Skewed distributions of lifetime reproductive success: beyond mean and variance

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.

Partitioning variance in reproductive success, within years and across lifetimes

Variance in reproductive success (s k 2 , with k = number of offspring) plays a large role in determining the rate of genetic drift and the scope within which selection acts. Various frameworks have been proposed to parse factors that contribute to s k 2 , but none has focused on age-specific values of ϕ = s k 2 / k ¯ , which indicate the degree to which reproductive skew is overdispersed (compared to the random Poisson expectation) among individuals of the same age and sex. Instead, within-age effects are generally lumped with residual variance and treated as "noise." Here, an ANOVA sums-of-squares framework is used to partition variance in annual and lifetime reproductive success into between-group and within-group components. For annual reproduction, the between-age effect depends on age-specific fecundity (b x), but relatively few empirical data are available on the within-age effect, which depends on ϕ x. By defining groups by age-at-death rather than age, the same ANOVA framework can be used to partition variance in lifetime reproductive success (LRS) into between-group and within-group components. Analytical methods are used to develop null-model expectations for random contributions to within-group and between-group components. For analysis of LRS, random variation in longevity appears as part of the between-group variance, and effects (if any) of skip breeding and persistent individual differences contribute to the within-group variance. Simulations are used to show that the methods for variance partitioning are asymptotically unbiased. Practical application is illustrated with empirical data for annual reproduction in American black bears and lifetime reproduction in Dutch great tits. Results show that overdispersed within-age variance (1) dominates annual s k 2 in both male and female black bears, (2) is the primary factor that reduces annual effective size to a fraction of the number of adults, and (3) represents most of the opportunity for selection. In contrast, about a quarter of the variance in LRS in great tits can be attributed to random variation in longevity, and most of the rest is due to modest differences in fecundity with age estimated for a single cohort of females. R code is provided that reads generic input files for annual and lifetime reproductive success and allows users to conduct variance partitioning with their own data.

Big boned: How fat storage and other adaptations influenced large theropod foraging ecology

Dinosaur foraging ecology has been the subject of scientific interest for decades, yet much of what we understand about it remains hypothetical. We wrote an agent-based model (ABM) to simulate meat energy sources present in dinosaur environments, including carcasses of giant sauropods, along with living, huntable prey. Theropod dinosaurs modeled in this environment (specifically allosauroids, and more particularly, Allosaurus Marsh, 1877) were instantiated with heritable traits favorable to either hunting success or scavenging success. If hunter phenotypes were more reproductively successful, their traits were propagated into the population through their offspring, resulting in predator specialists. If selective pressure favored scavenger phenotypes, the population would evolve to acquire most of their calories from carrion. Data generated from this model strongly suggest that theropods in sauropod-dominated systems evolved to detect carcasses, consume and store large quantities of fat, and dominate carcass sites. Broadly speaking, selective forces did not favor predatory adaptations, because sauropod carrion resource pools, as we modeled them, were too profitable for prey-based resource pools to be significant. This is the first research to test selective pressure patterns in dinosaurs, and the first to estimate theropod mass based on metabolic constraints.

Advancing methods for the biodemography of aging within social contexts

Several social dimensions including social integration, status, early-life adversity, and their interactions across the life course can predict health, reproduction, and mortality in humans. Accordingly, the social environment plays a fundamental role in the emergence of phenotypes driving the evolution of aging. Recent work placing human social gradients on a biological continuum with other species provides a useful evolutionary context for aging questions, but there is still a need for a unified evolutionary framework linking health and aging within social contexts. Here, we summarize current challenges to understand the role of the social environment in human life courses. Next, we review recent advances in comparative biodemography and propose a biodemographic perspective to address socially driven health phenotype distributions and their evolutionary consequences using a nonhuman primate population. This new comparative approach uses evolutionary demography to address the joint dynamics of populations, social dimensions, phenotypes, and life history parameters. The long-term goal is to advance our understanding of the link between individual social environments, population-level outcomes, and the evolution of aging.

Why is measuring and predicting fitness under genomic conflict so hard?

