Evidence for a postreproductive phase in female false killer whales Pseudorca crassidens

Background A substantial period of life after reproduction ends, known as postreproductive lifespan (PRLS), is at odds with classical life history theory and its causes and mechanisms have puzzled evolutionary biologists for decades. Prolonged PRLS has been confirmed in only two non-human mammals, both odontocete cetaceans in the family Delphinidae. We investigate the evidence for PRLS in a third species, the false killer whale, Pseudorca crassidens, using a quantitative measure of PRLS and morphological evidence from reproductive tissues. Results We examined specimens from false killer whales from combined strandings (South Africa, 1981) and harvest (Japan 1979-80) and found morphological evidence of changes in the activity of the ovaries in relation to age. Ovulation had ceased in 50% of whales over 45 years, and all whales over 55 years old had ovaries classified as postreproductive. We also calculated a measure of PRLS, known as postreproductive representation (PrR) as an indication of the effect of inter-population demographic variability. PrR for the combined sample was 0.14, whereas the mean of the simulated distribution for PrR under the null hypothesis of no PRLS was 0.02. The 99th percentile of the simulated distribution was 0.08 and no simulated value exceeded 0.13. These results suggest that PrR was convincingly different from the measures simulated under the null hypothesis. Conclusions We found morphological and statistical evidence for PRLS in South African and Japanese pods of false killer whales, suggesting that this species is the third non-human mammal in which this phenomenon has been demonstrated in wild populations. Nonetheless, our estimate for PrR in false killer whales (0.14) is lower than the single values available for the short-finned pilot whale (0.28) and the killer whale (0.22) and is more similar to working Asian elephants (0.13). Electronic supplementary material The online version of this article (doi:10.1186/s12983-017-0208-y) contains supplementary material, which is available to authorized users.


Background
Animals are said to have a postreproductive lifespan (PRLS) when reproductive senescence occurs faster than general somatic senescence (Alberts et al., 2013;. We define the onset of PRLS as the age at which ovulation ceases permanently, or in populations where this parameter is measurable, the age at last birth. PRLS is at odds with the classical life history model, and the adaptive causes and mechanisms have puzzled evolutionary biologists for decades (Williams, 1957), leading to legnthy debate.
Most of the research has focused on humans (e.g., Hawkes et al. (1998); Lahdenperä et al. (2004)), but a detectable PRLS has also been reported in a diversity of taxa. For example, Jones et al. (2014) compared standardized patterns of fecundity with age for 11 mammals, 12 other vertebrates, 10 invertebrates, 12 vascular plants and a green alga. In addition to humans, they reported a PRLS in killer whales Orcinus orca, bdelloid rotifers Macrotrachela sp., nematode worms Caenorhabditis elegans and Bali mynah birds Leucopsar rothschildi and concluded that their results led support to claims (e.g., Cohen (2004) for mammals) that the phenomenon may be widespread. In contrast, Levitis and Lackey (2011) claim that the apparently wide distribution of a significant PRLS is a methodological artefact. They identified shortcomings of the common practice of using postreproductive time (PrT), measured in units of time between last parturition and death, as a population measure of postreproductive lifespan. Notably, they found a false-positive rate of 47%.
Levitis and Lackey (2011) introduced a measure termed postreproductive representation (PrR), the proportion of adult lifespan that is postreproductive. The formulation of PrR utilizes age-specific rates from a life table and therefore allows for valid quantitative comparisons between populations with different demographic parameters. In addition, the authors make available procedures for comparing the point estimate for PrR to a null distribution representing the expected range of PrR under the assumption of no PRLS. Lahdenperä et al. (2014) calculated the PrR for working Asian elephants and found it was higher than populations of three long-lived, non-human primates living in wild or semi-wild conditions (Papio hamadryas, Macaca fuscata and Pan troglodytes) but much lower than for the shortfinned pilot whale, Globicephala macrorhynchus. Thus two species of toothed whales from the family Delphinidae (short-finned pilot whales ; Kasuya (1984, 1986)  According to life history theory there should be no selection for living beyond the end of one's ability to reproduce (Williams, 1957;Hamilton, 1966). The relatively large number of postreproductive females seen in pilot and killer whale groups and the fact that these species have matrilineal social systems suggest that the phenomenon is adaptive (Whitehead and Mann, 2000;McAuliffe and Whitehead, 2005;Ward et al., 2009;. We outline some of the adaptive hypotheses that assume a functional role for PRLS. According to the "Grandmother hypothesis", selection will favour a prolonged life after reproductive cessation with postreproductive females increasing their inclusive fitness by directly investing in and providing additional parental care to grand offspring (Hawkes et al., 1998). The "Stop early or mother" hypothesis proposes that selection acts to terminate reproductive ability ahead of natural mortality and the increased maternal risk of bearing offspring, and that postreproductive females gain greater fitness success by helping to improve the survival of their existing offspring than they would through continued reproduction. Central to both of these theories, and to adaptive menopause theories in general (Austad, 1994), is the assumption that there is a continually increasing risk of maternal mortality with age, and that the prolonged PRLS results from a trade-off between bearing and rearing. The main difference between the "Stop early" and the "Grandmother" hypotheses lies in whether postreproductive females enhance the survival of offspring only, or if there is also a grand-offspring benefit. Ward et al. (2009) andFoster et al. (2012) used longitudinal data from resident killer whales off British Columbia and Washington to test these hypotheses and showed that postreproductive females had little effect on their daughter's reproductive success but that both postreproductive and reproductive mothers increase their own offspring's survival, particularly the survival of male offspring.
Postreproductive females may serve as a reservoir of social/cultural information, ecological knowledge and provide leadership; the "Wisdom of the Elders" hypothesis (McAuliffe and Whitehead, 2005;. Although still a relatively under-researched topic, culture is likely to be an integral aspect of the lives of matrilineal whales (Whitehead, 1998;Rendell and Whitehead, 2001;Whitehead and Rendell, 2014) and offers an insight into the adaptive role of older, postreproductive females.  provide convincing support for the "Wisdom of the elders" hypothesis using longitudinal data from killer whales from one of the two populations studied by Ward et al. (2009) andFoster et al. (2012). They demonstrate that postreproductive females lead groups during collective movements, especially during times when prey productivity is low and that they are more likely to lead their sons than their daughters. Thus postreproductive female killer whales can act as reservoirs of ecological knowledge and buffer their kin, particularly their sons, against environmental hardships. The observation that this practice invests more in sons than daughters supports models of the evolution on menopause based on kinship dynamics. Johnstone and Cant (2010), who showed that very different social structures can give rise to an increase in local relatedness with female age, favoring late-life helping rather than bearing. Their analysis helps to explain why PRLS has evolved in humans and some odontocete cetaceans, rather than amongst long-lived, social mammals more generically.
In this paper, we use data from carcasses to examine evidence for a substantial female PRLS in a third odontocete, the false killer whale, Pseudorca crassidens, also a member of the family Delphinidae. We first examine the biological evidence for impaired reproductive performance with age, and then test whether a postulated postreproductive phase is supported statistically using the approach outlined by Levitis and Lackey (2011). Based on the results of our analyses, we conclude that there is strong evidence for a prolonged PRLS in female false killer whales.

