Avoiding extinction under nonlinear environmental change: models of evolutionary rescue with plasticity

Rapid environmental changes are putting numerous species at risk of extinction. For migration-limited species, persistence depends on either phenotypic plasticity or evolutionary adaptation (evolutionary rescue). Current theory on evolutionary rescue typically assumes linear environmental change. Yet accelerating environmental change may pose a bigger threat. Here, we present a model of a species encountering an environment with accelerating or decelerating change, to which it can adapt through evolution or phenotypic plasticity (within-generational or transgenerational). We show that unless either form of plasticity is sufficiently strong or adaptive genetic variation is sufficiently plentiful, accelerating or decelerating environmental change increases extinction risk compared to linear environmental change for the same mean rate of environmental change.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

Inbreeding–environment interactions increase extinction risk

Being able to accurately estimate the persistence time of populations of endangered plants and animals is central to conservation biology and is of considerable importance in informing land-use decisions. Genetic deterioration (due to inbreeding and random genetic drift) and environmental deterioration (e.g. climate change, pollution and introduced species) clearly contribute to population extinction, however, considerable recent evidence suggests that interactions between genetic deterioration and environmental stress are ubiquitous. The importance of these interactions for potentially reducing persistence times has not been quantified and has not been taken into account by major conservation organizations. Using a computer simulation, we determined that including reasonable estimates of the inbreeding–environment interaction reduces persistence times by 17.5–28.5% (mean=23%) for a wide range of carrying capacities, assumptions concerning the number of lethal equivalents and different regimes for the frequency and magnitude of the stressful environment. We note that the proportional decrease in persistence time with inclusion of the interactions becomes larger (i.e. the interaction becomes more important) as absolute time to extinction gets larger. Thus, inclusion of the interaction is important and surprisingly may be most needed when populations are of intermediate size and are considered relatively safe from environmental and genetic stresses acting independently.     

Sex‐specific selection under environmental stress in seed beetles

Sexual selection can increase rates of adaptation by imposing strong selection in males, thereby allowing efficient purging of the mutation load on population fitness at a low demographic cost. Indeed, sexual selection tends to be male‐biased throughout the animal kingdom, but little empirical work has explored the ecological sensitivity of this sex difference. In this study, we generated theoretical predictions of sex‐specific strengths of selection, environmental sensitivities and genotype‐by‐environment interactions and tested them in seed beetles by manipulating either larval host plant or rearing temperature. Using fourteen isofemale lines, we measured sex‐specific reductions in fitness components, genotype‐by‐environment interactions and the strength of selection (variance in fitness) in the juvenile and adult stage. As predicted, variance in fitness increased with stress, was consistently greater in males than females for adult reproductive success (implying strong sexual selection), but was similar in the sexes in terms of juvenile survival across all levels of stress. Although genetic variance in fitness increased in magnitude under severe stress, heritability decreased and particularly so in males. Moreover, genotype‐by‐environment interactions for fitness were common but specific to the type of stress, sex and life stage, suggesting that new environments may change the relative alignment and strength of selection in males and females. Our study thus exemplifies how environmental stress can influence the relative forces of natural and sexual selection, as well as concomitant changes in genetic variance in fitness, which are predicted to have consequences for rates of adaptation in sexual populations.     

Mating patterns influence vulnerability to the extinction vortex

Earth's biodiversity is undergoing mass extinction due to anthropogenic compounding of environmental, demographic and genetic stresses. These different stresses can trap populations within a reinforcing feedback loop known as the extinction vortex, in which synergistic pressures build upon one another through time, driving down population viability. Sexual selection, the widespread evolutionary force arising from competition, choice and reproductive variance within animal mating patterns could have vital consequences for population viability and the extinction vortex: (a) if sexual selection reinforces natural selection to fix ‘good genes’ and purge ‘bad genes’, then mating patterns encouraging competition and choice may help protect populations from extinction; (b) by contrast, if mating patterns create load through evolutionary or ecological conflict, then population viability could be further reduced by sexual selection. We test between these opposing theories using replicate populations of the model insect Tribolium castaneum exposed to over 10 years of experimental evolution under monogamous versus polyandrous mating patterns. After a 95‐generation history of divergence in sexual selection, we compared fitness and extinction of monogamous versus polyandrous populations through an experimental extinction vortex comprising 15 generations of cycling environmental and genetic stresses. Results showed that lineages from monogamous evolutionary backgrounds, with limited opportunities for sexual selection, showed rapid declines in fitness and complete extinction through the vortex. By contrast, fitness of populations from the history of polyandry, with stronger opportunities for sexual selection, declined slowly, with 60% of populations surviving by the study end. The three vortex stresses of (a) nutritional deprivation, (b) thermal stress and (c) genetic bottlenecking had similar impacts on fitness declines and extinction risk, with an overall sigmoid decline in survival through time. We therefore reveal sexual selection as an important force behind lineages facing extinction threats, identifying the relevance of natural mating patterns for conservation management.     

