Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.     

Interspecific differences in stochastic population dynamics explains variation in Taylor's temporal power law

Taylor’s power law, i.e. that the slope for the increase in variance with mean population size is between 1 and 2 at a logarithmic scale, provides one of the few quantitative relationships in population ecology, yet the underlying ecological mechanisms are only poorly understood. Stochastic theory of population dynamics predicts that demographic and environmental stochasticity will affect the slope differently. In a stable environment under the influence of demographic stochasticity alone the slope will be equal to 1. In large populations in which demographic variance will have a negligible effect on the dynamics the slope will approach 2. In addition, the slope will also be influenced by how the strength of density dependence is related to mean population size. To disentangle the relative contribution of these processes we estimate the mean‐variance relationship for a large number of populations of British birds. The variance in population size of most species decreased with the mean due to decreased influence of demographic stochasticity at larger population sizes. Interspecific differences in demographic stochasticity was the main factor influencing variation in slopes of Taylor’s power law among species through a significant negative relationship between the slope and demographic variance. In addition, slopes were influenced by interspecific variation in life history parameters such as adult survival and clutch size. These analyses show that Taylor’s power law is generated from an interplay between stochastic and density dependent factors, modulated by life history.     

Demographic stochasticity alters expected outcomes in experimental and simulated non‐neutral communities

Theory has shown that the effects of demographic stochasticity on communities may depend on the magnitude of fitness differences between species. In particular, it has been suggested that demographic stochasticity has the potential to significantly alter competitive outcomes when fitness differences are small (nearly neutral), but that it has negligible effects when fitness differences are large (highly non‐neutral). Here we test such theory experimentally and extend it to examine how demographic stochasticity affects exclusion frequency and mean densities of consumers in simple, but non‐neutral, consumer–resource communities. We used experimental microcosms of protists and rotifers feeding on a bacterial resource to test how varying absolute population sizes (a driver of demographic stochasticity) affected the probability of competitive exclusion of the weakest competitor. To explore whether demographic stochasticity could explain our experimental results, and to generalize beyond our experiment, we paired the experiment with a continuous‐time stochastic model of resource competition, which we simulated for 11 different fitness inequalities between competiting consumers. Consistent with theory, in both our experiments and our simulations we found that demographic stochasticity altered competitive outcomes in communities where fitness differences were small. However, we also found that demographic stochasticity alone could affect communities in other ways, even when fitness differences between competitors were large. Specifically, demographic stochasticity altered mean densities of both weak and strong competitors in experimental and simulated communities. These findings highlight how demographic stochasticity can change both competitive outcomes in non‐neutral communities and the processes underlying overall community dynamics.     

Extinction in relation to demographic and environmental stochasticity in age-structured models

The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.     

Tissue‐disruption‐induced cellular stochasticity and epigenetic drift: Common origins of aging and cancer?

Age‐related and cancer‐related epigenomic modifications have been associated with enhanced cell‐to‐cell gene expression variability that characterizes increased cellular stochasticity. Since gene expression variability appears to be highly reduced by—and epigenetic and phenotypic stability acquired through—direct or long‐range cellular interactions during cell differentiation, we propose a common origin for aging and cancer in the failure to control cellular stochasticity by cell–cell interactions. Tissue‐disruption‐induced cellular stochasticity associated with epigenetic drift would be at the origin of organ dysfunction because of an increase in phenotypic variation among cells, ultimately leading to cell death and organ failure through a loss of coordination in cellular functions, and eventually to cancerization. We propose mechanistic research perspectives to corroborate this hypothesis and explore its evolutionary consequences, highlighting a positive correlation between the median age of mass loss onset (a proxy for the onset of organ aging) and the median age at cancer diagnosis.     

