Will small population sizes warn us of impending extinctions?

Several models are used to show that population sizes are often relatively insensitive to deteriorating environmental conditions over most of the range of environments that allow population persistence. As conditions continue to worsen in these cases, equilibrium population sizes ultimately decline rapidly toward extinction from sizes similar to or larger than those before environmental decline began. Consumer-resource models predict that equilibrium or average population size can increase with deteriorating environmental conditions over a large part of the range of the environmental parameter that allows persistence. The initial insensitivity or increase in the population of the focal species occurs because changes in the populations of other components of the food web compensate for the decline in one or more fitness components of the focal population. However, the compensatory processes are generally nonlinear and often approach their limits abruptly rather than gradually. When there is steady directional change in the environment, populations lag behind the equilibrium population size specified by current environmental conditions. The environmental variable can then decline below the level required for population persistence while the population size is still close to or greater than its original value. Efficient consumers and self-reproducing resources are especially likely to produce this outcome. More complex models with adaptive behavior, additional consumers, or additional resources often exhibit similar trajectories of population size under environmental deterioration.     

The average lifetime of a population in a varying environment

I derive an approximate formula relating the average time to extinction of a population in a varying environment to its initial size, its equilibrium size (if it is self-regulated), its innate capacity for natural increase, and the impact upon it of environmental variation. The greater the impact of environmental variation, the more slowly a population's prospective lifetime increases with increase in its equilibrium size. The lifetimes of populations greatly influenced by environmental variation are more sensitive to the relative amplitude of fluctuation in their numbers than to their equilibrium size. Since species tend to avoid competitive displacement by specializing, rendering themselves more sensitive to environmental change, and since populations are no more likely to risk extinction in one environment than in another, the degree to which a community's populations fluctuate will be unrelated to environmental stability.     

Rapid convergence to an equilibrium state in kleptoparasitic populations

Previous papers have modelled the behaviour of populations which are subject to kleptoparasitism, and found those ecological situations in which kleptoparasitism should occur. Individuals were considered to be in one of several states, and an equilibrium distribution for the population was found. It was then assumed, for analytical purposes but without proof, that the population was actually in that equilibrium. In this paper, we show that the equilibrium is a stable one, and that it is reached in a relatively short time for all reasonable values of the ecological parameters. Thus, a population may be expected to spend most of the time in equilibrium, and this assumption of these previous works is justified.Research of the first author supported by EPSRC.The authors are also members of The Centre for the Study of Evolution, at the University of Sussex.     

Environmental marginality and geographic range limits: a case study with Arabidopsis lyrata ssp. lyrata

Understanding the factors that govern the distribution of species is a central goal of evolutionary ecology. It is commonly assumed that geographic range limits reflect ecological niche limits and that species experience increasingly marginal conditions towards the edge of their ranges. Using spatial data and ecological niche models we tested these hypotheses in Arabidopsis lyrata. Specifically, we asked whether range limits coincide with predicted niche limits in this system and whether the suitability of sites declines towards the edge of the species’ range in North America. We further explored patterns of environmental change towards the edge of the range and asked whether genome‐wide patterns of genetic diversity decline with increasing peripherality and environmental marginality. Our results suggest that latitudinal range limits coincide with niche limits. Populations experienced increasingly marginal environments towards these limits – though patterns of environmental change were more complex than most theoretical models for range limits assume. Genomic diversity declined towards the edge of the species’ range and with increasing distance from the estimated centre of the species’ niche in environmental space, but not with the suitability of sites based on niche model predictions. Thus while latitudinal range limits in this system are broadly associated with niche limits, the link between environmental conditions and genetic diversity (and thus the adaptive potential of populations) is less clear.     

Modeling the dynamics of natural rotifer populations: Phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete non-linear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.     

Population and prehistory I: Food-dependent population growth in constant environments

We present a demographic model that describes the feedbacks between food supply, human mortality and fertility rates, and labor availability in expanding populations, where arable land area is not limiting. This model provides a quantitative framework to describe how environment, technology, and culture interact to influence the fates of preindustrial agricultural populations. We present equilibrium conditions and derive approximations for the equilibrium population growth rate, food availability, and other food-dependent measures of population well-being. We examine how the approximations respond to environmental changes and to human choices, and find that the impact of environmental quality depends upon whether it manifests through agricultural yield or maximum (food-independent) survival rates. Human choices can complement or offset environmental effects: greater labor investments increase both population growth and well-being, and therefore can counteract lower agricultural yield, while fertility control decreases the growth rate but can increase or decrease well-being. Finally we establish equilibrium stability criteria, and argue that the potential for loss of local stability at low population growth rates could have important consequences for populations that suffer significant environmental or demographic shocks.     

