Autocorrelated environmental variation and the establishment of invasive species

Environmental parameters such as temperature and rainfall have a positively autocorrelated variance structure which makes it likely that runs of good or bad conditions will occur. It has previously been demonstrated that such autocorrelated environmental variance can increase the probability of extinction in small populations, in much the same way that increased variance without autocorrelation can increase extinction risk. As a result, it has also been suggested that positive autocorrelation will decrease the probability that a species will establish in a novel location. We suggest that describing the probability of invasion success as the probability of indefinite persistence may be an inappropriate definition of risk. Economic or ecological damage may be associated with a population that initially reaches high densities before going extinct in the new location. In addition, such populations may spread to new locations before extirpation. We use a modeling approach to examine the effect of positively autocorrelated conditions on the probability that small populations will reach large size before extinction. We find that where variance is high and the geometric mean of the population growth rate is low, autocorrelation increases the risk that a population will pass a an upper threshold density, even when extinction probability is unaffected. Therefore species classified as having low probability of invasion risk on the basis of population growth rates measured in low variance environments may actually have quite a substantial probability of establishing a large population for a period of time. The mechanism behind the effect is the disproportionate influence of short runs of good conditions initially following introduction.     

The effect of selection history on extinction risk during severe environmental change

Environments rarely remain the same over time, and populations are therefore frequently at risk of going extinct when changes are significant enough to reduce fitness. Although many studies have investigated what attributes of the new environments and of the populations experiencing these changes will affect their probability of going extinct, limited work has been directed towards determining the role of population history on the probability of going extinct during severe environmental change. Here, we compare the extinction risk of populations with a history of selection in a benign environment, to populations with a history of selection in one or two stressful environments. We exposed spores and lines of the green alga Chlamydomonas reinhardtii from these three different histories to a range of severe environmental changes. We found that the extinction risk was higher for populations with a history of selection in stressful environments compared to populations with a history of selection in a benign environment. This effect was not due to differences in initial population sizes. Finally, the rates of extinction were highly repeatable within histories, indicating strong historical contingency of extinction risk. Hence, information on the selection history of a population can be used to predict their probability of going extinct during environmental change.     

Temporal autocorrelation in host density increases establishment success of parasitoids in an experimental system

Environmental variation is classically expected to affect negatively population growth and to increase extinction risk, and it has been identified as a major determinant of establishment failures in the field. Yet, recent theoretical investigations have shown that the structure of environmental variation and more precisely the presence of positive temporal autocorrelation might alter this prediction. This is particularly likely to affect the establishment dynamics of biological control agents in the field, as host–parasitoid interactions are expected to induce temporal autocorrelation in host abundance. In the case where parasitoid populations display overcompensatory dynamics, the presence of such positive temporal autocorrelation should increase their establishment success in a variable environment. We tested this prediction in laboratory microcosms by introducing parasitoids to hosts whose abundances were manipulated to simulate uncorrelated or positively autocorrelated variations in carrying capacity. We found that environmental variability decreased population size and increased parasitoid population variance, which is classically expected to extinction risk. However, although exposed to significant environmental variation, we found that parasitoid populations experiencing positive temporal autocorrelation in host abundance were more likely to persist than populations exposed to uncorrelated variation. These results confirm that environmental variation is a key determinant of extinction dynamics that can have counterintuitive effects depending on its autocorrelation structure.     

An updated perspective on the role of environmental autocorrelation in animal populations

Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study, we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.     

Extinction dynamics and the regional persistence of a tree frog metapopulation

The concept of a metapopulation acknowledges local extinctions as a natural part of the dynamics of a patchily distributed population. However, if extinctions are not balanced by recolonizations or if there is a high degree of spatial synchrony of local extinctions, this poses a threat to and will reduce the metapopulation persistence time. Here we show that, in a metapopulation network of 378 pond patches used by the tree frog (Hyla arborea), even though extinctions are frequent (mean extinction probability p(e) = 0.24) they pose no threat to the metapopulation as they are balanced by recolonizations (p(c) = 0.33). In any one year there was a pattern of large populations tending to persist while small populations became extinct. The total number of individuals belonging to populations that went extinct was small (< 5%) compared with those populations that persisted. A spatial autocorrelation analysis indicated no clustering of local extinctions. The tree frog metapopulation studied consisted of a set of larger, persistent populations mixed with smaller populations characterized by high turnover dynamics.     

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.     

