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The capacity of natural selection to generate adaptive changes is (according to the fundamental theorem of natural selection) proportional to the additive genetic variance in fitness. In spite of its importance for development of new adaptations to a changing environment, processes affecting the magnitude of the genetic variance in fitness-related traits are poorly understood. Here, we show that the red-white colour polymorphism in female barn owls is subject to density-dependent selection at the phenotypic and genotypic level. The diallelic melanocortin-1 receptor gene explained a large amount of the phenotypic variance in reddish coloration in the females ( R 2 = 59.8 % ). Red individuals (RR genotype) were selected for at low densities, while white individuals (WW genotype) were favoured at high densities and were less sensitive to changes in density. We show that this density-dependent selection favours white individuals and predicts fixation of the white allele in this population at longer time scales without immigration or other selective forces. Still, fluctuating population density will cause selection to fluctuate and periodically favour red individuals. These results suggest how balancing selection caused by fluctuations in population density can be a general mechanism affecting the level of additive genetic variance in natural populations.

Seasonality and long-term environmental variability afect species diversity through their efects on the dynamics of species. To investigate such efects, we ftted a dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution to an assemblage of freshwater zooplankton sampled fve times a year (June–October) during the ice-free period over 28 years (1990–2017) in Lake Atnsjøen (Norway). By applying a multivariate stochastic community dynamics model for describing the fuctuations in abundances, we show that the community dynamics was driven by environmental variability in spring (i.e., June). In contrast, community-level ecological heterogeneity is highest in autumn. The autumn months (i.e., September and October) that rearranged the community are most likely crucial months to monitor long-term changes in community structure. Indeed, noises from early summer are fltered away, making it easier to track long-term changes. The community returned faster towards equilibrium when ecological heterogeneity was the highest (i.e., in September and October). This occurred because of stronger density-regulation in months with highest ecological heterogeneity. The community responded to the long-term warming of water temperature with decreasing species diversity and increasing abundance. Unevenness associated with variabilities in abundances might afect species interactions within the community. These can have consequences for the stability and functioning of the ecosystem. Freshwater · Lognormal distribution · Similarity · Return to equilibrium · Time-series

Here, we propose a theory for the structure of communities of competing species. We include ecologically realistic assumptions, such as density dependence and stochastic fluctuations in the environment, and analyze how evolution caused by

Achieving sustainable harvesting of natural populations depends on our ability to predict population responses to the combined effects of harvesting and environmental fluctuations while accounting for other internal and external factors that influence population dynamics in time and space. Here, we review recent research showing how spatial patterns and interspecific interactions can influence population responses to harvesting in fluctuating environments. We highlight several pathways through which harvesting can, often inadvertently, influence the dynamics and resilience to environmental fluctuations of both harvested and surrounding non-harvested populations and species. For instance, spatial models have shown that harvesting is expected to influence the spatial synchrony of population fluctuations, both of the harvested species and its competitors, predators and prey, with implications for population extinction risk. Dispersal and interspecific interactions can cause responses to harvesting in areas and species that are not themselves harvested. Harvesting that selectively targets certain groups of individuals, either intentionally or through for example spatially biased harvesting, can amplify environmentally induced population fluctuations by biasing the population structure towards individuals that are more sensitive to environmental variation. On the other hand, harvesting can in some cases buffer populations against the density-dependent effects of harsh climatic conditions, which are probably more common than previously acknowledged. Recent advances in modeling are providing new predictions that are highly relevant under global warming and now need to be tested empirically. We discuss how knowledge of these pathways can be used to increase the sustainability of harvesting.

Harvesting can magnify the destabilizing effects of environmental perturbations on population dynamics and, thereby, increase extinction risk. However, population-dynamic theory predicts that impacts of harvesting depend on the type and strength of density-dependent regulation. Here, we used logistic population growth models and an empirical reindeer case study to show that low to moderate harvesting can actually buffer populations against environmental perturbations. This occurs because of density-dependent environmental stochasticity, where negative environmental impacts on vital rates are amplified at high population density due to intraspecific resource competition. Simulations from our population models show that even low levels of harvesting may prevent overabundance, thereby dampening population fluctuations and reducing the risk of population collapse and quasi-extinction following environmental perturbations. Thus, depending on the species’ life history and the strength of density-dependent environmental drivers, low to moderate harvesting can improve population resistance to increased climate variability and extreme weather expected under global warming.

Many populations of especially long-lived species show large temporal variation in age structure, which can complicate estimating of important population parameters. This occurs because it can be difficult to disentangle whether variation in numbers is due to fluctuations in the environment or caused by changes in the age distribution. This chapter shows that fluctuations in the total reproductive value of the population, that is, the sum of all individual reproductive values, often provide a good description of the population dynamics but still is not confounded by fluctuations in age structure. Because the change in the total reproductive rate is exactly equal to the growth rate of the population, this quantity enables decomposition of the long-run growth rate into stochastic components caused by age-specific variation in demographic and environmental stochasticity. The chapter illustrates the practical application of this approach in stochastic demography by analyses of the dynamics of several populations of birds and mammals. It puts a strong focus on these methods being particularly useful in viability analyses of small populations of vulnerable or endangered species.

