On the interpretation and application of mean times to extinction

As a metric of population viability, conservation biologists routinely predict the mean time to extinction (MTE). Interpretation of MTE depends on the underlying distribution of times to extinction (DTE). Despite claims to the contrary, all information regarding extinction risk can be obtained from this single statistic, the MTE, provided the DTE is exponential. We discuss the proper interpretation of MTE and illustrate how to calculate any population viability statistic when only the MTE is known and the DTE is assumed to be exponential. We also discuss the restrictive assumptions underlying the exponential DTE and the conditions under which alternative models for the DTE are preferable to the conventional (exponential) model. Despite superficial similarities between the exponential and alternative DTEs, several key differences can lead to substantially different interpretations of the MTE.     

Evolutionary age and risk of extinction in the global avifauna

Species at high risk of extinction are not distributed at random among higher taxa. Here we demonstrate that there is a positive relationship between the proportion of species in a taxon which are considered to be threatened and the evolutionary age of that taxon, both for the global avifauna and the avifauna of the New World. The potential mechanisms and consequences of the relationship are examined.     

Community extinction patterns in coloured environments

Understanding community responses to environmental variation is a fundamental aspect of ecological research, with direct ecological, conservation and economic implications. Here, we examined the role of the magnitude, correlation and autocorrelation structures of environmental variation on species' extinction risk (ER), and the probability of actual extinction events in model competitive communities. Both ER and probability increased with increasing positive autocorrelation when species responded independently to the environment, yet both decreased with a strong correlation between species-specific responses. These results are framed in terms of the synchrony between--and magnitude of variation within--species population sizes and are explained in terms of differences in noise amplification under different conditions. The simulation results are robust to changes in the strength of interspecific density dependence, and whether noise affects density-independent or density-dependent population processes. Similar patterns arose under different ranges of noise severity when these different model assumptions were examined. We compared our results with those from an analytically derived solution, which failed to capture many features of the simulation results.     

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

种群生存力分析（PVA）的方法与应用

随着人们对资源的加速利用,生境丧失和破碎化导致物种濒危问题日益严重.以岛屿生物地理学为理论起源的种群生存力分析（PVA）,通过分析和模拟种群动态过程并建立灭绝概率与种群数量之间的关系,为濒危物种保护提供了重要的理论依据和研究途径.在过去的几十年中,种群生存力分析已成为保护生物学中一项重要的研究内容.目前种群生存力分析发展稳定,但对其实际预测能力和准确性尚存质疑,应用方面也有待进一步发展.种群生存力分析的进一步完善还需要在理论和方法上的创新,特别是籍于景观生态学和可持续性科学的理念,将空间分析手段、经济社会因素纳入到物种和种群的预测和管理上,从而使其具有更完整的理论基础和更高的实用价值.为此,本文对种群生存力分析的历史、基本概念、研究方法、模型应用和准确性进行了综述,并提出了有关的研究展望.     

A method for validating stochastic models of population viability: a case study of the mountain pygmy-possum (Burramys parvus)

1.  A method of validating stochastic models of population viability is proposed, based on assessing the mean and variance of the predicted population size.
2.  The method is illustrated with a model of the population dynamics of the mountain pygmy-possum ( Burramys parvus Broom 1895), based on annual census data collected from a single population in the Snowy Mountains of New South Wales, Australia between 1986 and 1997. The model incorporates density-dependence in survivorship and recruitment, and demographic and environmental stochasticity.
3.  The model appeared to make reasonable predictions for the three populations that were used for validation, provided the equilibrium population size was estimated accurately. This may require that differences in habitat quality between populations be taken into account.
4.  Following validation, the model was given new parameters using the additional data from the three populations, and the risk of population decline within the next 100 years was assessed. Although populations as small as 15 females are predicted to be relatively safe from extinction caused by stochastic processes, B. parvus appears vulnerable to loss of habitat and reductions in the population growth rate.
5.  The approach used in this paper is one of few attempts to validate a model of population viability using field data, and demonstrates that some aspects of stochastic population models can be tested.     

When does parameter drift decrease the uncertainty in extinction risk estimates?

Halley (2003) proposed that parameter drift decreases the uncertainty in long‐range extinction risk estimates, because drift mitigates the extreme sensitivity of estimated risk to estimated mean growth rate. However, parameter drift has a second, opposing effect: it increases the uncertainty in parameter estimates from a given data set. When both effects are taken into account, parameter drift can increase, sometimes substantially, the uncertainty in risk estimates. The net effect depends sensitively on the type of drift and on which model parameters must be estimated from observational data on the population at risk. In general, unless many parameters are estimated from independent data, parameter drift increases the uncertainty in extinction risk. These findings suggest that more mechanistic PVA models, using long‐term data on key environmental variables and experiments to quantify their demographic impacts, offer the best prospects for escaping the high data requirements when extinction risk is estimated from observational data.     

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.     

