Constant mortality and fertility over age in Hydra

Ralf Schaible; Alexander Scheuerlein; Maciej J. Dańko; Jutta Gampe; Daniel E. Martínez; James W. Vaupel

doi:10.1073/pnas.1521002112

New Research In

Contributed by James W. Vaupel, October 28, 2015 (sent for review April 4, 2015; reviewed by Thomas B. L. Kirkwood, Robert E. Steele, and Kenneth W. Wachter)

Significance

How an organism changes with age and why the pattern of change differs across species are questions that have intrigued biologists since Aristotle. Patterns of change can be described by trajectories of birth and death rates over age. For humans and many other mammals, mortality increases and fertility declines with age among adults. For other species, however, a remarkable variety of patterns has been observed. Although roughly constant mortality and fertility trajectories have been reported for some species, the data are problematic because sample sizes are small, especially at older ages. Here, we present compelling evidence for constant mortality and reproduction of Hydra using data from careful, large-scale studies over 8 y with 2,256 individuals.

Abstract

Senescence, the increase in mortality and decline in fertility with age after maturity, was thought to be inevitable for all multicellular species capable of repeated breeding. Recent theoretical advances and compilations of data suggest that mortality and fertility trajectories can go up or down, or remain constant with age, but the data are scanty and problematic. Here, we present compelling evidence for constant age-specific death and reproduction rates in Hydra, a basal metazoan, in a set of experiments comprising more than 3.9 million days of observations of individual Hydra. Our data show that 2,256 Hydra from two closely related species in two laboratories in 12 cohorts, with cohort age ranging from 0 to more than 41 y, have extremely low, constant rates of mortality. Fertility rates for Hydra did not systematically decline with advancing age. This falsifies the universality of the theories of the evolution of aging that posit that all species deteriorate with age after maturity. The nonsenescent life history of Hydra implies levels of maintenance and repair that are sufficient to prevent the accumulation of damage for at least decades after maturity, far longer than the short life expectancy of Hydra in the wild. A high proportion of stem cells, constant and rapid cell turnover, few cell types, a simple body plan, and the fact that the germ line is not segregated from the soma are characteristics of Hydra that may make nonsenescence feasible. Nonsenescence may be optimal because lifetime reproduction may be enhanced more by extending adult life spans than by increasing daily fertility.

The classic genetic theories of the evolution of aging formulated by Medawar (1) and Williams (2), mathematically specified by Hamilton (3), and further explained by Charlesworth and Williamson (4) predict increasing mortality and decreasing fertility from maturity for iteroparous multicellular species. As Hamilton (3) put it, senescence starting at maturity is inevitable. Subsequent theoretical advances by Kirkwood (5, 6) and others (7 ⇓–9) allow a more nuanced range of possibilities. Hamilton (3), however, continues to be widely cited, usually uncritically and as dogma.

Compilations of data (10, 11) suggest a variety of age trajectories of mortality and reproduction among organisms, including nonsenescence with constant age-specific death and fertility rates. Constant mortality after the age of reproductive maturity has been reported in field studies of some species of vertebrates (e.g., great tits, collared flycatchers) and nonvertebrates (e.g., hermit crabs, red abalone) (11), and may be common in plants (10, 11). These empirical studies, however, are problematic because sample sizes are small, especially at older ages to which few individuals in the wild survive (12 ⇓–14). Even at ages just after maturity, sample sizes for species observed in the wild are too small to detect whether mortality and fertility are indeed constant or are changing gradually.

To conclusively demonstrate that senescence starting at maturity is not universal for all iteroparous multicellular species, i.e., to refute Hamilton’s (3) canonical assertion, a study is needed that follows large numbers of individuals from maturity to advanced ages. If large populations are kept under benign conditions in laboratories or other protected environments, some individuals live to older ages, permitting detection of mortality increases and fertility decreases with age in, for example, nematode worms, Drosophila, medflies, and rodents (15, 16), as well as in humans. Hence, we tested the hypothesis that Hydra mortality and fertility are constant over age by following large populations under controlled conditions for extended periods that greatly exceed the life expectancy of Hydra in the wild.

Constant mortality in a population can be observed even if the risk of death rises with age for all surviving individuals in the population—if some individuals are frailer than others with a higher chance of death at any specific age. In this case, aging of the survivors will increase average mortality while the death of frailer individuals will lower average mortality for the surviving cohort: the two processes can balance each other (17, 18). To determine whether individuals are deteriorating with age, it is informative to study aging on the individual level. This cannot be done by observing deaths alone because individuals die only once. Individual aging can, however, be studied by observing repeated reproductive events. If an individual’s fertility is constant or increasing with age, then this is strong evidence that the individual, on balance, is not deteriorating with age. Hence, we carefully studied fertility via asexual reproduction of individual Hydra. Deaths in Hydra under laboratory conditions turned out to be so rare that it is unlikely that compositional change could account for constant mortality over age, but evidence that fertility does not decline with age reinforces the conclusion that Hydra do not suffer senescence.

The Cnidaria (Hydrozoa), which include the freshwater Hydra, are classified at the root of multicellular animal life. A Hydra polyp consists of a small sack with two tissue layers, an endoderm and ectoderm, tentacles and a mouth at the top, and a foot at the bottom (19). Three distinct stem cell lineages are present: epithelial stem cells (endoderm and ectoderm lineages), which produce epidermal and digestive cells, and interstitial stem cells, which are the precursors of all of the remaining somatic and germ cell types. Although there is some evidence that interstitial stem cells have a tendency to function as precursors of germ cells (20), these specific cell lineages can be generated de novo from multipotent interstitial stem cells throughout the life span of an individual. Hence, Hydra, like plants, do not have a clear distinction between a germ line and a soma (21).

