Many species are experiencing sustained environmental change mainly due to human activities. The unusual rate and extent of anthropogenic alterations of the environment may exceed the capacity of developmental, genetic, and demographic mechanisms that populations have evolved to deal with environmental change. To begin to understand the limits to population persistence, we present a simple evolutionary model for the critical rate of environmental change beyond which a population must decline and go extinct. We use this model to highlight the major determinants of extinction risk in a changing environment, and identify research needs for improved predictions based on projected changes in environmental variables. Two key parameters relating the environment to population biology have not yet received sufficient attention. Phenotypic plasticity, the direct influence of environment on the development of individual phenotypes, is increasingly considered an important component of phenotypic change in the wild and should be incorporated in models of population persistence. Environmental sensitivity of selection, the change in the optimum phenotype with the environment, still crucially needs empirical assessment. We use environmental tolerance curves and other examples of ecological and evolutionary responses to climate change to illustrate how these mechanistic approaches can be developed for predictive purposes.

Global climate change, over-exploitation, and habitat alteration are causing sustained and consistent pressures on wild populations [1]. Because of habitat fragmentation, many species will not be able to track their preferred environment in space, and must therefore adapt in situ to avoid extinction. What determines the maximum rate of environmental change that populations can cope with? Understanding this will inform both models and management plans about where critical thresholds lie or what might affect the potential resilience of particular species or ecological communities.

Two main approaches exist for studying the impact of environmental change on species persistence—niche modelling and mechanistic population modelling. On the one hand, “climate envelope models” (or “niche models”) are correlative and focused on the environment. Their conceptual background traces to Hutchinson's multidimensional representation of the niche [2]. They use measurements of environmental variables and records of species presence and absence to infer abiotic correlates of the realized niche of a species. By projecting this niche on a map with environmental data, the spatial locations that satisfy the basic requirements of the species are identified. Niche models have been combined with climate projections to predict range shifts and extinction rates [3]. Aside from the methodological caveats of this approach (changing covariance of environmental variables [4], population demography not in equilibrium with changing climate [5], spatial scale of the analysis [6],[7], and source-sink dynamics allowing individuals to exist outside their niche [8]), its major drawback is that it does not account for the biological processes underlying adaptation of a species to its environment. It cannot identify or incorporate the biological differences among species that determine whether or not they can persist in situ. While a new generation of “process-based” (or “mechanistic”) niche models is being developed to overcome these limitations [9]–[11], they currently rely on simplified demographic processes and generally overlook evolution in response to climate change (but see [12]). Niche modelling is thus currently more suited to understand changes in the distribution of suitable environments for a species at a continental scale than to predict population persistence or guide conservation plans.

On the other hand, mechanistic population modelling focuses on the biological processes that underlie population persistence. By combining evolutionary genetics and demography, the conditions that allow a population to maintain a positive intrinsic growth rate in the face of environmental change can be predicted theoretically [13],[14] and studied empirically [15]. The main focus of mechanistic population studies is not environmental variables, but ecologically important phenotypic traits (morphology, physiology, phenology, or behaviour) that affect population growth through their influence on life history. In contrast to niche modelling, this approach allows identification of factors that potentially limit population persistence in a changing environment. However, unless environmental variables are included, as well as phenotypic traits, this approach cannot be used to project the fate of populations.

Here, we propose a model of evolution and population growth to address how demographic and evolutionary constraints limit the persistence of a geographically isolated population under sustained environmental change. This model generalizes an earlier one by Lynch and Lande [13] by including phenotypic plasticity (see Box 1–Glossary) and an explicit environmental variable such as temperature. We use it to highlight the determinants of extinction risk and to identify research needs for a more predictive approach to population persistence in a changing environment. Research directed towards key determinants of extinction risk that are often overlooked in current empirical work may allow population biologists to take advantage of abundant environmental data in order to begin developing predictions about population persistence under alternative scenarios of climate change [16], which can help to guide conservation policies and management plans.