Evolutionary rescue under demographic and environmental stochasticity

Populations suffer two types of stochasticity: demographic stochasticity, from sampling error in offspring number, and environmental stochasticity, from temporal variation in the growth rate. By modelling evolution through phenotypic selection following an abrupt environmental change, we investigate how genetic and demographic dynamics, as well as effects on population survival of the genetic variance and of the strength of stabilizing selection, differ under the two types of stochasticity. We show that population survival probability declines sharply with stronger stabilizing selection under demographic stochasticity, but declines more continuously when environmental stochasticity is strengthened. However, the genetic variance that confers the highest population survival probability differs little under demographic and environmental stochasticity. Since the influence of demographic stochasticity is stronger when population size is smaller, a slow initial decline of genetic variance, which allows quicker evolution, is important for population persistence. In contrast, the influence of environmental stochasticity is population-size-independent, so higher initial fitness becomes important for survival under strong environmental stochasticity. The two types of stochasticity interact in a more than multiplicative way in reducing the population survival probability. Our work suggests the importance of explicitly distinguishing and measuring the forms of stochasticity during evolutionary rescue.     

Measurement error and estimates of population extinction risk

It is common to estimate the extinction probability for a vulnerable population using methods that are based on the mean and variance of the long‐term population growth rate. The numerical values of these two parameters are estimated from time series of population censuses. However, the proportion of a population that is registered at each census is typically not constant but will vary among years because of stochastic factors such as weather conditions at the time of sampling. Here, we analyse how such sampling errors influence estimates of extinction risk and find sampling errors to produce two opposite effects. Measurement errors lead to an exaggerated overall variance, but also introduce negative autocorrelations in the time series (which means that estimates of annual growth rates tend to alternate in size). If time series data are treated properly these two effects exactly counter balance. We advocate routinely incorporating a measure of among year correlations in estimating population extinction risk.     

Inbreeding and extinction: The effect of environmental stress and lineage

Human activities are simultaneously decreasing the size of wildlife populations (causing inbreeding) and increasing the level of stress that wildlife populations must face. Inbreeding reduces population fitness and increases extinction risk. However, very little information on the impact of stressful environments on extinction risk under inbreeding is available. We evaluated the impact of full sib inbreeding on extinction risk, using Drosophila melanogaster, in a benign and three stressful environments. The three stressful environments involved the addition to the medium of copper sulfate, methanol or alternating copper sulfate and methanol. There were 128 replicate populations for each of the four treatments. Under inbreeding, extinction rates were significantly higher in all three stressful environments compared with the benign environment. The percent extinct at generation eight (F = 0.826) for the four treatments were: 62.5% in the benign environment, 75.8%in the copper sulfate environment, 82.8% in the methanol environment, and 83.6% in the variable stress environment. However, the extinction rate in the variable stress environment did not differ significantly from the constant stress environments. Highly significant differences, among lineages, in extinction risk were detected. The results of this study indicate that wild populations are more vulnerable to inbreeding than indicated by extrapolation from captive environments.     

Effects of environmental variation on extinction and establishment

Theoretical models predict that increasing environmental variation increases the probability of extinction, decreases the probability of establishment, and influences the distribution of times to extinction or establishment. We conducted an experiment with 281 independent populations of Daphnia magna under controlled laboratory conditions to test these predictions. Consistent with the theory, the fraction of populations going extinct increased and the fraction of populations establishing self‐sustaining populations decreased under higher levels of environmental variation compared with controls. Time to extinction decreased under higher levels of environmental variation, but we found no effect on time to establishment. These results are consistent with theoretical predictions from models of extinction. They therefore support the use of stochastic population models to predict the fates of introductions of non‐indigenous species or native endangered species based on historic fluctuations and/or expected future conditions.     

