Predicting the time to quasi-extinction for populations far below their carrying capacity

Populations threatened by extinction are often far below their carrying capacity. A population collapse or quasi-extinction is defined to occur when the population size reaches some given lower density. If this density is chosen to be large enough for the demographic stochasticity to be ignored compared to environmental stochasticity, then the logarithm of the population size may be modelled by a Brownian motion until quasi-extinction occurs. The normal-gamma mixture of inverse Gaussian distributions can then be applied to define prediction intervals for the time to quasi-extinction in such processes. A similar mixture is used to predict the population size at a finite time for the same process provided that quasi-extinction has not occurred before that time. Stochastic simulations indicate that the coverage of the prediction interval is very close to the probability calculated theoretically. As an illustration, the method is applied to predict the time to extinction of a declining population of white stork in southwestern Germany.     

The role of age of first breeding in modeling raptor reintroductions

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A statistical approach to quasi-extinction forecasting

Forecasting population decline to a certain critical threshold (the quasi-extinction risk) is one of the central objectives of population viability analysis (PVA), and such predictions figure prominently in the decisions of major conservation organizations. In this paper, we argue that accurate forecasting of a population's quasi-extinction risk does not necessarily require knowledge of the underlying biological mechanisms. Because of the stochastic and multiplicative nature of population growth, the ensemble behaviour of population trajectories converges to common statistical forms across a wide variety of stochastic population processes. This paper provides a theoretical basis for this argument. We show that the quasi-extinction surfaces of a variety of complex stochastic population processes (including age-structured, density-dependent and spatially structured populations) can be modelled by a simple stochastic approximation: the stochastic exponential growth process overlaid with Gaussian errors. Using simulated and real data, we show that this model can be estimated with 20-30 years of data and can provide relatively unbiased quasi-extinction risk with confidence intervals considerably smaller than (0,1). This was found to be true even for simulated data derived from some of the noisiest population processes (density-dependent feedback, species interactions and strong age-structure cycling). A key advantage of statistical models is that their parameters and the uncertainty of those parameters can be estimated from time series data using standard statistical methods. In contrast for most species of conservation concern, biologically realistic models must often be specified rather than estimated because of the limited data available for all the various parameters. Biologically realistic models will always have a prominent place in PVA for evaluating specific management options which affect a single segment of a population, a single demographic rate, or different geographic areas. However, for forecasting quasi-extinction risk, statistical models that are based on the convergent statistical properties of population processes offer many advantages over biologically realistic models.     

植物种群生存力分析研究进展

对十多年来国外植物PVA的研究进行了综合评述;具体分析了影响植物种群生存力的各种随机性因子及确定性因子;总结了植物PVA研究的方法步骤及采用的模拟模型;探讨了植物PVA的难点,PVA对管理措施的评价效果;并提出对今后植物PVA的研究展望,认为PVA是研究濒危植物种群灭绝及评价管理或保护措施的有力工具;发展描述复杂种间关系的多种种的PVA模型以及包含多个影响因素的PVA应用模型是未来植物PVA的研究方向。     

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.     

Stabilizing Spatially-Structured Populations through Adaptive Limiter Control

Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems are not applicable to real, biological populations. This is because such methods typically require detailed knowledge of system specific parameters and the ability to manipulate them in real time; conditions often not met by most real populations. Moreover, real populations are often noisy and extinction-prone, which can sometimes render such methods ineffective. Here, we investigate a control strategy, which works by perturbing the population size, and is robust to reasonable amounts of noise and extinction probability. This strategy, called the Adaptive Limiter Control (ALC), has been previously shown to increase constancy and persistence of laboratory populations and metapopulations of Drosophila melanogaster. Here, we present a detailed numerical investigation of the effects of ALC on the fluctuations and persistence of metapopulations. We show that at high migration rates, application of ALC does not require a priori information about the population growth rates. We also show that ALC can stabilize metapopulations even when applied to as low as one-tenth of the total number of subpopulations. Moreover, ALC is effective even when the subpopulations have high extinction rates: conditions under which another control algorithm had previously failed to attain stability. Importantly, ALC not only reduces the fluctuation in metapopulation sizes, but also the global extinction probability. Finally, the method is robust to moderate levels of noise in the dynamics and the carrying capacity of the environment. These results, coupled with our earlier empirical findings, establish ALC to be a strong candidate for stabilizing real biological metapopulations.     