Non-local competition drives both rapid divergence and prolonged stasis in a model of speciation in populations with degenerate resource consumption

The theory of speciation is dominated by adaptationist thinking, with less attention to mechanisms that do not affect species adaptation. Degeneracy – the imperfect specificity of interactions between diverse elements of biological systems and their environments – is key to the adaptability of populations. A mathematical model was explored in which population and resource were distributed one-dimensionally according to trait value. Resource consumption was degenerate – neither strictly location-specific nor location-independent. As a result, the competition for resources among the elements of the population was non-local. Two modeling approaches, a modified differential-integral Verhulstian equation and a cellular automata model, showed similar results: narrower degeneracy led to divergent dynamics with suppression of intermediate forms, whereas broader degeneracy led to suppression of diversifying forms, resulting in population stasis with increasing phenotypic homogeneity. Such behaviors did not increase overall adaptation because they continued after the model populations achieved maximal resource consumption rates, suggesting that degeneracy-driven distributed competition for resources rather than selective pressure toward more efficient resource exploitation was the driving force. The solutions were stable in the presence of limited environmental stochastic variability or heritable phenotypic variability. A conclusion was made that both dynamic diversification and static homogeneity of populations may be outcomes of the same process – distributed competition for resource not affecting the overall adaptation – with the difference between them defined by the spread of trait degeneracy in a given environment. Thus, biological degeneracy is a driving force of both speciation and stasis in biology, which, by themselves, are not necessarily adaptive in nature.     

Where am I and why? Synthesizing range biology and the eco‐evolutionary dynamics of dispersal

Although generations of researchers have studied the factors that limit the distributions of species, we still do not seem to understand this phenomenon comprehensively. Traditionally, species’ ranges have been seen as the consequence of abiotic conditions and local adaptation to the environment. However, during the last years it has become more and more evident that biotic factors – such as intra‐ and interspecific interactions or the dispersal capacity of species – and even rapidly occurring evolutionary processes can strongly influence the range of a species and its potential to spread to new habitats. Relevant eco‐evolutionary forces can be found at all hierarchical levels: from landscapes to communities via populations, individuals and genes. We here use the metapopulation concept to develop a framework that allows us to synthesize this broad spectrum of different factors. Since species’ ranges are the result of a dynamic equilibrium of colonization and local extinction events, the importance of dispersal is immediately clear. We highlight the complex interrelations and feedbacks between ecological and evolutionary forces that shape dispersal and result in non‐trivial and partially counter‐intuitive range dynamics. Our concept synthesizes current knowledge on range biology and the eco‐evolutionary dynamics of dispersal. Synthesis What factors are responsible for the dynamics of species' ranges? Answering this question has never been more important than today, in the light of rapid environmental changes. Surprisingly, the ecological and evolutionary dynamics of dispersal – which represent the driving forces behind range formation – have rarely been considered in this context. We here present a framework that closes this gap. Dispersal evolution may be responsible for highly complex and non‐trivial range dynamics. In order to understand these, and possibly provide projections of future range positions, it is crucial to take the ecological and evolutionary dynamics of dispersal into account.     

Population size and identity influence the reaction norm of the rare,endemic plant Cochlearia bavarica across a gradient of environmental stress

Habitat degradation and loss can result in population decline and genetic erosion, limiting the ability of organisms to cope with environmental change, whether this is through evolutionary genetic response (requiring genetic variation) or through phenotypic plasticity (i.e., the ability of a given genotype to express a variable phenotype across environments). Here we address the question whether plants from small populations are less plastic or more susceptible to environmental stress than plants from large populations. We collected seed families from small (<100) versus large natural populations (>1,000 flowering plants) of the rare, endemic plant Cochlearia bavarica (Brassicaceae). We exposed the seedlings to a range of environments, created by manipulating water supply and light intensity in a 2 x 2 factorial design in the greenhouse. We monitored plant growth and survival for 300 days. Significant effects of offspring environment on offspring characters demonstrated that there is phenotypic plasticity in the responses to environmental stress in this species. Significant effects of population size group, but mainly of population identity within the population size groups, and of maternal plant identity within populations indicated variation due to genetic (plus potentially maternal) variation for offspring traits. The environment x maternal plant identity interaction was rarely significant, providing little evidence for genetically- (plus potentially maternally-) based variation in plasticity within populations. However, significant environment x population-size-group and environment x population-identity interactions suggested that populations differed in the amount of plasticity, the mean amount being smaller in small populations than in large populations. Whereas on day 210 the differences between small and large populations were largest in the environment in which plants grew biggest (i.e., under benign conditions), on day 270 the difference was largest in stressful environments. These results show that population size and population identity can affect growth and survival differently across environmental stress gradients. Moreover, these effects can themselves be modified by time-dependent variation in the interaction between plants and their environment.     

