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.     

Metapopulation extinction risk is increased by environmental stochasticity and assemblage complexity

Extinction risk is a key area of investigation for contemporary ecologists and conservation biologists. Practical conservation efforts for vulnerable species can be considerably enhanced by thoroughly understanding the ecological processes that interact to determine species persistence or extinction. Theory has highlighted the importance of both extrinsic environmental factors and intrinsic demographic processes. In laboratory microcosms, single-species single-habitat patch experimental designs have been widely used to validate the theoretical prediction that environmental heterogeneity can increase extinction risk. Here, we develop on this theme by testing the effects of fluctuating resource levels in experimental multispecies metapopulations. We compare a three-species host-parasitoid assemblage that exhibits apparent competition to the individual pairwise, host-parasitoid interactions. Existing theory is broadly supported for two-species assemblages: environmental stochasticity reduces trophic interaction persistence time, while metapopulation structure increases persistence time. However, with increasing assemblage complexity, the effects of trophic interactions mask environmental impacts and persistence time is further reduced, regardless of resource renewal regime. We relate our findings to recent theory, highlighting the importance of taking into account both intrinsic and extrinsic factors, over a range of spatial scales, in order to understand resource-consumer dynamics.     

Predicting patterns of long‐term adaptation and extinction with population genetics

Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short‐term transition from imminent doom to evolutionary rescue. But extinction can result from failure to adapt not only to catastrophes, but also to a backlog of environmental challenges. We model long‐term adaptation to long series of small challenges, where fitter populations reach higher population sizes. The population's long‐term fitness dynamic is well approximated by a simple stochastic Markov chain model. Long‐term persistence occurs when the rate of adaptation exceeds the rate of environmental deterioration for some genotypes. Long‐term persistence times are consistent with typical fossil species persistence times of several million years. Immediately preceding extinction, fitness declines rapidly, appearing as though a catastrophe disrupted a stably established population, even though gradual evolutionary processes are responsible. New populations go through an establishment phase where, despite being demographically viable, their extinction risk is elevated. Should the population survive long enough, extinction risk later becomes constant over time.     

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.     

Does inbreeding affect the extinction risk of small populations?: predictions from Drosophila

A fundamental assumption underlying the importance of genetic risks within conservation biology is that inbreeding increases the extinction probability of populations. Although inbreeding has been shown to have a detrimental impact on individual fitness, its contribution to extinction is still poorly understood. We have studied the consequences of different levels of prior inbreeding for the persistence of small populations using Drosophila melanogaster as a model organism. To this end, we determined the extinction rate of small vial populations differing in the level of inbreeding under both optimal and stress conditions, i.e. high temperature stress and ethanol stress. We show that inbred populations have a significantly higher short‐term probability of extinction than non‐inbred populations, even for low levels of inbreeding, and that the extinction probability increases with increasing inbreeding levels. In addition, we observed that the effects of inbreeding become greatly enhanced under stressful environmental conditions. More importantly, our results show that the impact of environmental stress becomes significantly greater for higher inbreeding levels, demonstrating explicitly that inbreeding and environmental stress are not independent but can act synergistically. These effects seem long lasting as the impact of prior inbreeding was still qualitatively the same after the inbred populations had been expanded to appreciable numbers and maintained as such for approximately 50 generations. Our observations have significant consequences for conservation biology.     

Forest fragmentation effects on patch occupancy and population viability of herbaceous plant species

Habitat fragmentation is one of the major threats to species diversity. In this review, we discuss how the genetic and demographic structure of fragmented populations of herbaceous forest plant species is affected by increased genetic drift and inbreeding, reduced mate availability, altered interactions with pollinators, and changed environmental conditions through edge effects. Reported changes in population genetic and demographic structure of fragmented plant populations have, however, not resulted in large-scale extinction of forest plants. The main reason for this is very likely the long-term persistence of small and isolated forest plant populations due to prolonged clonal growth and long generation times. Consequently, the persistence of small forest plant populations in a changing landscape may have resulted in an extinction debt, that is, in a distribution of forest plant species reflecting the historical landscape configuration rather than the present one. In some cases, fragmentation appears to affect ecosystem integrity rather than short-term population viability due to the opposition of different fragmentation-induced ecological effects. We finally discuss extinction and colonization dynamics of forest plant species at the regional scale and suggest that the use of the metapopulation concept, both because of its heuristic power and conservation applications, may be fruitful.     