The adult size of individual Hydra can vary depending on the environment (e.g., food and temperature), but growth is always determinate: Hydra reach adult size when lateral bud formation starts (22). Although sexual reproduction has been observed, Hydra generally reproduce clonally via forming buds from somatic cells of all three lineages that initiate new individuals (23). After detachment from their mother, these buds are independent, self-maintaining, reproductive individuals termed ramets that all share the same genome (22, 23). The collective population of ramets that share the same genome is termed a genet (24). A new genet is created by sexual reproduction. Genet age may substantially exceed the age of the individual ramets that are alive at a given moment. From the perspective of evolutionary theories of senescence, the genet is subject to natural selection and hence is of fundamental interest (25).

In the pioneering study of aging in Hydra (26), the only major study to date, individuals were collected from the field, yielding an assortment of genets of unknown and most likely different ages. A total of 145 individuals was followed. Weekly fertility (from asexual reproduction) varied erratically and differed substantially among cohorts. The fluctuations arose, in part, from the small initial cohort sizes of 20–50 polyps. The small sample sizes were further reduced by high early mortality in two of the four cohorts and by accidental deaths.

Here, we report results from a study using 2,256 individuals observed in 12 cohorts in two different laboratories, Pomona (P) and Rostock (R), over a period of 2,925 d (more than 3.9 million Hydra days). Individuals from three Hydra strains (Hydra magnipapillata strain 105, nine cohorts; Hydra vulgaris strain AEP, two cohorts; and Hydra vulgaris strain ARG45a, one cohort) were cultured individually under controlled laboratory conditions with constant food supply. Genet age of individuals when the experiments were initiated in the nine strain-105 cohorts was at least 33 y, whereas the genet age of individuals in one of the strain-AEP cohorts was a year or less, because the population was produced from eggs. Genet age of individuals in the other two Hydra vulgaris strains is unknown.

Results

Death rates in all cohorts were constant (Fig. 1 and Table 1) and very low. Independent of their laboratory or strain origin, 10 of the 12 cohorts had the same annual probability of death of 0.006 with an average of one annual death in 167 individuals (Fig. 1 A and B, and Table 1). Two cohorts of the at least 33-y-old genet strain had an even lower constant annual probability of death of 0.0009, which differed statistically from all of the other populations (Fig. 1C and Fig. S1). It is remarkable that death rates were independent of genet age. The Rostock cohorts, which were assayed as successive generations of a founder cohort, maintained constant low death rates, indicating that mother’s age did not matter (Table 1, cohorts R1–R9, and Fig. S1). Moreover, death rates of the Rostock cohorts with genet age of 41 y were also indistinguishable from death rates in a Pomona cohort with genet age of a year or less (Table 1, cohort P1, and Fig. S1). Assuming that the mortality rates we measured over ages from 0 to 41 y are representative, such low levels of mortality imply that 5% of individuals still would be alive after between 494 and 3,376 y, depending on the cohort (Table 1).

Fig. 1.

Demographic trajectories. Survivorship and mortality of Hydra by age. Survivorship (Kaplan–Meier estimator; Upper) and annual probability of death (Lower) in 12 Hydra cohorts. (A) Combined data of the three Pomona cohorts. Cohort P1: H. vulgaris strain AEP first generation, 22 individuals derived from fertilized eggs, observed after they were fully grown at 30 d of age; combined with 98 individuals that were raised from buds of the first generation. Cohort P2: 150 H. vulgaris strain ARG45a. Cohort P3: 150 H. vulgaris buds from strain AEP. (B) Combined data of a subset of Rostock cohorts that had the same annual probability of death as the Pomona cohorts. R1–R3 and R6–R9 (1,428 individuals, H. magnipapillata strain 105). (C) Rostock cohorts R4 and R5 (408 individuals, H. magnipapillata strain 105) that differed from the other Rostock and all Pomona cohorts.

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Table 1.

General statistics for all cohorts in the study

Fig. S1.

Estimated daily hazard of mortality per cohort and 95% confidence intervals.

Fertility was assessed as monthly averages of the daily number of buds produced by asexual reproduction. Because mortality was so low, changes in the composition of the cohorts were negligible. Levels of fertility were higher and fluctuated more in the three Pomona cohorts (P1–P3; Fig. 2), which were kept at higher feeding rates than the nine H. magnipapillata strain 105 cohorts in Rostock (Fig. 3). Although fertility increases with age for the individuals studied were somewhat more frequent than decreases (Table 2), reproduction rates for most individual Hydra (80%; Table 2) were constant, at least when assessed over several years. This is particularly apparent in the sequentially initiated Rostock cohorts, for which it was possible to separate the effects of age from fluctuations over calendar time in laboratory environments. These fluctuations are driven by some environmental (laboratory) conditions and can be substantial. This also appears to be the case in the Pomona cohorts, although for these cohorts we are not able to separate laboratory effects from cohort effects.

Fig. 2.

Demographic trajectories. Fertility of Hydra by age in three Pomona cohorts. Fertility expressed as smoothed daily budding rates. Cohort P1: 120 buds of H. vulgaris strain AEP; cohort P2: 150 buds of H. vulgaris strain ARG45a; cohort P3: 150 H. vulgaris buds from strain AEP.

Fig. 3.

Demographic trajectories. Fertility of Hydra by age in nine Rostock cohorts. Smoothed monthly budding rates of Rostock cohorts controlled for environmental effects. (A) Cohorts R1, R2, R3, R7, R8, and R9 had identical shapes of the budding curve, but differed in the level of monthly budding. (B) Cohorts R4 and R5. Both cohorts had an identical shape but also differed in the monthly budding. (C) Cohort R6. The shapes of the cohorts listed in B and C were significantly different from A.

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Table 2.