Study species
False killer whales are distributed globally in tropical and warm temperate seas and are occasionally sighted in cold temperate regions (Baird, 2002). They are typically pelagic, although they also use the shallow waters around oceanic islands, such as the Hawaiian Islands (Baird et al., 2008;Baird, 2016). Their propensity to mass strand and the affiliative behaviour of stranded individuals has been taken as an indicator of their extreme sociality (Baird, 2002). False killer whales usually travel in groups of 20 to 100 and long-term (at least 15 year) association patterns between individuals have been documented (Baird et al., 2008;Baird, 2016).
The social structure of false killer whales groups is not known and the dispersal patterns of male false killer whales from their natal school is poorly understood (Ferreira et al., 2014). The stranded and shore drive samples are characterised by few large juvenile and sub-adults (Kasuya, 1986;Alonso et al., 1999;Ferreira et al., 2014). In contrast to short-finned pilot whales (see ) aggregations of maturing males have not been observed.

Data collection
Reproductive tissues are expected to degrade with age as females cease to be reproductively active. To test this hypothesis in false killer whales, we analysed samples from the ovaries and mammary glands. We investigated age-related trends in 1) ovarian weight per kg of body mass, 2) ovarian activity, 3) mammary gland thickness, and 4) the occurrence of pregnancy based on the presence of corpora lutea of pregnancy (CLP).
We used the database analyzed by Ferreira et al. (2014), who compared age and reproductive information from false killer whales stranded in South Africa in 1981, with similar material from animals examined from drive fisheries in Japan . The South African material was collected from 65 false killer whales that stranded en masse on the west coast of the Western Cape Province on 19 August, 1981. Of these, 56 were found over a 1.5 km stretch of beach in St Helena Bay (32.781 • S 18.1 • E). As scientists reached the site only two days after the stranding event was reported, the material was not fresh and fixation was suboptimal. Data are available from 41 (including 37 mature) females. The Japanese material originated from six schools driven ashore at Iki Island (33.8 • N 129.718 • E) in February and March of 1979 and 1980, designed as culling operations to reduce fishery interactions (Kasuya, 1985). In each case, as many false killer whales as possible were randomly examined. Data are available for 96 (including 76 mature) females. (Ferreira et al., 2014) concluded that although patterns of growth appeared similar, both sexes were 10%-20% larger in Japan than South Africa. Additionally, initial ovulation and apparent pregnancy rates were lower in animals from South Africa, possibly because of impaired reproductive performance in the stranded school. Survival rates were not calculated separately but the overall age compositions did not suggest any great differences in longevity or survival (see Fig. 2 in Ferreira et al. (2014)). In order to increase sample size, data from South African and Japanese females have been combined (n = 83) for most of the following sections. Only where there were obvious differences have the analyses been separated by population.

