Postreproductive lifespans are rare in mammals

Abstract A species has a post‐reproductive stage if, like humans, a female entering the adult population can expect to live a substantial proportion of their life after their last reproductive event. However, it is conceptually and statistically challenging to distinguish these true post‐reproductive stages from the usual processes of senescence, which can result in females occasionally surviving past their last reproductive event. Hence, despite considerable interest, the taxonomic prevalence of post‐reproductive stages remains unclear and debated. In this study we use life tables constructed from published data on wild populations of mammals, and statistical measures of post‐reproductive lifespans, to distinguish true post‐reproductive stages from artefacts of senescence and demography in 52 species. We find post‐reproductive stages are rare in mammals and are limited to humans and a few species of toothed whales. By resolving this long‐standing debate, we hope to provide clarity for researchers in the field of evolutionary biology and a solid foundation for further studies investigating the evolution and adaptive significance of this unusual life history trait.


| INTRODUCTION
An intuitive understanding of life history theory might lead to the prediction that the most effective way for an organism to maximize its fitness is to reproduce until the end of life. Contrary to this expectation, females of some species-notably humans-cease reproduction well before the end of life. The origin and evolution of female postreproductive lifespan have stimulated discussion and debate on the evolution of senescence, the selective forces impacting life histories, and the structure of human and nonhuman animal societies Hamilton, 1966;Hawkes & Coxworth, 2013; Johnstone & Cant, 2010;Williams, 1957). However, despite widespread interest, researchers are in disagreement about the taxonomic prevalence of extended postreproductive lifespans. Some studies suggest that postreproductive life is a common trait in mammals (Cohen, 2004;Finch & Holmes, 2010;Holmes & Ottinger, 2003;Nichols, Zecherle, & Arbuckle, 2016;Walker & Herndon, 2008), whereas others maintain that postreproductive lifespans are limited to humans and some species of toothed whale (Alberts et al., 2013;Austad, 1994Austad, , 1997Foote, 2008;Levitis, Burger, & Lackey, 2013). This confusion has been caused by: (i) past difficulties in defining postreproductive lifespans (reviewed in (Levitis et al., 2013)) and (ii) using data from captive populations (discussed in ).
Defining postreproductive life is hindered by the conceptual difficulty of separating the postreproductive traits of interest from artifacts of senescence (Levitis et al., 2013). The postreproductive trait of interest is usually, either implicitly or explicitly, an extended postreproductive lifespan where females undergo menopause and terminate reproduction: called by Levitis et al. (2013) (and hereafter) a postreproductive stage. More formally, we define a species as having a postreproductive stage if a female entering the adult population can expect, on average, to live long enough to spend some of their life postreproductive. A great advantage of this definition is that this individual level trait can be scaled up to that of the population. In a population of females with postreproductive stages, a substantial proportion of females in the population will be postreproductive at any given time. This definition has clear ecological and evolutionary implications and can be unambiguously applied to taxonomically diverse species.
Aging theory predicts that in general the rates of senescence of physiological systems, including the reproductive system, are expected to be approximately simultaneous and proportional (Williams, 1957).
In contrast, for a species to have a postreproductive stage, the processes of somatic and reproductive senescence need to have become decoupled to an extent that results in females regularly living beyond their reproductive lifespan for an extended period (Levitis et al., 2013).
However-even in species without a postreproductive stage-natural variation in the relative timing of senescence of reproductive and somatic systems has the potential to result in some females occasionally living for a short time after their last reproductive event (termed postreproductive viability by (Levitis et al., 2013)). Senescence, along with chance and variation, can therefore result in some individual females in a population displaying short postreproductive lifespans. Such post reproductive viability has often mistakenly been referred to as akin to a true postreproductive stage in which the processes of somatic and reproductive senescence have become decoupled (e.g. Nichols et al., 2016). It is therefore important to distinguish the usual processes of senescence from true postreproductive stages.
Evidence of a postreproductive stage is often presented from captive populations. However, in many species, captive individuals have reduced increased survival because the risks of predation and starvation, and disease are greatly reduced (Tidière et al., 2016). Captivity can, therefore, extend rare and short postreproductive periods to mimic a postreproductive life history strategy (for examples of long postreproductive lifespans in captivity: (Cohen, 2004)). Captive breeding can also disrupt and shorten female reproductive lifespans compared to natural conditions (Hermes, Hildebrandt, & Göritz, 2004).
However, these artificially prolonged postreproductive lifespans are the outcome of increased survival in captive conditions, not natural selection. Rather, the postreproductive lifespans observed in captive populations are an artifact of the low-risk environment and the usual processes of senescence.
In this study, we compare patterns of reproductive and somatic senescence across fifty-two wild mammalian populations and distinguish postreproductive life history strategies from the rare and short postreproductive lifespans that are artifacts of senescence. We do this using a population-level measure: postreproductive representation (PrR) (Levitis & Lackey, 2011) which calculates the proportion of adult female years being lived by postreproductive females (Levitis & Lackey, 2011). Unlike other measures of postreproductive lifespan, PrR incorporates both the proportion of the population surviving to become postreproductive and their life expectancy upon becoming postreproductive (Levitis & Lackey, 2011), which provides a robust and statistically testable null hypothesis: that the proportion of adult female years being lived in the population is not statistically different than expected by chance. Moreover, PrR provides a measure that is directly comparable between species that differ in their total lifespans (Levitis & Lackey, 2011). Using PrR, we distinguish postreproductive life history strategies from artifacts of reproductive senescence and determine the prevalence of this unusual life history strategy in mammals. Using only data from wild animal populations, we avoid artifacts of artificially long lifespans that are observed in captive populations.