Use of population viability analysis models for Atlantic and Pacific salmon recovery planning

Uncertainty and risk abound in making natural resource management decisions. Population viability analysis (PVA) includes a variety of qualitative or quantitative analyses to predict the future status of a population or collection of populations and to predict the risk of extinction (or quasi-extinction) over time given some assumptions of the factors driving population dynamics. In this paper, we review the various PVA models applied to Atlantic and Pacific salmon for determination of listing under the Endangered Species Act and in planning recovery actions. We also review the numerous cautions involved in developing PVA models and in interpreting their results. There have been a larger number of PVA models applied to Pacific salmon compared to Atlantic salmon due to the greater geographic range and number of species of Pacific salmon. Models for both Atlantic and Pacific salmon have ranged from simple models that view populations as simply a number of organisms to complex age- or stage-structured models depending on the purpose of the model and available data for model parameterization. The real value of PVA models to salmon conservation is not in making absolute predictions of the risk of extinction, but rather in evaluating relative effects of management alternatives on extinction risk and informing decision making within an adaptive management framework. As computing power, quantitative techniques, and knowledge of mechanistic linkages between terrestrial, freshwater, and marine environments advance, PVA models will become an even more powerful tool in conservation planning for salmon species.     

种群生存力分析:准确性和保护应用

目前已提出了五类估计濒危物种绝灭风险的种群生存力分析模型 ,即 :分析模型、单种群确定性模型、单种群随机模型、异质种群模型和显空间模型。模型的选择取决于物种的生活史特征和可用的数据。与用于保护实践的其他方法相比 ,种群生存力分析 (PVA)是相对准确的量化工具。然而 ,一些濒危物种种群统计学数据质量差和种群动态的有关假说模糊不清可能影响到模型预测的准确性 ,因此 ,要谨慎地使用PVA。在西方国家 ,PVA在濒危物种保护计划和管理中应用越来越广泛。它主要用于 :( 1)预测濒危物种未来的种群大小 ;( 2 )估计一定时间内物种的绝灭风险 ;( 3 )评估一套保护措施 ,确定哪个能使种群的存活时间最长 ;( 4)探索不同假说对小种群动态的影响 ;( 5 )指导濒危动物野外数据的搜集工作。我国的濒危物种很多 ,然而开展PVA研究的濒危物种却很少。应大力发展适合于模拟我国特有濒危物种及其保护问题的PVA模型     

The importance of inverse density dependence in population viability analysis: an example using threatened woodland caribou in Canada

[First paragraph]Population viability analysis (PVA) refers to a group of analytical and modelling approaches for assessing the risk of population extinction. PVA is commonly used to estimate absolute time to extinction or probability of persistence under either current or novel conditions. However, the amount of information of species specific biology as well as the dynamics of small populations needed to confidently estimate population persistence is high, a fact often overlooked in the light of increasing availability of easy-to-use software packages.     

