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.

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.

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.

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.

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.

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.

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.

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.

Evolution of stochastic demography with life history tradeoffs in density-dependent age-structured populations.

We analyze the stochastic demography and evolution of a density-dependent age- (or stage-) structured population in a fluctuating environment. A positive linear combination of age classes (e.g., weighted by body mass) is assumed to act as the single variable of population size, [Formula: see text], exerting density dependence on age-specific vital rates through an increasing function of population size. The environment fluctuates in a stationary distribution with no autocorrelation. We show by analysis and simulation of age structure, under assumptions often met by vertebrate populations, that the stochastic dynamics of population size can be accurately approximated by a univariate model governed by three key demographic parameters: the intrinsic rate of increase and carrying capacity in the average environment, [Formula: see text] and [Formula: see text], and the environmental variance in population growth rate, [Formula: see text] Allowing these parameters to be genetically variable and to evolve, but assuming that a fourth parameter, [Formula: see text], measuring the nonlinearity of density dependence, remains constant, the expected evolution maximizes [Formula: see text] This shows that the magnitude of environmental stochasticity governs the classical trade-off between selection for higher [Formula: see text] versus higher [Formula: see text] However, selection also acts to decrease [Formula: see text], so the simple life-history trade-off between [Formula: see text]- and [Formula: see text]-selection may be obscured by additional trade-offs between them and [Formula: see text] Under the classical logistic model of population growth with linear density dependence ([Formula: see text]), life-history evolution in a fluctuating environment tends to maximize the average population size.

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.

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.

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.

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.

Modelling time to population extinction when individual reproduction is autocorrelated.

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.

Extinction Risk and Lack of Evolutionary Rescue under Resource Depletion or Area Reduction.

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.

How are species interactions structured in species-rich communities? A new method for analysing time-series data.

Estimation of intra- and interspecific interactions from time-series on species-rich communities is challenging due to the high number of potentially interacting species pairs. The previously proposed sparse interactions model overcomes this challenge by assuming that most species pairs do not interact. We propose an alternative model that does not assume that any of the interactions are necessarily zero, but summarizes the influences of individual species by a small number of community-level drivers. The community-level drivers are defined as linear combinations of species abundances, and they may thus represent e.g. the total abundance of all species or the relative proportions of different functional groups. We show with simulated and real data how our approach can be used to compare different hypotheses on community structure. In an empirical example using aquatic microorganisms, the community-level drivers model clearly outperformed the sparse interactions model in predicting independent validation data.

Spatial synchrony and harvesting in fluctuating populations:Relaxing the small noise assumption.

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.

Evidence for r- and K-selection in a wild bird population: a reciprocal link between ecology and evolution.

Understanding the variation in selection pressure on key life-history traits is crucial in our rapidly changing world. Density is rarely considered as a selective agent. To study its importance, we partition phenotypic selection in fluctuating environments into components representing the population growth rate at low densities and the strength of density dependence, using a new stochastic modelling framework. We analysed the number of eggs laid per season in a small song-bird, the great tit, and found balancing selection favouring large clutch sizes at small population densities and smaller clutches in years with large populations. A significant interaction between clutch size and population size in the regression for the Malthusian fitness reveals that those females producing large clutch sizes at small population sizes also are those that show the strongest reduction in fitness when population size is increased. This provides empirical support for ongoing r- and K-selection in this population, favouring phenotypes with large growth rates r at small population sizes and phenotypes with high competitive skills when populations are close to the carrying capacity K This selection causes long-term fluctuations around a stable mean clutch size caused by variation in population size, implying that r- and K-selection is an important mechanism influencing phenotypic evolution in fluctuating environments. This provides a general link between ecological dynamics and evolutionary processes, operating through a joint influence of density dependence and environmental stochasticity on fluctuations in population size.

Density dependence in an age-structured population of great tits: identifying the critical age classes.

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.