Field procedures
Ferreira et al. (2014) described the procedures used in collecting material in both localities. Attempts were made to collect one to three adjacent teeth from the center of the lower jaw of each animal, and these were fixed in 10% buffered formalin (Japan) or in 70% ethanol (South Africa). Where possible, the depth of the mammary gland was measured and the presence/absence of milk recorded, the diameters of both uterine cornua measured and the length and sex of any foetus present recorded. Samples of mammary gland and uterus were taken for histology where appropriate. Both ovaries were collected and the presence of corpora lutea, corpora albicantia or large follicles recorded before the ovaries were fixed in 10% buffered formalin.

Age determination from teeth
Teeth were sectioned longitudinally through the center of the pulp cavity to a thickness of 40 -50µm (Ferreira et al., 2014). Sections were then decalcified and stained with haematoxylin before mounting in Canada Balsam. Whales were aged by counting the growth layers in dentine and/or cementum at a magnification of 20 -100x (and without reference to other biological data). Growth layer groups (GLGs) in the dentine and cementum were assumed to be deposited annually (Kasuya and Matsui, 1984). The median values of three independent GLG counts in the dentine and cementum were taken, and where discrepancies between dentinal and cemental counts occurred, the growth layers in both tissues were repeatedly checked until a good agreement was reached between the two counts. The ages of older individuals with closed pulp cavities were determined using cemental GLG counts only. The ages of individuals below 10 years were estimated to the nearest 0.25 year by comparing the thickness of the first and last postnatal dentinal layers, while in older whales the ages were determined to the nearest n ± 0.5 year (where n is integer). All age-related data analyses relate to these age estimates, though data have been grouped where necessary.

Analysis of reproductive tissue: ovaries and mammary glands
The medulla and cortex of all ovaries were hand-sliced at 1-2 mm intervals and examined macroscopically for various indices of follicular development (non-atretic follicles < 1 mm in diameter), ovulation (corpora lutea of ovulation -CLO, corpora albcantia), pregnancy (corpora lutea of pregnancy, CLP) and follicular atresia (atretic Graafian follicles, corpora atretica). The numbers of corpora lutea, corpora albicantia, and corpora atretica were counted. The diameters of all corpora and Graafian follicles were measured to the nearest 0.1 mm on three planes using vernier calipers, and the mean taken as the cube root of the product of the three. Corpora albicantia were classified as young, medium or old according to the characteristics used by . Macroscopically visible Graafian follicles (i.e. those > 1 mm in diameter) were classified as atretic or non-atretic on the basis of the macroscopic thickness of the follicle walls. Perrin and Donovan (1984)(Appendix A) provide a detailed description of the terminology.

Classification of individuals into reproductive categories
Females were classed as mature if they: (a) contained at least one corpus luteum or corpus albicans in the ovaries, and\or (b) were pregnant or lactating. Pregnancy was determined either by the visible presence of a foetus (or knowledge of its abortion), or the presence of a corpus luteum and evidence from endometrial histology or the presence of a fragment of placenta or umbilical cord that the female had been carrying a foetus. Lactating females were those with: (1) field observations of milk in the mammary gland, or (2) in which histology suggested that the gland was active (Ferreira et al., 2014). Ovulating females were those with an active corpus luteum in the ovaries but no signs of pregnancy: the size distribution of these corpora lutea of ovulation tended to be bimodal, with some having diameters ≥ 29.6 mm and others diameters ≥ 39.3 mm, and as the latter group coincided with the size range for known corpora lutea of pregnancy, it is possible that some of the larger corpora lutea of ovulation may actually have been undiagnosed corpora lutea of pregnancy (perhaps associated with very small undetected embryos). Resting females were those with at least one corpus luteum or corpus albicans in the ovaries but no intimation of pregnancy or lactation.