There are three mechanisms by which a population can persist when its local environment changes: dispersal to track its preferred environment in space, genetic evolution to the new local conditions, or phenotypic plasticity [17],[18]. Using the model in Box 2 and Text S1, we give an overview of the determinants of extinction risk for an isolated population with a restricted geographic range under sustained environmental change, assuming dispersal is not possible. We consider cases where all other possible factors influencing extinction risk (demographic and environmental stochasticity, inbreeding depression, genetic drift [19]) can be ignored relative to the impact of sustained environmental change. The determinants of extinction risk then belong to three main classes.

(1) Demographic properties of the population. These are components of the population growth rate that are not affected by adaptation to the changing environment. They include the generation time, T, and the maximum intrinsic rate of increase r_max (per unit time) of a population with optimum mean phenotype. Even if these parameters are not affected by the environmental change, they do constrain the rate of adaptation. Populations with longer generations must evolve faster per generation to adapt to a given rate of environmental change, and populations with a low r_max will reach extinction before they can adapt to rapid environmental change [13]–[15],[20]. The specific influence of each of these variables on extinction risk across taxa also depends on their covariation. Broad-scale studies of life-history traits indicate that the per-generation intrinsic rate of increase is of the same order of magnitude across several taxa, whereas r_max per unit time is roughly inversely proportional to the generation time [21]–[23]. As a consequence, the critical rate of environmental change should be generally lower for species with longer generation times, which will be at greater extinction risk.

(2) Evolutionary potential. This measures how fast genetic evolution occurs for a given deviation of the mean phenotype from the optimum. The strength of stabilizing selection γ measures how the mean fitness decreases with the squared deviation from the optimum and also determines the strength of directional selection for a given deviation from the optimum. Stronger stabilizing selection (larger γ), although causing increased mortality, allows faster environmental change to be tolerated by causing faster evolution [13]. The genetic variance, the product of phenotypic variance σ² and heritability h², determines how much genetic evolution is caused by a given strength of selection. Higher genetic variance allows persistence under stronger environmental change, because it allows the population to track its phenotypic optimum more closely. Although we focus on a single trait for simplicity, this may actually be a linear combination of measurable traits. In this case, the genetic variances of the original traits and their genetic covariances affect the magnitude of the genetic response to selection in any phenotypic direction [24],[25].

(3) Biological impact of the environment. This links the environment to the biology of individuals in the species. Phenotypic plasticity describes the direct impact of the environment on the development of individual phenotypes. It may involve morphological, physiological or behavioural responses, which can occur on different time scales. For continuous environmental variables, plasticity usually is modelled using reaction norms, where the phenotype of a given genotype is plotted as a function of the environment [26]. We focus on linear reaction norms for simplicity, although reaction norms can be non-linear [27],[28] (see below). With linear reaction norms, the slope b quantifies the degree of plasticity. The environmental sensitivity of selection, B, measures how the optimum phenotype changes with the environment, which for simplicity we also assume is a linear relationship. With no cost of plasticity, populations with b closer to B are likely to persist under higher rates of environmental change.

This model can be combined with environmental projections to ask whether future rates of environmental change will threaten the persistence of particular populations or species. Application of the model requires multiple steps, which previously have been undertaken in isolation or in combination, although all have rarely been completed together.

A relationship between an environmental variable and a measure of selection, either observed in the wild or derived from an experiment, has been argued to be the strongest evidence for the cause of natural selection [54]. Quantification of this relationship is required to predict population evolution and persistence in a changing environment. Most of the studies highlighted above compared selective pressures among discrete environmental states, often interpreted as stresses (but see [39]). Current global change, however, mainly involves continuous environmental variables for which precise time series and projections are available. The environmental sensitivity of selection should therefore be estimated by measuring phenotypic selection along a continuous environmental gradient. Apart from measuring a fundamental parameter of the model, this would also allow its basic assumptions to be tested. In particular, our model (like previous ones) assumes that environmental change primarily alters the optimum phenotype with little impact on the width of the fitness function (Figure 1), but this assumption has hardly ever been tested empirically.