Environmental fluctuations promote intraspecific diversity and population persistence via inflationary effects

The impact of temporal variation in the environment, specifically the amount of temporal autocorrelation, on population processes is of growing interest in ecology and evolutionary biology. It was recently discovered that temporal autocorrelation in the environment can significantly increase the abundance of populations that would otherwise have low, or even negative long‐term growth rates (via so‐called ‘inflationary effects’), provided that immigration from another source prevents extinction. Here we use a mathematical model to ask whether inflationary effects can also increase population persistence without immigration if different phenotypes within that population partition growth over time and buffer each other from extinction via mutation. Using a combination of analytical and numerical methods, we find that environmental autocorrelation can inflate the abundance of phenotypes that would otherwise be excluded from the population, provided that phenotypes are sufficiently different in their use of the environment. This inflation of abundance at the phenotypic level also generates an inflation of abundance at the population level. Remarkably, intraspecific inflationary effects can increase both phenotypic and whole population abundance even if one or all phenotypes are maladapted to the environment, as long as mutations prevent phenotypic extinction during periods of poor environmental conditions. Given the prevalence of temporally autocorrelated environmental variables in nature, intraspecific inflationary effects have the potential to be of widespread importance for population persistence as well as the maintenance of intraspecific diversity.     

Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

Trophic interactions affect the population dynamics and risk of extinction of basal species in food webs

This paper addresses effects of trophic complexity on basal species, in a Lotka–Volterra model with stochasticity. We use simple food web modules, with three trophic levels, and expose every species to random environmental stochasticity and analyze (1) the effect of the position of strong trophic interactions on temporal fluctuations in basal species’ abundances and (2) the relationship between fluctuation patterns and extinction risk. First, the numerical simulations showed that basal species do not simply track the environment, i.e. species dynamics do not simply mirror the characteristics of the applied environmental stochasticity. Second, the extinction risk of species was related to the fluctuation patterns of the species.More specifically, we show (i) that despite being forced by random stochasticity without temporal autocorrelation (i.e. white noise), there is significant temporal autocorrelation in the time series of all basal species’ abundances (i.e. the spectra of basal species are red-shifted), (ii) the degree of temporal autocorrelation in basal species time series is affected by food web structure and (iii) the degree of temporal autocorrelation tend to be correlated to the extinction risks of basal species.Our results emphasize the role of food web structure and species interactions in modifying the response of species to environmental variability. To shed some light on the mechanisms we compare the observed pattern in abundances of basal species with analytically predicted patterns and show that the change in the predicted pattern due to the addition of strong trophic interactions is correlated to the extinction risk of the basal species. We conclude that much remain to be understood about the mechanisms behind the interaction among environmental variability, species interactions, population dynamics and vulnerability before we quantitatively can predict, for example, effects of climate change on species and ecological communities. Here, however, we point out a new possible approach for identifying species that are vulnerable to environmental stochasticity by checking the degree of temporal autocorrelation in the time series of species. Increased autocorrelation in population fluctuations can be an indication of increased extinction risk.     

Mating system affects population performance and extinction risk under environmental challenge

Failure of organisms to adapt to sudden environmental changes may lead to extinction. The type of mating system, by affecting fertility and the strength of sexual selection, may have a major impact on a population''s chances to adapt and survive. Here, we use experimental evolution in bulb mites (Rhizoglyphus robini) to examine the effects of the mating system on population performance under environmental change. We demonstrate that populations in which monogamy was enforced suffered a dramatic fitness decline when evolving at an increased temperature, whereas the negative effects of change in a thermal environment were alleviated in polygamous populations. Strikingly, within 17 generations, all monogamous populations experiencing higher temperature went extinct, whereas all polygamous populations survived. Our results show that the mating system may have dramatic effects on the risk of extinction under environmental change.     

Incorporating the temporal autocorrelation of demographic rates into structured population models

Population dynamics are typically temporally autocorrelated: population sizes are positively or negatively correlated with past population sizes. Previous studies have found that positive temporal autocorrelation increases the risk of extinction due to ‘inertia’ that prolongs downward fluctuations in population size. However, temporal autocorrelation has not yet been analyzed at the level of life cycle transitions. We developed an R package, colorednoise, which creates stochastic matrix population projections with distinct temporal autocorrelation values for each matrix element. We used it to analyze long-term demographic data on 25 populations from the COMADRE and COMPADRE databases and simulate their stochastic dynamics. We found a broad range of temporal autocorrelation across species, populations and life cycle stages. The number of stage-classes in the matrix strongly affected the temporal autocorrelation of the growth rate. In the plant populations, reproduction transitions had more negative temporal autocorrelation than survival transitions, and matrices dominated by positive temporal autocorrelation had higher extinction risk, while in animal populations transition type was not associated with noise color. Our results indicate that temporal autocorrelation varies across life cycle transitions, even among populations of the same species. We present the colorednoise package for researchers to analyze the temporal autocorrelation of structured demographic rates.     