Trends in reproductive materials
Weights of both ovaries were available for 55 females from Japan. Ovary weights of non-pregnant, non-ovulating females (i.e. without an active corpus luteum) have been expressed as a proportion of estimated body weight (g/kg). Ovarian weights were averaged and grouped into 8 age classes due to the sparseness of the data (Fig. 1). Age-classes were 5-years with the exception of the first one. The youngest individual in the dataset was 8.25 years old, so the first category included animals age 8.25 up to, and including, 14.5. Similarly, the last category included animals aged 51.0 years or older, with the oldest animal aged at 63.5 years, since there were only two individuals older than 59.5 years. These were 5 years wide; 8.25-14.5 year-olds, 15.0-20.5 year-olds, 21.0-26.5 year-olds, 27.0-32.5 year-olds, 33.0-38.5 year-olds, 39.0-44.5 year-olds, 45.0-50.5 year-olds and individuals aged 51.0 or older. This grouping was used in all analyses of reproductive tissues. All statistical analysis was carried out in R (R Core Team, 2016).
We used linear regression models to examine (1) trends in ovarian weights per kg of body mass as a function of age class, (2) trends in mammary gland thickness in different reproductive categories (lactating vs non-lactating) and with age in years, (3) trends in the number of Graafian follicles and the percentage of those that were atretic as a function of age class, and (4) to test for a trend between the total number of corpora albicantia and age in years. In all cases, age was determined by GLGs. We were only able to compare the number of corpora lutea representing pregnancy and ovulation in two age classes (5), younger than 25yr and older than 25yr, using a test for proportions (R Core Team, 2016). This was because of a very small sample size of 26 individuals. We ran power analyses on all models using the pwr package in R (Champely, 2015).

Construction of the life table
The calculation of Postreproductive Representation (PrR) required data on age-specific fecundity and survival, as well as the cohort size in each age class. The parameters of the life table were estimated based on those published in Caughley (1977): lx: the survival or the probability of surviving to the exact age x dx: the frequency of mortality or the probability of dying during the age interval x, x+1 qx: the mortality rate or the proportion of animals alive at age x that die before age x+1 px: the survival rate or the proportion of animals at age x that survive to age x+1 Age specific survival and fecundity were derived for animals in each age or year class, ranging from age 8 to 63. Younger animals were grossly underrepresented and do not appear in the life table (Additional file 2).
Age data were available from a combined data set of 91 females from South Africa and Japan. Observed age frequency data were converted to a cumulative frequency distribution representing the number of individuals observed to be alive in each age group from an initial cohort size of 91 (i.e., the number of whales >8 years old).
To avoid violating the requirements of a static life table (i.e. that the frequency of each age class x is equal to or greater than x+1; (Caughley, 1977), the frequency distribution of animals in the different age classes was smoothed using a logistic regression model before constructing the life table. This approach provided all age classes with values and fulfilled the requirements of the static life table. Smoothing of age distributions is often done by use of a log-polynomial model (with a logged response variable, counts of animals in an age class, and polynomial terms of the explanatory variable, age), whereby terms are added sequentially and the adequacy of the model is checked via the F-statistic. In our data, there was no evidence for variability in the survival rate with age and the model used was a linear regression model of the form log(y) = a + bx.
Survival information was available from a dataset including animals between the ages of 8 and 63, and age classes of 1 year. In contrast, fecundity information for P.crassidens was available from a combined dataset on pregnancy rate in animals from South Africa and Japan, where data were pooled into age classes. Age classes for fecundity started at 8.25, ended at 56.25 years and were 6 years wide, resulting in 9 categories. This approach boosted the number of data points within each category. The effect of different grouping regimes was investigated during exploratory analysis and its effect was found to be negligible.
In order to obtain a complete life table including age specific survival and fecundity, we applied a data-driven regression model to the fecundity data to estimate the pregnancy rate for each age class in the survival data. This model was implemented with the sm package in R (Bowman and Azzalini, 2014). The smoothing parameter (h: the standard deviation of the normal kernel function used; Bowman and Azzalini (2014)) for the regression was estimated during model fitting to be 5.46, however the result for PrR was not sensitive to the choice of h in either direction when the change was within 3 units of the model estimated h.