Genomic conflict between the sexes is caused by differences in the optimal male and female reproductive strategies, and is a major contributor to genetic, phenotypic, and life history variation. While early experimental work appeared to strongly support the sexual conflict paradigm, recent work has produced more ambiguous results. Recent advances in experimental evolution studies combined with theoretical arguments can shed light on why measuring fitness under a conflict is so challenging, including the incidental alteration of mating dynamics, demographic effects, and inherent complexity in what quantity selection maximizes. We stress that non-intuitive results do not necessarily mean the absence of conflict, and follow-up experiments to determine why a priori predictions failed can ultimately teach us more than if they had been confirmed.

Hurricanes affect diversification among individual life courses of a primate population

Extreme climatic events may influence individual-level variability in phenotypes, survival and reproduction, and thereby drive the pace of evolution. Climate models predict increases in the frequency of intense hurricanes, but no study has measured their impact on individual life courses within animal populations. We used 45 years of demographic data of rhesus macaques to quantify the influence of major hurricanes on reproductive life courses using multiple metrics of dynamic heterogeneity accounting for life course variability and life-history trait variances. To reduce intraspecific competition, individuals may explore new reproductive stages during years of major hurricanes, resulting in higher temporal variation in reproductive trajectories. Alternatively, individuals may opt for a single optimal life-history strategy due to trade-offs between survival and reproduction. Our results show that heterogeneity in reproductive life courses increased by 4% during years of major hurricanes, despite a 2% reduction in the asymptotic growth rate due to an average decrease in mean fertility and survival by that is, shortened life courses and reduced reproductive output. In agreement with this, the population is expected to achieve stable population dynamics faster after being perturbed by a hurricane (ρ = 1.512 ; 95% CI: 1.488, 1.538), relative to ordinary yearsρ = 1.482 ; 1.475 , 1.490 . Our work suggests that natural disasters force individuals into new demographic roles to potentially reduce competition during unfavourable environments where mean reproduction and survival are compromised. Variance in lifetime reproductive success and longevity are differently affected by hurricanes, and such variability is mostly driven by survival.

Physiological tipping points in the relationship between foraging success and lifetime fitness of a long-lived mammal

Although anthropogenic change is often gradual, the impacts on animal populations may be precipitous if physiological processes create tipping points between energy gain, reproduction or survival. We use 25 years of behavioural, diet and demographic data from elephant seals to characterise their relationships with lifetime fitness. Survival and reproduction increased with mass gain during long foraging trips preceding the pupping seasons, and there was a threshold where individuals that gained an additional 4.8% of their body mass (26 kg, from 206 to 232 kg) increased lifetime reproductive success three-fold (from 1.8 to 4.9 pups). This was due to a two-fold increase in pupping probability (30% to 76%) and a 7% increase in reproductive lifespan (6.0 to 6.4 years). The sharp threshold between mass gain and reproduction may explain reproductive failure observed in many species and demonstrates how small, gradual reductions in prey from anthropogenic disturbance could have profound implications for animal populations.

When the going gets tough, the tough get going: Effect of extreme climate on an Antarctic seabird's life history

Individuals differ in many ways. Most produce few offspring; a handful produce many. Some die early; others live to old age. It is tempting to attribute these differences in outcomes to differences in individual traits, and thus in the demographic rates experienced. However, there is more to individual variation than meets the eye of the biologist. Even among individuals sharing identical traits, life history outcomes (life expectancy and lifetime reproduction) will vary due to individual stochasticity, that is to chance. Quantifying the contributions of heterogeneity and chance is essential to understand natural variability. Interindividual differences vary across environmental conditions, hence heterogeneity and stochasticity depend on environmental conditions. We show that favourable conditions increase the contributions of individual stochasticity, and reduce the contributions of heterogeneity, to variance in demographic outcomes in a seabird population. The opposite is true under poor conditions. This result has important consequence for understanding the ecology and evolution of life history strategies.