The Effect of an Upper Limit to Population Size on Persistence Time

For a population with density-independent vital rates in a randomly varying environment, previous authors have calculated the probability that population size will first drop to some specified (arbitrary) low level at a given time (the first passage time distribution (FPTD), which may be interpreted as a distribution of extinction times). In this paper, we study the FPTD For a stochastic model of density-independent population growth which includes a hard upper limit to population size. We discuss the conditions under which this distribution may be approximated by the FPTD of a Wiener process with a reflecting boundary condition, for which an exact calculation is presented in an appendix. We compare the FPTD of the new model with its counterpart in the model without an upper limit. The most important effects of introducing the upper limit are: (a) ultimate extinction becomes certain; (b) if the long run growth rate in the absence of the upper boundary was small but positive, extinction within ecologically significant times is likely; (c) for larger values of the long run growth rate, persistence over ecologically significant times is almost certain. We discuss the implications of result (b) for conservation. Result (c) establishes that "density-vague" regulation can produce persistent, but bounded, populations.     

Demographic factors and genetic variation influence population persistence under environmental change

Population persistence has been studied in a conservation context to predict the fate of small or declining populations. Persistence models have explored effects on extinction of random demographic and environmental fluctuations, but in the face of directional environmental change they should also integrate factors affecting whether a population can adapt. Here, we examine the population‐size dependence of demographic and genetic factors and their likely contributions to extinction time under scenarios of environmental change. Parameter estimates were derived from experimental populations of the rainforest species, Drosophila birchii, held in the lab for 10 generations at census sizes of 20, 100 and 1000, and later exposed to five generations of heat‐knockdown selection. Under a model of directional change in the thermal environment, rapid extinction of populations of size 20 was caused by a combination of low growth rate (r) and high stochasticity in r. Populations of 100 had significantly higher reproductive output, lower stochasticity in r and more additive genetic variance (V_A) than populations of 20, but they were predicted to persist less well than the largest size class. Even populations of 1000 persisted only a few hundred generations under realistic estimates of environmental change because of low V_A for heat‐knockdown resistance. The experimental results document population‐size dependence of demographic and adaptability factors. The simulations illustrate a threshold influence of demographic factors on population persistence, while genetic variance has a more elastic impact on persistence under environmental change.     

Negative environmental perturbations may improve species persistence

Among the factors proximally involved in the extinction of small isolated populations, genetic deterioration and temporal variation in environmental quality have been the subjects of intensive research in ecological and evolutionary sciences. However, previous theoretical studies and population viability assessments generally assumed a strict dichotomy between these two types of threat. Yet a number of empirical studies have recently suggested that the effects of genetic deterioration and environmental variation should not be considered independently, by demonstrating that the main effect of inbreeding depression lies with its tendency to exacerbate the deleterious consequences of environmental stress. Capitalizing on these results, I developed a stochastic model to examine the impact of random environmental perturbations on the persistence time of small isolated populations subject to inbreeding depression and mutation accumulation. The model assumes that spontaneous deleterious mutations have more severe effects when perturbations occur, which results in more efficient purging of the mutation load. Under this assumption, I find that negative perturbations may paradoxically improve middle- and long-term species persistence for realistic frequency of occurrence and severity distribution.     

Predicting extinction risks for plants: environmental stochasticity can save declining populations

An emerging generalization from theoretical and empirical studies on conservation biology is that high levels of environmental stochasticity increase the likelihood of population extinction. However, coexistence theory has illustrated that there are circumstances under which environmental stochasticity can increase the chance of population persistence. These theoretical studies have shown that the sign of the effect of environmental stochasticity on population persistence is determined by interactions between life history and environmental stochasticity. These interactions mean that the stochastic and deterministic rates of population growth might differ fundamentally. Although difficult to demonstrate in real systems, observed life histories and variance in the vital rates of populations suggest that this phenomenon is likely to be common, and is therefore of much relevance to conservation biologists.     

Metapopulation dynamics: Does it help to have more of the same?

With the interest in conservation biology shifting towards processes from patterns, and to populations from communities, the theory of metapopulation dynamics is replacing the equilibrium theory of island biogeography as the population ecology paradigm in conservation biology. The simplest models of metapopulation dynamics make predictions about the effects of habitat fragmentation - size and isolation of habitat patches - on metapopulation persistence. The simple models may be enriched by considerations of the effects of demographic and environmental stochasticity on the size and extinction probability of local populations. Environmental stochasticity affects populations at two levels: it makes local extinctions more probable, and it also decreases metapopulation persistence time by increasing the correlation of extinction events across populations. Some controversy has arisen over the significance of correlated extinctions, and how they may affect the optimal subdivision of metapopulations to maximize their persistence time.     