Darwinian selection leads to Gaia

The Gaia hypothesis, in its strongest form, states that the Earth's atmosphere, oceans, and biota form a tightly coupled system that maintains environmental conditions close to optimal for life. According to Gaia theory, optimal conditions are intrinsic, immutable properties of living organisms. It is assumed that the role of Darwinian selection is to favor organisms that act to stabilize environmental conditions at these optimal levels. In this paper, an alternative form of Gaia theory based on more traditional Darwinian principles is proposed. In the new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions. A simple Daisyworld model is used to illustrate this convergence phenomenon. Sensitivity analysis of the Daisyworld model suggests that in stable ecosystems, the convergence of equilibrium and optimal conditions is inevitable, provided there are no externally driven shocks to the system. The end result may appear to be the product of a cooperative venture, but is in fact the outcome of Darwinian selection acting upon "selfish" organisms.     

Non‐equilibrium in plant distribution models – only an issue for introduced or dispersal limited species?

Species distribution models rely on the assumption that species' distributions are at equilibrium with environmental conditions within a region – i.e. they occur in all suitable habitats. If this assumption holds, species occurrence should be predictable from measures of the environment. Introduced species may be poor candidates for distribution models due to their presumed lack of equilibrium within the landscapes they occupy, although predicting their potential distributions is often of critical importance to natural resource managers. We determined if the accuracy of species distribution models differed between 17 native and 17 introduced riparian plant species in the western United States. We also assessed if model accuracy was associated with both environmental and biological factors that can influence dispersal. We used Random Forests to model species distributions and linear regression to determine if model accuracy was associated with dispersal‐related traits. Model accuracy for introduced species was higher than that for native species. Dispersal‐related traits did not affect model accuracy or improvement, though two other traits, family affiliation and rarity on the landscape, did have an effect. Distance‐based measures of dispersal potential improved model fit equally for both native and introduced species and for species with a variety of dispersal traits, suggesting that the importance of regional propagule pressure is relatively constant across species with different dispersal opportunities. Several lines of future questioning are suggested by our results, including why introduced species may in some cases produce more accurate distribution models than native species and how species dispersal traits relate to distribution model accuracy at different spatial scales.     

MALADAPTATION AS A SOURCE OF SENESCENCE IN HABITATS VARIABLE IN SPACE AND TIME

In this study, we use a quantitative genetics model of structured populations to investigate the evolution of senescence in a variable environment. Adaptation to local environments depends on phenotypic traits whose optimal values vary with age and with environmental conditions. We study different scenarios of environmental heterogeneity, where the environment changes abruptly, gradually, or cyclically with time and where the environment is heterogeneous in space with different populations connected by migration. The strength of selection decreases with age, which predicts slower adaptation of traits expressed late in the life cycle, potentially generating stronger senescence in habitats where selection changes in space or in time. This prediction is however complicated by the fact that the genetic variance also increases with age. Using numerical calculations, we found that the rate of senescence is generally increased when the environment varies. In particular, migration between different habitats is a source of senescence in heterogeneous landscapes. We also show that the rate of senescence can vary transiently when the population is not at equilibrium, with possible implications for experimental evolution and the study of invasive species. Our results highlight the need to study age‐specific adaptation, as a changing environment can have a different impact on different age classes.     