Individual fertility

Controlling for fluctuations in the laboratory age-specific budding rates for the Rostock cohorts eventually reached a cohort-specific constant level. However, the shape of the trajectories was different among cohorts and three groups could be identified (Fig. 3). Group A (cohorts R1–R3 and R7–R9) had a “burn-in” phase during which monthly budding rates gradually increased over 2 y to reach a constant level that differed among cohorts. This burn-in phase was extended in group B (cohorts R4 and R5): fertility remained low during the first 2.5 y and then rose to a fertility rate similar to the other Rostock cohorts of group A with around 0.6 buds per month. Both cohorts in group B differed from all of the others with respect to their significantly lower death rates (Fig. 1C). Finally, group C (cohort R6) had high fertility just after establishment that subsequently declined to a low and constant value. Mortality and asexual reproduction remained low and constant regardless of whether eggs or sperm were produced (as in all Pomona cohorts) or not (as in all Rostock cohorts).

Discussion

The mortality profile of Hydra—as shown in this 8-y study of various strains kept in two different laboratories—is remarkable. Death rates that are low and constant irrespective of ramet and genet age (which ranged from 0 to 41 y), are features that no other species across the tree of life, up until now, has been conclusively shown to have achieved. Our mortality data are consistent with the results of the shorter and much smaller, pioneering study by Martínez (26). His laboratory-kept strains of Hydra (145 individuals) showed no detectable increase in mortality with age over an observational period of 4 y. Jones et al. (11) reported constant rates of mortality in species other than Hydra (e.g., red abalone and the great tit) based on much less conclusive data and at a much higher level than the rates for Hydra that are presented here. There is no a priori reason, however, to suspect that other species are not capable of achieving life histories of low and constant mortality. Possible candidates are organisms with long recorded life spans, such as sponges, corals, ascidians, and some plants (14). Available data, however, are too sparse to provide the statistical power necessary to conclusively demonstrate constant low mortality.

Reproduction rates of Hydra in our study were constant after an initial phase of increasing or decreasing fertility. Feeding regime affected fertility but did not affect mortality. In a previous study of H. magnipapillata, Schaible et al. (27) found that budding increased linearly with food intake, whereas survival without food (a proxy for the investment in somatic maintenance) was unaffected by previous feeding conditions. Hence, Hydra may prioritize the investment of available resources to levels of maintenance that ensure very low mortality and then use excess resources to produce buds.

Although the isogenic Rostock cohorts were kept under constant feeding conditions, there was variation in the level of fertility. A significant part of these differences may be attributable to chance variation in the physiology of successive isogenic generations (28). This has been documented in other species kept in a constant environment (28 ⇓–30).

Life history traits of Hydra in this study did not vary independently of each other. The two cohorts with significantly lower death rates showed decreased fertility in the first 2.5 y (Figs. 1C and 3, group B). This implies that some individuals under constant conditions are able, at least temporarily, to boost their investment in maintenance at the expense of reduced fertility.

The key finding of our study is that Hydra appear to be able to maintain themselves without accumulating damage and mutations, such that constant (and very low) mortality and approximately constant fertility levels persist over extended periods of time under laboratory conditions—up to 8 y for the individuals (ramets) that we observed and up to at least 41 y in the genets. These durations are much longer than the life expectancy of an adult polyp in the wild. We have not been able to observe survival of individual polyps, but we have been able to roughly estimate population size. Some field studies (31 ⇓–33) and results of our own observations in a pond we studied in Northern Germany show a considerable seasonal fluctuation in Hydra abundance. Early in the season (March, April), population density increases with an abundance peak in June; during this period, buds and immature Hydra are numerous. The population crashes in July and August: no or very few individuals can be observed. At the end of the season in October, the Hydra populations somewhat recover. During winter, Hydra abundance is constant at a low level depending on the duration of the low temperature period and the thickness of the ice cover. Hence, it seems likely that nearly all Hydra born over the course of a year—mostly born in March through June and, to a lesser extent, October—live a few months or less. We conclude that, although there may be some polyps in the wild that are many years old, the average individual at maturity faces a short life numbered in weeks rather than in years.

How and why can Hydra in the laboratory achieve a life history without senescence for an extended period of years? We cannot rule out senescence starting at an age beyond the period we could observe. Because the canonical genetic theories of the evolution of aging—mutation accumulation and antagonistic pleiotropy—predict that senescence should start at maturity and should increase as survivorship declines, we can, however, conclude that these theories do not hold for all species. Theories that permit senescence to start at ages later than maturity cannot be ruled out, although an explanation of why senescence could be delayed so long in Hydra is called for. Because the germ line is not segregated from the soma in Hydra, the disposable soma theory, which allows late-onset senescence, is not directly applicable, but some version of it might hold for Hydra. Sophisticated recent research on the mathematics of the process of mutation accumulation (9, 34) may provide such an explanation. Instead of a delay in eventual senescence to an age vastly higher than average life expectancy, the alternative and simpler hypothesis would be that Hydra are able to maintain themselves for indefinitely long durations.

Nonsenescence may be feasible because of the simplicity of the Hydra body plan and cellular processes, at least compared with more complex animals. Most Hydra cells are continually proliferating stem cells that are never silenced (35). The natural turnover of cellular material in Hydra, which is complete after 3–4 wk (36), is a potent way of preventing the accumulation of damage such as metabolic wastes that cannot be transported out of the cell. Dańko et al. (37) show in a theoretical model that cell turnover, high fraction of stem cells, together with damage-dependent cell selection are capable of preventing senescence in Hydra. In addition to this high cellular turnover, Hydra has developed a high level of emergency repair sensu Kirkwood (6) and can completely regenerate even after most body and tissue structures are destroyed (38). Furthermore, Hydra must be able to repair more routine damage, maintain the integrity of their telomeres, and sustain an efficient and robust immune system (23). These traits carry immediate selective advantages in an environment where dangers due to stochastic environmental hazards, predation, and infection are severe (23).