Harvesting can magnify the destabilizing effects of environmental perturbations on population dynamics and, thereby, increase extinction risk. However, population-dynamic theory predicts that impacts of harvesting depend on the type and strength of density-dependent regulation. Here, we used population models for a range of life histories and an empirical reindeer case study to show that harvesting can actually buffer populations against environmental perturbations. This occurs because of density-dependent environmental stochasticity, where negative environmental impacts on vital rates are amplified at high population density due to intra-specific resource competition. Simulations from our population models show that even low levels of proportional harvesting may prevent overabundance, thereby dampening population fluctuations and reducing the risk of population collapse and quasi-extinction induced by environmental perturbations. Thus, depending on the species’ life history and the strength of density-dependent environmental drivers, harvesting can improve population resistance to increased climate variability and extreme weather expected under global warming.

The degree of spatial autocorrelation in population fluctuations increases with dispersal and geographical covariation in the environment, and decreases with strength of density dependence. Because the effects of these processes can vary throughout an individual’s lifespan, we studied how spatial autocorrelation in abundance changed with age in three marine fish species in the Barents Sea. We found large interspecific differences in age-dependent patterns of spatial autocorrelation in density. Spatial autocorrelation increased with age in cod, the reverse trend was found in beaked redfish, while it remained constant among age classes in haddock. We also accounted for the average effect of local cohort dynamics, i.e. the expected local density of an age class given last year’s local density of the cohort, with the goal of disentangling spatial autocorrelation patterns acting on an age class from those formed during younger age classes and being carried over. We found that the spatial autocorrelation pattern of older age classes became increasingly determined by the distribution of the cohort during the previous year. Lastly, we found high degrees of autocorrelation over long distances for the three species, suggesting the presence of far-reaching autocorrelating processes on these populations. We discuss how differences in the species’ life history strategies could cause the observed differences in age-specific variation in spatial autocorrelation. As spatial autocorrelation can differ among age classes, our study indicates that fluctuations in age structure can influence the spatio-temporal variation in abundance of marine fish populations.

Adaptive topography is a central concept in evolutionary biology, describing how the mean fitness of a population changes with gene frequencies or mean phenotypes.We use expected population size as a quantity to be maximized by natural selection to show that selection on pairwise combinations of reproductive traits of collared flycatchers caused by fluctuations in population size generated an adaptive topography with distinct peaks often located at intermediate phenotypes. This occurred because r- and K-selection made phenotypes favored at small densities different from those with higher fitness at population sizes close to the carrying capacity K. Fitness decreased rapidly with a delay in the timing of egg laying, with a densitydependent effect especially occurring among early-laying females. The number of fledglings maximizing fitness was larger at small population sizes than when close to K. Finally, there was directional selection for large fledglings independent of population size. We suggest that these patterns can be explained by increased competition for some limiting resources or access to favorable nest sites at high population densities. Thus, r- and K-selection based on expected population size as an evolutionary maximization criterion may influence life-history evolution and constrain the selective responses to changes in the environment.

Since COVID-19 spread globally in early 2020 and was declared a pandemic by the World Health Organization (WHO) in March, many countries are managing the local epidemics effectively through intervention measures that limit transmission. The challenges of immigration of new infections into regions and asymptomatic infections remain. Standard deterministic compartmental models are inappropriate for sub- or peri-critical epidemics (reproductive number close to or less than one), so individual-based models are often used by simulating transmission from an infected person to others. However, to be realistic, these models require a large number of parameters, each with its own set of uncertainties and lack of analytic tractability. Here, we apply stochastic age-structured Leslie theory with a long history in ecological research to provide some new insights to epidemic dynamics fuelled by external imports. We model the dynamics of an epidemic when R 0 is below one, representing COVID-19 transmission following the successful application of intervention measures, and the transmission dynamics expected when infections migrate into a region. The model framework allows more rapid prediction of the shape and size of an epidemic to improve scaling of the response. During an epidemic when the numbers of infected individuals are rapidly changing, this will help clarify the situation of the pandemic and guide faster and more effective intervention.

International audience; The effects of harvest and fluctuating environment on interdependent predators and prey are complex and not well-known. We define a stochastic model where the predators and prey dynamically interact. The novelty of the model holds on the fact that predators and prey dynamics are simultaneously affected by correlated environmental noises. Interacting predators and prey are harvested using a proportional threshold harvesting strategy that accounts for stochastic population dynamics. Optimal yield of prey can be obtained with identical harvesting strategies when the predators and prey responded to the environment similarly (i.e., synchrony between species) and differently (i.e., asynchrony between species). Remarkably, our study demonstrates that two different harvesting strategies, the proportional harvesting strategy for the prey and the proportional threshold harvesting strategy for the predators, are needed to optimize the annual yield of predators and prey when both species are harvested simultaneously. Our study finds optimal strategies for harvesting interacting species affected by environmental variations (i.e., correlated noises) with parameters representing the joint dynamics of predators and prey at a stable state.