Population characteristics predict responses in moose body mass to temporal variation in the environment

1. A general problem in population ecology is to predict under which conditions stochastic variation in the environment has the stronger effect on ecological processes. By analysing temporal variation in a fitness-related trait, body mass, in 21 Norwegian moose Alces alces (L.) populations, we examined whether the influence of temporal variation in different environmental variables were related to different parameters that were assumed to reflect important characteristics of the fundamental niche space of the moose. 2. Body mass during autumn was positively related to early access to fresh vegetation in spring, and to variables reflecting slow phenological development (low June temperature, a long spring with a slow plant progression during spring). In contrast, variables related to food quantity and winter conditions had only a minor influence on temporal variation in body mass. 3. The magnitude of the effects of environmental variation on body mass was larger in populations with small mean body mass or living at higher densities than in populations with large-sized individuals or living at lower densities. 4. These results indicate that the strongest influence of environmental stochasticity on moose body mass occurs towards the borders of the fundamental niche space, and suggests that populations living under good environmental conditions are partly buffered against fluctuations in environmental conditions.     

Environmental change,mutational load and the advantage of sexual reproduction

There is evidence that asexual reproduction has a long-term disadvantage when compared to sexual reproduction. This disadvantage is usually assumed to arise from the more efficient incorporation of advantageous mutations by sexual populations. We consider here the effect on asexual and sexual populations of changes in the fitness of harmful mutations. It is shown that the re-establishment of equilibrium following environmental change is generally faster in sexual populations, and that the mutational load experienced by the sexual population can be significantly less during this period than that experienced by an asexual one. Changes in the fitness of harmful mutations may therefore impose a greater long-term disadvantage on asexual populations than those which are sexual.     

Natural selection drives parallel divergence in the mountain plant Heliosperma pusillum s.l

The evolution of species or ecotypes can occur gradually through neutral and adaptive genetic changes. To explore the influence of natural selection during early phases of divergence, morphological and ecological discontinuity and its adaptive significance were investigated in six pairs of alpine and independently evolved montane populations of Heliosperma pusillum s.l.; the latter are usually taxonomically recognised at the species rank in spite of their highly debatable taxonomic value. We tested whether environmental conditions – characterised by Landolt indicator values from vegetation surveys and temperature measurements – and morphology of alpine and montane populations differ discretely and in parallel across six population pairs. By reciprocal transplantation experiments in natural environments in two population pairs and in climate chambers for five population pairs we compared fitness of native versus non‐native individuals. Alpine and montane populations differed in environmental conditions and morphology within each pair. Morphological differentiation occurred in parallel and correlated with environmental, but not with genetic distances. In both environments, native individuals had higher establishment success and plant size. Differentiation of the independently evolved montane populations is driven by natural selection and parallel, independent adaptation in response to drought, lower irradiance and higher, less fluctuating temperatures in montane populations. Our study system exemplifies rapid, parallel evolution leading to morphologically and ecologically strongly divergent, though fully interfertile, ecotypes.     

Population of origin and environment interact to determine oomycete infections in spotted salamander populations

Spatial variation in disease risk in wild populations can depend both on environmental and genetic factors. Understanding the various contributions of each factor requires experimental manipulation of both the environment and genetic composition of populations under natural field conditions. We first examined natural patterns of oomycete composition and infection in the eggs of 13 populations of the spotted salamander Ambystoma maculatum. We then performed a fully factorial field transplant of the eggs of six populations to separate the contributions from population of origin and the environment on oomycete resistance in spotted salamanders. Among wild ponds, we found strong variation in oomycete infections in spotted salamander populations and differences in the composition of oomycete communities. In transplant experiments, salamander populations differed in their resistance to oomycete infections via a significant interaction between population of origin and environment. However, not all populations were locally adapted to local conditions. One population was significantly adapted to its home environment, and another one was significantly maladapted. These population effects could originate from differential adaptation of salamander populations to local oomycete communities or environmental conditions that mediate resistance, local adaptation and maladaptation of oomycetes to hosts, or from maternal transmission. Accounting for both environment and population of origin will often be necessary to understand disease dynamics in wild populations.     

Environmental dependence of inbreeding depression and purging in Drosophila melanogaster

