The natural history of luck: A synthesis study of structured population models.

Chance pervades life. In turn, life histories are described by probabilities (e.g. survival and breeding) and averages across individuals (e.g. mean growth rate and age at maturity). In this study, we explored patterns of luck in lifetime outcomes by analysing structured population models for a wide array of plant and animal species. We calculated four response variables: variance and skewness in both lifespan and lifetime reproductive output (LRO), and partitioned them into contributions from different forms of luck. We examined relationships among response variables and a variety of life history traits. We found that variance in lifespan and variance in LRO were positively correlated across taxa, but that variance and skewness were negatively correlated for both lifespan and LRO. The most important life history trait was longevity, which shaped variance and skew in LRO through its effects on variance in lifespan. We found that luck in survival, growth, and fecundity all contributed to variance in LRO, but skew in LRO was overwhelmingly due to survival luck. Rapidly growing populations have larger variances in LRO and lifespan than shrinking populations. Our results indicate that luck-induced genetic drift may be most severe in recovering populations of species with long mature lifespan and high iteroparity.

The Contributions of Maternal Age Heterogeneity to Variance in Lifetime Reproductive Output.

AbstractVariance among individuals in fitness components reflects both genuine heterogeneity between individuals and stochasticity in events experienced along the life cycle. Maternal age represents a form of heterogeneity that affects both the mean and the variance of lifetime reproductive output (LRO). Here, we quantify the relative contribution of maternal age heterogeneity to the variance in LRO using individual-level laboratory data on the rotifer Brachionus manjavacas to parameterize a multistate age × maternal age matrix model. In B. manjavacas, advanced maternal age has large negative effects on offspring survival and fertility. We used multistate Markov chains with rewards to quantify the contributions to variance in LRO of heterogeneity and of the stochasticity inherent in the outcomes of probabilistic transitions and reproductive events. Under laboratory conditions, maternal age heterogeneity contributes 26% of the variance in LRO. The contribution changes when mortality and fertility are reduced to mimic more ecologically relevant environments. Over the parameter space where populations are near stationarity, maternal age heterogeneity contributes an average of 3% of the variance. Thus, the contributions of maternal age heterogeneity and individual stochasticity can be expected to depend strongly on environmental conditions; over most of the parameter space, the variance in LRO is dominated by stochasticity.

An inconvenient tooth: Evaluating female choice in multiple paternity using an evolutionarily and ecologically important vertebrate clade.

Understanding mating systems is a pillar of behavioural ecology, placing the complex interactions between females and males into a reproductive context. The field of multiple paternity, the phenomenon whereby many sires contribute to an individual litter, has traditionally viewed females as passive players in a male-male competitive framework. With the emergence of feminist perspectives in ecological fields, novel alternative mechanisms and evolutionary theories across invertebrate and vertebrate taxa recognize females are active stakeholders in the reproductive process. Despite their evolutionary significance, ecological diversity and myriad reproductive modes, elasmobranch (sharks, skates and rays) research lags behind other fields regarding complex biological processes, such as multiple paternity which is often ascribed to convenience polyandry. Here, we layout hypotheses and resynthesize multiple paternity literature from a female and life history perspective to highlight how alternative mechanisms influence the predominance of multiple paternity across elasmobranchs. We draw upon parallels in other invertebrate and vertebrate taxa to demonstrate how female elasmobranchs can influence multiple paternity outcomes that benefit their reproductive success. Our article challenges dogma that has resulted from years of dismissing the female perspective as important and provides a framework for future advancement using more holistic approaches to studying mating systems.

Diet influences latitudinal gradients in life-history traits, but not reproductive output, in ectotherms.

Aim: Latitudinal gradients in life-history traits are apparent in many taxa and are expected to be strong for ectotherms that have temperature-driven constraints on performance and fitness. The strength of these gradients, however, should also be affected by diet. Because diet type (carnivory, omnivory, herbivory) influences accessibility to nutrition and assimilation efficiency, we aim to study how diet affects latitudinal gradients in lifetime reproductive output and the underlying life-history traits in ectotherms. Location: Global. Time period: Recent. Major taxa studied: Lizards (Reptilia, Squamata, Sauria). Methods: We used empirical (352 species) and phylogenetically imputed data (563 species) to analyse the interactive effects of latitude and diet on life-history traits (longevity, age at maturity, reproductive life span, hatchling mass, clutch/brood size, clutch/brood frequency, female mass) and lifetime reproductive output of lizards. Results: Lifetime reproductive output does not significantly differ in lizards across diet types, and only carnivores exhibit a small increase at higher latitudes. Diet type, however, influences latitudinal patterns of individual life-history traits. Carnivores exhibit a shift towards 'slower-paced' life histories at higher latitudes for most traits (increased longevity, age at maturity, reproductive life span, and decreased clutch frequency). By contrast, herbivores either display 'faster-paced' life histories (reduction in reproductive life span, hatchling mass, female mass) or no change (clutch frequency, clutch size, age at maturity) at higher latitudes. Omnivores exhibit intermediate and muted latitudinal patterns. Main conclusions: We suggest that the nutritional challenges of herbivory, compounded by thermal constraints at higher latitudes, may explain differences in life-history characteristics of herbivorous ectotherms. Intermediate patterns exhibited by omnivores highlight how flexibility in diet can buffer environmental challenges at higher latitudes. Our results indicate that lizards with different diet types display various trends in their life histories across latitudes, which eventually balance out to result in similar reproductive outputs throughout their lifetime, with little benefits to carnivory.