Nonsenescence for an extended period after maturity may be a stable evolutionary strategy because in Hydra the germ line is not segregated from the soma (21). Mutations in Hydra cells may be transmitted via budding to subsequent generations. Consequently, and similarly to the protection of the germ line in organisms that segregate the germ line from the soma, maintenance and repair of cells is critical to prevent the accumulation of damage (2, 5). If clonal reproduction is initiated by soma cells (instead of parthenogenesis that proceeds from an egg through the full morphogenetic course), this imperative may require prolonged high maintenance over many consecutive generations, as seen in our Hydra dataset. Despite high levels of maintenance, the integrity of the stem cell lineages might slowly undergo deterioration through the accumulation of damage (39). This damage might be negligible or neutral in the environment at the time but might be detrimental over a long time period or if the environment changes. At an extended timescale spanning decades or perhaps hundreds or thousands of years, however, the quality of the gametes might deteriorate, as demonstrated by Ally et al. (40) in stands of poplar clones. The life span of a Hydra genet therefore might be limited by mutation accumulation over sufficiently long timescales. Under these circumstances, occasional sexual reproduction might counteract the deterioration and restore viability of the gametes.

How Hydra maintain constant mortality over the course of life is an important question. Equally important is: why is it evolutionarily optimal for Hydra to do so—and at such a low level of mortality? As noted above, because many of the cells of a Hydra may be involved in reproduction, high levels of maintenance and repair are favored by evolution—consistent with Kirkwood’s disposable soma theory (14, 41). If long life in the laboratory is a byproduct of the exigencies of reproduction by asexual budding and of the need to regenerate damaged or lost body parts, then many such species that do not sequester the germ line may experience low and constant mortality under protected conditions.

It is known, however, that some of these species show a decline in age-specific survival with age—they senesce. This is well documented for the asexual metazoans Paranais litoralis (Oligochaeta) and Stenostomum incaudatum (Turbellaria) (42) and some species of plants (43, 44). In addition, unrepaired damage has been shown to accumulate over consecutive generations in unicellular species, such as Escherichia coli (45, 46) and fission (47) and budding yeast (48).

Thus, the fact that Hydra does not sequester the germ line may not be sufficient to explain the high levels of maintenance and repair that are prerequisites for nonsenescence. Additional factors may be required. Nonsenescence might have evolved as an adaptive strategy if a few fortunate Hydra are sheltered in rare niches and it is these individuals that ensure the continuity of the population (49, 50). Although no data are available, it is possible that some Hydra in the wild survive for many years and these Hydra are crucial for the species’ evolutionary fitness.

In sum, evolution pressures that favor high levels of maintenance and repair in Hydra together with a capacity for regeneration and for preventing deterioration may have jointly favored the Hydra’s life history of nonsenescence. Our experiments provide compelling evidence that death and reproduction rates for Hydra, under laboratory conditions, are constant over age. Why remains an enigma, but glimmers of explanation beckon.

The title of Martínez’s pioneering study (26) is “Mortality Patterns Suggest Lack of Senescence in Hydra”; in contrast, the title of this article is “Constant Mortality and Fertility over Age in Hydra.” The earlier study was suggestive; this study is conclusive over the period of observation. The earlier study focused on mortality; this study shows that both mortality and fertility are constant. Researchers could dismiss the earlier study as small, incomplete, and inconclusive—and could continue to assert, citing Hamilton (3), that for all multicellular organisms with repeated reproduction mortality inevitably rises with age starting at maturity and fertility inevitably falls. This view is no longer tenable.

Materials and Methods

Empirical Data.

Mortality and fertility data are from assays of nine cohorts of Hydra magnipapillata strain 105 at the Max Planck Institute for Demographic Research (Rostock, Germany), and three cohorts with individuals of Hydra vulgaris strains AEP (two cohorts) and ARG45a, at Pomona College (Claremont, CA), with 2,256 individuals started since 2006. Each individual was cultured in isolation in plastic multiwell culture plates under identical laboratory conditions. Deaths because of catastrophic or natural death (see below) and asexual reproduction via the production of new buds were assessed daily.

Rostock cohorts (R1–R9; 1,836 individuals; 3.26 million Hydra days) were initiated sequentially with an interval of about 6 mo, producing cohorts of different ramet ages at a given time. Genet age for the Rostock cohorts was more than 33 y at the start of the study. Pomona cohorts (P1–P3; 420 individuals; 0.63 million Hydra days) were initiated at the same time and ramets had the same age. The genet age of individuals in one of the strain-AEP cohorts was a year or less, because the population was produced from eggs. Genet age of individuals in the other two Hydra vulgaris strains is unknown. See SI Materials and Methods for further details.

Definitions of Death.

In the course of the experiment, we observed two types of death, “natural death” and “catastrophic death.” Natural deaths occurred in individuals that died in the absence of extrinsic forces. This happened over the course of four stages: (i) Hydra were less mobile and took longer to capture the three shrimp that were provided as food; (ii) after 2–5 d, tentacles shortened and took the shape of clubs; the polyps got more transparent; (iii) after an additional 2–5 d, the whole polyps shortened in length and completely ceased locomotion; and (iv) after an additional 2–5 d, the polyps were completely dissolved in the buffer solution. In contrast, catastrophic deaths occurred suddenly and with human impact, for example, when individuals became attached to the lid of the culture dish and dried out subsequently or when individuals were lost during buffer change or by accidentally dropping the culture dish.

Mortality Analysis for All Cohorts.

For each of the cohorts (nine in Rostock, three in Pomona), the following models for the age-specific hazard of death μ(x), where x is age (in days), were fitted:Constant hazard(exponential distribution):μ(x)=λ,Weibull−Makeham hazard:μ(x)=axb+c,Gompertz−Makeham hazard:μ(x)=aebx+c.

Parameters were estimated by maximizing the log-likelihood function. Catastrophic deaths were treated as right-censored observations (at the respective age at death), and individuals alive at the end of study were right-censored at their age at the end of the observation period.