Calculating postreproductive representation (PrR)
PrR (Levitis and Lackey, 2011) is equal to the ratio T M/T B, where T M is the expected number of postreproductive years lived by an average newborn, and T B the expected number of adult years lived by an average newborn. T M is defined as the product of the remaining life expectancy once 95% of lifetime fecundity has been realised (age M ) and the number of individuals surviving to that exact age. T B is defined as the product of the remaining life expectancy once 5% of lifetime fecundity has been realised (age B) and the number of individuals surviving to that exact age.
Even though the inputs and calculations for PrR are described in terms of expected demographic rates for newborn animals, Levitis and Lackey (2011) note that this measure is independent of infant and juvenile mortality but dependent on survival through the reproductive and postreproductive phases, making the method particularly suitable for comparing populations with different pre-reproductive mortality. Based on this premise, we assume that the theory and application are equally relevant in cases where the demographic information is missing for the first few cohorts, as in the dataset analysed here.
One of the advantages of PrR is that it makes it possible to make inferences about the value of PrR obtained for a given species or population. Together the model-based survival and smoothed fecundity information for P.crassidens were used to estimate PrR for our sample. We used code provided by Levitis and Lackey (2011) to obtain a null distribution for the values of PrR one might expect to obtain based on these data, if the null hypothesis of no postreproductive lifespan were true. Due to the opportunistic nature of the data used, there were some gaps in the life table. Ten age classes (18% of the 56 age classes in the life table) were empty. These gaps created problems in the application of the simulation routine, which stochastically generates individual life histories based on the survival and fecundity probabilities in the life table and the initial cohort size in the observed dataset. The first empty age class in the data occurs at age 11, with the result that no individuals were simulated to survive past age 11. To overcome this problem, we made previously empty age classes contain a single individual. We ran the simulation for 1000 populations with the same number of individuals as in the observed dataset (n = 91) and compared the observed PrR to the mean of the null distribution of PrR. The test statistic for the difference between the two estimates was obtained by taking the difference of the means and dividing it by the square root of the sum of the standard deviations for each sample.
Under this methodology, there is no natural way to produce an estimate of the uncertainty associated with the point estimate of PrR for a life table, because it comes from a single population. The life table for P.crassidens was constructed based on combined data from two populations (a healthy population from 6 harvested schools, and a population with potentially impaired vital rates from 1 stranded school) with similar survival, but divergent fecundity rates (Ferreira et al., 2014). This approach made it possible to calculate point estimates and null distributions for PrR based on the combined dataset and for South Africa and Japan separately. In the absence of a formal measure of uncertainty in PrR, we offer the two separate point estimates as an indication of the range that PrR can take on for P.crassidens under widely differing scenarios for reproductive rates (Fig. 6).

Ovarian weights
We found no evidence of age-rated changes in the ovarian size (ovary weight per kg of body weight) of false killer whales, however, there was very low power to detect a significant effect (F 7,47 = 2.09, p-value for the difference in ovary weight in no 2 groups being substantially different from zero equal to 0.53). Fig. 1 indicates that ovary weights increased with age up to about 26 years, but this trend was not statistically significant. With our sample size there was a 11% chance of detecting an effect of the observed size (0.03) at the 5% level if it was actually there.

Mammary gland development with age
There was strong evidence that the gland in lactating females was significantly thicker than that in mature, non-lactating females (Ferreira et al. (2014) and this study: F 2,29 = 7.04, p-value for no difference in mammary gland thickness between lactating and non-lactating individuals < 0.01). Measurements of mammary gland thickness were available for 38 mature females and averaged 2.5 cm (mean, range 0.9-4.2 cm). There was sufficient power to conclude that this result was robust for the observed effect size and sample size (99% probability of detecting the effect at the 5% level). However, there was no evidence to support a decline in mammary gland thickness with age (Additional file 1), despite reasonable power to detect a significant effect of the observed size with the sample size (78% probability of detecting an effect of size 1 at the 5% level).

Follicular development and atresia with age
The number of macroscopically-visible Graafian follicles in mature females varied greatly between individuals, with 42.2% (35 out of 83) having none. The number of Graafian follicles remained on average high in the first three age groups (8.25-26.5 year-olds: median 1, mean 29.5±10.12 SE), but above 27 years of age the number declined markedly (17.0-51.0+ year-olds: median 1, mean 7.01±3.77 SE) ( Fig.  2 broken line). Despite the spike in Graafian follicles in the age group 33.0-38.5 year-olds, there was evidence for an overall decrease in Graafian follicles with age (F 1,81 = 5.446, p < 0.03) and there was sufficient power to conclude that this trend was robust (99>% chance of detecting an effect of size 4.4 at the 5% level). Follicular atresia gradually increased with age, but not markedly in older individuals. The number of corpora atretica per female showed a progressive increase with age (F 1,81 = 5.06, p < 0.03), as did the mean percentage of follicles that were atretic, resulting from the atresia of luteinized Graafian follicles (Fig. 2 solid line). There was sufficient power to judge this result to be robust (99% chance of detecting an effect of 0.5 at the 5% level).

