ±5% to ±30% (Fig. 8) reveals that the sign of the mortality rate differences between the captive and reference cohorts determines whether the average age in the field population is over- or underestimated. Thus, mean age is: (i) underestimated if age-specific mortality in the reference cohort is less than age-specific mortality in the captive cohort; and (ii) overestimated if mortality in the reference cohort is greater than mortality in the captive cohort. Inasmuch as the medflies captured in the field experienced lower mortality at older ages than the captive cohort, this finding suggests that the average age in wild medfly populations were slightly underestimated (i.e. the actual mean ages in wild populations were older than the estimated mean ages).
Demographic selection model
Calculations suggest that frailty selection would not easily account for the observed differences in mean remaining lifetimes between wild-caught and reference cohorts. The usual approach (Vaupel et al., 1979) assumes a lifetime frailty factor multiplying an individual's hazard rate at all ages, with a gamma distribution of factors across the population. High early mortality in the wild before capture would remove frail flies from the population, leaving less frail, intrinsically longer-lived survivors after capture. The frailty model predicts how much of an increment in initial mortality would have to added to the rates of the reference life table to extend further life expectancy at ages like 80 up to the levels observed in the once-wild samples. It turns out in our setting that there is a lower bound on the required increment which holds across choices for the unknown variance in initial frailty. For the female sample, the increment would be as much or more than 99%. Extremely long-lived flies must have been young when captured. Such a level for young-age mortality is far in excess of plausible rates in the wild, which are thought to be on the order of 3% per day or 24% over 10 days.
The increment required for the mechanism of frailty selection to explain away the difference in late-life survival is too great to be credible. The standard frailty model (Vaupel et al., 1979) sets the hazard rate applying to an individual at age a equal to the product of a baseline hazard function and an individual frailty multiplier Z, where Z is drawn from a gamma distribution with unit mean and shape parameter k, corresponding to a variance of 1/k. In our notation, M(a) is the cumulative hazard up to age a in the hypothetical baseline schedule for the mortality of always-captive flies. W is an increment to the cumulative hazard contributed by extra mortality in the wild over and above baseline, here assumed to be concentrated at or near age zero. la is the survival schedule for the reference life table, assumed to be produced by frailty selection operating on the baseline hazard function; Sa is the survival schedule produced by frailty selection operating in the presence of the precapture increment W along with subsequent mortality corresponding to M(a). Under the model, the survival schedules produced by frailty selection are given by Laplace transforms of the gamma frailty distribution:
- la= (kk)(M(a) +k)−k (1)
- Sa= (kk)(W+M(a) +k)−k= (kk)(W+k(la)−1/k)−k(2)
Further life expectancy at age 80 in the presence of the increment W is given by the integral over a > 80 of Sa /S80. The integrand approaches la /l80 for all a both as the gamma shape parameter k goes to zero and as k goes to infinity, so further life expectancy has some maximum value at some intermediate value of k for each fixed value of W. We evaluate la by setting it equal to the empirical survival schedule for the reference life table, extended into the open-ended interval beyond the last observed death with a hazard estimated from the last 10 observed waiting times at 0.200 per day. For each k we calculate the value of W required to raise further life expectancy at 80 from 16.669 to 24.163. These values are bounded below by W = 4.591. The required increment to mortality is therefore at least 1 – exp(–W) = 0.9899.
This conclusion is strengthened by the expectation that a substantial portion of precapture mortality in the wild is bound to be exogenous, imposed by accident without a close relationship to individual frailty. Adding exogenous mortality to the extra mortalities required for frailty selection would produce even more extreme levels. Furthermore, the effect of extra precapture mortality on mean frailty among survivors would tend to taper with age, whereas the differences in observed survival curves appear to grow with age at extreme ages. Thus, while frailty selection may well operate to some extent, it is not likely to account for the main finding of extraordinary survival among once-wild flies.
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This research was supported by the National Institute on Aging/National Institutes of Health through grants P01 AG022500-01 and P01 AG08761-10. We thank N. Zoudas C. Ioannous, A. Protogerou, A. Diamandidis, and M. Giannakou for technical assistance in Greece, Roger Vargas, Boaz Yuval, Deborah Roach, Ronald Lee, Freerk Molleman, Carol Horvitz, Steven Orzack, James Anderson, and Shripad Tuljapurkar for comments on earlier drafts, and Leslie Sandberg for editorial assistance.
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- Top of page
- Experimental procedures
- Supporting Information
Appendix S1 Empirical and statistical results of medfly trap capture bias study.
Appendix S2 Medfly remaining lifetimes.
Appendix S2 Sensitivity analysis of deconvolution model.
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