Classical theory in population genetics includes derivation of the stationary distribution of allele frequencies under balance between selection, genetic drift, and mutation. Here we investigate the simplest generalization of these single locus models to quantitative genetics with many loci, assuming simple additive effects on a set of phenotypes and a linear approximation to the fitness function. Genetic effects and pleiotropy are simulated by a prescribed stochastic model. Our goal is to analyze the structure of the G-matrix at stasis when the model is not very close to being neutral. The smallest eigenvalue of the G-matrix is practically zero by Fisher's fundamental theorem for natural selection and the fitness function is approximately a linear function of the corresponding eigenvector. Evolution of genetic trade-offs is closely linked to the fitness function. If a single locus never codes for more than two traits, then additive genetic covariance between two phenotype components always has the opposite sign of the product of their coefficients in the fitness function under no mutation, a pattern that is likely to occur frequently also in more complex models. In our major examples only 1-2 percent of the loci are over-dominant for fitness, but they still account for practically all dominance variance in fitness as well as all contributions to the G-matrix. These analyses show that the structure of the G-matrix reveals important information about the contribution of different traits to fitness.

Many species show synchronous fluctuations in population size over large geographical areas, which are likely to increase their regional extinction risk. Here we examine how the degree of spatial synchrony in population dynamics is affected by trophic interactions using a two-species predator-prey model with spatially correlated environmental noise. We show that the predator has a larger spatial scale of population synchrony than the prey if the population fluctuations of both species are mainly determined by the direct effect of stochastic environmental variations in the prey. This result implies that in ecosystems regulated from the bottom up, the spatial scale of synchrony of the predator population increases beyond the scale of the spatial autocorrelation in the environmental noise and in the prey fluctuations. Harvesting the prey increases the spatial scale of population synchrony of the predator, while harvesting the predator reduces the spatial scale of the population fluctuations of its prey. Hence, the development of sustainable harvesting strategies should also consider the impact on unharvested species at other trophic levels as well as human perturbations of ecosystems, whether the result of exploitation or an effect on dispersal processes, as they can affect food web structures and trophic interactions over large geographical areas.

Levels of random genetic drift are influenced by demographic factors, such as mating system, sex ratio and age structure. The effective population size (Ne) is a useful measure for quantifying genetic drift. Evaluating relative contributions of different demographic factors to Ne is therefore important to identify what makes a population vulnerable to loss of genetic variation. Until recently, models for estimating Ne have required many simplifying assumptions, making them unsuitable for this task. Here, using data from a small, harvested moose population, we demonstrate the use of a stochastic demographic framework allowing for fluctuations in both population size and age distribution to estimate and decompose the total demographic variance and hence the ratio of effective to total population size (Ne/N) into components originating from sex, age, survival and reproduction. We not only show which components contribute most to Ne/N currently, but also which components have the greatest potential for changing Ne/N. In this relatively long‐lived polygynous system we show that Ne/N is most sensitive to the demographic variance of older males, and that both reproductive autocorrelations (i.e., a tendency for the same individuals to be successful several years in a row) and covariance between survival and reproduction contribute to decreasing Ne/N (increasing genetic drift). These conditions are common in nature and can be caused by common hunting strategies. Thus, the framework presented here has great potential to increase our understanding of the demographic processes that contribute to genetic drift and viability of populations, and to inform management decisions. © 2019 The Authors. Molecular Ecology published by John Wiley & Sons Ltd This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Many animal populations providing ecosystem services, including harvest, live in seasonal environments and migrate between seasonally distinct ranges. Unfortunately, two major sources of human-induced global change threaten these populations: climate change and anthropogenic barriers. Anthropogenic infrastructure developments present a global threat to animal migrations through increased migration mortality or behavioral avoidance. Climate change alters the seasonal and spatial dynamics of resources and therefore the effects of migration on population performance. We formulated a population model with ideal-free migration to investigate changes in population size and harvest yield due to barriers and seasonal dynamics. The model predicted an increasing proportion of migrants when the difference between areas in seasonality or carrying capacity increased. Both migration cost and behavioral avoidance of barriers substantially reduced population size and harvest yields. Not surprisingly, the negative effects of barriers were largest when the population benefited most from migration. Despite the overall decline in harvest yield from a migratory population due to barriers, barriers could result in locally increased yield from the resident population following reduced competition from migrants. Our approach and results enhance the understanding of how global warming and infrastructure development worldwide may change population dynamics and harvest offtake affecting livelihoods and rural economies. Seasonal migration · Ideal-free distribution · Anthropogenic infrastructure · Mobile agent–based ecosystem services © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creativecommonshorg/licenses/by/4.0/.

