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.     

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.     

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.     

Variation in Allee effects: evidence,unknowns, and directions forward

Allee effects, positive effects of population size or density on per-capita fitness, are of broad interest in ecology and conservation due to their importance to the persistence of small populations and to range boundary dynamics. A number of recent studies have highlighted the importance of spatiotemporal variation in Allee effects and the resulting impacts on population dynamics. These advances challenge conventional understanding of Allee effects by reframing them as a dynamic factor affecting populations instead of a static condition. First, we synthesize evidence for variation in Allee effects and highlight potential mechanisms. Second, we emphasize the “Allee slope,” i.e., the magnitude of the positive effect of density on the per-capita growth rate, as a metric for demographic Allee effects. The more commonly used quantitative metric, the Allee threshold, provides only a partial picture of the underlying forces acting on population growth despite its implications for population extinction. Third, we identify remaining unknowns and strategies for addressing them. Outstanding questions about variation in Allee effects fall broadly under three categories: (1) characterizing patterns of natural variability; (2) understanding mechanisms of variation; and (3) implications for populations, including applications to conservation and management. Future insights are best achieved through robust interactions between theory and empiricism, especially through mechanistic models. Understanding spatiotemporal variation in the demographic processes contributing to the dynamics of small populations is a critical step in the advancement of population ecology.     

Phenotypic plasticity and population viability: the importance of environmental predictability

Phenotypic plasticity plays a key role in modulating how environmental variation influences population dynamics, but we have only rudimentary understanding of how plasticity interacts with the magnitude and predictability of environmental variation to affect population dynamics and persistence. We developed a stochastic individual-based model, in which phenotypes could respond to a temporally fluctuating environmental cue and fitness depended on the match between the phenotype and a randomly fluctuating trait optimum, to assess the absolute fitness and population dynamic consequences of plasticity under different levels of environmental stochasticity and cue reliability. When cue and optimum were tightly correlated, plasticity buffered absolute fitness from environmental variability, and population size remained high and relatively invariant. In contrast, when this correlation weakened and environmental variability was high, strong plasticity reduced population size, and populations with excessively strong plasticity had substantially greater extinction probability. Given that environments might become more variable and unpredictable in the future owing to anthropogenic influences, reaction norms that evolved under historic selective regimes could imperil populations in novel or changing environmental contexts. We suggest that demographic models (e.g. population viability analyses) would benefit from a more explicit consideration of how phenotypic plasticity influences population responses to environmental change.     

Consequences of Environmental Fluctuations on Taylor’s Power Law and Implications for the Dynamics and Persistence of Populations

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor’s power law relationship. We showed that the combined effects of environmental/demographic noises and the scaling of population size variability interact with the population dynamics and affect the mean time to extinction.     

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.     

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.     

Environmental variation, stochastic extinction, and competitive coexistence

Understanding how environmental fluctuations affect population persistence is essential for predicting the ecological impacts of expected future increases in climate variability. However, two bodies of theory make opposite predictions about the effect of environmental variation on persistence. Single-species theory, common in conservation biology and population viability analyses, suggests that environmental variation increases the risk of stochastic extinction. By contrast, coexistence theory has shown that environmental variation can buffer inferior competitors against competitive exclusion through a storage effect. We reconcile these two perspectives by showing that in the presence of demographic stochasticity, environmental variation can increase the chance of extinction while simultaneously stabilizing coexistence. Our stochastic simulations of a two-species storage effect model reveal a unimodal relationship between environmental variation and coexistence time, implying maximum coexistence at intermediate levels of environmental variation. The unimodal pattern reflects the fact that the stabilizing influence of the storage effect accumulates rapidly at low levels of environmental variation, whereas the risk of extinction due to the combined effects of environmental variation and demographic stochasticity increases most rapidly at higher levels of variation. Future increases in environmental variation could either increase or decrease an inferior competitor's expected persistence time, depending on the distance between the present level of environmental variation and the optimal level anticipated by this theory.     

Harvested populations are more variable only in more variable environments

The interaction between environmental variation and population dynamics is of major importance, particularly for managed and economically important species, and especially given contemporary changes in climate variability. Recent analyses of exploited animal populations contested whether exploitation or environmental variation has the greatest influence on the stability of population dynamics, with consequences for variation in yield and extinction risk. Theoretical studies however have shown that harvesting can increase or decrease population variability depending on environmental variation, and requested controlled empirical studies to test predictions. Here, we use an invertebrate model species in experimental microcosms to explore the interaction between selective harvesting and environmental variation in food availability in affecting the variability of stage‐structured animal populations over 20 generations. In a constant food environment, harvesting adults had negligible impact on population variability or population size, but in the variable food environments, harvesting adults increased population variability and reduced its size. The impact of harvesting on population variability differed between proportional and threshold harvesting, between randomly and periodically varying environments, and at different points of the time series. Our study suggests that predicting the responses to selective harvesting is sensitive to the demographic structures and processes that emerge in environments with different patterns of environmental variation.     