Spatially heterogeneous stochasticity and the adaptive diversification of dormancy

Diversified bet‐hedging, a strategy that leads several individuals with the same genotype to express distinct phenotypes in a given generation, is now well established as a common evolutionary response to environmental stochasticity. Life‐history traits defined as diversified bet‐hedging (e.g. germination or diapause strategies) display marked differences between populations in spatial proximity. In order to find out whether such differences can be explained by local adaptations to spatially heterogeneous environmental stochasticity, we explored the evolution of bet‐hedging dormancy strategies in a metapopulation using a two‐patch model with patch differences in stochastic juvenile survival. We found that spatial differences in the level of environmental stochasticity, restricted dispersal, increased fragmentation and intermediate survival during dormancy all favour the adaptive diversification of bet‐hedging dormancy strategies. Density dependency also plays a major role in the diversification of dormancy strategies because: (i) it may interact locally with environmental stochasticity and amplify its effects; however, (ii) it can also generate chaotic population dynamics that may impede diversification. Our work proposes new hypotheses to explain the spatial patterns of bet‐hedging strategies that we hope will encourage new empirical studies of this topic.     

Demographic variance in heterogeneous populations: matrix models and sensitivity analysis

The demographic consequences of stochasticity in processes such as survival and reproduction are modulated by the heterogeneity within the population. Therefore, to study effects of stochasticity on population growth and extinction risk, it is critical to use structured population models in which the most important sources of heterogeneity (e.g. age, size, developmental stage) are incorporated as i‐state variables. Demographic stochasticity in heterogeneous populations has often been studied using one of two approaches: multitype branching processes and diffusion approximations. Here, we link these approaches, through the demographic stochasticity in age‐ or stage‐structured matrix population models. We derive the demographic variance, σ²_d, which measures the per capita contribution to the variance in population growth increment, and we show how it can be decomposed into contributions from transition probabilities and fertility across ages or stages. Furthermore, using matrix calculus we derive the sensitivity of σ²_d to age‐ or stage‐specific mortality and fertility. We apply the methods to an extensive set of data from age‐classified human populations (long‐term time‐series for Sweden, Japan and the Netherlands; two hunter–gatherer populations, and the high‐fertility Hutterites), and to a size‐classified population of the herbaceous plant Calathea ovandensis. For the human populations our analysis reveals substantial temporal changes in the demographic variance as well as its main components across age. These new methods provide a powerful approach for calculating the demographic variance for any structured model, and for analyzing its main components and sensitivities. This will make possible new analyses of demographic variance across different kinds of heterogeneity in different life cycles, which will in turn improve our understanding of mechanisms underpinning extinction risk and other important biological outcomes.     

Simulating viability of a spadefoot toad Pelobates fuscus metapopulation in a landscape fragmented by a road

A stochastic simulation model allowing for demographic and environmental stochasticity was developed in order to predict the dynamics of a Pelobates fuscus metapopulation. The metapopulation (consisting of ca 1000 adult individuals) was intensively studied in the field for a period of four years and the simulation model was parameterised (sex ratio, age‐specific survival rates, fecundity and dispersal between subpopulations) using field data. A sensitivity analysis revealed that a change in the juvenile yearly survival rate has a relatively larger effect on subpopulation persistence than adult survival rate and fecundity rate have. The probability of subpopulation persistence for one hundred years increased from 0 to 0.6 with a change in juvenile yearly survival rate from 0.35 to 0.40. Varying dispersal rate (from 0 to 1% of the individuals in a subpopulation moving to another subpopulation within a year) showed that four of the five subpopulations are dependent on the last one for persistence, indicating a source‐sink structure of the metapopulation. The subpopulation with the highest estimated juvenile survival has a far higher persistence probability than the others; they in turn would go extinct were it not for the occasional input of individuals from the source subpopulation. The source‐sink structure was also apparent when simulating the isolation effect of the road: persistence of the subpopulation isolated by the road decreases markedly with only a 20% decrease in the number of individuals dispersing to this pond. Environmental stochasticity decreases persistence time of the source subpopulation, but increases persistence time of the unstable ones. This is probably due to the presence of overcompensating density‐dependent factors affecting the subpopulations and to the more general effect of stochasticity: it may temporarily change reproduction and mortality rates, increase time to extinction for unstable subpopulations through a rescue effect; and decrease time to extinction for the more stable subpopulations.     