Regression of corpora albicantia with age
Old corpora albicantia likely persist in the ovaries of false killer whales throughout life, whereas young and medium corpora albicantia apparently represent progressive stages in their regression (Ferreira et al., 2014). There was strong evidence that the numbers of old corpora albicantia in an individual's ovaries continued to increase linearly with age (F 1,73 = 75.4, p < 0.01) (Fig.3 A) and there was enough power to conclude this trend was robust (99>% chance of detecting an effect of size 0.3 at the 5% level). The maximum number of old corpora albicantia was 22 (in an individual 55.5 year old), whereas the maximum number of medium or young corpora albicantia in any individual was only 3 and showed no signs of accumulating except in newly mature individuals (Fig. 3 B). Only 2 of the 31 females over 40 years of age had any young corpora albicantia: the oldest female was a 48.5 years old resting female and the second oldest female was aged 40.5 years and was ovulating/lactating. None of the 15 females older than 48.5 years contained a young corpus albicans and the oldest female with a medium corpus albicans was 55.5 years old. This pattern suggested the onset of a reduction in the rate of successful ovulation in animals at some point after 41 years of age, although the shape of this trend is not known.

Trend in pregnancy rate and successful ovulations with age
The relative frequencies of corpora lutea of ovulation and pregnancy were available for 26 known-age female false killer whales using combined data from Japan and South Africa (accessory corpora lutea have been excluded) (Fig. 4). The data were not sufficient to compare the relative frequencies across the 8 age groups used in the other analyses of reproductive tissue so the data were split into two groups: animals up to 25 years old and animals older than 25 years. This cutoff was chosen so that the sample sizes were equal. The frequency of corpora lutea of pregnancy relative to those of ovulation was greater in females up to 25 years of age compared to older females (mean difference 0.38, SE 0.18). The relative frequencies were compared in the two age groups to test whether ovulation was less likely to be followed by pregnancy in older animals. There was insufficient evidence to support a true difference between the groups (χ 2 = 2.52, p = 0.11) but there was also low power to detect a trend (10% chance of detecting an effect of size 0.38 at the 5% level). We would need a sample size of approximately 108 individuals to have an 80% chance of detecting that same trend at the 5% level.

The life table
In order to increase sample size, age-specific pregnancy rates were investigated for both the Japanese and South African samples (Table 1). Even so, data had to be binned by age group to obtain sufficient resolution. The apparent pregnancy rate rose from 16.7% in newly mature whales to 50% in females aged 20 -26 years, declining thereafter to 15.4% in 38 -44 years old females. The oldest pregnant female was 43.5 years old. None of the 23 whales 44-63 years old was pregnant. Mean age specific fecundity was estimated at 0.16 (SE 0.06, max. 0.50). We used the smoothed proportion of pregnant females from Table 1 to calculate age-specific fecundity, sensu (Levitis and Lackey, 2011): the total number of offspring of both sexes born to all individuals within an age class (Fig. 5).

Postreproductive representation (PrR)
For the combined population ages at which an animal has reached 5% and 95% of its reproductive potential were found to be 10 and 40 years respectively (5th and 95th fecundity quantiles), and the age at which an animal has lived 95% of its lifespan was found to be 56 years. The exact value of PrR for this population was found to be 0.25. This value was substantially different to the mean of the null distribution for PrR (0.03±0.0009 mean and SE) under the null hypothesis of no post reproductive lifespan, for which the 95% percentile was 0.10 and no simulated value exceeded 0.20. In calculating separate point estimates for each population, representing different fecundity scenarios, we found that the evidence in favour of postreproductive lifespan strengthens when the data from South Africa are considered on their own (PrR = 0.44), and remains effectively unchanged if data from Japan are considered on their own (PrR = 0.22) .The test statistic for the difference in the combined dataset was found to be 256 standard deviations from zero, and the p-value was effectively zero. This constitutes strong evidence for a postreproductive lifespan in false killer whales.
Assuming mature females that are resting with no young or medium corpora albicantia and no non-atretic macroscopic follicles in their ovaries have ceased ovulation, our sample included 15 postreproductive females. The ages of the 14 animals for which an age estimate was available ranged from 34.5 to 63.5 (mean 50.9 ± 2.5 SE) years, with 50% of whales over 45 years, and all whales over 55 years old being postreproductive (Fig. 6). The maximum ages of whales in both samples were similar, 63.5 and 62.5 years, in females from South Africa and Japan respectively (Fig. 6).

