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

Variety is the spice of life: nongenetic variation in life histories influences population growth and evolvability

Individual vital rates, such as mortality and birth rates, are key determinants of lifetime reproductive success, and variability in these rates shapes population dynamics. Previous studies have found that this vital rate heterogeneity can influence demographic properties, including population growth rates. However, the explicit effects of the variation within and the covariance between vital rates that can also vary throughout the lifespan on population growth remain unknown. Here, we explore the analytical consequences of nongenetic heterogeneity on long-term population growth rates and rates of evolution by modifying traditional age-structured population projection matrices to incorporate variation among individual vital rates. The model allows vital rates to be permanent throughout life ("fixed condition") or to change over the lifespan ("dynamic condition"). We reduce the complexity associated with adding individual heterogeneity to age-structured models through a novel application of matrix collapsing ("phenotypic collapsing"), showing how to collapse in a manner that preserves the asymptotic and transient dynamics of the original matrix. The main conclusion is that nongenetic individual heterogeneity can strongly impact the long-term growth rate and rates of evolution. The magnitude and sign of this impact depend heavily on how the heterogeneity covaries across the lifespan of an organism. Our results emphasize that nongenetic variation cannot simply be viewed as random noise, but rather that it has consistent, predictable effects on fitness and evolvability.

What's luck got to do with it? A generative model for examining the role of stochasticity in age-at-death, with implications for bioarchaeology

INTRODUCTION

The role of "luck" in determining individual exposure to health insults is a critical component of the processes that shape age-at-death distributions in mortality samples but is difficult to address using traditional bioarcheological analysis of skeletal materials. The present study introduces a computer simulation approach to modeling stochasticity's contribution to the mortality schedule of a simulated cohort.

METHODS

The present study employs an agent-based model of 15,100 individuals across a 120 year period to examine the predictive value of birth frailty on age-at-death when varying the likelihood of exposure to health insults.

RESULTS

Birth frailty, when accounting for varying exposure likelihood scenarios, was found to account for 18.7% of the observed variation in individual age-at-death. Analysis stratified by exposure likelihood demonstrated that birth frailty alone explains 10.2%-12.1% of the variation observed across exposure likelihood scenarios, with the stochasticity associated with exposure to health insults (i.e., severity of health insult) and mortality likelihood driving the majority of variation observed.

CONCLUSIONS

Stochasticity of stressor exposure and intrinsic stressor severity are underappreciated but powerful drivers of mortality in this simulation. This study demonstrates the potential value of simulation modeling for bioarchaeological research.

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.

Adaption, neutrality and life-course diversity

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non-genetic and also non-environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non-genetic, non-environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life-course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non-genetic non-environmental variation.

Ecological Drivers of Community Cohesion

From protocellular to societal, networks of living systems are complex and multiscale. Discerning the factors that facilitate assembly of these intricate interdependencies using pairwise interactions can be nearly impossible. To facilitate a greater understanding, we developed a mathematical and computational model based on a synthetic four-strain Saccharomyces cerevisiae interdependent system. Specifically, we aimed to provide a greater understanding of how ecological factors influence community dynamics. By leveraging transiently structured ecologies, we were able to drive community cohesion. We show how ecological interventions could reverse or slow the extinction rate of a cohesive community. An interconnected system first needs to persist long enough to be a subject of natural selection. Our emulation of Darwin's "warm little ponds" with an ecology governed by transient compartmentalization provided the necessary persistence. Our results reveal utility across scales of organization, stressing the importance of cyclic processes in major evolutionary transitions, engineering of synthetic microbial consortia, and conservation biology. IMPORTANCE We are facing unprecedented disruption and collapse of ecosystems across the globe. To have any hope of mitigating this phenomenon, a much greater understanding of ecosystem dynamics is required. However, ecosystems are typically composed of highly dynamic networks of individual species. These interactions are further modulated by abiotic and biotic factors that vary temporally and spatially. Thus, ecological dynamics are obfuscated by this complexity. Here, we developed a theoretical model, informed by a synthetic experimental system, of Darwin's "warm little ponds." This cycling four-species system seeks to elucidate the ecological factors that drive or inhibit interaction. We show that these factors could provide an essential tool for avoiding the accelerating ecological collapse. Our study also provides a starting point to develop a more encompassing model to inform conservation efforts.

Individual stochasticity in the life history strategies of animals and plants

The life histories of organisms are expressed as rates of development, reproduction, and survival. However, individuals may experience differential outcomes for the same set of rates. Such individual stochasticity generates variance around familiar mean measures of life history traits, such as life expectancy and the reproductive number R0. By writing life cycles as Markov chains, we calculate variance and other indices of variability for longevity, lifetime reproductive output (LRO), age at offspring production, and age at maturity for 83 animal and 332 plant populations from the Comadre and Compadre matrix databases. We find that the magnitude within and variability between populations in variance indices in LRO, especially, are surprisingly high. We furthermore use principal components analysis to assess how the inclusion of variance indices of different demographic outcomes affects life history constraints. We find that these indices, to a similar or greater degree than the mean, explain the variation in life history strategies among plants and animals.

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.

Quantifying the effect of genetic, environmental and individual demographic stochastic variability for population dynamics in Plantago lanceolata

Simple demographic events, the survival and reproduction of individuals, drive population dynamics. These demographic events are influenced by genetic and environmental parameters, and are the focus of many evolutionary and ecological investigations that aim to predict and understand population change. However, such a focus often neglects the stochastic events that individuals experience throughout their lives. These stochastic events also influence survival and reproduction and thereby evolutionary and ecological dynamics. Here, we illustrate the influence of such non-selective demographic variability on population dynamics using population projection models of an experimental population of Plantago lanceolata. Our analysis shows that the variability in survival and reproduction among individuals is largely due to demographic stochastic variation with only modest effects of differences in environment, genes, and their interaction. Common expectations of population growth, based on expected lifetime reproduction and generation time, can be misleading when demographic stochastic variation is large. Large demographic stochastic variation exhibited within genotypes can lower population growth and slow evolutionary adaptive dynamics. Our results accompany recent investigations that call for more focus on stochastic variation in fitness components, such as survival, reproduction, and functional traits, rather than dismissal of this variation as uninformative noise.

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.

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.