| Data
We constructed life tables for fifty-two placental mammal species using published data on wild and unprovisioned populations (Table 1).
We aimed to have as broad a taxonomic representation as possible among mammals, but age-specific data are difficult to collect for wild animals. Hence, species with available data are usually long-lived mammals of commercial, conservation, or scientific interest.
We used both age-specific survival and age-specific fertility data to construct life tables. Data were collected from the literature searches in Google Scholar and Web of Science. As search terms, we used the species common and scientific names in conjunction with data-specific terms such as "age-specific fecundity/fertility," "agespecific mortality," "reproduction," "survival," "age structure," and "life table." Data were used for analysis if the description of the population and methods were clear enough to be confident of their accuracy and interpretation. These types of age-specific survival and fecundity data included in this analysis are described below.

| Creating life tables: survival
Life tables are a widespread approach used to quantify life history in animals (e.g., Carey, 1993;Deevey, 1947;Erickson, Currie, Inouye, & Winn, 2006;Promislow & Harvey, 1990). At their simplest, life tables-in biology-are used to provide estimates of the rate of an animal's mortality and fecundity through their life. The construction of life tables therefore relies on deriving age-specific estimates of survival and reproduction. The age-specific data that we use to construct our life tables fall into three categories which we will call: longitudinal complete, longitudinal censored, and census data ( Table 2). These three types of data are defined below.
Longitudinal complete data require following all individuals for their entire lives. For wild populations, this is usually derived from long-term field studies where animals born into the population are individually identifiable and tracked until death. In a longitudinal complete study, the exact year of birth and age at death are known. For each age category, the total number of individuals observed at age x (N x ) is therefore known. From these data, other life table metrics can be derived (Carey, 1993;Krebs, 1998;Wachter, 2014) such as the probability of surviving to a given age (l x ), the probability of surviving through an age (p x ), and life expectancy at age x (e x ). Fourteen of the T A B L E 1 Postreproductive representation (PrR) for 52 species of placental mammal (for simplicity defined and referred to as species rather than subspecies or ecotypes). PrR represents the proportion of adult female years being lived by postreproductive females. Asterix (*) shows those that are significantly different from 0 (p < .05). Ex at maturity is the expected lifespan for a female reaching sexual maturity. Age M is the age at which 95% of population lifetime fecundity has been reached, and Ex at maturity shows the expected lifespan of females who reach age M. Demography indicates the dispersal system for group living species, asocial represents species found in groups but without evidence of coherent social groups. Note: as postreproductive life expectancy scales with total lifespan, in short-lived species there may be survival past the end of reproduction but on scales shorter than a year, so e M will still be 0   (Wachter, 2014)): assigning individuals to age bins to create a monotonically decreasing age structure. These age bins were then used to estimate N x (assuming mortality is equally spread through the binned range), which was in turn used to derive life tables (Krebs, 1998). This method assumes the population is at a stable age structure; an assumption violated if the population is growing or shrinking (Krebs, 1998). In the absence of detailed population growth data for most species, we model each species with census data under three growth scenarios: stable population (population growth (r) = 0), a population in serious decline (r = −0.1, approximately a decline of 10% per year), and a population in a period of rapid growth (r up to 0.1, the exact value depends on the species and some population growth scenarios are impossible for a given age structure). All life table statistics and derived statistics were calculated for all three population growth scenarios. Life tables for twenty-seven mammal species in this study were based on census data (Table 2).