Peak shifts and extinction under sex-specific selection

A well-known property of sexual selection combined with a cross-sex genetic correlation (r_mf) is that it can facilitate a peak shift on the adaptive landscape. How do these diversifying effects of sexual selection + r_mf balance with the constraints imposed by such sexual antagonism, to affect the macroevolution of sexual dimorphism? Here, I extend existing quantitative genetic models of evolution on complex adaptive landscapes. Beyond recovering classical predictions for the conditions promoting a peak shift, I show that when r_mf is moderate to strong, relatively weak sexual selection is required to induce a peak shift in males only. Increasing the strength of sexual selection leads to a sexually concordant peak shift, suggesting that macroevolutionary rates of sexual dimorphism may be largely decoupled from the strength of within-population sexual selection. Accounting explicitly for demography further reveals that sex-specific peak shifts may be more likely to be successful than concordant shifts in the face of extinction, especially when natural selection is strong. An overarching conclusion is that macroevolutionary patterns of sexual dimorphism are unlikely to be readily explained by within-population estimates of selection or constraint alone.     

Estimate of population extinction risk and its application to ecological risk management

Environmental threats, such as habitat size reduction or environmental pollution, may not cause immediate extinction of a population but may shorten the expected time to extinction. We developed a method to estimate the mean time to extinction for a density-dependent population with environmental fluctuation and to compare the impacts of different risk factors. We first derived a formula of the mean extinction time for a population with logistic growth and environmental and demographic stochasticities expressed as a stochastic differential equation model (canonical model). The relative importance of different risk factors is evaluated by the decrease in the mean extinction time. We studied an approximated formula for the reduction in habitat size that enhances extinction risk by the same magnitude as a given decrease in survivorship caused by toxic chemical exposure. In a large population (large K) or in a slowly growing population (small r), a small decrease in survivorship can cause the extinction risk to increase, corresponding to a significant reduction in the habitat size. Finally, we studied an approximate maximum likelihood estimate of three parameters (intrinsic growth rate r, carrying capacity K, and environmental stochasticity σ ² _e ) from time series data. By Monte Carlo sampling, we can remove the bias very effectively and determine the confidence interval. We discuss here how the reliability of the estimate changes with the length of time series. If we know the intrinsic rate of population growth r, the mean extinction time is estimated quite accurately even when only a short time series is available for parameter estimation. Received: March 31, 1999 / Accepted: November 9, 1999     

Linear analysis solves two puzzles in population dynamics: the route to extinction and extinction in coloured environments

In this paper, we give simple explanations to two unsolved puzzles that have emerged in recent theoretical studies in population dynamics. First, the tendency of some model populations to go extinct from high population densities, and second, the positive effect of autocorrelated environments on extinction risks for some model populations. Both phenomena are given general explanations by simple, linear, sto-chastic models. We emphasize the predictive and explanatory power of such models.     

Phylogenetic,spatial and environmental components of extinction risk in carnivores

Aim Extinction risk is non‐randomly distributed across phylogeny and space and is influenced by environmental conditions. We quantified the relative contribution of these factors to extinction risk to unveil the underlying macroecological processes and derive predictive models. Location Global. Methods Based on the IUCN global assessments, we divided 192 carnivore species into two dichotomous classes representing different levels of extinction risk. We used spatial proximity, phylogenetic relationship and environmental variables together with phylogenetic eigenvector regression and spatial eigenvector filters to model and predict threat status. Results Our full models explained between 57% and 96% of the variance in extinction risk. Phylogeny and spatial proximity roughly explained between 21% and 70% of the total variation in all analyses, while the explanatory power of environmental conditions was relatively weaker (up to 15%). Phylogeny and spatial proximity contributed equally to the explained variance in the lower threat level, while spatial proximity was the most important factor in the models of the higher threat level. Prediction of threat status achieved 97% correct assignments. Main conclusions Our approach differs fundamentally from current studies of extinction risk because it does not necessarily rely on life‐history information. We clearly show that instead of treating phylogenetic inertia and spatial signal as statistical nuisances, space and phylogeny should be viewed as very useful in explaining a wide range of phenomena in comparative studies.     

Minimum viable population sizes and global extinction risk are unrelated

Theoretical and empirical work has shown that once reduced in size and geographical range, species face a considerably elevated risk of extinction. We predict minimum viable population sizes (MVP) for 1198 species based on long-term time-series data and model-averaged population dynamics simulations. The median MVP estimate was 1377 individuals (90% probability of persistence over 100 years) but the overall distribution was wide and strongly positively skewed. Factors commonly cited as correlating with extinction risk failed to predict MVP but were able to predict successfully the probability of World Conservation Union Listing. MVPs were most strongly related to local environmental variation rather than a species' intrinsic ecological and life history attributes. Further, the large variation in MVP across species is unrelated to (or at least dwarfed by) the anthropogenic threats that drive the global biodiversity crisis by causing once-abundant species to decline.     

