Life-history traits and effective population size in species with overlapping generations revisited: the importance of adult mortality

Abstract

The relationship between life-history traits and the key eco-evolutionary parameters effective population size (Ne) and Ne/N is revisited for iteroparous species with overlapping generations, with a focus on the annual rate of adult mortality (d). Analytical methods based on populations with arbitrarily long adult lifespans are used to evaluate the influence of d on Ne, Ne/N and the factors that determine these parameters: adult abundance (N), generation length (T), age at maturity (α), the ratio of variance to mean reproductive success in one season by individuals of the same age (φ) and lifetime variance in reproductive success of individuals in a cohort (Vk•). Although the resulting estimators of N, T and Vk• are upwardly biased for species with short adult lifespans, the estimate of Ne/N is largely unbiased because biases in T are compensated for by biases in Vk• and N. For the first time, the contrasting effects of T and Vk• on Ne and Ne/N are jointly considered with respect to d and φ. A simple function of d and α based on the assumption of constant vital rates is shown to be a robust predictor (R(2)=0.78) of Ne/N in an empirical data set of life tables for 63 animal and plant species with diverse life histories. Results presented here should provide important context for interpreting the surge of genetically based estimates of Ne that has been fueled by the genomics revolution.

Figure 1

Typical patterns of Type I survival in species with adult lifespans of 5, 10, 20 and 40 years. Annual mortality at age of maturity was d_α=0.05; d_x increased each year by the proportion λ that was chosen to produce cumulative survivorship of l_x=0.01 at the maximum age. The filled circles are , the constant mortality rate that would produce the same cumulative survivorship over the adult lifespan.

Figure 2

Relationship between adult survival (assumed to be constant at annual rate 1−d) and generation length (T) and lifetime variance in reproductive success (V_k•). These are analytical and numerical results based on relationships in Equations (8), (9), (11) and (12). Three scenarios are considered: constant fecundity (m) with φ=1; fecundity that is proportional to age (m_x=βx) with φ=1; and m_x and φ both proportional to age. Changes in φ do not affect generation length, and hence in the last scenario the curve for T vs 1−d is also given by the black dashed line. When survival is constant with age, the rate of increase of adult N with increasing survival is identical to the rate of increase in T with constant vital rates (solid black curve).

Figure 3

Bias in estimates of key demographic parameters when applying analytical results based on infinite series to populations with finite adult lifespan. These scenarios used constant adult mortality at the levels indicated, constant φ=1 and either constant fecundity (top) or fecundity proportional to age (bottom). ‘Estimated' parameters were based on the expectations from infinite series analysis and ‘True' values were calculated for the actual time series using the AgeNe method described by Waples et al. (2011).

Figure 4

Bias in estimates of N_e and N_e/N when applying analytical results based on infinite series to populations with finite adult lifespan. These scenarios used constant adult mortality at the levels indicated, constant φ=1 and either constant fecundity (top) or fecundity proportional to age (bottom). ‘Estimated' parameters were based on the expectations from infinite series analysis and ‘True' values were calculated for the actual time series using the AgeNe method described by Waples et al. (2011).

Figure 5

Bias in estimates of adult census size and generation length when assuming constant survival for species with Type I survivorship. These scenarios used constant fecundity and survivorship followed the Gompertz functions depicted in Figure 1. True parameters were calculated for the observed data using the AgeNe method described by Waples et al. (2011) and the estimates were calculated using the values in Supplementary Table S2 to represent mortality in Equations (4) and (7), assuming α=1.

Figure 6

Relationship between annual survival (s=1−d, assumed to be constant) and predicted N_e/N, for scenarios involving different combinations of age at maturity, φ and fecundity (constant or proportional to age). Predictions for constant fecundity use Equation (14) and those for fecundity proportional to age use Equation (18).

Figure 7

Estimates of N_e/N compared with the true ratio for 63 species with diverse life histories. True parameters were calculated using the life tables compiled by Waples et al. (2013), with modifications as described in Methods and shown in Supplementary Table S1. Estimates of N_e/N were calculated from Equation (14) using the actual age at maturity and the values of shown in Supplementary Table S1.

Figure 8

Relationship between estimated and true N_e/N for individual species, using data from Figure 7. The top panel show results for all 63 species; the bottom panel shows results only for species with survival that is constant with age, or nearly so. Some outlier species are identified. The legend indicates general patterns of age-specific survival and fecundity. ‘Flat'=constant with age; ‘UpFlat'=increasing in the first few years after maturity before leveling off; ‘Up'=increasing with age; ‘other'=decreasing with age, complex patterns or different patterns in males and females.