Effects of habitat size and quality on equilibrium density and extinction time of Sorex araneus populations

1. The effects of changes in habitat size and quality on the expected population density and the expected time to extinction of Sorex araneus are studied by means of mathematical models that incorporate demographic stochasticity.
2. Habitat size is characterized by the number of territories, while habitat quality is represented by the expected number of offspring produced during the lifetime of an individual.
3. The expected population density of S. araneus is shown to be mainly influenced by the habitat size. The expected time to extinction of S. araneus populations due to demographic stochasticity, on the other hand, is much more affected by the habitat quality.
4. In a more general setting we demonstrate that, irrespective of the actual species under consideration, the likelihood of extinction as a consequence of demographic stochasticity is more effectively countered by increasing the reproductive success and survival of individuals then by increasing total population size.     

Sex and stochasticity affect range expansion of experimental invasions

Understanding and predicting range expansion are key objectives in many basic and applied contexts. Among dioecious organisms, there is strong evidence for sex differences in dispersal, which could alter the sex ratio at the expansion's leading edge. However, demographic stochasticity could also affect leading‐edge sex ratios, perhaps overwhelming sex‐biased dispersal. We used insects in laboratory mesocosms to test the effects of sex‐biased dispersal on range expansion, and a simulation model to explore interactive effects of sex‐biased dispersal and demographic stochasticity. Sex‐biased dispersal created spatial clines in the sex ratio, which influenced offspring production at the front and altered invasion velocity. Increasing female dispersal relative to males accelerated spread, despite the prediction that demographic stochasticity would weaken a signal of sex‐biased dispersal. Our results provide the first experimental evidence for an influence of sex‐biased dispersal on invasion velocity, highlighting the value of accounting for sex structure in studies of range expansion.     

Recent exposure to environmental stochasticity does not determine the demographic resilience of natural populations

Escalating climatic and anthropogenic pressures expose ecosystems worldwide to increasingly stochastic environments. Yet, our ability to forecast the responses of natural populations to this increased environmental stochasticity is impeded by a limited understanding of how exposure to stochastic environments shapes demographic resilience. Here, we test the association between local environmental stochasticity and the resilience attributes (e.g. resistance, recovery) of 2242 natural populations across 369 animal and plant species. Contrary to the assumption that past exposure to frequent environmental shifts confers a greater ability to cope with current and future global change, we illustrate how recent environmental stochasticity regimes from the past 50 years do not predict the inherent resistance or recovery potential of natural populations. Instead, demographic resilience is strongly predicted by the phylogenetic relatedness among species, with survival and developmental investments shaping their responses to environmental stochasticity. Accordingly, our findings suggest that demographic resilience is a consequence of evolutionary processes and/or deep-time environmental regimes, rather than recent-past experiences.     

The effect of phenotypic variation on metapopulation persistence

Demographic stochasticity (due to the probabilistic nature of the birth–death process) and demographic heterogeneity (between-individual differences in demographic parameters) have long been seen as factors affecting extinction risk. While demographic stochasticity can be independent of underlying species traits, demographic heterogeneity may strongly depend on phenotypic variation. However, how phenotypic variation can affect extinction risk is largely unknown. Here, I develop a stochastic metapopulation model that takes into account the effects of demographic stochasticity and phenotypic variation in the traits controlling colonization rates to assess what the effect of phenotypic variation may be on the persistence of the metapopulation. Although phenotypic variation can lead to a decrease in metapopulation persistence under some conditions, it also may lead to an increase in persistence whenever phenotypic mismatch—or the distance between the optimal trait value and the population mean—is large. This mismatch can in turn arise from a variety of ecological and evolutionary reasons, including weak selection or a recent history of invasion. Last, the effect of phenotypic variation has a deterministic component on colonization rates, and a stochastic component on persistence through colonization rates, but both are important to understand the overall effect. These results have important implications for the conservation of threatened species and management practices that may historically have overlooked phenotypic variation as unimportant noise around mean values of interest.     