T A B L E 1 (Continued)
Conversely, fin whales (Balaenoptera physalus) were hunted intensively during the period of modern whaling which increased mortality and is unlikely to have left the natural population parameters intact (Aguilar, 2000). The demographic parameters for fin whales should therefore be interpreted with caution.

| Creating life tables: fecundity
In this study, we are interested in the presence or absence of female reproductive activity at a given ages rather than broader declines in fecundity with age. We therefore define fecundity as the proportion of reproductive females at a given age who are reproductively ac- Because fecundity is reported as a proportion, it is vulnerable to small sample sizes returning highly variable changes in f x values. This is a particular problem at later ages, when N x is lower. To account for this, fecundity data were smoothed by weighting the magnitude in fecundity change between x and x + 1 by the number of individuals sampled at x+1.
T A B L E 2 Summary of types of data used to construct the life tables used in this study. Superscript indicates the form of pregnancy data used to calculate f x , Y = observations of accompanying young, P = females were pregnant, P/B = combined pregnancy and birth data, and G = maternity of offspring inferred using genetic tools

| Calculating postreproductive representation
PrR is calculated as the proportion of adult female years in the population being lived by postreproductive individuals (Levitis & Lackey, 2011  Age M is the age at which 95% of population fecundity has been completed, independent of mortality (Levitis & Lackey, 2011). That is, age M represents the minimum age at which population fecundity (in our case total reproductive active females) of all females up to and including the age in question is greater than or equal to 95% of the total population fecundity of the total female population of all ages (equation 2). Ninety-five percent of population is used to remove the influence of demographic outliers.
Postreproductive years are calculated as the female years However, due to inconsistency in the reporting of early life survival in different species, we define age B as the youngest age at which females are observed reproducing in the species. Fixing age B allows consistent comparison between species. PrR is particularly suited for interspecific comparison because it is unitless and is therefore independent of the longevity of the species in question (Levitis & Lackey, 2011).
We also test the statistical significance of the calculated value of PrR for each species. As discussed above, the expectation of senescence is that the rates of aging of different biological systems are expected to be approximately simultaneous and proportional and shaped by the risks of extrinsic mortality (Williams, 1957). The null hypothesis is therefore that survival (l x )-the combined effect of intrinsic and extrinsic mortality on a population-and fecundity (f x ) should decline at the same rate, that is, PrR = 0 (Levitis & Lackey, 2011). We test this by simulating 9999 populations of 1000 individuals in which this null hypothesis is true and comparing this to our observed data (Levitis & Lackey, 2011). Significance is calculated separately for each species by generating null populations based on that species' demographic parameters. The reported p values (Table 1) indicate the number of times that this simulated PrR was greater than or equal to the observed PrR (with the sample included in the numerator and denominator; see equation 1 in (Ruxton & Neuhäuser, 2013)).
In natural conditions, the usual processes of senescence can result in rare and/or brief female survival past last reproduction. These populations will have a low PrR which is unlikely to be significantly different from that expected by chance. In contrast, for species with a postreproductive life history strategy, a large proportion of females will be postreproductive resulting in a high PrR, significantly different from zero (Levitis & Lackey, 2011;Levitis et al., 2013).