Measurement of selection in several environments may be difficult to carry out in the field because of lack of control over environmental parameters. For some species such measurements could be performed in controlled laboratory conditions, provided the relationship between fitness in the laboratory and in the wild can be established. Alternatively, performance can be measured in the laboratory and the relationship between performance and fitness assessed in the wild [55].

Studies of thermal tolerance curves in ectotherms commonly measure fitness in continuous environments. However, these studies generally relate fitness (or performance) directly to the environment, which makes it difficult to produce evolutionary predictions and to test them experimentally [56]. Modelling tolerance curves with an underlying phenotypic trait subject to natural selection and phenotypic plasticity may prove more fruitful, since it should allow predictions about the dynamics of tolerance curve evolution (Box 3).

Our model includes a number of simplifying assumptions. We assume a constant shape of the fitness function across environments, allowing only the optimum phenotype to change with the environment. However, the strength of stabilizing selection around the optimum phenotype γ may depend on the environment (Figure 1, third column, second row). Furthermore the maximum fitness r_max may generally be lower in more extreme environments because of physiological constraints, such that the ridge in Figure 1 would have an intermediate maximum. This was shown to occur in a recent comparative study of thermal tolerance curves among several insect taxa, where the maximum fitness was lower for species that had their optimum at a lower temperature [67]. Other demographic parameters including the generation time T may change with the environment. Genotype × environment interaction (or genetic variance in plasticity) can cause the genetic variance (h²σ²) to depend on the environment [68]–[71]. Although these mechanisms are not included in our simple model, they all can be analyzed theoretically and studied empirically, and should be included where they are suspected to be important.

Plasticity itself may evolve if it varies genetically, and new environments can cause directional selection on plasticity [72],[73]. However, more information is needed about plasticity and its inheritance in extreme environments before the evolution of plasticity can be included in the analysis of persistence under sustained environmental change.

Finally, we considered a population that cannot disperse nor receive migrants from other populations experiencing different environments. We focused on this situation because it is one that is most commonly overlooked in niche modelling studies. Our model thus applies best to species with habitats restricted by dispersal barriers or species which disperse slowly relative to the rate of environmental change [74]. At the other extreme, a population may be able to persist by following its preferred environment in space without any evolution, as assumed in niche modelling, but this is very unlikely for species occupying fragmented habitats. For populations that can both disperse and evolve in response to a changing environment, gene flow among populations with different environments may limit local adaptation and restrict the geographic range of the population or even cause extinction [74],[75].

Our aim was to describe an approach based on evolutionary and demographic mechanisms that can be used to make predictions on population persistence in a changing environment and to highlight the most important variables to measure. While this approach is obviously more costly and time-consuming than niche modelling, its results are also likely to be more useful for specific purposes because it explicitly incorporates the factors that limit population response to environmental change.

The feasibility of such a mechanistic approach has been demonstrated by a few recent studies. Deutsch et al. [76] used thermal tolerance curves to predict the fitness consequence of climate change for many species of terrestrial insects across latitudes, but without explicitly considering phenotypic plasticity or genetic evolution. Kearney et al. [12] combined biophysical models of energy transfers with measures of heritability of egg desiccation to predict how climate change would affect the distribution of the mosquito Aedes aegiptii in Australia. Egg desiccation was treated as a threshold trait, but the possibility of phenotypic plasticity or evolution of the threshold was not considered. These encouraging efforts call for more empirical studies where genetic evolution and phenotypic plasticity are combined with demography to make predictions about population persistence in a changing environment. The simple approach we have outlined is a necessary step towards a more specific and comprehensive understanding of the influence of environmental change on population extinction.