There has been much recent research interest in the existence of a major axis of life‐history variation along a fast–slow continuum within almost all major taxonomic groups. Eco‐evolutionary models of density‐dependent selection provide a general explanation for such observations of interspecific variation in the "pace of life." One issue, however, is that some large‐bodied long‐lived “slow” species (e.g., trees and large fish) often show an explosive “fast” type of reproduction with many small offspring, and species with “fast” adult life stages can have comparatively “slow” offspring life stages (e.g., mayflies). We attempt to explain such life‐history evolution using the same eco‐evolutionary modeling approach but with two life stages, separating adult reproductive strategies from offspring survival strategies. When the population dynamics in the two life stages are closely linked and affect each other, density‐dependent selection occurs in parallel on both reproduction and survival, producing the usual one‐dimensional fast–slow continuum (e.g., houseflies to blue whales). However, strong density dependence at either the adult reproduction or offspring survival life stage creates quasi‐independent population dynamics, allowing fast‐type reproduction alongside slow‐type survival (e.g., trees and large fish), or the perhaps rarer slow‐type reproduction alongside fast‐type survival (e.g., mayflies—short‐lived adults producing few long‐lived offspring). Therefore, most types of species life histories in nature can potentially be explained via the eco‐evolutionary consequences of density‐dependent selection given the possible separation of demographic effects at different life stages., Our model demonstrates how density dependence can uncouple the eco‐evolutionary dynamics of adult reproduction versus offspring survival to allow independent life‐history (fast vs. slow) evolution at different life stages. The normal simple fast–slow life‐history continuum can thus be modified into more complex life histories, such as those seen in most trees and large fish with large‐bodied long‐lived “slow” adults but explosive “fast” reproduction with many small offspring. We therefore show that fast–slow density‐dependent selection theory has the potential to explain even the most complex types of life‐history strategies seen in nature.

We have in this study analysed bird communities across Norway with a heterogeneous species abundance model, where dynamical parameters can vary among species. Similarity in community composition over time, used as a measure of temporal β-diversity or the turnover rate, was then estimated. When we account for heterogeneity in dynamical parameters among species it will affect how we estimate environmental stochasticity, and, subsequently, how the temporal dynamics is modelled. In addition, spatial variation in species abundance within a sampling area can obscure the temporal dynamics of communities. By inadvertently including small-scale spatial variation within sampling areas in the sample noise term, it will be difficult to correctly detect changes in community structure, or species abundance similarity, in time. Using Norwegian bird communities as a case study, we have shown how to interpret the sample correlation of the bivariate Poisson lognormal distribution, fitted to pairs of transects, and why separation of the transects into spatially similar subgroups can be beneficial. This approach also makes us able to account for sampling error and over-dispersion relative to Poisson sampling. The partitioning of the variance of the species abundance distributions showed that heterogeneity among species in temporal dynamics accounted for roughly 75% of the variation, close to estimates for other taxa. High temporal similarity can be interpreted as a low baseline turnover rate, which is important when studying changes to ecosystems due to e.g. anthropogenic effects. Furthermore, the environmental stochasticity was more realistically estimated in this heterogeneous model. This is essential for predicting the dynamics of species abundances forward in time. β-diversity Environmental stochasticity Heterogeneous species abundance models Over-dispersion Temporal community dynamics

Harvesting in space affects, in general, the spatial scale of the synchrony in the population fluctuations, which determines the size of the areas subjected to simultaneous quasi-extinction risk. Here we show that harvesting reduces the population synchrony scale if it depends more strongly on population fluctuations than the density dependence of the growth rate in the absence of harvesting. We show that constant and proportional harvesting always increases the spatial scale, using a theta-logistic model for density regulation. We also provide exact scaling results under harvesting for the Beverton–Holt and the Ricker stock-recruitment models that are commonly applied, e.g. in fisheries. Our results indicate that harvest in areas with large abundances should be encouraged to avoid increase of the spatial scale of synchrony in the population fluctuations that can lead to unexpected quasi-extinction of populations over large areas. Our results quantify this harvesting impact giving the resulting scales of spatial synchrony of population fluctuations. This emphasizes the importance of estimating the form of density dependence as well as the dependency of harvest upon population density of exploited populations, in order to get reliable predictions of the size of areas that can undergo simultaneous quasi-extinction.

We analyze a spatial age-structured model with density regulation, age specific dispersal, stochasticity in vital rates and proportional harvesting. We include two age classes, juveniles and adults, where juveniles are subject to logistic density dependence. There are environmental stochastic effects with arbitrary spatial scales on all birth and death rates, and individuals of both age classes are subject to density independent dispersal with given rates and specified distributions of dispersal distances. We show how to simulate the joint density fields of the age classes and derive results for the spatial scales of all spatial autocovariance functions for densities. A general result is that the squared scale has an additive term equal to the squared scale of the environmental noise, corresponding to the Moran effect, as well as additive terms proportional to the dispersal rate and variance of dispersal distance for the age classes and approximately inversely proportional to the strength of density regulation. We show that the optimal harvesting strategy in the deterministic case is to harvest only juveniles when their relative value (e.g. financial) is large, and otherwise only adults. With increasing environmental stochasticity there is an interval of increasing length of values of juveniles relative to adults where both age classes should be harvested. Harvesting generally tends to increase all spatial scales of the autocovariances of densities.