| RESULTS
Three of the 52 mammal species have a postreproductive representation significantly greater than 0 ( Figure 1; Table 1
Our comparative analysis shows that postreproductive stages are rare in mammals and are confined to a limited number of species. In this study of 52 species of mammals, we report significant postreproductive stages in humans, killer whales, and short-finned pilot whales.
Some recent evidence also suggests that a third cetacean, false killer whales (Pseudorca crassidens), may also have a postreproductive stage (Photopoulou, Ferreira, Best, Kasuya, & Marsh, 2017). Far from being a common life history strategy, current evidence suggests that postreproductive stages are limited to humans and a few species of toothed whale.
Although our analysis shows that postreproductive life history strategies are rare in mammals, postreproductive viability may be more common. Postreproductive viability, survival after the end of reproduction, is indicated in many species by nonzero expected survival years F I G U R E 1 Proportion of female years in the population being lived by postreproductive individuals, scaled by maximum female age in 52 species of mammal. Each bar (right) shows the proportion of female years in the population being lived by reproductive (green) and post reproductive (orange) females. The length of the bar is equivalent to the maximum female lifespan of the species. A significant proportion of adult females years being lived by postreproductives is indicated by an asterisk (*). Species are ordered by family according to (Meredith et al., 2011) and within family alphabetically. Phylogeny (left) represents the relationships between mammalian orders (Meredith et al., 2011), branches are unscaled. after 95% of lifetime fecundity has been completed (e B in Table 2).
The apparent ubiquity of postreproductive viability underlines the importance of using appropriate methods to distinguish these short and rarely occurring artifacts of senescence from postreproductive life history strategies.
In this study, we have shown that in humans, killer whales, and short-finned pilot whales, greater than 25% of adult female years in a population are being lived by postreproductive females. This is far beyond what is expected by the general process of senescence and is likely to be the result of active selection on female life history.
Indeed in humans and killer whales-the two best-studied species with a postreproductive stage-there is substantial evidence that the postreproductive stage has evolved in response to a trade-off between both the inclusive fitness benefits and costs experienced by old females . In both humans and killer whales, older females provide benefits to the survival and reproduction of their offspring and grand-offspring (Blurton Jones, 2016;Foster et al., 2012;Hawkes, O'Connell, Blurton Jones, Alvarez, & Charnov, 1998;Lahdenperä, Lummaa, Helle, Helle, & Russell, 2004). However, numerous examples of cooperative breeders demonstrate that the ability to help relatives does not alone lead to the evolution of postreproductive stages (Koenig & Dickinson, 2016). Humans and killer whales have social systems that might predispose females to evolve a postreproductive life history strategy. In ancestral humans, dispersal is thought to have been female-biased (Copeland et al., 2011;Lalueza-Fox et al., 2011;Marlow, 2004) and in resident ecotype killer whales, both males and females are philopatric remaining with their natal group for their entire life (Bigg, Olesiuk, Ellis, Ford, & Balcomb, 1990). Under both these dispersal systems, a females' distant relatives are replaced with her offspring and grand-offspring as she ages, increasing her average relatedness to her local group. These age-related changes in local relatedness, kinship dynamics, can select for intergenerational conflict over reproduction (the reproductive conflict hypothesis (Cant & Johnstone, 2008)), which when taken together with the benefits of helping in late life, can select for the evolution of menopause (Cant & Johnstone, 2008;Johnstone & Cant, 2010). Under human and killer whale demography, reproductive conflict is predicted to select for harming behavior in early adulthood and helping behavior in late life (Cant & Johnstone, 2008;Johnstone & Cant, 2010). In killer whales, for example, older females lead their group at times of low resource abundance . Moreover, in both humans and killer whales, older females suffer costs by reproducing at the same time as their daughters, which will select for reproductive restraint and cessation in late life (Croft et al., 2017;Lahdenperä, Gillespie, Lummaa, & Russell, 2012).
Dispersal patterns, and their resultant kinship dynamics, are not enough in themselves to drive the evolution of a postreproductive stage. In this study, we see that mammals other than humans, killer whales, and short-finned pilot whales have either female-biased dispersal or bisexual philopatry but do not have a postreproductive stage (Table 1). The costs and benefits of helping relatives and ceasing reproduction are driven by older females being able to increase their inclusive fitness by aiding relatives (e.g., mother and grandmother effects (Hawkes et al., 1998)) and require a fitness cost of continued reproduction from intergenerational conflict (e.g., (Lahdenperä et al., 2012;Croft et al., 2017)).
Without both these costs and benefits, postreproductive life histories are not expected to evolve, even given age-related increases in local relatedness (Cant & Johnstone, 2008;Johnstone & Cant, 2010). The rarity of postreproductive life histories in mammals is likely to reflect the unusual behavioral and demographic circumstances required for it to be a beneficial strategy. It is also interesting to note that all three species we have found to have a postreproductive stage are relatively long-lived (although importantly not all long-lived species have postreproductive stages).
More research is needed to establish if, for mammals, a relatively slow life history is a necessary condition for postreproductive stages to be beneficial.
Advances in our understanding of the evolution and processes of senescence (Lemaître & Gaillard, 2017;Nussey, Froy, Lemaitre, Gaillard, & Austad, 2013) have made it clear that rare and short survival beyond reproductive lifespan is not an adaptive strategy.
Rather natural variation in the rate of senescence of various systems (reproductive and somatic) is likely to result in occasional and brief survival of females beyond their last reproductive event (Levitis et al., 2013). In contrast, the prolonged postreproductive life of female humans and some toothed whales is far beyond what we expect from the general processes of senescence (Levitis et al., 2013).
Unlike previous studies investigating the taxonomic prevalence of postreproductive life histories, we have been able to differentiate both conceptually and statistically, postreproductive stages from senescence. In contrast to some previous studies (Cohen, 2004;Finch & Holmes, 2010;Holmes & Ottinger, 2003;Nichols et al., 2016;Walker & Herndon, 2008), we found postreproductive stages to be rare in mammals. This rarity is likely to reflect our conceptual and methodological separation of postreproductive stages from the natural process of senescence. In this study, we have clarified the taxonomic prevalence of postreproductive stages, allowing future studies to be put in an evolutionary context.

ACKNOWLEDGMENTS
We would like to acknowledge the efforts of scientists who collected the raw data used in this paper. In particular we thank Dave Ellifrit, Erin Heydenrich, Astrid van Ginneken and other staff at the Center for Whale Research for killer whale demographic data, and, we thank the Banded Mongoose Research Project for access to unpublished data. We also thank colleagues in the Centre for Research in Animal Behaviour at the University of Exeter for useful discussions and input. We would also like the three anonymous reviewers for their constructive comments which improved the manuscript.

COMPETING INTERESTS
We have no competing interests.