Using Bayesian Population Viability Analysis to Define Relevant Conservation Objectives

Adaptive management provides a useful framework for managing natural resources in the face of uncertainty. An important component of adaptive management is identifying clear, measurable conservation objectives that reflect the desired outcomes of stakeholders. A common objective is to have a sustainable population, or metapopulation, but it can be difficult to quantify a threshold above which such a population is likely to persist. We performed a Bayesian metapopulation viability analysis (BMPVA) using a dynamic occupancy model to quantify the characteristics of two wood frog (Lithobates sylvatica) metapopulations resulting in sustainable populations, and we demonstrate how the results could be used to define meaningful objectives that serve as the basis of adaptive management. We explored scenarios involving metapopulations with different numbers of patches (pools) using estimates of breeding occurrence and successful metamorphosis from two study areas to estimate the probability of quasi-extinction and calculate the proportion of vernal pools producing metamorphs. Our results suggest that ≥50 pools are required to ensure long-term persistence with approximately 16% of pools producing metamorphs in stable metapopulations. We demonstrate one way to incorporate the BMPVA results into a utility function that balances the trade-offs between ecological and financial objectives, which can be used in an adaptive management framework to make optimal, transparent decisions. Our approach provides a framework for using a standard method (i.e., PVA) and available information to inform a formal decision process to determine optimal and timely management policies.     

Extirpation Risk of an Isolated Black Bear Population Under Different Management Scenarios

ABSTRACT Habitat loss and anthropogenic mortality are recognized as threats to populations of large carnivores worldwide, yet their relative importance to extinction risk has rarely been quantified. We used population viability analysis (PVA) to estimate extinction probability of an isolated population of black bears (Ursus americanus) on the Bruce Peninsula, Ontario, Canada under different management scenarios. We used random-effects analysis of variance to estimate components of variance in extinction risk explained by 4 management actions: 1) preventing habitat destruction, 2) reducing or eliminating incidental non-natural mortality, 3) reducing or eliminating harvest, and 4) reducing the fraction of reproducing females in the harvest. Habitat area reductions had the greatest effect on risk despite uncertainty in bear density. Incidental non-natural mortality had a greater effect than the rate or age and sex distribution of harvest. Quantifying the variation in outputs of PVA models associated with different management options is an improvement over qualitative comparisons of relative risk and enhances the applicability of PVA to management. This study highlights the importance of protecting habitats on adjacent private lands when reserves are too small to support populations of bears, and of protecting reproducing females from non-natural mortality—results that could aid managers of other large carnivores in focusing management efforts to ensure persistence of populations.     

Estimating Sustainable Harvest in Wolverine Populations Using Logistic Regression

Abstract: Population viability analysis (PVA) is a common tool to evaluate population vulnerability. However, most techniques require reliable estimates of underlying population parameters, which are often difficult to obtain and PVA are, therefore, best used in a qualitative context. Logistic regression is a powerful alternative to traditional PVA methods but has received surprisingly limited attention. Logistic regression fits regression equations to binary output from PVA models at a specific point in time to predict probability of a binary response over a range of parameter values. We used logistic regression on output from stochastic population models to evaluate the relative importance of demographic parameters for wolverine (Gulo gulo) populations and to estimate sustainable harvest in a wolverine population in Alaska. Our analysis indicated that adult survival is the most important demographic parameter to reliably estimate in wolverine populations because it had a greater effect on population persistence than did both fecundity and subadult survival. In accordance with this, harvest rate had a greater effect on population persistence than did any of the other harvest- and migration-related variables we tested. Furthermore, a high proportion of harvested females strengthened the effect of harvest. Hypothetical wolverine populations suffered high probabilities of both extinction and population decline over a range of realistic population sizes and harvest regimes. We suggest that harvested wolverine populations must be regarded as sink populations and that source populations in combination with sufficient dispersal corridors must be secured for any wolverine harvest to be sustainable.     