Implication of climate change for the persistence of raptors in arid savanna

Arid savannas are regarded as one of the ecosystems most likely to be affected by climate change. In these dry conditions, even top predators like raptors are affected by water availability and precipitation. However, few research initiatives have addressed the question of how climate change will affect population dynamics and extinction risk of particular species in arid ecosystems. Here, we use an individual‐oriented modeling approach to conduct experiments on the population dynamics of long lived raptors. We investigate the potential impact of precipitation variation caused by climate change on raptors in arid savanna using the tawny eagle (Aquila rapax) in the southern Kalahari as a case study. We simulated various modifications of precipitation scenarios predicted for climate change, such as lowered annual precipitation mean, increased inter‐annual variation and increased auto‐correlation in precipitation. We found a high impact of these modifications on extinction risk of tawny eagles, with reduced population persistence in most cases. Decreased mean annual precipitation and increased inter‐annual variation both caused dramatic decreases in population persistence. Increased auto‐correlation in precipitation led only to slightly accelerated extinction of simulated populations. Finally, for various patterns of periodically fluctuating precipitation, we found both increased and decreased population persistence. In summary, our results suggest that the impacts on raptor population dynamics and survival caused by climate change in arid savannas will be great. We emphasize that even if under climate change the mean annual precipitation remains constant but the inter‐annual variation increases the persistence of raptor populations in arid savannas will decrease considerably. This suggests a new dimension of climate change driven impacts on population persistence and consequently on biodiversity. However, more investigations on particular species and/or species groups are needed to increase our understanding of how climate change will impact population dynamics and how this will influence species diversity and biodiversity.     

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.     

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 phenotypic variation on metapopulation persistence

Demographic stochasticity (due to the probabilistic nature of the birth–death process) and demographic heterogeneity (between-individual differences in demographic parameters) have long been seen as factors affecting extinction risk. While demographic stochasticity can be independent of underlying species traits, demographic heterogeneity may strongly depend on phenotypic variation. However, how phenotypic variation can affect extinction risk is largely unknown. Here, I develop a stochastic metapopulation model that takes into account the effects of demographic stochasticity and phenotypic variation in the traits controlling colonization rates to assess what the effect of phenotypic variation may be on the persistence of the metapopulation. Although phenotypic variation can lead to a decrease in metapopulation persistence under some conditions, it also may lead to an increase in persistence whenever phenotypic mismatch—or the distance between the optimal trait value and the population mean—is large. This mismatch can in turn arise from a variety of ecological and evolutionary reasons, including weak selection or a recent history of invasion. Last, the effect of phenotypic variation has a deterministic component on colonization rates, and a stochastic component on persistence through colonization rates, but both are important to understand the overall effect. These results have important implications for the conservation of threatened species and management practices that may historically have overlooked phenotypic variation as unimportant noise around mean values of interest.     

Population Genetic Consequences of the Allee Effect and the Role of Offspring-Number Variation

A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. But many species are repeatedly introduced to the same location and eventually one population may overcome the Allee effect by chance. With the help of stochastic models, we investigate how much genetic diversity such successful populations harbor on average and how this depends on offspring-number variation, an important source of stochastic variability in population size. We find that with increasing variability, the Allee effect increasingly promotes genetic diversity in successful populations. Successful Allee-effect populations with highly variable population dynamics escape rapidly from the region of small population sizes and do not linger around the critical population size. Therefore, they are exposed to relatively little genetic drift. It is also conceivable, however, that an Allee effect itself leads to an increase in offspring-number variation. In this case, successful populations with an Allee effect can exhibit less genetic diversity despite growing faster at small population sizes. Unlike in many classical population genetics models, the role of offspring-number variation for the population genetic consequences of the Allee effect cannot be accounted for by an effective-population-size correction. Thus, our results highlight the importance of detailed biological knowledge, in this case on the probability distribution of family sizes, when predicting the evolutionary potential of newly founded populations or when using genetic data to reconstruct their demographic history.     

Life history and population size variability in a relict plant. Different routes towards long-term persistence

A central tenet of conservation biology is that population size affects the persistence of populations. However, many narrow endemic species combine small population ranges and sizes with long persistence, thereby challenging this tenet. I examined the performance of three different-sized populations of Petrocoptis pseudoviscosa (Caryophyllaceae), a palaeoendemic rupicolous herb distributed along a small valley in the Spanish Pyrenees. Reproductive and demographic parameters were recorded over 6 years, and deterministic and stochastic matrix models were constructed to explore population dynamics and extinction risk. Populations differed greatly in structure, fecundity, recruitment, survival rate, and life span. Strong differentiation in life-history parameters and their temporal variability resulted in differential population vulnerability under current conditions and simulated global changes such as habitat fragmentation or higher climatic fluctuations. This study provides insights into the capacity of narrow endemics to survive both at extreme environmental conditions and at small population sizes. When dealing with species conservation, the population size–extinction risk relationship may be too simplistic for ancient, ecologically restricted organisms, and some knowledge of life history may be most important to assess their future.     

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.     

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.     

Density-dependent demographic variation determines extinction rate of experimental populations

Understanding population extinctions is a chief goal of ecological theory. While stochastic theories of population growth are commonly used to forecast extinction, models used for prediction have not been adequately tested with experimental data. In a previously published experiment, variation in available food was experimentally manipulated in 281 laboratory populations of Daphnia magna to test hypothesized effects of environmental variation on population persistence. Here, half of those data were used to select and fit a stochastic model of population growth to predict extinctions of populations in the other half. When density-dependent demographic stochasticity was detected and incorporated in simple stochastic models, rates of population extinction were accurately predicted or only slightly biased. However, when density-dependent demographic stochasticity was not accounted for, as is usual when forecasting extinction of threatened and endangered species, predicted extinction rates were severely biased. Thus, an experimental demonstration shows that reliable estimates of extinction risk may be obtained for populations in variable environments if high-quality data are available for model selection and if density-dependent demographic stochasticity is accounted for. These results suggest that further consideration of density-dependent demographic stochasticity is required if predicted extinction rates are to be relied upon for conservation planning.