Fish species richness in spring‐fed ponds: effects of habitat size versus isolation in temporally variable environments

1. Species richness in a habitat patch is determined by immigration (regional) and extinction (local) processes, and understanding their relative importance is crucial for conservation of biodiversity. In this study, we applied the Island Biogeography concept to spring ponds connected to a river in southwestern Japan to examine how immigration and extinction processes interact to determine fish species richness in temporally variable environments. 2. Fish censuses were conducted 15 times in 13 study ponds at 1–4 month intervals from August 1998 through October 2000. Effects of habitat size (pond area), isolation (distance from the river) and temporal environmental variability (water level fluctuation) on (i) species richness, (ii) immigration and extinction rates and (iii) population size and persistence of each fish species were assessed. 3. The results revealed predominant effects of distance on species richness, immigration/extinction rates and population size and persistence. Species richness decreased with increasing distance but was not related to either pond area or water level fluctuation. A negative effect of distance on immigration rate was detected, while neither pond area nor water level fluctuation had significant effects on extinction rate. Further, population size and persistence of four species increased with decreasing distance, suggesting that, in ponds close to the river, immigrants from the river reduce the probability of extinction (i.e. provide a rescue effect), contributing to the maintenance of high species richness. 4. Overall results emphasise the importance of immigration processes, rather than extinction, in shaping patterns of species richness in our system. The predominant importance of immigration was probably because of (i) high temporal variability that negates habitat‐size effects and (ii) continuous immigration that easily compensates for local extinctions. Our results suggest that consideration of regional factors (e.g. connectivity, locations of source populations and barriers to colonisation) is crucial for conservation and restoration of local habitats.     

Will small population sizes warn us of impending extinctions?

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

Which traits promote persistence of feral GM crops? Part 2: implications of metapopulation structure

Transgenes may spread from crops into the environment via the establishment of feral populations, often initiated by seed spill from transport lorries or farm machinery. Locally, such populations are often subject to large environmental variability and usually do not persist longer than a few years. Because secondary feral populations may arise from seed dispersal to adjacent sites, the dynamics of such populations should be studied in a metapopulation context. We study a structured metapopulation model with local dispersal, mimicking a string of roadside subpopulations of a feral crop. Population growth is assumed to be subject to local disturbances, introducing spatially random environmental stochasticity. Our aim is to understand the role of dispersal and environmental variability in the dynamics of such ephemeral populations. We determine the effect of dispersal on the extinction boundary and on the distribution of persistence times, and investigate the influence of spatially correlated disturbances as opposed to spatially random disturbances. We find that, given spatially random disturbances, dispersal slows down the decline of the metapopulation and results in the occurrence of long-lasting local populations which remain more or less static in space. We identify which life history traits, if changed by genetic modification, have the largest impact on the population growth rate and persistence times. For oilseed rape, these are seed bank survival and dormancy. Combining our findings with literature data on transgene-induced life history changes, we predict that persistence is promoted by transgenes for oil-modifications (high stearate or high laurate) and, possibly, for insect resistence (Bt). Transgenic tolerance to glufosinate herbicide is predicted to reduce persistence.     

Genetic estimates of contemporary effective population size: what can they tell us about the importance of genetic stochasticity for wild population persistence?

Genetic stochasticity due to small population size contributes to population extinction, especially when population fragmentation disrupts gene flow. Estimates of effective population size ( N _e) can therefore be informative about population persistence, but there is a need for an assessment of their consistency and informative relevance. Here we review the body of empirical estimates of N _e for wild populations obtained with the temporal genetic method and published since Frankham's (1995 ) review. Theoretical considerations have identified important sources of bias for this analytical approach, and we use empirical data to investigate the extent of these biases. We find that particularly model selection and sampling require more attention in future studies.
We report a median unbiased N _e estimate of 260 (among 83 studies) and find that this median estimate tends to be smaller for populations of conservation concern, which may therefore be more sensitive to genetic stochasticity. Furthermore, we report a median N _e/ N ratio of 0.14, and find that this ratio may actually be higher for small populations, suggesting changes in biological interactions at low population abundances. We confirm the role of gene flow in countering genetic stochasticity by finding that N _e correlates strongest with neutral genetic metrics when populations can be considered isolated. This underlines the importance of gene flow for the estimation of N _e, and of population connectivity for conservation in general. Reductions in contemporary gene flow due to ongoing habitat fragmentation will likely increase the prevalence of genetic stochasticity, which should therefore remain a focal point in the conservation of biodiversity.     