Sex‐specific effects of inbreeding in wild‐caught Drosophila melanogaster under benign and stressful conditions

In animal populations, sib mating is often the primary source of inbreeding depression (ID). We used recently wild‐caught Drosophila melanogaster to test whether such ID is amplified by environmental stress and, in males, by sexual selection. We also investigated whether increased ID because of stress (increased larval competition) persisted beyond the stressed stage and whether the effects of stress and sexual selection interacted. Sib mating resulted in substantial cumulative fitness losses (egg to adult reproduction) of 50% (benign) and 73% (stressed). Stress increased ID during the larval period (23% vs. 63%), but not during post‐stress reproductive stages (36% vs. 31%), indicating larval stress may have purged some adult genetic load (although ID was uncorrelated across stages). Sexual selection exacerbated inbreeding depression, with inbred male offspring suffering a higher reproductive cost than females, independent of stress (57% vs. 14% benign, 49% vs. 11% stress).     

Genes under weaker stabilizing selection increase network evolvability and rapid regulatory adaptation to an environmental shift

Regulatory networks play a central role in the modulation of gene expression, the control of cellular differentiation, and the emergence of complex phenotypes. Regulatory networks could constrain or facilitate evolutionary adaptation in gene expression levels. Here, we model the adaptation of regulatory networks and gene expression levels to a shift in the environment that alters the optimal expression level of a single gene. Our analyses show signatures of natural selection on regulatory networks that both constrain and facilitate rapid evolution of gene expression level towards new optima. The analyses are interpreted from the standpoint of neutral expectations and illustrate the challenge to making inferences about network adaptation. Furthermore, we examine the consequence of variable stabilizing selection across genes on the strength and direction of interactions in regulatory networks and in their subsequent adaptation. We observe that directional selection on a highly constrained gene previously under strong stabilizing selection was more efficient when the gene was embedded within a network of partners under relaxed stabilizing selection pressure. The observation leads to the expectation that evolutionarily resilient regulatory networks will contain optimal ratios of genes whose expression is under weak and strong stabilizing selection. Altogether, our results suggest that the variable strengths of stabilizing selection across genes within regulatory networks might itself contribute to the long‐term adaptation of complex phenotypes.     

The consequences of polyandry for population viability,extinction risk and conservation

Polyandry, by elevating sexual conflict and selecting for reduced male care relative to monandry, may exacerbate the cost of sex and thereby seriously impact population fitness. On the other hand, polyandry has a number of possible population-level benefits over monandry, such as increased sexual selection leading to faster adaptation and a reduced mutation load. Here, we review existing information on how female fitness evolves under polyandry and how this influences population dynamics. In balance, it is far from clear whether polyandry has a net positive or negative effect on female fitness, but we also stress that its effects on individuals may not have visible demographic consequences. In populations that produce many more offspring than can possibly survive and breed, offspring gained or lost as a result of polyandry may not affect population size. Such ecological ‘masking’ of changes in population fitness could hide a response that only manifests under adverse environmental conditions (e.g. anthropogenic change). Surprisingly few studies have attempted to link mating system variation to population dynamics, and in general we urge researchers to consider the ecological consequences of evolutionary processes.     

Assortative Mating and Fertility in two Drosophila subobscura Strains with different Mitochondrial DNA Haplotypes

The mating pattern and female fertility on the two main mitochondrial DNA haplotypes (I and II) of Drosophila subobscura were studied, in an attempt to find possible differences between them in relation to sexual selection or isolation that could explain the populational dynamics and the co-existence of these two strains in nature. The mating pattern indicated an assortative mating in population cages, where couples of the same haplotype, mainly those of haplotype I, mated more often. However, the significations detected in laboratory conditions disappeared in wild populations, where random mating was the rule. The female fertility also showed differences in the laboratory compared to the wild, since couples with haplotype I males were more efficient in the laboratory populations. These results, together with others that we previously obtained, either point to selection acting directly on the mtDNA or to the presence of some kind of cytonuclear co-adaptation in these two haplotypes, although this must be modulated by other factors that change with the seasons and time. The end result could well be a balance of opposite forces acting on both haplotypes.