The log-likelihood function for the unknown parameter(s) θ is given by ln⁡L(θ)=∑i=1n[δiln μ(xi;θ)−H(xi;θ)], where n is the sample size, xi is the age at death or right-censoring of individual i, the parameter vector θ is either θ=λ (for the exponential), θ=(a,b) (for Weibull and Gompertz), or θ=(a,b,c) (for Weibull–Makeham and Gompertz–Makeham). The event indicator δi is =1 for deaths, and =0 for right-censored observations. H(xi, θ) is the integrated hazard of the model (51).

All multiparameter models contain the constant-hazard model as a special case; that is, the exponential model is nested in the multiparameter models. Whether the exponential distribution is appropriate or not was assessed by a likelihood ratio test (52). The exponential model was rejected (at the significance level α=0.05) only for the first Rostock cohort (R1). We left-truncated all individuals at age 400 d (only in this first cohort) and analyzed mortality beyond this age (Table S1). Consequently, the log-likelihood was adjusted for left truncation at ui (=400) as ln⁡L(θ)=∑i=1n[δiln μ(xi;θ)−H(xi; θ)+H(ui;θ)].

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Table S1.

Estimated model parameters, log-likelihood values, P values LRT

The maximum-likelihood estimates for an exponential distribution can be derived analytically (number of deaths divided by total time at risk) (51); however, for the multiparameter models, maximization of the log-likelihood has to be performed numerically. All log-likelihood functions were optimized using Matlab (53) (Nelder–Mead simplex method).

In the next step, we estimated the cohort-specific hazard levels and calculated 95% confidence intervals. The confidence interval for each λ is based on the likelihood ratio statistic. It is preferred over confidence intervals based on large-sample normal approximations if the log-likelihood function shows a lack of symmetry, which is the case here. The confidence interval is given by those values of λ for which the statistic ln⁡R(λ)=2⋅[ln⁡L(λ^)−ln⁡L(λ)] is smaller than the (1−α)-quantile of the χ2 distribution with df = 1. For (1−α)=0.95, this critical value is C = 3.8415. The value λ^ is the maximum-likelihood estimate for each sample. The limits for the confidence intervals were determined numerically by using the function uniroot in R (54). The results are shown in Fig. S1.

We tested whether different cohorts, within each laboratory, share the same constant level of mortality. This was done via a likelihood ratio test (LRT) and confirmed by a Kolmogorov–Smirnov test (Table S2). Identical hazard levels were rejected for the Rostock cohorts (LRT statistic: 19.5862; P value: 0.0120; df = 8) and for the Pomona cohorts (LRT statistic: 6.2277; df = 2; P value: 0.0444). Rejection of a common hazard level for the Rostock cohorts is due to a comparatively low level of mortality in cohorts R4 and R5 (one death for 435,219 and 387,478 d of exposure, respectively) (Fig. S1). In Pomona, cohort P1 shows higher mortality than cohorts P2 and P3.

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Table S2.

Summary of the results of the KS test statistic

If cohorts R4 and R5 are excluded, a common hazard level across the remaining 10 cohorts (3 in Pomona, 7 in Rostock) is not rejected (LRT statistic: 12.4170; df = 9; P value: 0.1908). The common level of mortality is estimated as λ^=1.6618e-05 (per day), with 95% confidence interval (1.2464e-05; 2.1605e-05). This level of mortality corresponds to an annual probability of death q=qx, x+365=1− e−365 λ^ = 0.006047, with a 95% confidence interval (0.004539; 0.007855). For the two cohorts R4 and R5, a common level of mortality can be assumed (LRT statistic: 0.0067; df = 1; P value: 0.9345), and the estimated hazard is λ^= 2.4310e-06 (per day) with a 95% confidence interval (4.0423e-07; 7.5066e-06). It corresponds to an annual probability of death q = 0.000887, 95% confidence interval (0.000148; 0.002736).

Fertility Analysis for Rostock Cohorts.

Unlike the Pomona cohorts, which were initiated at the same time and had the same age, the Rostock cohorts were initiated sequentially with an interval of about 6 mo, producing cohorts of different ages at a given time. We were therefore able to separate the effect of age (denoted by x) and calendar time (denoted by t). For each of the Rostock cohorts (1–9), we calculated the monthly number of buds (1 mo = 30 d) and the total time of exposure in each month. The budding rate was estimated by a Poisson model making the following assumptions: If y(c,x,t) denotes the observed number of buds in cohort c at age x and time t, then the y(c,x,t) are viewed as realizations from Poisson variables with expected value m(c,x,t), which is given by the product of the budding rate λ(c,x,t) and the exposure time e(c,x,t) of the cohort at age x and time t: m(c,x,t)=E(y(c,x,t))=λ(c,x,t)⋅e(c,x,t).

How the budding rates λ(c,x,t) change with age x and potentially differ by cohort c is the core of the analysis. To allow for overdispersion that might be introduced by within-cohort heterogeneity, we allow the scale parameter ϕ of the Poisson distribution to be >1 and hence the variance to be larger than the mean of the Poisson variates. The dependence of the rates on age is assumed to be smooth, and the smooth terms are represented by penalized regression splines. Modeling was done on a log scale for the rates, as usual for Poisson regression. The potential shared effects of calendar time t were modeled as a random (intercept) effect bt for ln λ(c,x), normally distributed with variance σt2: ln⁡λ(c,x,t)= ln⁡λ(c,x)+bt.

Several models for the cohort- and age-specific rates λ(c,x) were considered, ranging from a single age-specific budding rate λ(x) for all cohorts to a model with separate smooth rates λ(c,x) for each single cohort. All resulting generalized additive mixed models (55) were estimated using the function gamm in the library mgcv of the statistical package R (54). Model comparisons were made based on the resulting Akaike information criterion (AIC). The model with the lowest AIC was chosen as the final model. This model results in three groups of cohorts, and within each group the shape of the age-specific budding rate is the same, however, possibly at different intensity [λ(c,x)= γcλg(x)].