Synergistic effects of an extreme weather event and habitat fragmentation on a specialised insect herbivore

Habitat fragmentation is considered to be one of the main causes of population decline and species extinction worldwide. Furthermore, habitat fragmentation can decrease the ability of populations to resist and to recover from environmental disturbances such as extreme weather events, which are expected to occur at an increasing rate as a result of climate change. In this study, we investigated how calcareous grassland fragmentation affected the impact of the climatically extreme summer of 2003 on egg deposition rates, population size variation and survival of the blue butterfly Cupido minimus, a specialist herbivore of Anthyllis vulneraria. Immediately after the 2003 summer heat wave, populations of the host plant declined in size; this was paralleled with decreases in population size of the herbivore and altered egg deposition rates. In 2006 at the end of the monitoring period, however, most A. vulneraria populations had recovered and only one population went extinct. In contrast, several butterfly populations had gone extinct between 2003 and 2006. Extinction probability was significantly related to initial population size, with small populations having a higher risk of extinction than large populations. These results support the prediction that species of higher trophic levels are more susceptible to extinction due to habitat fragmentation and severe disturbances.     

Effects of founding genetic variation on adaptation to a novel resource

Population genetic theory predicts that adaptation in novel environments is enhanced by genetic variation for fitness. However, theory also predicts that under strong selection, demographic stochasticity can drive populations to extinction before they can adapt. We exposed wheat-adapted populations of the flour beetle (Tribolium castaneum) to a novel suboptimal corn resource, to test the effects of founding genetic variation on population decline and subsequent extinction or adaptation. As previously reported, genetically diverse populations were less likely to go extinct. Here, we show that among surviving populations, genetically diverse groups recovered faster after the initial population decline. Within two years, surviving populations significantly increased their fitness on corn via increased fecundity, increased egg survival, faster larval development, and higher rate of egg cannibalism. However, founding genetic variation only enhanced the increase in fecundity, despite existing genetic variation-and apparent lack of trade-offs-for egg survival and larval development time. Thus, during adaptation to novel habitats the positive impact of genetic variation may be restricted to only a few traits, although change in many life-history traits may be necessary to avoid extinction. Despite severe initial maladaptation and low population size, genetic diversity can thus overcome the predicted high extinction risk in new habitats.     

Scaling of the mean and variance of population dynamics under fluctuating regimes

Theoretical ecologists have long sought to understand how the persistence of populations depends on the interactions between exogenous (biotic and abiotic) and endogenous (e.g., demographic and genetic) drivers of population dynamics. Recent work focuses on the autocorrelation structure of environmental perturbations and its effects on the persistence of populations. Accurate estimation of extinction times and especially determination of the mechanisms affecting extinction times is important for biodiversity conservation. Here we examine the interaction between environmental fluctuations and the scaling effect of the mean population size with its variance. We investigate how interactions between environmental and demographic stochasticity can affect the mean time to extinction, change optimal patch size dynamics, and how it can alter the often-assumed linear relationship between the census size and the effective population size. The importance of the correlation between environmental and demographic variation depends on the relative importance of the two types of variation. We found the correlation to be important when the two types of variation were approximately equal; however, the importance of the correlation diminishes as one source of variation dominates. The implications of these findings are discussed from a conservation and eco-evolutionary point of view.     

Extinctions in competitive communities forced by coloured environmental variation

Understanding the relationships between environmental fluctuations, population dynamics and species interactions in natural communities is of vital theoretical and practical importance. This knowledge is essential in assessing extinction risks in communities that are, for example, pressed by changing environmental conditions and increasing exploitation. We developed a model of density dependent population renewal, in a Lotka–Volterra competitive community context, to explore the significance of interspecific interactions, demographic stochasticity, population growth rate and species abundance on extinction risk in populations under various autocorrelation (colour) regimes of environmental forcing. These factors were evaluated in two cases, where either a single species or the whole community was affected by the external forcing. Species' susceptibility to environmental noise with different autocorrelation structure depended markedly on population dynamics, species' position in the abundance hierarchy and how similarly community members responded to external forcing. We also found interactions between demographic stochasticity and environmental noise leading to a reversal in extinction probabilities from under- to overcompensatory dynamics. We compare our results with studies of single species populations and contrast possible mechanisms leading to extinctions. Our findings indicate that abundance rank, the form of population dynamics, and the colour of environmental variation interact in affecting species extinction risk. These interactions are further modified by interspecific interactions within competitive communities as the interactions filter and modulate the environmental noise.     