Increased Extinction Potential of Insular Fish Populations with Reduced Life History Variation and Low Genetic Diversity

Theoretical work has shown that reduced phenotypic heterogeneity leads to population instability and can increase extinction potential, yet few examples exist of natural populations that illustrate how varying levels expressed diversity may influence population persistence, particularly during periods of stochastic environmental fluctuation. In this study, we assess levels of expressed variation and genetic diversity among demographically independent populations of tidewater goby (Eucyclogobius newberryi), show that reductions in both factors typically coincide, and describe how low levels of diversity contribute to the extinction risk of these isolated populations. We illustrate that, for this annual species, continuous reproduction is a safeguard against reproductive failure by any one population segment, as natural, stochastically driven salinity increases frequently result in high mortality among juvenile individuals. Several study populations deviated from the natural pattern of year-round reproduction typical for the species, rendering those with severely truncated reproductive periods vulnerable to extinction in the event of environmental fluctuation. In contrast, demographically diverse populations are more likely to persist through such periods through the continuous presence of adults with broader physiological tolerance to abrupt salinity changes. Notably, we found a significant correlation between genetic diversity and demographic variation in the study populations, which could be the result of population stressors that restrict both of these diversity measures simultaneously, or suggestive of a causative relationship between these population characteristics. These findings demonstrate the importance of biocomplexity at the population level, and assert that the maintenance of diversity contributes to population resilience and conservation of this endangered species.     

Stress and adaptation in conservation genetics

Stress, adaptation and evolution are major concerns in conservation biology. Stresses from pollution, climatic changes, disease etc. may affect population persistence. Further, stress typically occurs when species are placed in captivity. Threatened species are usually managed to conserve their ability to adapt to environmental changes, whilst species in captivity undergo adaptations that are deleterious upon reintroduction into the wild. In model studies using Drosophila melanogaster, we have found that; (a) inbreeding and loss of genetic variation reduced resistance to the stress of disease, (b) extinction rates under inbreeding are elevated by stress, (c) adaptive evolutionary potential in an increasingly stressful environment is reduced in small population, (d) rates of inbreeding are elevated under stressful conditions, (e) genetic adaptation to captivity reduces fitness when populations are reintroduced into the 'wild', and (f) the deleterious effects of adaptation on reintroduction success can be reduced by population fragmentation.     

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。     

Regional dynamics and dispersal in the vascular plant Silene viscosa (L.) inhabiting small islands

We investigated and compared the patch occupancy and colonisation and extinction over a 40-yr period in the vascular plant Silene viscosa in two archipelagos off the Swedish east coast. We also assessed the importance of regional vs local dynamics for regional persistence by examining factors affecting colonisation and extinction processes.
We found an effect of isolation on the patch occupancy in 1957, but this effect disappeared 1997. The effect of isolation was not detected when analysing colonisations and extinctions during the 40-yr period separately, which suggests that the colonisations and extinctions since 1957 have changed the patch occupancy of S. viscosa . The change in the patch occupancy is attributed to an increased colonisation, presumably mediated by the increase of the greylag goose Anser anser . The large amplitude of population size change, the high persistence of populations during a 40-yr period, and the long term persistence for some populations all suggest that the distribution pattern approximates a distribution that is expected to be generated from an Island-Mainland model, where a number of large populations are persistent and a number of smaller populations are more prone to extinction due to catastrophes (nesting cormorants) and environmental stochasticity (summer drought). Most evidence suggests that regional processes are of less importance than local processes for regional persistence on a time scale of 40 yr for S. viscosa .     

Demographic consequences of population subdivision on the long-furred woolly mouse opossum (Micoureus paraguayanus) from the Atlantic Forest

Habitat destruction and fragmentation severely affected the Atlantic Forest. Formerly contiguous populations may become subdivided into a larger number of smaller populations, threatening their long-term persistence. The computer package VORTEX was used to simulate the consequences of habitat fragmentation and population subdivision on Micoureus paraguayanus, an endemic arboreal marsupial of the Atlantic Forest. Scenarios simulated hypothetical populations of 100 and 2000 animals being partitioned into 1–10 populations, linked by varying rates of inter-patch dispersal, and also evaluated male-biased dispersal. Results demonstrated that a single population was more stable than an ensemble of populations of equal size, irrespective of dispersal rate. Small populations (10–20 individuals) exhibited high instability due to demographic stochasticity, and were characterized by high rates of extinction, smaller values for metapopulation growth and larger fluctuations in population size and growth rate. Dispersal effects on metapopulation persistence were related to the size of the populations and to the sexes that were capable of dispersing. Male-biased dispersal had no noticeable effects on metapopulation extinction dynamics, whereas scenarios modelling dispersal by both sexes positively affected metapopulation dynamics through higher growth rates, smaller fluctuations in growth rate, larger final metapopulation sizes and lower probabilities of extinction. The present study highlights the complex relationships between metapopulation size, population subdivision, habitat fragmentation, rate of inter-patch dispersal and sex-biased dispersal and indicates the importance of gaining a better understanding of dispersal and its interactions with correlations between disturbance events.