SI Methods and Materials

Description of the Hydra Species We Used.

The Hydra strains Hydra magnipapillata strain 105 and Hydra vulgaris strain AEP and strain ARG45a belong into the same phylogenetic vulgaris cluster (56, 57). During experiments, all H. magnipapillata individuals reproduced only asexually via budding, whereas H. vulgaris reproduced both sexually and asexually.

Rostock Cohorts.

Description of the cohorts.

Rostock cohort R1 was initiated in 2006 from a lineage that was started in 1973 with one polyp caught in the wild (H. magnipapillata strain 105) (58). As it is unknown how long that individual had reproduced clonally before it was collected, we set 33 y to be the minimum age of this lineage at the beginning of the study. The lineage has been propagated asexually until today. To compare the budding and death rates between the parental and the subsequent generations of buds, about every 6 mo buds of the individuals of the first three cohorts were kept and transferred to form a new cohort. Lineage age was identical to genet age for the Rostock cohort and ranged between ∼33 and ∼37 y.

H. magnipapillata strain 105 is well adapted to laboratory conditions. The Rostock laboratory stock culture was founded in March 2005 by budding from a single polyp (a member of the clone strain 105 from the University of California, Irvine). On March 1, 2006, individuals for the first R1 were derived by budding from the stock culture. This process of building the R1 cohort of 204 polyp individuals was finished after 55 d. About 6 mo later, on September 11, 2006, R2, with 204 individuals was established and was finished after 99 d by budding from the individuals of R1. On March 16, 2007, R3 was established from R1 and R2, and was finished after 110 d. Subsequent cohorts were all derived from the first three Rostock cohorts and were separated on January 10, 2008 (R4, finished after 67 d), September 9, 2008 (R5, finished after 36 d), April 1, 2009 (R6, finished after 119 d), and January 1, 2010 (R7, finished after 73 d), November 1, 2010 (R8, finished after 67 d), and April 1, 2011 (R9, finished after 55 d).

Culture conditions.

Single polyps were cultured and fed under identical and constant laboratory conditions to standardize macroenvironmental parameters and minimize microenvironmental conditions. Every individual was cultured in isolation in plastic multiwell culture plates using a medium containing 0.05 mM NaHCO₃, 1 mM CaCl₂, 0.1 mM MgCl₂, 0.001 mM MgSO₄, and 0.003 mM KNO₃ in deionized water. The medium was changed after every feeding time. The experiments were conducted in an incubator with constant temperature at 18 °C and a 12-h light/dark cycle. Hydra polyps for the Rostock cohorts were each fed with three freshly hatched nauplii of brine shrimp (Artemia salina) (2 d posthatching) three times per week. The Artemia were fed directly to the Hydra to ensure that each individual received the same amount of food. All of the polyps in all cohorts were checked for complete food intake after feeding, and any uneaten food remains were discarded. All budding events were recorded and the buds discarded as soon as they detached from the mother. No sexually active Hydra were found in any of the Rostock cohorts.

Pomona Cohorts.

Description of the cohorts.

Pomona cohort P1 consisted of 22 individuals hatched from an egg (“Pomona 1”) and their first generation of buds. The genet age of those individuals varied between 30 d for the hatchlings and up to 6 mo for the buds. The genet age for the individuals of the strains ARG 45a (cohort P2) and AEP (cohort P3) of the species Hydra vulgaris (Pallas 1766) (59) cannot be estimated. After the egg hatches, the hatchling grows rapidly for the first ∼30 d to mature into a miniature polyp. According to Grassi et al. (60), hatchlings incur elevated daily mortality that first increases with age (until the age of 30 d) but then tapers off to a low level. Because we started observing only successfully hatched individuals, we estimated the age of these at 30 d. The first generations of buds from Pomona 1 were combined with their parents in cohort P1. The age of those individuals varied between 3 and 6 mo. The genet age for the individuals of the strains ARG 45a (cohort P2) and AEP (cohort P3) of the species H. vulgaris cannot be estimated. Both cohorts consisted of 150 individuals. Cohort P2 was established from individuals of strain ARG45a, which were collected in 2006 from an Argentinian creek (Buenos Aires Province, S 30° 02.877′ W 062° 07.695′). Cohort P3 was established from individuals of strain AEP, which were derived from crosses between two individuals of H. vulgaris. One of these was collected the 1980s in Philadelphia, Pennsylvania, and the other one at the same time in Susanville, California (61).

Culture conditions.

Lab protocols for Pomona cohorts were identical to those for Rostock cohorts, except that Pomona cohorts were fed three times a week (Monday, Wednesday, and Friday) with freshly hatched (∼1-d-old) brine shrimp using a Pasteur pipette to deliver approximately five to eight shrimp into the tentacles of the Hydra. At the time of feeding, new offspring were counted and removed from the dishes. The Hydra were allowed to digest the shrimp for a minimum of 4 h and were then transferred to clean cell culture dishes. In the Pomona cohorts, all individuals were sexually active but the amount of sexual reproduction was not quantified.

Mortality Analysis: Kolmogorov–Smirnov Tests.

Komogorov–Smirnov (KS) tests were performed for each cohort in two versions. First, for ages at death, where catastrophic deaths were not considered, and second for all ages at death, including catastrophic deaths. In both cases, the parameter λc of the exponential distribution was determined by maximum likelihood. The expected proportion of deaths pc at the age ec at the end of the study, when surviving individuals were right-censored, was calculated from the corresponding cumulative distribution function: pc=1−exp{−λcec}. Due to the staggered entry of the individual Hydra into the cohorts, the age ec is the age of the latest born survivor at the end of the study.

Should the null hypothesis of an exponential distribution hold, then the transformed sample ui=1−exp{−λcxi}, where the xi are the observed ages at death, would follow a uniform distribution over (0, pc). This hypothesis was tested via a KS test using the function ks.test in R. (Ties were broken by adding a uniformly distributed random number in ±10−6.)