Pathways to extinction: beyond the error threshold

Since the introduction of the quasispecies and the error catastrophe concepts for molecular evolution by Eigen and their subsequent application to viral populations, increased mutagenesis has become a common strategy to cause the extinction of viral infectivity. Nevertheless, the high complexity of virus populations has shown that viral extinction can occur through several other pathways apart from crossing an error threshold. Increases in the mutation rate enhance the appearance of defective forms and promote the selection of mechanisms that are able to counteract the accelerated appearance of mutations. Current models of viral evolution take into account more realistic scenarios that consider compensatory and lethal mutations, a highly redundant genotype-to-phenotype map, rough fitness landscapes relating phenotype and fitness, and where phenotype is described as a set of interdependent traits. Further, viral populations cannot be understood without specifying the characteristics of the environment where they evolve and adapt. Altogether, it turns out that the pathways through which viral quasispecies go extinct are multiple and diverse.     

Dynamics of escape mutants

We use multi-type Galton-Watson branching processes to model the evolution of populations that, due to a small reproductive ratio of the individuals, are doomed to extinction. Yet, mutations occurring during the reproduction process, may lead to the appearance of new types of individuals that are able to escape extinction. We provide examples of such populations in medical, biological and environmental contexts and give results on (i) the probability of escape/extinction, (ii) the distribution of the waiting time to produce the first individual whose lineage does not get extinct and (iii) the distribution of the time it takes for the number of mutants to reach a high level. Special attention is dedicated to the case where the probability of mutation is very small and approximations for (i)-(iii) are derived.     

Infectious disease in animal metapopulations: the importance of environmental transmission

Motivated by an array of infectious diseases that threaten wildlife populations, a simple metapopulation model (subpopulations connected by animal movement) is developed, which allows for both movement-based and environmental transmission. The model demonstrates that for a range of plausible parameterizations of environmental transmission, increased movement rate of animals between discrete habitats can lead to a decrease in the overall proportion of sites that are occupied. This can limit the ability of the rescue effect to ensure locally extinct populations become recolonized and can drive metapopulations down in size so that extinction by mechanisms other than disease may become more likely. It further highlights that, in the context of environmental transmission, the environmental persistence time of pathogens and the probability of acquiring infection by environmental transmission can affect host metapopulations both qualitatively and quantitatively. Additional spillover sources of infection from alternate reservoir hosts are also included in the model and a synthesis of all three types of transmission, acting alone or in combination, is performed revealing that movement-based transmission is the only necessary condition for a decline in the proportion of occupied sites with increasing movement rate, but that the presence of other types of transmission can reverse this qualitative result. By including the previously neglected role of environmental transmission, this work contributes to the general discussion of when dispersal by wild animals is beneficial or detrimental to populations experiencing infectious disease.     

Estimating population trends using population viability analyses for the conservation ofCapra pyrenaica

Large herbivore populations can suffer important oscillations with considerable effects on ecosystem functions and services, yet our capacity to predict population fate is limited and conditional upon the availability of data. This study investigated the interannual variation in the growth rate of populations ofCapra pyrenaica Schinz, 1838, and its extinction risk by comparing the dynamics of populations that were stable for more than two decades (Gredos and Tortosa-Beceite), populations that had increased recently (Tejeda-Almijara), and populations that were in decline (Cazorla-Segura) or extinct (the Pyrenees population; hereafter, bucardo). To estimate quasi-extinction threshold assessments (50% of population extinct in this study), which have implications for the conservation of the species, we used empirical data and the predictions derived from several theoretical models. The results indicate that when variance of log population growth rate reaches a specific threshold, the probability of quasi-extinction increased drastically. ForC. pyrenaica, we recommend keeping population variance < 0.05, which will reduce the likelihood that the irruptive oscillations caused by environmental and demographic stochasticity will put the population at risk. Models to predict the dynamics ofC. pyrenaica populations should incorporate temporal stochasticity because, in this study, it strongly increased the likelihood that a population declined.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.