Predicting extinction risks under climate change: coupling stochastic population models with dynamic bioclimatic habitat models

Species responses to climate change may be influenced by changes in available habitat, as well as population processes, species interactions and interactions between demographic and landscape dynamics. Current methods for assessing these responses fail to provide an integrated view of these influences because they deal with habitat change or population dynamics, but rarely both. In this study, we linked a time series of habitat suitability models with spatially explicit stochastic population models to explore factors that influence the viability of plant species populations under stable and changing climate scenarios in South African fynbos, a global biodiversity hot spot. Results indicate that complex interactions between life history, disturbance regime and distribution pattern mediate species extinction risks under climate change. Our novel mechanistic approach allows more complete and direct appraisal of future biotic responses than do static bioclimatic habitat modelling approaches, and will ultimately support development of more effective conservation strategies to mitigate biodiversity losses due to climate change.     

Linear analysis solves two puzzles in population dynamics: the route to extinction and extinction in coloured environments

In this paper, we give simple explanations to two unsolved puzzles that have emerged in recent theoretical studies in population dynamics. First, the tendency of some model populations to go extinct from high population densities, and second, the positive effect of autocorrelated environments on extinction risks for some model populations. Both phenomena are given general explanations by simple, linear, sto-chastic models. We emphasize the predictive and explanatory power of such models.     

Viability in a pink environment: why "white noise" models can be dangerous

Analysis of long time series suggests that environmental fluctuations may be accurately represented by 1/ f   noise (pink noise), where temporal correlation is found at several scales, and the range of fluctuations increases over time. Previous studies on the effects of coloured noise on population dynamics used first or second order autoregressive noise. I examined the importance of coloured noise for extinction risk using true 1/ f   noise. I also considered the problem of estimating extinction risk with a limited sample of environmental variation. Pink noise environments increased extinction risk in random walk models where environmental variation affected the growth rate. However, pink noise environments decreased extinction risk in the Ricker model where environmental variation modified the carrying capacity. Underestimation of environmental variance almost always yielded underestimation of extinction risk. For either population viability analysis or management, we should carefully consider the long-term behaviour of the environment as well as how we include environmental noise in population models.     

Density dependence in resource exploitation: empirical test of Levins' metapopulation model

Levins' model of metapopulation dynamics is modified to incorporate variable degrees of density dependence in the per capita exploitation of resource patches. We demonstrate a simple means of testing for this density dependence in a sample of metapopulations, each at its equilibrium balance of local colonization to extinction. The fraction of habitable unoccupied patches equilibrates to a constant number under the null model of density independent colonization, and to a constant proportion under strong density dependence. We compare the null model to two density dependent alternatives, using data on exploitation of nest boxes by collared flycatchers Ficedula albicollis . The analysis shows how predicted trends in the equilibrium unoccupied fraction are similar for both spatial interference and net immigration. This needs to be recognized, since the null hypothesis of a constant unused resource applies also to the dynamics of consumable resources, where it is expressed in a constant stock of uneaten prey at the dynamic equilibrium of predators to prey.     

Allee effects and extinction in a lattice model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which the probability of extinction is greatly increased. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.     

Assessing human impact despite uncertainty:viability of the northern spotted owl metapopulation in the northwestern USA

We demonstrate the effect of uncertainty (resulting from lack of information or measurement error) on the assessment of human impact, with an analysis of the viability of the northern spotted owl throughout its range in the United States. We developed a spatially-explicit, stage-structured, stochastic metapopulation model of the northern spotted owl throughout its range in the United States. We evaluated the viability of the metapopulation using measures such as risk of decline and time to extinction. We incorporated uncertainty in the form of parameter ranges, and used them to estimate upper and lower bounds on the estimated viability of the species. We analysed the effect of this type of uncertainty on the assessment of human impact by comparing the species' viability under current conditions and under an assumed loss of spotted owl habitat in the next 100 years. The ranges of parameters were quite large and resulted in a wide range of risks of extinction. Despite this uncertainty, the results were sensitive to parameters related to habitat loss: under all assumptions and combinations of parameters, the model predicted that habitat loss results in substantially higher risks of metapopulation decline. This result demonstrated that even with relatively large uncertainties, risk-based model results can be used to assess human impact reliably.     

Comparison of methods for detecting bottlenecks from microsatellite loci

This paper describes simulation tests to compare methods for detecting recent bottlenecks using microsatellite data. This study considers both type I error (detecting a bottleneck when there wasn’t one) and type II error (failing to detect a bottleneck when there was one) under a variety of scenarios. The two most promising methods were the range in allele size conditioned on the number of alleles, M _k , and heterozygosity given the number of alleles, H _k , under a two-phase mutation model; in most of the simulations one of these two methods had the lowest type I and type II error relative to other methods. M _k was the method most likely to correctly identify a bottleneck when a bottleneck lasted several generations, the population had made a demographic recovery, and mutation rates were high or pre-bottleneck population sizes were large. On the other hand H _k was most likely to correctly identify a bottleneck when a bottleneck was more recent and less severe and when mutation rates were low or pre-bottleneck population sizes were small. Both methods were prone to type I errors when assumptions of the model were violated, but it may be easier to design a conservative heterozygosity test than a conservative ratio test.