Cohort R3 is the only cohort for which the KS test rejects the exponential distribution at the 5% level, if catastrophic deaths are excluded (Table S2). In cohort R1, due to a careless visitor who threw a whole plate down, six individuals were killed on the same day; this heaping leads to the rejection of the null hypothesis in this case.

Acknowledgments

R.S., A.S., M.J.D., J.G., and J.W.V. thank Jessica Metcalf, Ellen Kalmbach, Nora Ibrahim, and David Thomson for constructive discussions and for setting up the experiments and devising the maintenance schedules of Hydra at the Max Planck Institute for Demographic Research (MPIDR); we are grateful to Antje Storek-Langbein and Uta Cleven for their help in the MPIDR laboratory. Owen Jones, Fernando Colchero, Boris Kramer, and Samuel Pavard at MPIDR provided valuable comments. D.E.M. thanks Caroline Crocker, Anthony Bellantuono, Abril Iñiguez, Amber Nierodi, and Ashley Brutto for their technical support at Pomona College. A portion of this work was funded by NIH Grant AG037965 (to D.E.M.). We acknowledge funding from the Max Planck Society for the experiments in both laboratories.

Footnotes

↵¹R.S. and A.S. contributed equally to this work.
↵²To whom correspondence may be addressed. Email: jwv{at}demogr.mpg.de or dem04747{at}pomona.edu.

Author contributions: R.S., J.G., D.E.M., and J.W.V. designed research; R.S. and D.E.M. performed research; A.S., M.J.D., and J.G. analyzed data; and R.S., A.S., and J.W.V. wrote the paper.
Reviewers: T.B.L.K., Newcastle University; R.E.S., University of California, Irvine; and K.W.W., University of California, Berkeley.
The authors declare no conflict of interest.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1521002112/-/DCSupplemental.

Freely available online through the PNAS open access option.

View Abstract

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Article Classifications

Biological Sciences
Evolution

[1] ↵
Medawar PB
(1952) An Unsolved Problem of Biology: An Inaugural Lecture Delivered at University College, London, 6 December, 1951 (H. K. Lewis and Company, London)
.

[2] Medawar PB

[3] ↵
Williams GC
(1957) Pleiotropy, natural-selection, and the evolution of senescence. Evolution 11(4):398–411
.
OpenUrl CrossRef

[4] Williams GC

[5] ↵
Hamilton WD
(1966) The moulding of senescence by natural selection. J Theor Biol 12(1):12–45
.
OpenUrl CrossRef PubMed

[6] Hamilton WD

[7] ↵
Charlesworth B,
Williamson JA
(1975) The probability of survival of a mutant gene in an age-structured population and implications for the evolution of life-histories. Genet Res 26(1):1–10
.
OpenUrl CrossRef PubMed

[8] Charlesworth B,

[9] Williamson JA

[10] ↵
Kirkwood TBL
(1977) Evolution of ageing. Nature 270(5635):301–304
.
OpenUrl CrossRef PubMed

[11] Kirkwood TBL

[12] ↵
Kirkwood TBL
(1981) Repair and Its Evolution Survival Versus Reproduction (Blackwell Scientific Publications, Oxford), pp 165–189
.

[13] Kirkwood TBL

[14] ↵
Baudisch A
(2008) Inevitable Senescence? Contributions to Evolutionary Demographic Theory (Springer, Berlin)
.

[15] Baudisch A

[16] ↵
Evans SN,
Steinsaltz D,
Wachter KW
(2013) A Mutation-Selection Model with Recombination for General Genotypes. Memoirs of the American Mathematical Society (American Mathematical Society, Providence, RI), Vol. 222, No. 1044
.

[17] Evans SN,

[18] Steinsaltz D,

[19] Wachter KW

[20] ↵
Wachter KW,
Steinsaltz D,
Evans SN
(2014) Evolutionary shaping of demographic schedules. Proc Natl Acad Sci USA 111(Suppl 3):10846–10853
.
OpenUrl Abstract/FREE Full Text

[21] Wachter KW,

[22] Steinsaltz D,

[23] Evans SN

[24] ↵
Baudisch A, et al.
(2013) The pace and shape of senescence in angiosperms. J Ecol 101(3):596–606
.
OpenUrl CrossRef

[25] Baudisch A, et al.

[26] ↵
Jones OR, et al.
(2014) Diversity of ageing across the tree of life. Nature 505(7482):169–173
.
OpenUrl CrossRef PubMed

[27] Jones OR, et al.

[28] ↵
Deevey ES Jr
(1947) Life tables for natural populations of animals. Q Rev Biol 22(4):283–314
.
OpenUrl CrossRef PubMed

[29] Deevey ES Jr

[30] ↵
Finch CE
(1990) Longevity, Senescence, and the Genome (Univ of Chicago Press, Chicago)
.

[31] Finch CE

[32] ↵
Kirkwood TBL,
Austad SN
(2000) Why do we age? Nature 408(6809):233–238
.
OpenUrl CrossRef PubMed

[33] Kirkwood TBL,

[34] Austad SN

[35] ↵
Carey JR,
Liedo P,
Orozco D,
Vaupel JW
(1992) Slowing of mortality rates at older ages in large medfly cohorts. Science 258(5081):457–461
.
OpenUrl Abstract/FREE Full Text

[36] Carey JR,

[37] Liedo P,

[38] Orozco D,

[39] Vaupel JW

[40] ↵
Vaupel JW, et al.
(1998) Biodemographic trajectories of longevity. Science 280(5365):855–860
.
OpenUrl Abstract/FREE Full Text

[41] Vaupel JW, et al.