种群生存力分析研究进展和趋势

种群生存力分析（PVA）是正在迅速发展的新方法,已成为保护生物学研究的热点。它主要研究随机干扰对小种群绝灭的影响,其目的是制定最小可存活种群（MVP）,把绝灭减少到可接受的水平。随机干扰可分四类;统计随机性,环境随机性,自然灾害和遗传随机性。确定MVP的方法有三种：理论模型,模拟模型,模拟模型和岛屿生物地理学方法。理论模型主要研究理想或特定条件下随机因素对种群的影响;模拟模型是利用计算机模拟种群绝灭过程;岛屿生物地理学方法主要分析岛屿物种的分布和存活,证实分析模型和模拟模型。已有大量的文献研究统计随机性,环境随机性和自然灾害的行为特征,但遗传因素与种群生存力之间的关系还不清楚。建立包括四种随机性的综合性模型,广泛地检验PVA模型,系统地研制目标种的遗传和生态特性以及MVP的实际应用是PVA的发展趋势。     

Allee effects,extinctions, and chaotic transients in simple population models

Discrete time single species models with overcompensating density dependence and an Allee effect due to predator satiation and mating limitation are investigated. The models exhibit four behaviors: persistence for all initial population densities, bistability in which a population persists for intermediate initial densities and otherwise goes extinct, extinction for all initial densities, and essential extinction in which "almost every" initial density leads to extinction. For fast-growing populations, these models show populations can persist at high levels of predation even though lower levels of predation lead to essential extinction. Alternatively, increasing the predator's handling time, the population's carrying capacity, or the likelihood of mating success may lead to essential extinction. In each of these cases, the mechanism behind these disappearances are chaotic dynamics driving populations below a critical threshold determined by the Allee effect. These disappearances are proceeded by chaotic transients that are proven to be approximately exponentially distributed in length and highly sensitive to initial population densities.     

Estimating demographic models for the range dynamics of plant species

Aims To better understand how demographic processes shape the range dynamics of woody plants (in this case, Proteaceae), we introduce a likelihood framework for fitting process‐based models of range dynamics to spatial abundance data. Location The fire‐prone Fynbos biome (Cape Floristic Region, South Africa). Methods Our process‐based models have a spatially explicit demographic submodel (describing dispersal, reproduction, mortality and local extinction) as well as an observation submodel (describing imperfect detection of individuals), and are constrained by species‐specific predictions of habitat distribution models and process‐based models for seed dispersal by wind. Free model parameters were varied to find parameter sets with the highest likelihood. After testing this approach with simulated data, we applied it to eight Proteaceae species that differ in breeding system (monoecy versus dioecy) and adult fire survival. We assess the importance of Allee effects and negative density dependence for range dynamics, by using the Akaike information criterion to select between alternative models fitted for the same species. Results The best model for all dioecious study species included Allee effects, whereas this was true for only one of four monoecious species. As expected, sprouters (in which adults survive fire) were estimated to have lower rates of reproduction and catastrophic population extinction than related non‐sprouters. Overcompensatory population dynamics seem important for three of four non‐sprouters. We also found good quantitative agreement between independent data and most estimates of reproduction, carrying capacity and extinction probability. Main conclusions This study shows that process‐based models can quantitatively describe how large‐scale abundance distributions arise from the movement and interaction of individuals. It stresses links between the life history, demography and range dynamics of Proteaceae: dioecious species seem more susceptible to Allee effects which reduce migration ability and increase local extinction risk, and sprouters seem to have high persistence of established populations, but their low reproduction limits habitat colonization and migration.     

How does intraspecific density regulation influence metapopulation synchrony and persistence?