Population level consequences of facultatively cooperative behaviour in a stochastic environment

The social environment in which individuals live affects their fitness and in turn population dynamics as a whole. Birds with facultative cooperative breeding can live in social groups with dominants, subordinate helpers that assist with the breeding of others, and subordinate non-helpers. Helping behaviour benefits dominants through increased reproductive rates and reduced extrinsic mortality, such that cooperative breeding might have evolved in response to unpredictable, harsh conditions affecting reproduction and/or survival of the dominants. Additionally, there may be different costs and benefits to both helpers and non-helpers, depending on the time-scale. For example, early-life costs might be compensated by later-life benefits. These differential effects are rarely analysed in the same study. We examined whether helping behaviour affects population persistence in a stochastic environment and whether there are direct fitness consequences of different life-history tactics adopted by helpers and non-helpers. We parameterised a matrix population model describing the population dynamics of female Seychelles warblers Acrocephalus sechellensis, birds that display facultative cooperative breeding. The stochastic density-dependent model is defined by a (st)age structure that includes life-history differences between helpers and non-helpers and thus can estimate the demographic mechanisms of direct benefits of helping behaviour. We found that population dynamics are strongly influenced by stochastic variation in the reproductive rates of the dominants, that helping behaviour promotes population persistence and that there are only early-life differences in the direct fitness of helpers and non-helpers. Through a matrix population model, we captured multiple demographic rates simultaneously and analysed their relative importance in determining population dynamics of these cooperative breeders. Disentangling early-life versus lifetime effects of individual tactics sheds new light on the costs and benefits of helping behaviour. For example, the finding that helpers and non-helpers have similar lifetime reproductive outputs and that differences in reproductive values between the two life-history tactics arise only in early life suggests that overall, helpers and non-helpers have a similar balance of costs and benefits when analysing direct benefits. We recommend analysing the consequence of different life-history tactics, during both early life and over the lifetime, as analyses of these different time frames may produce conflicting results.

The kinship matrix: inferring the kinship structure of a population from its demography

The familial structure of a population and the relatedness of its individuals are determined by its demography. There is, however, no general method to infer kinship directly from the life cycle of a structured population. Yet, this question is central to fields such as ecology, evolution and conservation, especially in contexts where there is a strong interdependence between familial structure and population dynamics. Here, we give a general formula to compute, from any matrix population model, the expected number of arbitrary kin (sisters, nieces, cousins, etc) of a focal individual ego, structured by the class of ego and of its kin. Central to our approach are classic but little-used tools known as genealogical matrices. Our method can be used to obtain both individual-based and population-wide metrics of kinship, as we illustrate. It also makes it possible to analyse the sensitivity of the kinship structure to the traits implemented in the model.

Slower environmental cycles maintain greater life-history variation within populations

Populations in nature are comprised of individual life histories, whose variation underpins ecological and evolutionary processes. Yet the forces of environmental selection that shape intrapopulation life-history variation are still not well-understood, and efforts have largely focused on random (stochastic) fluctuations of the environment. However, a ubiquitous mode of environmental fluctuation in nature is cyclical, whose periodicities can change independently of stochasticity. Here, we test theoretically based hypotheses for whether shortened ('Fast') or lengthened ('Slow') environmental cycles should generate higher intrapopulation variation of life history phenotypes. We show, through a combination of agent-based modelling and a multi-generational laboratory selection experiment using the tidepool copepod Tigriopus californicus, that slower environmental cycles maintain higher levels of intrapopulation variation. Surprisingly, the effect of environmental periodicity on variation was much stronger than that of stochasticity. Thus, our results show that periodicity is an important facet of fluctuating environments for life-history variation.

Demystifying individual heterogeneity

Among-individual variation in vital rates, such as mortality and birth rates, exists in nearly all populations. Recent studies suggest that this individual heterogeneity produces substantial life-history and fitness differences among individuals, which in turn scale up to influence population dynamics. However, our ability to understand the consequences of individual heterogeneity is limited by inconsistencies across conceptual frameworks in the field. Studies of individual heterogeneity remain filled with contradicting and ambiguous terminology that introduces risks of misunderstandings, conflicting models and unreliable conclusions. Here, we synthesise the existing literature into a single and comparatively straightforward framework with explicit terminology and definitions. This work introduces a distinction between potential vital rates and realised vital rates to develop a coherent framework that maps directly onto mathematical models of individual heterogeneity. We suggest the terms "fixed condition" and "dynamic condition" be used to distinguish potential vital rates that are permanent from those that can change throughout an individual's life. To illustrate, we connect the framework to quantitative genetics models and to common classes of statistical models used to infer individual heterogeneity. We also develop a population projection matrix model that provides an example of how our definitions are translated into precise quantitative terms.