Habitat‐driven life history variation in an amphibian metapopulation

Life‐history theory states that, during the lifetime of an individual, resources are allocated to either somatic maintenance or reproduction. Resource allocation tradeoffs determine the evolution and ecology of life‐history strategies and determine an organisms’ position along the fast–slow continuum. Theory predicts that environmental stochasticity is an important driver of resource allocation and therefore life‐history evolution. Highly stochastic environments are expected to increase uncertainty in reproductive success and select for iteroparity and a slowing down of the life history. To date, most empirical studies have used comparisons among species to examine these theoretical predictions. By contrast, few have investigated how environmental stochasticity affects life‐history strategies at the intraspecific level. In this study, we examined how variation in breeding site stochasticity (among‐year variability in pond volume and hydroperiod) promotes the co‐occurrence of different life‐history strategies in a spatially structured population, and determines life‐history position along the fast–slow continuum in the yellow‐bellied toad Bombina variegata. We collected mark–recapture data from a metapopulation and used multievent capture–recapture models to estimate survival, recruitment and breeding probabilities. We found higher survival and longer lifespans in populations inhabiting variable sites compared to those breeding in stable ones. In addition, probabilities of recruitment and skipping a breeding event were higher in variable sites. The temporal variance of survival and recruitment probabilities, as well as the probability to skip breeding, was higher in variable sites. Taken together, these findings indicate that populations breeding in variable sites experienced a slowing down of the life‐history. Our study thus revealed similarities in the macroevolutionary and microevolutionary processes shaping life‐history evolution.     

Can life history predict the effect of demographic stochasticity on extinction risk?

Demographic stochasticity is important in determining extinction risks of small populations, but it is largely unknown how its effect depends on the life histories of species. We modeled effects of demographic stochasticity on extinction risk in a broad range of generalized life histories, using matrix models and branching processes. Extinction risks of life histories varied greatly in their sensitivity to demographic stochasticity. Comparing life histories, extinction risk generally increased with increasing fecundity and decreased with higher ages of maturation. Effects of adult survival depended on age of maturation. At lower ages of maturation, extinction risk peaked at intermediate levels of adult survival, but it increased along with adult survival at higher ages of maturation. These differences were largely explained by differences in sensitivities of population growth to perturbations of life-history traits. Juvenile survival rate contributed most to total demographic variance in the majority of life histories. Our general results confirmed earlier findings, suggesting that empirical patterns can be explained by a relatively simple model. Thus, basic life-history information can be used to assign life-history-specific sensitivity to demographic stochasticity. This is of great value when assessing the vulnerability of small populations.     

Genetic rescue in a severely inbred wolf population

Natural populations are becoming increasingly fragmented which is expected to affect their viability due to inbreeding depression, reduced genetic diversity and increased sensitivity to demographic and environmental stochasticity. In small and highly inbred populations, the introduction of only a few immigrants may increase vital rates significantly. However, very few studies have quantified the long‐term success of immigrants and inbred individuals in natural populations. Following an episode of natural immigration to the isolated, severely inbred Scandinavian wolf (Canis lupus) population, we demonstrate significantly higher pairing and breeding success for offspring to immigrants compared to offspring from native, inbred pairs. We argue that inbreeding depression is the underlying mechanism for the profound difference in breeding success. Highly inbred wolves may have lower survival during natal dispersal as well as competitive disadvantage to find a partner. Our study is one of the first to quantify and compare the reproductive success of first‐generation offspring from migrants vs. native, inbred individuals in a natural population. Indeed, our data demonstrate the profound impact single immigrants can have in small, inbred populations, and represent one of very few documented cases of genetic rescue in a population of large carnivores.     

Colonization in metapopulations: a review of theory and observations

In metapopulation dynamics turnover of populations in isolated patches may be frequent. Regional survival of a species in such a system with frequent extinctions hinges on its colonization ability. Colonization is more than just dispersal; when a propagule reaches a new patch it faces higher extinction probabilities than does an established population. Extinction models as well as empirical data suggest that a large propagule with a potential for rapid increase in a varying environment, or with a low mortality rate in an environment perceived as constant, has a higher probability of successful colonization. Large variation in population size when it is still small increases the risk of failure. Factors introducing such variation are demographic stochasticity and environmental variation. It is hard to single out demographic traits that ensure good colonizing ability, since colonization can be achieved in many different ways, but generalists and species with self-fertilization seem to be superior.     

