A measure for describing and comparing post-reproductive lifespan as a population trait

Abstract

1. While-classical life-history theory does not predict post-reproductive lifespan (PRLS), it has been detected in a great number of taxa, leading to the view that it is a broadly conserved trait, and attempts to reconcile theory with these observations. We suggest an alternative: the apparently wide distribution of significant PRLS is an artifact of insufficient methods.2. PRLS is traditionally measured in units of time between each individual's last parturition and death, after excluding those individuals for whom this interval is short. A mean of this measure is then calculated as a population value. We show this traditional population measure (which we denote PrT) to be inconsistently calculated, inherently biased, strongly correlated with overall longevity, uninformative on the importance of PRLS in a population's life-history, unable to use the most-commonly available form of relevant data and without a realistic null hypothesis. Using data altered to ensure that the null hypothesis is true, we find a false positive rate of 0.47 for PrT.3. We propose an alternative population measure, using life-table methods. Post-reproductive Representation (PrR) is the proportion of adult years lived which are post-reproductive. We briefly derive PrR and discuss its properties. We employ a demographic simulation, based on the null hypothesis of simultaneous and proportional decline in survivorship and fecundity, to produce a null distribution for PrR based on the age-specific rates of a population.4. In an example analysis, using data on 84 populations of human and non-human primates, we demonstrate the ability of PrR to represent the effects of artificial protection from mortality and of humanness on PRLS. PrR is found to be higher for all human populations under a wide range of conditions than for any non-human primate in our sample. A strong effect of artificial protection is found, but humans under the most-adverse conditions still achieve PrR of >0.3.5. PrT should not be used as a population measure, and should be used as an individual measure only with great caution. The use of PrR as an intuitive, statistically valid and intercomparable population life-history measure is encouraged.

Figure 1

Age-specific survival for populations with identical Post-reproductive Times are shown. Populations A (red line) and B (blue dashed line) both begin reproducing at age=0, reach reproductive cessation at age=10, and both experience 50% annual mortality in years 10 and above. Population A experiences no mortality prior to reproductive cessation, while Population B experiences 20% annual mortality. 16.6% of years lived by population A are post-reproductive, compared to 4.5% of years lived by B. However, PrT for each population is one year. For both these populations the ratio of PrT to fertile lifespan is 1/10.

Figure 2

Post-reproductive time (PrT) scales with life expectancy at birth. A measure of PrT (e_M) plotted against life expectancy at birth (e₀) for 63 species of captive primates. Data are from the International Species Information System. The majority of information in these interspecies comparisons of PrT is attributable to the overall longevity of the organisms (Adjusted R-squared: 0.67), not to variation in the representation of post-reproductive individuals in the populations, indicating that PRLS is of limited value for comparisons between species with different overall longevities. The upper outlier in this graph is the Brown Wooly Monkey, Lagothrix lagotricha, a species known to be difficult to breed in captivity (Mooney and Lee 1999), and without exceptional PRLS as measured by PrR or ecological reason to expect unusual PRLS.

Figure 3

A null hypothesis for Post-reproductive representation (PrR) is generated by altering the observed survivorship curve (solid black line), such that its decline after the age of maximum fecundity is proportional to the decline of age-specific fecundity (solid blue line). This new curve is employed to calculate yearly survival probabilities (p_x) for a population in which survivorship and fecundity decline in parallel. 1000 populations are simulated using these altered survival probabilities. PrR is calculated for each, generating the null distribution against which the observed value can be compared. We illustrate this process for two chimpanzee populations. Each dashed multicolored line is the survivorship curve (l_x) for a single simulated population. Wild chimpanzee (A) survivorship decline is at the low end of their null distribution. Zoo chimpanzees (B) live significantly longer than is expected based on their rate of reproductive senescence. The larger sample size in B leads to a tighter null distribution.

Figure 4

Post-reproductive representation (T_M/T_B) for humans (top) and non-human primates (bottom) under varying circumstances. Primate populations are wild Pan troglodytes and Papio cyanocephalus, semi-wild Macaca fuscata and 66 zoo populations. While both humans and non-humans reveal increasing PrR in increasingly tailored habitats, all human populations experience greater PrR than any non-human population, and no primates but humans experience substantial PrR under natural conditions.