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.     

Establishment success and extinction risk in autocorrelated environments

We consider establishment success (and extinction risk of small populations) in fluctuating environments, by means of an inhomogeneous branching process model. In this model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period individuals reproduce independently and have random numbers of offspring. Expected numbers of offspring vary over reproduction periods due to random environmental changes. Previous simulation results indicated that there is a positive autocorrelation between the establishment probabilities of invaders in successive reproduction periods when environmental states are independently distributed. This result was never formally proved. In this paper we prove that this is indeed true, regardless of the form of the distribution of environmental states or the offspring distribution (under a monotonicity condition, which holds for biologically realistic models). Furthermore, we prove that it is also true for positively autocorrelated environmental states. We show by a counterexample that in environments with a strong negative autocorrelation establishment probabilities can be negatively autocorrelated. This was further examined through simulations. Our results imply that in independent, positively autocorrelated and weakly negatively autocorrelated environments the probability of success of invasion in different independently varying sites is the highest, followed by sequential invasion. For environments with a strong negative autocorrelation, sequential invasion has the highest probability of success. Effects of autocorrelation were further examined with simulations. From the results it appears that the expected length of 'runs of bad luck' is the most crucial factor for establishment success.     

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.     

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.     

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.     

Demographic stochasticity and temporal autocorrelation in the dynamics of structured populations

Populations can show temporal autocorrelation in the dynamics arising from different mechanisms, including fluctuations in the demographic structure. This autocorrelation is often treated as a complicating factor in the analyses of stochastic population growth and extinction risk. However, it also reflects important information about the demographic structure. Here, we consider how temporal autocorrelation is related to demographic stochasticity in structured populations. Demographic stochasticity arises from inherent randomness in the demographic processes of individuals, like survival and reproduction, and the resulting impact on population growth is measured by the demographic variance. Earlier studies have shown that population structure have positive or negative effects on the demographic variance compared to a model where the structure is ignored. Here, we derive a new expression for the demographic variance of a structured population, using the temporal autocorrelation function of the population growth rate. We show that the relative difference in demographic variance when the structure is included or ignored (the effect of structure on demographic variance) is approximately twice the sum of the autocorrelations. We demonstrate the result for a simple hypothetical example, as well as a set of empirical examples using age‐structured models of 24 mammals from the demographic database COMADRE. In the empirical examples, the sum of the autocorrelation function was negative in all cases, indicating that age structure generally has a negative effect on the demographic variance (i.e. the demographic variance is lower compared to that of a model where the structure is ignored). Other kinds of structure, such as spatial heterogeneity affecting fecundity, can have positive effects on the demographic variance, and the sum of the autocorrelations will then be positive. These results yield new insights into the complex interplay between population structure, demographic variance, and temporal autocorrelation, that shapes the population dynamics and extinction risk of populations.     

Bet-hedging applications for conservation

One of the early tenets of conservation biology is that population viability is enhanced by maintaining multiple populations of a species. The strength of this tenet is justified by principles of bet-hedging. Management strategies that reduce variance in population size will also reduce risk of extinction. Asynchrony in population fluctuations in independent populations reduces variance in the aggregate of populations whereas environmental correlation among areas increases the risk that all populations will go extinct. We review the theoretical rationale of bet-hedging and suggest applications for conservation management of least terns in Nebraska and grizzly bears in the northern Rocky Mountains of the United States. The risk of extinction for least terns will be reduced if we can sustain the small central Platte River population in addition to the larger population on the lower Platte. Similarly, by restoring grizzly bears to the Bitterroot wilderness of Idaho and Montana can reduce the probability of extinction for grizzly bears in the Rocky Mountains of the United States by as much as 69–93%.     

The effective size of fluctuating populations

We consider a Wright-Fisher model whose population size is an autocorrelated stochastic process. Our interest is in the effects of autocorrelated fluctuations of the population size on the effective size. We define the inbreeding effective size and the variance effective size and show that these effective sizes are the same for this model. In the literature, it is said that the effective size is equal to the harmonic mean of population size when the size fluctuates. We will show, however, that the effective size is not the same as the harmonic mean of population size unless the fluctuations of population size are uncorrelated. The effective size is larger (resp. smaller) than the harmonic mean when the fluctuations of population size are positively (resp. negatively) autocorrelated. Further, we obtain some asymptotic expressions for effective size when the population size is very large and/or the autocorrelation of the fluctuation is very strong.     

How is extinction risk related to population-size variability over time? A family of models for species with repeated extinction and immigration

It is well known that for an isolated population, the probability of extinction is positively related to population size variation: more variation is associated with more extinction. What, then, is the relation of extinction to population size variation for a population embedded in a metapopulation and subjected to repeated extinction and recolonization? In this case, the extinction risk can be measured by the extinction rate, the frequency at which local extinction occurs. Using several population dynamics models with immigration, we find, in general, a negative correlation between extinction and variation. More precisely, with increasing length of the time series, an initially negative regression coefficient first becomes more negative, then becomes less negative, and eventually attains positive values before decreasing again to 0. This pattern holds under substantial variation in values of parameters representing species and environmental properties. It is also rather robust to census interval length and the fraction of missed individuals but fails to hold for high thresholds (population size values below which extinction is deemed to occur) when quasi extinction rather than true extinction is represented. The few departures from the initial negative correlation correspond to populations at risk: low growth rate or frequent catastrophes.     