The evolution of dispersal under demographic stochasticity

Temporal and spatial variations of the environment are important factors favoring the evolution of dispersal. With few exceptions, these variations have been considered to be exclusively fluctuations of habitat quality. However, since the presence of conspecifics forms part of an individual's environment, demographic stochasticity may be a component of this variability as well, in particular when local populations are small. To study this effect, we analyzed the evolution of juvenile dispersal in a metapopulation model in which habitat quality is constant in space and time but occupancy fluctuates because of demographic stochasticity. Our analysis extends previous studies in that it includes competition of resources and competition for space. Also, juvenile dispersal is not given by a fixed probability but is made conditional on the presence of free territories in a patch, whereas individuals born in full patches will always disperse. Using a combination of analytical and numerical approaches, we show that demographic stochasticity in itself may provide enough variability to favor dispersal even from patches that are not fully occupied. However, there is no simple relationship between the evolution of dispersal and various indicators of demographic stochasticity. Selected dispersal depends on all aspects of the life-history profile, including kin selection.     

Demographic stochasticity and temporal autocorrelation in the dynamics of structured populations

Populations can show temporal autocorrelation in the dynamics arising from different mechanisms, including fluctuations in the demographic structure. This autocorrelation is often treated as a complicating factor in the analyses of stochastic population growth and extinction risk. However, it also reflects important information about the demographic structure. Here, we consider how temporal autocorrelation is related to demographic stochasticity in structured populations. Demographic stochasticity arises from inherent randomness in the demographic processes of individuals, like survival and reproduction, and the resulting impact on population growth is measured by the demographic variance. Earlier studies have shown that population structure have positive or negative effects on the demographic variance compared to a model where the structure is ignored. Here, we derive a new expression for the demographic variance of a structured population, using the temporal autocorrelation function of the population growth rate. We show that the relative difference in demographic variance when the structure is included or ignored (the effect of structure on demographic variance) is approximately twice the sum of the autocorrelations. We demonstrate the result for a simple hypothetical example, as well as a set of empirical examples using age‐structured models of 24 mammals from the demographic database COMADRE. In the empirical examples, the sum of the autocorrelation function was negative in all cases, indicating that age structure generally has a negative effect on the demographic variance (i.e. the demographic variance is lower compared to that of a model where the structure is ignored). Other kinds of structure, such as spatial heterogeneity affecting fecundity, can have positive effects on the demographic variance, and the sum of the autocorrelations will then be positive. These results yield new insights into the complex interplay between population structure, demographic variance, and temporal autocorrelation, that shapes the population dynamics and extinction risk of populations.     

The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species

Invasive species are a serious threat to biodiversity worldwide and predicting whether an introduced species will first establish and then become invasive can be useful to preserve ecosystem services. Establishment is influenced by multiple factors, such as the interactions between the introduced individuals and the resident community, and demographic and environmental stochasticity. Field observations are often incomplete or biased. This, together with an imperfect knowledge of the ecological traits of the introduced species, makes the prediction of establishment challenging. Methods that consider the combined effects of these factors on our ability to predict the establishment of an introduced species are currently lacking. We develop an inference framework to assess the combined effects of demographic stochasticity and parameter uncertainty on our ability to predict the probability of establishment following the introduction of a small number of individuals. We find that even moderate levels of demographic stochasticity influence both the probability of establishment, and, crucially, our ability to correctly predict that probability. We also find that estimation of the demographic parameters of an introduced species is fundamental to obtain precise estimates of the interaction parameters. For typical values of demographic stochasticity, the drop in our ability to predict an establishment can be 30% when having priors on the demographic parameters compared to having their accurate values. The results from our study illustrate how demographic stochasticity may bias the prediction of the probability of establishment. Our method can be applied to estimate probability of establishment of introduced species in field scenarios, where time series data and prior information on the demographic traits of the introduced species are available.     

Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density-regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance-related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.