Variance as a life history outcome: Sensitivity analysis of the contributions of stochasticity and heterogeneity.

Variance in life history outcomes among individuals is a requirement for natural selection, and a determinant of the ecological dynamics of populations. Heterogeneity among individuals will cause such variance, but so will the inherently stochastic nature of their demography. The relative contributions of these variance components - stochasticity and heterogeneity - to life history outcomes are presented here in a general, demographic calculation. A general formulation of sensitivity analysis is provided for the relationship between the variance components and the demographic rates within the life cycle. We illustrate these novel methods with two examples; the variance in longevity within and between frailty groups in a laboratory population of fruit flies, and the variance in lifetime reproductive output within and between initial environment states in a perennial herb in a stochastic fire environment. In fruit flies, an increase in mortality would increase the variance due to stochasticity and reduce that due to heterogeneity. In the plant example, increasing mortality reduces, and increasing fertility increases both variance components. Sensitivity analyses such as these can provide a powerful tool in identifying patterns among life history stages and heterogeneity groups and their contributions to variance in life history outcomes.

Bio-energetic modeling of medium-sized cetaceans shows high sensitivity to disturbance in seasons of low resource supply.

Understanding the full scope of human impact on wildlife populations requires a framework to assess the population-level repercussions of nonlethal disturbance. The Population Consequences of Disturbance (PCoD) framework provides such an approach, by linking the effects of disturbance on the behavior and physiology of individuals to their population-level consequences. Bio-energetic models have been used as implementations of PCoD, as these integrate the behavioral and physiological state of an individual with the state of the environment, to mediate between disturbance and biological significant changes in vital rates (survival, growth, and reproduction). To assess which levels of disturbance lead to adverse effects on population growth rate requires a bio-energetic model that covers the complete life cycle of the organism under study. In a density-independent setting, the expected lifetime reproductive output of a single female can then be used to predict the level of disturbance that leads to population decline. Here, we present such a model for a medium-sized cetacean, the long-finned pilot whale (Globicephala melas). Disturbance is modeled as a yearly recurrent period of no resource feeding for the pilot whale female and her calf. Short periods of disturbance lead to the pre-weaned death of the first one or more calves of the young female. Higher disturbance levels also affect survival of calves produced later in the life of the female, in addition to degrading female survival. The level of disturbance that leads to a negative population growth rate strongly depends on the available resources in the environment. This has important repercussion for the timing of disturbance if resource availability fluctuates seasonally. The model predicts that pilot whales can tolerate on average three times longer periods of disturbance in seasons of high resource availability, compared to disturbance happening when resources are low. Although our model is specifically parameterized for pilot whales, it provides useful insights into the general consequences of nonlethal disturbance. If appropriate data on life history and energetics are available, it can be used to provide management advice for specific species or populations.

Reproductive skipping as an optimal life history strategy in the southern elephant seal, Mirounga leonina.

Intermittent breeding by which organisms skip some current reproductive opportunities in order to enhance future reproductive success is a common life history trade-off among long-lived, iteroparous species. The southern elephant seal Mirounga leonina engages in intermediate breeding when body condition is low. While it is anticipated that this strategy may increase the lifetime reproductive output of this species, the conditions under which reproductive skipping are predicted to occur are not clear. Here I develop a dynamic state variable model based on published data that examines when southern elephant seals are predicted to optimally skip reproduction in order to maximize lifetime reproductive output as a function of current body mass, maternal age, and survivorship. I demonstrate that the optimal reproductive strategy for this species can include reproductive skipping, and that the conditions where this is optimal depend on patterns of mass-dependent adult female survival. I further show that intermittent breeding can increase lifetime reproductive output, and that the magnitude of this benefit increases with the ability of individual animals to replenish depleted body mass through foraging. Finally, I show that when the environment is variable and foraging is reduced in bad years, the benefit of adopting an optimal strategy that includes reproductive skipping increases asymptotically with the frequency of bad years. These results highlight the importance of characterizing the pattern of adult survival in this species, as well as the need to identify other factors that may influence the prevalence and benefits of reproductive skipping.

Lifetime reproductive output: individual stochasticity, variance, and sensitivity analysis.

Lifetime reproductive output (LRO) determines per-generation growth rates, establishes criteria for population growth or decline, and is an important component of fitness. Empirical measurements of LRO reveal high variance among individuals. This variance may result from genuine heterogeneity in individual properties, or from individual stochasticity, the outcome of probabilistic demographic events during the life cycle. To evaluate the extent of individual stochasticity requires the calculation of the statistics of LRO from a demographic model. Mean LRO is routinely calculated (as the net reproductive rate), but the calculation of variances has only recently received attention. Here, we present a complete, exact, analytical, closed-form solution for all the moments of LRO, for age- and stage-classified populations. Previous studies have relied on simulation, iterative solutions, or closed-form analytical solutions that capture only part of the sources of variance. We also present the sensitivity and elasticity of all of the statistics of LRO to parameters defining survival, stage transitions, and (st)age-specific fertility. Selection can operate on variance in LRO only if the variance results from genetic heterogeneity. The potential opportunity for selection is quantified by Crow's index I , the ratio of the variance to the square of the mean. But variance due to individual stochasticity is only an apparent opportunity for selection. In a comparison of a range of age-classified models for human populations, we find that proportional increases in mortality have very small effects on the mean and variance of LRO, but large positive effects on I . Proportional increases in fertility increase both the mean and variance of LRO, but reduce I . For a size-classified tree population, the elasticity of both mean and variance of LRO to stage-specific mortality are negative; the elasticities to stage-specific fertility are positive.