Significance We derive a univariate approximation for the growth of a density-dependent age-structured population in a fluctuating environment. Its accuracy is demonstrated by comparison with simulations of the age-structured model under assumptions applicable to many vertebrate populations. This facilitates extension to age-structured populations of recent theory on the evolution of stochastic population dynamics, showing that evolution tends to maximize a simple function of three key population parameters: the maximum population growth rate and carrying capacity in the average environment, r 0 and K , and the variance of population growth rate, σ e 2 . Regardless of the complexity of trade-offs among these parameters, for the classical logistic model of population growth, evolution in a fluctuating environment tends to maximize the average population size.

In spatio-temporal population dynamic models, the most important concept, in addition to mean and variance of local density fluctuations, is the spatial scale of fluctuations in density expressed by studying the spatial autocovariance function. Analytical formulas for this scale in models with local density regulation, dispersal and spatially autocorrelated noise, are rather simple when based on asymptotic theory giving linear models in the limit as the environmental variance approaches zero. The accuracy of these analytical small noise approximations has, however, not been investigated theoretically. Here, we work out improved approximations for the scale as well the spatial autocorrelation function using non-linear logistic local dynamics and going to the next order of approximation with respect to the environmental variance. Generally, it turns out that the asymptotic results are remarkably accurate under moderate fluctuations in density but may be inaccurate for very large fluctuations. For populations with small dispersal capacity, the main error comes from the fact that the logistic dynamics is non-linear, and this error is partly wiped out as dispersal increases. Proportional harvesting has a large effect on the dynamics in spatial as well as non-spatial models, increasing population fluctuations and their spatial scale. The optimal harvesting rate with respect to expected yield per time unit, however, is only to a small extent affected by the magnitude of population fluctuations unless these are very large, so that asymptotic results are applicable over a large range of population fluctuations.

Evolutionary adaptations following environmental deterioration can sometimes rescue populations from extinction. Here we provide a scenario in which such evolutionary rescue will be difficult. Using a rather general model for fluctuating r- and K-selection in a density-dependent population, we show that reduction of available resources will not necessarily induce evolution of adaptations to counteract such changes provided that density regulation acts through available resources per individual. In large populations, resource depletion may induce a change in stationary distribution of population size while the optimal phenotype remains unchanged. Under a period of continuous reduction in available resources, increased strength of K-selection will occur in the sense that individuals are able to live and reproduce under less favorable conditions. Smaller growth rates as a consequence of K-selection and trade-offs between intrinsic growth rate r and carrying capacity K may then have a considerable negative effect on the persistence of the population even after the reduction of available resources is stopped. This negative effect comes in addition to the purely ecological effect of reduced time to extinction because of a reduction in K and increased demographic stochasticity. Continuous reduction in the available area or in available resources per individual may result in long-run maladaptation even if demographic noise increases and, finally but too late, induces r-selection.

A general assumption in quantitative genetics is the existence of an intermediate phenotype with higher mean individual fitness in the average environment than more extreme phenotypes. Here, we investigate the evolvability and presence of such a phenotype in wild bird populations from an eleven-year experiment with four years of artificial selection for long and short tarsus length, a proxy for body size. The experiment resulted in strong selection in the imposed directions. However, artificial selection was counteracted by reduced production of recruits in offspring of artificially selected parents. This resulted in weak natural selection against extreme trait values. Significant responses to artificial selection were observed at both the phenotypic and genetic level, followed by a significant return toward preexperimental means. During artificial selection, the annual observed phenotypic response closely followed the predicted response from quantitative genetic theory (ryears = 0.96, rcohorts = 0.56). The rapid return to preexperimental means was induced by three interacting mechanisms: selection for an intermediate phenotype, immigration, and recombination between selected and unselected individuals. The results of this study demonstrates the evolvability of phenotypes and that selection may favor an intermediate phenotype in wild 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.

Understanding how environmental variation affects phenotypic evolution requires models based on ecologically realistic assumptions that include variation in population size and specific mechanisms by which environmental fluctuations affect selection. Here we generalize quantitative genetic theory for environmentally induced stochastic selection to include general forms of frequency- and density-dependent selection. We show how the relevant fitness measure under stochastic selection relates to Fisher's fundamental theorem of natural selection, and present a general class of models in which density regulation acts through total use of resources rather than just population size. In this model, there is a constant adaptive topography for expected evolution, and the function maximized in the long run is the expected factor restricting population growth. This allows us to generalize several previous results and to explain why apparently " K -selected" species with slow life histories often have low carrying capacities. Our joint analysis of density- and frequency-dependent selection reveals more clearly the relationship between population dynamics and phenotypic evolution, enabling a broader range of eco-evolutionary analyses of some of the most interesting problems in evolution in the face of environmental variation.