Intraspecific density regulation influences the synchronization of local population dynamics through dispersal. Spatial synchrony in turn may jeopardize metapopulation persistence. Joining results from previous studies suggests that spatial synchrony is highest at moderate over-compensation and is low at compensating and at very strong over-compensating density regulation. We scrutinize this supposition of a unimodal relationship using a process-based metapopulation model with explicit local population dynamics. We extend the usually studied range of density regulation to under-compensation and analyse resulting metapopulation persistence. We find peaks of spatial synchrony not only at over-compensatory but also under-compensatory density regulation and show that effects of local density compensation on synchrony follow a bimodal rather than unimodal relationship. Persistence of metapopulations however, shows a unimodal relationship with a broad plateau of high persistence from compensatory to over-compensatory density regulation. This range of high persistence comprises both levels of low and high spatial synchrony. Thus, not synchrony alone jeopardizes metapopulation persistence, but only in interplay with high local extinction risk. The functional forms of the relations of density compensation with spatial synchrony and persistence are robust to increases in dispersal mortality, landscape dynamics, or density dependence of dispersal. However, with each of these increases the maxima of spatial synchrony and persistence shift to higher over-compensation and levels of synchrony are reduced. Overall, for over-compensation high landscape connectivity has negative effects while for under-compensation connectivity affects persistence positively. This emphasizes the importance of species life-history traits for management decisions with regard to landscape connectivity: while dispersal corridors are essential for species with under-compensatory density regulation, they may have detrimental effects for endangered species with over-compensation.     

Does colonization asymmetry matter in metapopulations?

Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.     

Overcoming Allee effects through evolutionary,genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.     

Stochastic population dynamics of a montane ground-dwelling squirrel

Understanding the causes and consequences of population fluctuations is a central goal of ecology. We used demographic data from a long-term (1990-2008) study and matrix population models to investigate factors and processes influencing the dynamics and persistence of a golden-mantled ground squirrel (Callospermophilus lateralis) population, inhabiting a dynamic subalpine habitat in Colorado, USA. The overall deterministic population growth rate λ was 0.94±SE 0.05 but it varied widely over time, ranging from 0.45±0.09 in 2006 to 1.50±0.12 in 2003, and was below replacement (λ<1) for 9 out of 18 years. The stochastic population growth rate λ(s) was 0.92, suggesting a declining population; however, the 95% CI on λ(s) included 1.0 (0.52-1.60). Stochastic elasticity analysis showed that survival of adult females, followed by survival of juvenile females and litter size, were potentially the most influential vital rates; analysis of life table response experiments revealed that the same three life history variables made the largest contributions to year-to year changes in λ. Population viability analysis revealed that, when the influences of density dependence and immigration were not considered, the population had a high (close to 1.0 in 50 years) probability of extinction. However, probability of extinction declined to as low as zero when density dependence and immigration were considered. Destabilizing effects of stochastic forces were counteracted by regulating effects of density dependence and rescue effects of immigration, which allowed our study population to bounce back from low densities and prevented extinction. These results suggest that dynamics and persistence of our study population are determined synergistically by density-dependence, stochastic forces, and immigration.     

Assessing Extinction Risk in Small Metapopulations of Golden‐headed Lion Tamarins (Leontopithecus chrysomelas) in Bahia State,Brazil

Golden‐headed lion tamarins (GHLTs; Leontopithecus chrysomelas) are endangered primates endemic to the Brazilian Atlantic Forest, where loss of forest and its connectivity threaten species survival. Understanding the role of habitat availability and configuration on population declines is critical for guiding proactive conservation for this, and other, endangered species. We conducted population viability analysis to assess vulnerability of ten GHLT metapopulations to habitat loss and small population size. Seven metapopulations had a low risk of extirpation (or local extinction) over the next 100 years assuming no further forest loss, and even small populations could persist with immediate protection. Three metapopulations had a moderate/high risk of extirpation, suggesting extinction debt may be evident in parts of the species’ range. When deforestation was assumed to continue at current rates, extirpation risk significantly increased while abundance and genetic diversity decreased for all metapopulations. Extirpation risk was significantly negatively correlated with the size of the largest patch available to metapopulations, underscoring the importance of large habitat patches for species persistence. Finally, we conducted sensitivity analysis using logistic regression, and our results showed that local extinction risk was sensitive to percentage of females breeding, adult female mortality, and dispersal rate and survival; conservation or research programs that target these aspects of the species’ biology/ecology could have a disproportionately important impact on species survival. We stress that efforts to protect populations and tracts of habitat of sufficient size throughout the species’ distribution will be important in the near‐term to protect the species from continuing decline and extinction.