Assessing the sensitivity and resistance of communities in a changing environment.

We propose that the ecological resilience of communities to permanent changes of the environment can be based on how variation in the overall abundance of individuals affects the number of species. Community sensitivity is defined as the ratio between the rate of change in the log expected number of species and the rate of change in the log expected number of individuals in the community. High community sensitivity means that small changes in the total abundance strongly impact the number of species. Community resistance is the proportional reduction in expected number of individuals that the community can sustain before expecting to lose one species. A small value of community resistance means that the community can only endure a small reduction in abundance before it is expected to lose one species. Based on long-term studies of four bird communities in European deciduous forests at different latitudes large differences were found in the resilience to environmental perturbations. Estimating the variance components of the species abundance distribution revealed how different processes contributed to the community sensitivity and resistance. Species heterogeneity in the population dynamics was the largest component, but its proportion varied among communities. Species-specific response to environmental fluctuations was the second major component of the variation in abundance. Estimates of community sensitivity and resistance based on data only from a single year were in general larger than those based on estimates from longer time series. Thus, our approach can provide rapid and conservative assessment of the resilience of communities to environmental changes also including only short-term data. This study shows that a general ecological mechanism, caused by increased strength of density dependence due to reduction in resource availability, can provide an intuitive measure of community resilience to environmental variation. Our analyses also illustrate the importance of including specific assumptions about how different processes affect community dynamics. For example, if stochastic fluctuations in the environment affect all species in a similar way, the sensitivity and resistance of the community to environmental changes will be different from communities in which all species show independent responses.

Density-dependent selection and the maintenance of colour polymorphism in barn owls.

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 ([Formula: see text]). 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.

Seasonal diversity dynamics of a boreal zooplankton community under climate impact.

Seasonality and long-term environmental variability affect species diversity through their effects on the dynamics of species. To investigate such effects, we fitted a dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution to an assemblage of freshwater zooplankton sampled five 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 fluctuations 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 filtered 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 affect species interactions within the community. These can have consequences for the stability and functioning of the ecosystem.

Harvesting can stabilise population fluctuations and buffer the impacts of extreme climatic events.

Harvesting can magnify the destabilising 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 intra-specific 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.

Age-dependent patterns of spatial autocorrelation in fish populations.

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.

The ecological dynamics of the coronavirus epidemics during transmission from outside sources when R 0 is successfully managed below one.

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.

An Evolutionary and Ecological Community Model for Distribution of Phenotypes and Abundances among Competing Species.

AbstractHere, 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 r- and K-selection will affect the packing of species in the phenotypic space as well as the species abundance distribution. Species-specific traits have the same matrix G of additive genetic variances and covariances, and evolution of mean traits is affected by fluctuations in population size of all species. In general, the model produces a shape of the distributions of log abundances that is skewed to the left, which is typical of most natural communities. Mean phenotypes of the species in the community are distributed approximately uniformly on the surface of a multidimensional sphere. However, environmental stochasticity generates selection that deviates species slightly from this surface; nonetheless, phenotypic distribution will be different from a random packing of species. This model of community evolution provides a theoretical framework that predicts a relationship between the structure of the phenotypic space and the form of species abundance distributions that can be compared against time series of variation in community structure.

Structure of the G-matrix in relation to phenotypic contributions to fitness.

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.

Density-Dependent Adaptive Topography in a Small Passerine Bird, the Collared Flycatcher.

AbstractAdaptive 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 density-dependent 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.

Phenotypic evolution in stochastic environments: The contribution of frequency- and density-dependent selection.

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.

Contrasting patterns of density-dependent selection at different life stages can create more than one fast-slow axis of life-history variation.

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.

Spatial Scales of Population Synchrony in Predator-Prey Systems.

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.

Spatial covariation of competing species in a fluctuating environment.

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.

Decomposing demographic contributions to the effective population size with moose as a case study.

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.

Spatial scaling of population synchrony in marine fish depends on their life history.

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.

Towards a predictive conservation biology: the devil is in the behaviour.

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'.

Ecological dynamics and large scale phenotypic differentiation in density-dependent populations.

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 r- and K-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.

Accounting for interspecific competition and age structure in demographic analyses of density dependence improves predictions of fluctuations in population size.

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.

The effect of harvesting on the spatial synchrony of population fluctuations.

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.

Spatial distribution and optimal harvesting of an age-structured population in a fluctuating environment.

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.