International audience; Understanding species coexistence has long been a major goal of ecology. Coexistence theory for two competing species posits that intraspecific density dependence should be stronger than interspecific density dependence. Great tits and blue tits are two bird species that compete for food resources and nesting cavities. On the basis of long-term monitoring of these two competing species at sites across Europe, combining observational and manipulative approaches, we show that the strength of density regulation is similar for both species, and that individuals have contrasting abilities to compete depending on their age. For great tits, density regulation is driven mainly by intraspecific competition. In contrast, for blue tits, interspecific competition contributes as much as intraspecific competition, consistent with asymmetric competition between the two species. In addition, including age-specific effects of intra-and interspecific competition in density-dependence models improves predictions of fluctuations in population size by up to three times.

One of the most important challenges in conservation biology is to predict the viability of populations of vulnerable and threatened species. This requires that the demographic stochasticity strongly affecting the ecological and evolutionary dynamics of especially small populations is correctly estimated and modelled. Here, we summarize theoretical evidence showing that the demographic variance in population dynamics is a key parameter determining the probability of extinction and also is directly linked to the magnitude of the genetic drift in the population. The demographic variance is dependent on the mating system, being larger in a polygynous than in monogamous populations. Understanding factors affecting intersexual differences in mating success is therefore essential in explaining variation in the demographic variance. We hypothesize that the strength of sexual selection, for example, quantified by the Bateman gradient, may be a useful predictor of the magnitude of the demographic stochasticity and hence the genetic drift in the population. We provide results from a field study of moose that support this claim. Thus, including central principles from behavioural ecology may increase the reliability of population viability analyses through an improvement of our understanding of factors affecting stochastic influences on population dynamics and evolutionary processes.This article is part of the theme issue ‘Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation’.

Understanding how stochastic fluctuations in the environment influence population dynamics is crucial for sustainable management of biological diversity. However, because species do not live in isolation, this requires knowledge of how species interactions influence population dynamics. In addition, spatial processes play an important role in shaping population dynamics. It is therefore important to improve our understanding of how these different factors act together to shape patterns of abundance across space within and among species. Here, we present a new analytical model for understanding patterns of covariation in space between interacting species in a stochastic environment. We show that the correlation between two species in how they experience the same environmental conditions determines how correlated fluctuations in their densities would be in the absence of competition. In other words, without competition, synchrony between the species is driven by the environment, similar to the Moran effect within a species. Competition between the two species causes their abundances to become less positively or more negatively correlated. The same strength of competition has a greater negative effect on the correlation between species when one of them has a more variable growth rate than the other. In addition, dispersal or other movement weakens the effect of competition on the interspecific correlation. Finally, we show that movement increases the distance over which the species are (positively or negatively) correlated, an effect that is stronger when the species are competitors, and that there is a close connection between the spatial scaling of population synchrony within a species and between species. Our results show that the relationships between the different factors influencing interspecific correlations in abundance are not simple linear ones, but this model allows us to disentangle them and predict how they will affect population fluctuations in different situations. © 2019 The Authors. Ecology published by Wiley Periodicals, Inc. on behalf of Ecological Society of America This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

International audience; Climate variation strongly influences fluctuations in size of avian populations. In this chapter, we show that it is difficult to predict how the abundance of birds will respond to climate change. A major reason for this is that most available time series of fluctuations in population size are in a statistical sense short, thus often resulting in large uncertainties in parameter estimates. We therefore argue that reliable population predictions must be based on models that capture how climate change will affect vital rates as well as including other processes (e.g. density-dependences) known to affect the population dynamics of the species in question. Our survey of examples of such forecast studies show that reliable predictions necessarily contain a high level of uncertainty. A major reason for this is that avian population dynamics are strongly influenced by environmental stochasticity, which is for most species, irrespective of their life history, the most important driver of fluctuations in population size. Credible population predictions must therefore assess the effects of such uncertainties as well as biases in population estimates.

The synchrony of population dynamics in space has important implications for ecological processes, for example affecting the spread of diseases, spatial distributions and risk of extinction. Here, we studied the relationship between spatial scaling in population dynamics and species position along the slow‐fast continuum of life history variation. Specifically, we explored how generation time, growth rate and mortality rate predicted the spatial scaling of abundance and yearly changes in abundance of eight marine fish species. Our results show that population dynamics of species' with ‘slow’ life histories are synchronised over greater distances than those of species with ‘fast’ life histories. These findings provide evidence for a relationship between the position of the species along the life history continuum and population dynamics in space, showing that the spatial distribution of abundance may be related to life history characteristics. This is the peer reviewed version of an article, which has been published in final form at [https://doi.org/10.1111/ele.13360]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. "