Modelling population persistence on islands: mammal introductions in the New Zealand archipelago

Islands are likely to differ in their susceptibility to colonization or invasion due to variation in factors that affect population persistence, including island area, climatic severity and habitat modification. We tested the importance of these factors in explaining the persistence of 164 introductions of six mammal species to 85 islands in the New Zealand archipelago using survival analysis and model selection techniques. As predicted by the theory of stochastic population growth, extinction risk was the greatest in the period immediately following introduction, declining rapidly to low probability by ca 25 years. This suggests that initially small populations were at greatest risk of extinction and that populations which survived for 25 years were likely to persist subsequently for much longer. Islands in the New Zealand archipelago become colder and windier with increasing latitude, and the probability of mammal populations persisting on islands declined steeply with increasing latitude. Hence, our results suggest that climatic suitability was an important determinant of the outcome of these invasions. The form of the relationship between latitude and persistence probability differed among species, emphasizing that the outcome of colonization attempts is species-environment specific.     

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.     

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.     

Spatial pattern of habitat quality modulates population persistence in fragmented landscapes

Habitat quality is one of the important factors determining population dynamics and persistence, yet few studies have examined the effects of spatial heterogeneity in within-patch habitat quality. In this paper, we use a spatially explicit agent-based model to investigate how habitat fragmentation and spatial pattern of within-patch habitat quality affect population dynamics and long-term persistence. We simulate three levels of habitat fragmentation (ranges from continuous to highly fragmented) and three types of spatial patterns in habitat quality within patches (i.e., negatively autocorrelated, randomly distributed, and positively autocorrelated). Hypothetical species differ in their niche specialization. The results demonstrate explicitly that the spatial pattern of within-patch habitat quality plays an important role in modulating the effects of habitat fragmentation on populations. Populations become less variable in size, and experience lower probability of extinction in landscapes with positively autocorrelated within-patch habitat quality. Specifically, specialized species are more vulnerable to habitat fragmentation, but this vulnerability is greatly mitigated by positively autocorrelated habitat quality within patches, in other words, exhibiting higher resistance to habitat fragmentation. The findings of this study suggest that managing habitat quality in existing habitat remnants is important to preserve species in habitats undergoing fragmentation, particularly for those with specialized habitat requirements.     

Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.     

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.     

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.     

Disease and the devil: density-dependent epidemiological processes explain historical population fluctuations in the Tasmanian devil

Australia's last mega-carnivore marsupial, the Tasmanian devil Sarcophilus harrisii , Dasyuridae is endemic to the island state of Tasmania. The recent appearance and rapid spread of a debilitating and usually lethal, cancer-like disease has raised concerns regarding the species' future. We used a demographic matrix modelling approach to evaluate the potential long-term implications of epidemics on this population. Both adult survival and temporally autocorrelated re-occurrence of disease were expressed as a function of female abundance. Large fluctuations in abundance resulted when disease outbreaks were conditioned to be density-dependent; however, this resulted in a low probability of quasi-extinction due to the dissipation of disease transmission at low densities. Epidemic stochasticity alone in an otherwise deterministic model resulted in major population cycles occurring every 77–146 yr, consistent with historical reports. Although epidemics in this species may not result in extinction directly, the contemporary presence of additional mortality sources during periods of low abundance may increase extinction risk.     

Latitudinal gradients in butterfly population variability are influenced by landscape heterogeneity

The variability of populations over time is positively associated with their risk of local extinction. Previous work has shown that populations at the high‐latitude boundary of species’ ranges show higher inter‐annual variability, consistent with increased sensitivity and exposure to adverse climatic conditions. However, patterns of population variability at both high‐ and low‐latitude species range boundaries have not yet been concurrently examined. Here, we assess the inter‐annual population variability of 28 butterfly species between 1994 and 2009 at 351 and 18 sites in the United Kingdom and Catalonia, Spain, respectively. Local population variability is examined with respect to the position of the species’ bioclimatic envelopes (i.e. whether the population falls within areas of the ‘core’ climatic suitability or is a climatically ‘marginal’ population), and in relation to local landscape heterogeneity, which may influence these range location – population dynamic relationships. We found that butterfly species consistently show latitudinal gradients in population variability, with increased variability in the more northerly UK. This pattern is even more marked for southerly distributed species with ‘marginal’ climatic suitability in the UK but ‘core’ climatic suitability in Catalonia. In addition, local landscape heterogeneity did influence these range location – population dynamic relationships. Habitat heterogeneity was associated with dampened population dynamics, especially for populations in the UK. Our results suggest that promoting habitat heterogeneity may promote the persistence of populations at high‐latitude range boundaries, which may potentially aid northwards expansion under climate warming. We did not find evidence that population variability increases towards southern range boundaries. Sample sizes for this region were low, but there was tentative evidence, in line with previous ecological theory, that local landscape heterogeneity may promote persistence in these retracting low‐latitude range boundary populations.     

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.     

Small variance in growth rates in annual plants has large effects on genetic drift

? Premise of the Study: Effective population size (N(e)) is a critical index of the evolutionary capacity of populations. Low N(e) indicates that standing genetic diversity is susceptible to loss via stochastic processes (and inbreeding) and is, therefore, unavailable for natural selection to act upon. Reported N(e) in plant populations is often quite low. What biological and ecological factors might produce such low N(e) ? Methods: We conducted a simulation model to test the effect of randomly assigned and autocorrelated growth rates of annual plants on plant-size distributions at the end of the growing season. Because plant size is directly correlated with reproductive output in annual plants, variation in plant size reflects variation in reproduction, and thus our modeled size distributions can be used to estimate N(e). ? Key Results: Randomly assigned growth rates had a negligble effect on N(e)/N. Autocorrelated growth rates decreased N(e)/N as the length of the growing season increased. This was the case even when the variance in growth rates was as low as 0.1% of the mean. ? Conclusions: While intrinsic plant biology can affect the degree of growth autocorrelation, ecological factors such as competition, herbivory, and abiotic stress can increase or decrease levels of growth autocorrelation. Ecological factors that increase growth autocorrelation can have significant effects on genetic drift within populations.