Discussion
The morphological and statistical evidence we have presented makes a strong case for the false killer whale being the third species of toothed whale from the family Delphinidae to have a prolonged postreproductive lifespan (PRLS).  and  used carcass analysis to demonstrate that female short-finned pilot whales cease to breed by 40 years of age but still have a mean life expectancy of 14 years. The ovaries of the females classified as postreproductive were senescent and histologically similar to post-menopausal human ovaries . Longitudinal demographic data indicate that female killer whales also live well beyond the age of reproductive cessation (Bigg, 1982;Olesiuk et al., 1990;Ward et al., 2009;Foster et al., 2012). Anatomical and life history data for sperm whales are also suggestive of a significant PRLS (Best et al., 1984) and there are indications that other odontocetes such as spotted and spinner dolphins (Perrin et al., 1976(Perrin et al., , 1977 may have a similar postreproductive phase. Nonetheless the evidence for all these additional species is inconclusive (Marsh and Kasuya, 1986).
The morphological evidence for a PRLS in the false killer whale includes: (1) the marked decline in macroscopically visible Graafian follicles in the ovaries of females above 38.5 years of age, and complete absence of such follicles from the ovaries of females over 57.5 years of age; and (2) the apparent reduction in the rate of successful ovulation in animals in their fifth and sixth decade of life as evidenced by lack of young corpora albicantia in their ovaries, a pattern suggesting an absence of ovulation in animals over 49 years of age. There was also weak evidence for an age-related decline in the ratio of corpora lutea of pregnancy to corpora lutea of ovulation, which would suggest that ovulation is less likely to be followed by pregnancy in older females, but the sample size was too small to show this convincingly.
The statistical evidence for a prolonged PRLS in false killer whales is also compelling, indicating that the PrR for the combined sample was 0.25, substantially different to the mean of the null distribution under the null hypothesis of no post reproductive lifespan. Evidence supporting a substantial postreproductive lifespan strengthened when the data from South Africa were considered on their own (PrR = 0.44), and remained effectively unchanged for the Japan-only data (PrR = 0.22). Lahdenperä et al. (2014) calculated the PrR several species of large mammals (see Fig. 6). Our data for the false killer whale span the single estimate for the other cetaceans that are accepted as having a significant PRLS (0.28 for the short-finned pilot whale), are much higher than the values for working Asian elephants (0.13) and three long-lived, non-human primates living in wild or semi-wild conditions (Pan troglodytes (0.018); Macaca fuscata (0.055); Papio hamadryas (0.084)) and but lower than pre-industrial Finns (0.51), which corresponds with patterns found in other historical or hunter-gatherer human populations (0.3-0.47) (see Lahdenperä et al. (2014) for details).
There is no single accepted indicator of the cessation of female reproduction. A decrease in ovulation and pregnancy rates with age is typical of many mammals, few of which show a prolonged postreproductive phase. An age-related decline in fertility is not just the result of changes in the ovaries, but is a consequence of the total sum of changes to the reproductive system. Thus, as Marsh and Kasuya (1986) point out, the existence of a postreproductive phase is best investigated on the basis of a variety of evidence, as we have done here. Oceanic marine mammals are notoriously difficult to study. Data from both stranded animals and shore-drive fisheries are suitable for investigating the existence of PRLS in such species as demonstrated here for false killer whales and by  and  for short-finned pilot whales.
Nonetheless, the relatively few young individuals (both mature and immature) in our false killer whale sample is a shortcoming and their inclusion would make the analysis more robust. However, it seems unlikely that young, sexually mature individuals are grossly underrepresented, based on the youngest mature animals present in the sample (South Africa) and the estimated age at which 50% of animals are mature (Japan). The calculation of PrR required that all age classes were represented. The fact that some age classes were not represented in our dataset made it necessary to make consequential adjustments to the data prior to analysis. These gaps were not at the extremes of the age distribution and ought not have affected our conclusions. In addition, the fact that the data from South Africa are from only 1 group limit robust population comparisons. It will be important to collect additional data from stranded animals to test if the results reported here apply to other social groups and populations of false killer whales.
False killer whales share several life history characteristics with the other toothed whales shown to have a prolonged PRLS. All have low life-time productivity, are sexually dimorphic (indicating male parental care is likely to be sparse or non-existent), and are known or believed to exist in stable matrilineal groups of closely related females, with strong mother-offspring associations and a long period of dependency (Bigg, 1982;Whitehead and Mann, 2000). With such low fecundity and prolonged maternal investment, survival, particularly adult survival, is likely the most important life history parameter as first pointed out by Eberhardt and Siniff (1977). Postreproductive females may help to ensure better calf survival through protection and provisioning of resources, nutri-tional and otherwise, and thereby increase their own inclusive fitness because members of a matrilineal pod are likely to be genetically related. Food sharing among false killer whales was reported by Connor and Norris (1982), and has frequently been observed in the longitudinal study around the Hawaiian Islands (Baird et al., 2008;Baird, 2016).
Lactation is also energetically expensive (Lockyer, 1981). Thus, in species with co-operative breeding, postreproductive females may relieve daughters from their lactating duties so that they can redirect their energies to producing more offspring. Another advantage of communal suckling is that if a lactating female should die, her calf can obtain milk from another lactating female, or alternatively, if the mother should lose its newborn calf, she could provide milk to and contribute to the survival of other nursing calves in the group. Best et al. (1984) suggested that communal suckling might occur in sperm whales, while Gordon (1987) described an observation of a sperm whale calf apparently suckling from two different females. Although there is no direct evidence of communal suckling in false killer whales, the presence of more lactating females than juveniles of presumed suckling age among the relatively less fertile South African whales  is suggestive. In species with low reproductive potential and stable groups of closely related females, communal suckling would seem an advantageous strategy. Communal suckling might also explain the lack of age-related decline of the thickness of mammary tissue observed in our study.
Longitudinal data are required to test hypotheses about the ways in which a PRLS might increase the inclusive fitness of a false killer whale population, as has been done for two killer whales populations off British Columbia and Washington by Ward et al. (2009);Foster et al. (2012);. Such data will be logistically challenging to collect for false killer whales (Baird et al., 2008) because of their pelagic lifestyle. The most promising source of such data is the long-term study of the for false killer whale population around the Hawaiian Islands (Baird et al., 2008;Baird, 2016). Understanding the way in which local relatedness changes with female age would be particularly informative from a theoretical perspective, given modelling by Johnstone and Cant (2010) showed that an increase in relatedness with female age can arise in species with very different social structures. It would be particularly informative, albeit logistically challenging, to obtain data about the change in female relatedness with age, social structure and evidence for a PRLS in other large social Delphinids such as Risso's dolphins (Grampus griseus), melon headed whales (Peponocephala electra), pygmy killer whales (Feresa attenuata) and pilot whales (Globicephala spp.).