Spatial differentiation of phenotypes is assumed to be determined by a combination of fluctuating selection producing adaptations to the local environment and a homogenizing effect of migration. We present a model with density regulation and a density-dependent fitness function affected by spatio-temporal variability in population size driven by spatially correlated fluctuations in the environment causing fluctuating - and -selection on a set of traits. We derive the variance in local mean phenotypes and show how the spatial scales of the correlations between the components of the mean phenotype depend on ecological parameters. The degree of spatial differentiation of phenotypes is strongly influenced by parameters affecting ecological dynamics. In the case of a one-dimensional character the geographical scale of variation in the mean phenotype has simply an additive term corresponding to the Moran effect in population dynamics as well as a term determined by dispersal and strength of local selection. The degree of phenotypic differentiation increases with decreasing strength of local density dependence and decreasing strength of local selection. These results imply that the form of the spatial autocorrelation function can reveal important information about ecological and evolutionary processes causing phenotypic differentiation in space. © 2019 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r-selection and K-selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r0 and the lifetime reproductive success (LRS) R0 , both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r0 and average lifetimes are small, whereas R0 dominates and lifetimes are larger under small noise. Thus, K-selection is closely linked to selection for large R0 so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r0 and R0 ) tend to be maximized at low and high densities, respectively, favoring density-dependent changes in the optimal life history.

Reliable estimates of effective population size Ne are of central importance in population genetics and evolutionary biology. For populations that fluctuate in size, harmonic mean population size is commonly used as a proxy for (multi-) generational effective size. This assumes no effects of density dependence on the ratio between effective and actual population size, which limits its potential application. Here, we introduce density dependence on vital rates in a demographic model of variance effective size. We derive an expression for the ratio Ne/N in a density-regulated population in a fluctuating environment. We show by simulations that yearly genetic drift is accurately predicted by our model, and not proportional to 1/(2N) as assumed by the harmonic mean model, where N is the total population size of mature individuals. We find a negative relationship between Ne/N and N. For a given N, the ratio depends on variance in reproductive success and the degree of resource limitation acting on the population growth rate. Finally, our model indicate that environmental stochasticity may affect Ne/N not only through fluctuations in N, but also for a given N at a given time. Our results show that estimates of effective population size must include effects of density dependence and environmental stochasticity.

International audience; Classical approaches for the analyses of density dependence assume that all the individuals in a population equally respond and equally contribute to density dependence. However, in age-structured populations, individuals of different ages may differ in their responses to changes in population size and how they contribute to density dependence affecting the growth rate of the whole population. Here we apply the concept of critical age classes, i.e., a specific scalar function that describes how one or a combination of several age classes affect the demographic rates negatively, in order to examine how total density dependence acting on the population growth rate depends on the age-specific population sizes. In a 38-yr dataset of an age-structured great tit (Parus major) population, we find that the age classes, including the youngest breeding females, were the critical age classes for density regulation. These age classes correspond to new breeders that attempt to take a territory and that have the strongest competitive effect on other breeding females. They strongly affected population growth rate and reduced recruitment and survival rates of all breeding females. We also show that depending on their age class, females may differently respond to varying density. In particular, the negative effect of the number of breeding females was stronger on recruitment rate of the youngest breeding females. These findings question the classical assumptions that all the individuals of a population can be treated as having an equal contribution to density regulation and that the effect of the number of individuals is age independent. Our results improve our understanding of density regulation in natural populations.

Here we analyze how dispersal, genetic drift, and adaptation to the local environment affect the geographical differentiation of a quantitative character through natural selection using a spatial dynamic model for the evolution of the distribution of mean breeding values in space and time. The variation in optimal phenotype is described by local Ornstein-Uhlenbeck processes with a given spatial autocorrelation. Selection and drift are assumed to be governed by phenotypic variation within areas with a given mean breeding value and constant additive genetic variance. Between such neighboring areas there will be white noise variation in mean breeding values, while the variation at larger distances has a spatial structure and a spatial scale that we investigate. The model is analyzed by solving balance equations for the stationary distribution of mean breeding values. We also present scaling results for the spatial autocovariance function for mean breeding values as well as that for the covariance between mean breeding value and the optimal phenotype expressing local adaption. Our results show in particular how these spatial scales depend on population density. For large densities the spatial scale of fluctuations in mean breeding values have similarities with corresponding results in population dynamics, where the effect of migration on spatial scales may be large if the local strength of density regulation is small. In our evolutionary model strength of density regulation corresponds to strength of local selection so that weak local selection may produce large spatial scales of autocovariances. Genetic drift and stochastic migration are shown to act through the population size within a characteristic area with much smaller variation in optimal phenotypes than in the whole population.

Empirical evidence strongly indicates that human exploitation has frequently led to rapid evolutionary changes in wild populations, yet the mechanisms involved are often poorly understood. Here, we applied a recently developed demographic framework for analyzing selection to data from a 20-year study of a wild population of moose, Alces alces. In this population, a genetic pedigree has been established all the way back to founders. We demonstrate harvest-induced directional selection for delayed birth dates in males and reduced body mass as calf in females. During the study period, birth date was delayed by 0.81 days per year for both sexes, whereas no significant changes occurred in calf body mass. Quantitative genetic analyses indicated that both traits harbored significant additive genetic variance. These results show that selective harvesting can induce strong selection that oppose natural selection. This may cause evolution of less favorable phenotypes that become maladaptive once harvesting ceases.