Distributions of LRS in varying environments

The lifetime reproductive success (LRS) of individuals is affected by random events such as death, realized growth or realized reproduction, and the outcomes of these events can differ even when individuals have identical probabilities. Another source of randomness arises when these probabilities also change over time in variable environments. For structured populations in stochastic environments, we extend our recent method to determine how birth environment and birth stage determine the random distribution of the LRS. Our results provide a null model that quantifies effects on LRS of just the birth size or stage. Using Roe deer Capreolus capreolus as a case study, we show that the effect of an individual's birth environment on LRS varies with the frequency of environments and their temporal autocorrelation, and that lifetime performance is affected by changes in the pattern of environmental states expected as a result of climate change.

How fitness consequences of early-life conditions vary with age in a long-lived seabird: A Bayesian multivariate analysis of age-specific reproductive values

Evolutionary theory suggests that individuals can benefit from deferring the fitness cost of developing under poor conditions to later in life. Although empirical evidence for delayed fitness costs of poor developmental conditions is abundant, individuals that die prematurely have not often been incorporated when estimating fitness, such that age-specific fitness costs, and therefore the relative importance of delayed fitness costs are actually unknown. We developed a Bayesian statistical framework to estimate age-specific reproductive values in relation to developmental conditions. We applied it to data obtained from a long-term longitudinal study of common terns Sterna hirundo, using sibling rank to describe variation in developmental conditions. Common terns have a maximum of three chicks, and later hatching chicks acquire less food, grow more slowly and have a lower fledging probability than their earlier hatched siblings. We estimated fitness costs in adulthood to constitute c. 45% and 70% of the total fitness costs of hatching third and second, respectively, compared to hatching first. This was due to third-ranked hatchlings experiencing especially high pre-fledging mortality, while second-ranked hatchlings had lower reproductive success in adulthood. Both groups had slightly lower adult survival. There was, however, no evidence for sibling rank-specific rates of senescence. We additionally found years with low fledgling production to be associated with particularly strong pre-fledging selection on sibling rank, and with increased adult survival to the next breeding season. This suggests that adults reduce parental allocation to reproduction in poor years, which disproportionately impacts low-ranked offspring. Interpreting these results, we suggest that selection at the level of the individual offspring for delaying fitness costs is counteracted by selection for parental reduction in brood size when resources are limiting.

Time and Chance: Using Age Partitioning to Understand How Luck Drives Variation in Reproductive Success

AbstractOver the course of individual lifetimes, luck usually explains a large fraction of the between-individual variation in life span or lifetime reproductive output (LRO) within a population, while variation in individual traits or "quality" explains much less. To understand how, where in the life cycle, and through which demographic processes luck trumps trait variation, we show how to partition by age the contributions of luck and trait variation to LRO variance and how to quantify three distinct components of luck. We apply these tools to several empirical case studies. We find that luck swamps effects of trait variation at all ages, primarily because of randomness in individual state dynamics ("state trajectory luck"). Luck early in life is most important. Very early state trajectory luck generally determines whether an individual ever breeds, likely by ensuring that they are not dead or doomed quickly. Less early luck drives variation in success among those breeding at least once. Consequently, the importance of luck often has a sharp peak early in life or it has two peaks. We suggest that ages or stages where the importance of luck peaks are potential targets for interventions to benefit a population of concern, different from those identified by eigenvalue elasticity analysis.

Taming fitness: Organism-environment interdependencies preclude long-term fitness forecasting

Fitness is a central but notoriously vexing concept in evolutionary biology. The propensity interpretation of fitness is often regarded as the least problematic account for fitness. It ties an individual's fitness to a probabilistic capacity to produce offspring. Fitness has a clear causal role in evolutionary dynamics under this account. Nevertheless, the propensity interpretation faces its share of problems. We discuss three of these. We first show that a single scalar value is an incomplete summary of a propensity. Second, we argue that the widespread method of "abstracting away" environmental idiosyncrasies by averaging over reproductive output in different environments is not a valid approach when environmental changes are irreversible. Third, we point out that expanding the range of applicability for fitness measures by averaging over more environments or longer time scales (so as to ensure environmental reversibility) reduces one's ability to distinguish selectively relevant differences among individuals because of mutation and eco-evolutionary feedbacks. This series of problems leads us to conclude that a general value of fitness that is both explanatory and predictive cannot be attained. We advocate for the use of propensity-compatible methods, such as adaptive dynamics, which can accommodate these difficulties.