[42] ↵
Vaupel JW,
Yashin AI
(1985) Heterogeneity’s ruses: Some surprising effects of selection on population dynamics. Am Stat 39(3):176–185
.
OpenUrl CrossRef PubMed

[43] Vaupel JW,

[44] Yashin AI

[45] ↵
Vaupel JW
(2010) Biodemography of human ageing. Nature 464(7288):536–542
.
OpenUrl CrossRef PubMed

[46] Vaupel JW

[47] ↵
Trembley A
(1744) Memoires pour Servir a l’Histoire d’un Genre de Polypes d’Eau Douce, a Bras en Forme de Cornes (Chez Durand, Paris)
.

[48] Trembley A

[49] ↵
Nishimiya-Fujisawa C,
Kobayashi S
(2012) Germline stem cells and sex determination in Hydra. Int J Dev Biol 56(6-8):499–508
.
OpenUrl CrossRef PubMed

[50] Nishimiya-Fujisawa C,

[51] Kobayashi S

[52] ↵
Bosch TCG,
David CN
(1987) Stem-cells of Hydra magnipapillata can differentiate into somatic cells and germ line cells. Dev Biol 121(1):182–191
.
OpenUrl CrossRef

[53] Bosch TCG,

[54] David CN

[55] ↵
Otto JJ,
Campbell RD
(1977) Tissue economics of hydra: Regulation of cell cycle, animal size and development by controlled feeding rates. J Cell Sci 28:117–132
.
OpenUrl Abstract/FREE Full Text

[56] Otto JJ,

[57] Campbell RD

[58] ↵
Schaible R,
Sussman M,
Kramer BH
(2014) Aging and potential for self-renewal: Hydra living in the age of aging—a mini-review. Gerontology 60(6):548–556
.
OpenUrl CrossRef PubMed

[59] Schaible R,

[60] Sussman M,

[61] Kramer BH

[62] ↵
Harper JL
(1977) Population Biology of Plants (Academic, London)
.

[63] Harper JL

[64] ↵
Orive ME
(1995) Senescence in organisms with clonal reproduction and complex life-histories. Am Nat 145(1):90–108
.
OpenUrl CrossRef

[65] Orive ME

[66] ↵
Martínez DE
(1998) Mortality patterns suggest lack of senescence in Hydra. Exp Gerontol 33(3):217–225
.
OpenUrl CrossRef PubMed

[67] Martínez DE

[68] ↵
Schaible R,
Ringelhan F,
Kramer BH,
Miethe T
(2011) Environmental challenges improve resource utilization for asexual reproduction and maintenance in hydra. Exp Gerontol 46(10):794–802
.
OpenUrl CrossRef PubMed

[69] Schaible R,

[70] Ringelhan F,

[71] Kramer BH,

[72] Miethe T

[73] ↵
Finch CE,
Kirkwood T
(2000) Chance, Development, and Aging (Oxford Univ Press, Oxford)
.

[74] Finch CE,

[75] Kirkwood T

[76] ↵
Rea SL,
Wu D,
Cypser JR,
Vaupel JW,
Johnson TE
(2005) A stress-sensitive reporter predicts longevity in isogenic populations of Caenorhabditis elegans. Nat Genet 37(8):894–898
.
OpenUrl CrossRef PubMed

[77] Rea SL,

[78] Wu D,

[79] Cypser JR,

[80] Vaupel JW,

[81] Johnson TE

[82] ↵
Sánchez-Blanco A,
Kim SK
(2011) Variable pathogenicity determines individual lifespan in Caenorhabditis elegans. PLoS Genet 7(4):e1002047
.
OpenUrl CrossRef PubMed

[83] Sánchez-Blanco A,

[84] Kim SK

[85] ↵
Welch PS,
Loomis HA
(1924) A limnological study of Hydra oligactis in Douglas Lake, Michigan. Trans Am Microsc Soc 43:203–235
.
OpenUrl

[86] Welch PS,

[87] Loomis HA

[88] ↵
Bell G,
Wolfe LM
(1985) Sexual and asexual reproduction in a natural population of Hydra pseudoligactis. Can J Zool 63(4):851–856
.
OpenUrl CrossRef

[89] Bell G,

[90] Wolfe LM

[91] ↵
Ribi G,
Tardent R,
Tardent P,
Scascighini C
(1985) Dynamics of hydra populations in Lake Zurich, Switzerland, and Lake Maggiore, Italy. Schweiz Z Hydrol 47(1):45–56
.
OpenUrl CrossRef

[92] Ribi G,

[93] Tardent R,

[94] Tardent P,

[95] Scascighini C

[96] ↵
Wachter KW,
Evans SN,
Steinsaltz D
(2013) The age-specific force of natural selection and biodemographic walls of death. Proc Natl Acad Sci USA 110(25):10141–10146
.
OpenUrl Abstract/FREE Full Text

[97] Wachter KW,

[98] Evans SN,

[99] Steinsaltz D

[100] ↵
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Constant mortality and fertility over age in Hydra

Significance

Abstract

Results

Discussion

Materials and Methods

Empirical Data.

Definitions of Death.

Mortality Analysis for All Cohorts.

Fertility Analysis for Rostock Cohorts.

SI Methods and Materials

Description of the Hydra Species We Used.

Rostock Cohorts.

Description of the cohorts.

Culture conditions.

Pomona Cohorts.

Description of the cohorts.

Culture conditions.

Mortality Analysis: Kolmogorov–Smirnov Tests.

Acknowledgments

Footnotes

References

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Constant mortality and fertility over age in Hydra

Significance

Abstract

Results

Discussion

Materials and Methods

Empirical Data.

Definitions of Death.

Mortality Analysis for All Cohorts.

Fertility Analysis for Rostock Cohorts.

SI Methods and Materials

Description of the Hydra Species We Used.

Rostock Cohorts.

Description of the cohorts.

Culture conditions.

Pomona Cohorts.

Description of the cohorts.

Culture conditions.

Mortality Analysis: Kolmogorov–Smirnov Tests.

Acknowledgments

Footnotes

References

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