Anthropogenic activity can cause changes in the population dynamics of species. The changes can be modelled by density dependent models with time varying parameters. The following study looks at the accuracy of model parameter estimates using primarily simulations, in addition to a real data set of Grey Heron. A key point is the amount of data required to detect deterministic changes, either step-wise or gradual, in parameters for species with different population dynamics. The theta-logistic model is used to simulate the data and fitted to realizations of step-wise change in growth rate, and a linear model is fitted to gradual or step-wise changes in carrying capacity. Bayesian analysis is applied to study the effect of different prior distributions on the strength of density regulation. The range of the data is especially important when trying to detect step-wise changes in growth rate. Detection of changes in carrying capacity depends on the dynamics of the population, e.g. it is difficult to observe change for species with long return time to equilibrium within short time frames. The estimates of change in carrying capacity can become more accurate using a strong prior on the strength of density regulation. However, the prior may give more conservative estimates, if the prior assumes a weak density regulation. The results provide ecologists and decision makers with a general idea of what to expect of analyses of time series data of populations in changing environments.

A general assumption in quantitative genetics is the existence of an intermediate phenotype with higher mean individual fitness in the average environment than more extreme phenotypes. Here, we investigate the evolvability and presence of such a phenotype in wild bird populations from an eleven-year experiment with four years of artificial selection for long and short tarsus length, a proxy for body size. The experiment resulted in strong selection in the imposed directions. However, artificial selection was counteracted by reduced production of recruits in offspring of artificially selected parents. This resulted in weak natural selection against extreme trait values. Significant responses to artificial selection were observed at both the phenotypic and genetic level, followed by a significant return toward preexperimental means. During artificial selection, the annual observed phenotypic response closely followed the predicted response from quantitative genetic theory (ryears = 0.96, rcohorts = 0.56). The rapid return to preexperimental means was induced by three interacting mechanisms: selection for an intermediate phenotype, immigration, and recombination between selected and unselected individuals. The results of this study demonstrates the evolvability of phenotypes and that selection may favor an intermediate phenotype in wild populations.

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age‐structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates. This is the peer reviewed version of an article, which has been published in final form at [https://doi.org/10.1111/ele.12834]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. "

Warmer winters alter the dynamics of a local bird population and reduce immigration rate due to density-dependent feedback., Climate change will affect the population dynamics of many species, yet the consequences for the long-term persistence of populations are poorly understood. A major reason for this is that density-dependent feedback effects caused by fluctuations in population size are considered independent of stochastic variation in the environment. We show that an interplay between winter temperature and population density can influence the persistence of a small passerine population under global warming. Although warmer winters favor an increased mean population size, density-dependent feedback can cause the local population to be less buffered against occasional poor environmental conditions (cold winters). This shows that it is essential to go beyond the population size and explore climate effects on the full dynamics to elaborate targeted management actions.

There is now considerable empirical evidence that evolutionary changes in many phenotypic characters, such as body mass, age at maturation, and timing of breeding, often occur in populations subject to intense harvesting over longer periods. Here, we analyze the evolutionary component of the selection due to nonselective harvesting, which will operate even under selective harvesting and may generate a large evolutionary response. If phenotype affects susceptibility to density dependence-for example, through resource limitation-then nonselective harvesting can induce evolutionary change through its effect on population density. We provide a model for evolution of a quantitative character in such a fluctuating density-dependent population, using the diffusion approximation to describe jointly the temporal changes in mean phenotype and log population size. We show how nonselective harvesting in particular generates r-selection governed by genetic variation in the strength of density regulation and the magnitude of population fluctuations. We show that r-selection caused by nonselective harvesting is proportional to the mean fraction of the population harvested. We then compare the short-term as well as the long-term evolutionary impact of nonselective harvesting for different harvesting strategies by using the mean harvest fraction for different strategies. This comparison is performed for three different harvesting strategies: constant, proportional, and threshold harvesting. The more ecologically sustainable strategies also produce smaller evolutionary changes.

An extension of the selection differential in the Robertson-Price equation for the mean phenotype in an age-structured population is provided. Temporal changes in the mean phenotype caused by transient fluctuations in the age-distribution and variation in mean phenotype among age classes, which can mistakenly be interpreted as selection, will disappear if reproductive value weighting is applied. Changes in any weighted mean phenotype in an age-structured population may be decomposed into between- and within-age class components. Using reproductive value weighting the between-age class component becomes pure noise, generated by previous genetic drift or fluctuating selection. This component, which we call transient quasi-selection, can therefore be omitted when estimating age-specific selection on fecundity or viability within age classes. The final response can be computed at the time of selection, but can not be observed until lifetime reproduction is realized unless the heritability is one. The generality of these results is illustrated further by our derivation of the selection differential for the continuous time age-structured model with general age-dependent weights. A simple simulation example as well as estimation of selection components in a house sparrow population illustrates the applicability of the theory to analyze selection on the mean phenotype in fluctuating age-structured populations.