Conclusions
We found compelling morphological and statistical evidence for PRLS in South African and Japanese pods of false killer whales, the third non-human mammal in which this phenomenon has been convincingly established in wild populations. Our estimates for the PrR of the false killer whale (0.22-0.44; Fig. 6) spanned the single value available for the short-finned pilot whale (0.28) and are comparable with estimates for historical or hunter-gather human populations (0.3-0.47). Our results suggest that it would be fruitful to investigate the age-related change in relatedness and social structure of false killer whales and other large social Delphinids in order to gain further theoretical insights into why some social large mammals exhibit a post-reproductive phase in the life history of females.     The fitted relationship between pregnancy rate and age, using data-driven regression, for female false killer whales from Japan, South Africa, and the combined dataset. The open diamonds represent females of known age from the combined dataset that were found to be postreproductive.  Lahdenperä et al. (2014) to include the estimate for false killer whales from this study. PrR values and maximum longevities in Asian elephants and humans from (Lahdenperä et al., 2014), other PrR-values were taken from Levitis and Lackey (2011). Maximum longevities in Macaca fuscata were sourced from Pavelka and Fedigan (1999), Pan troglodytes from Hill et al. (2001), Papio hamadryas from Bronikowski et al. (2002) and Globicephala macrorhyncus from , as in the original version of the figure. Tables   Table 1: Variation in apparent pregnancy rates of Japanese and South African false killer whales with age. Labels Pregnant and Pregnant a are used to denote the presence of a foetus, and no foetus but corpus luteum ≥ 3.93mm thick, respectively (see Materials and Methods).

Additional Files
Additional file 1 -Thickness of mammary gland in false killer whales (South Africa) in relation to age and reproductive status. Figure S1. Thickness of mammary gland in false killer whales (South Africa) in relation to age and reproductive status. Open circles are used to represent animals that were not lactating (NL) and closed circles animals for those that were lactating (L). We fitted a linear regression model to mammary gland thickness with age and reproductive class (lactating, non-lactating) as explanatory variables. The dashed horizontal line is the fitted mean mammary gland thickness in non-lactating animals, and the solid line is the fitted mean thickness for lactating animals. The grey bands around each fitted mean are the 95% confidence intervals for the estimate. The figure shows that there is some evidence for greater mammary gland thickness in lactating animals but there was no evidence for a change with age in either.
Additional file 2 -Life table for Pseudorca crassidens Table S1. The life table for the combined dataset for specimens from Japan and South Africa. Age classes are 1 year wide, n denotes the number of animals of each age class in the original data, cumulativen denotes the number of animals at least n years of age, S is the estimated age-specific survival, repro is the number of reproductively active animals, post − repro is the number of confirmed postreproductive animals.