Elimination or reduction of inbreeding depression by natural selection at the contributing loci (purging) has been hypothesized to effectively mitigate the negative effects of inbreeding in small isolated populations. This may, however, only be valid when the environmental conditions are relatively constant. We tested this assumption using Drosophila melanogaster as a model organism. By means of chromosome balancers, chromosomes were sampled from a wild population and their viability was estimated in both homozygous and heterozygous conditions in a favourable environment. Around 50% of the chromosomes were found to carry a lethal or sublethal mutation, which upon inbreeding would cause a considerable amount of inbreeding depression. These detrimentals were artificially purged by selecting only chromosomes that in homozygous condition had a viability comparable to that of the heterozygotes (quasi-normals), thereby removing most deleterious recessive alleles. Next, these quasi-normals were tested both for egg-to-adult viability and for total fitness under different environmental stress conditions: high-temperature stress, DDT stress, ethanol stress, and crowding. Under these altered stressful conditions, particularly for high temperature and DDT, novel recessive deleterious effects were expressed that were not apparent under control conditions. Some of these chromosomes were even found to carry lethal or near-lethal mutations under stress. Compared with heterozygotes, homozygotes showed on average 25% additional reduction in total fitness. Our results show that, except for mutations that affect fitness under all environmental conditions, inbreeding depression may be due to different loci in different environments. Hence purging of deleterious recessive alleles can be effective only for the particular environment in which the purging occurred, because additional load will become expressed under changing environmental conditions. These results not only indicate that inbreeding depression is environment dependent, but also that inbreeding depression may become more severe under changing stressful conditions. These observations have significant consequences for conservation biology.     

Social competition as a driver of phenotype–environment correlations: implications for ecology and evolution

While it is universally recognised that environmental factors can cause phenotypic trait variation via phenotypic plasticity, the extent to which causal processes operate in the reverse direction has received less consideration. In fact individuals are often active agents in determining the environments, and hence the selective regimes, they experience. There are several important mechanisms by which this can occur, including habitat selection and niche construction, that are expected to result in phenotype–environment correlations (i.e. non-random assortment of phenotypes across heterogeneous environments). Here we highlight an additional mechanism – intraspecific competition for preferred environments – that may be widespread, and has implications for phenotypic evolution that are currently underappreciated. Under this mechanism, variation among individuals in traits determining their competitive ability leads to phenotype–environment correlation; more competitive phenotypes are able to acquire better patches. Based on a concise review of the empirical evidence we argue that competition-induced phenotype–environment correlations are likely to be common in natural populations before highlighting the major implications of this for studies of natural selection and microevolution. We focus particularly on two central issues. First, competition-induced phenotype–environment correlation leads to the expectation that positive feedback loops will amplify phenotypic and fitness variation among competing individuals. As a result of being able to acquire a better environment, winners gain more resources and even better phenotypes – at the expense of losers. The distinction between individual quality and environmental quality that is commonly made by researchers in evolutionary ecology thus becomes untenable. Second, if differences among individuals in competitive ability are underpinned by heritable traits, competition results in both genotype–environment correlations and an expectation of indirect genetic effects (IGEs) on resource-dependent life-history traits. Theory tells us that these IGEs will act as (partial) constraints, reducing the amount of genetic variance available to facilitate evolutionary adaptation. Failure to recognise this will lead to systematic overestimation of the adaptive potential of populations. To understand the importance of these issues for ecological and evolutionary processes in natural populations we therefore need to identify and quantify competition-induced phenotype–environment correlations in our study systems. We conclude that both fundamental and applied research will benefit from an improved understanding of when and how social competition causes non-random distribution of phenotypes, and genotypes, across heterogeneous environments.     

Climate adaptation is not enough: warming does not facilitate success of southern tundra plant populations in the high Arctic

Rapidly rising temperatures are expected to cause latitudinal and elevational range shifts as species track their optimal climate north and upward. However, a lack of adaptation to environmental conditions other than climate – for example photoperiod, biotic interactions, or edaphic conditions – might limit the success of immigrants in a new location despite hospitable climatic conditions. Here, we present one of the first direct experimental tests of the hypothesis that warmer temperatures at northern latitudes will confer a fitness advantage to southern immigrants relative to native populations. As rates of warming in the Arctic are more than double the global average, understanding the impacts of warming in Arctic ecosystems is especially urgent. We established experimentally warmed and nonwarmed common garden plots at Alexandra Fiord, Ellesmere Island in the Canadian High Arctic with seeds of two forb species (Oxyria digyna and Papaver radicatum) originating from three to five populations at different latitudes across the Arctic. We found that plants from the local populations generally had higher survival and obtained a greater maximum size than foreign individuals, regardless of warming treatment. Phenological traits varied with latitude of the source population, such that southern populations demonstrated substantially delayed leaf‐out and senescence relative to northern populations. Our results suggest that environmental conditions other than temperature may influence the ability of foreign populations and species to establish at more northerly latitudes as the climate warms, potentially leading to lags in northward range shifts for some species.