Measurement error and estimates of population extinction risk

It is common to estimate the extinction probability for a vulnerable population using methods that are based on the mean and variance of the long‐term population growth rate. The numerical values of these two parameters are estimated from time series of population censuses. However, the proportion of a population that is registered at each census is typically not constant but will vary among years because of stochastic factors such as weather conditions at the time of sampling. Here, we analyse how such sampling errors influence estimates of extinction risk and find sampling errors to produce two opposite effects. Measurement errors lead to an exaggerated overall variance, but also introduce negative autocorrelations in the time series (which means that estimates of annual growth rates tend to alternate in size). If time series data are treated properly these two effects exactly counter balance. We advocate routinely incorporating a measure of among year correlations in estimating population extinction risk.     

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.     

Scaling the extinction vortex: Body size as a predictor of population dynamics close to extinction events

1. Mutual reinforcement between abiotic and biotic factors can drive small populations into a catastrophic downward spiral to extinction—a process known as the “extinction vortex.” However, empirical studies investigating extinction dynamics in relation to species'' traits have been lacking.
2. We assembled a database of 35 vertebrate populations monitored to extirpation over a period of at least ten years, represented by 32 different species, including 25 birds, five mammals, and two reptiles. We supplemented these population time series with species‐specific mean adult body size to investigate whether this key intrinsic trait affects the dynamics of populations declining toward extinction.
3. We performed three analyses to quantify the effects of adult body size on three characteristics of population dynamics: time to extinction, population growth rate, and residual variability in population growth rate.
4. Our results provide support for the existence of extinction vortex dynamics in extirpated populations. We show that populations typically decline nonlinearly to extinction, while both the rate of population decline and variability in population growth rate increase as extinction is approached. Our results also suggest that smaller‐bodied species are particularly prone to the extinction vortex, with larger increases in rates of population decline and population growth rate variability when compared to larger‐bodied species.
5. Our results reaffirm and extend our understanding of extinction dynamics in real‐life extirpated populations. In particular, we suggest that smaller‐bodied species may be at greater risk of rapid collapse to extinction than larger‐bodied species, and thus, management of smaller‐bodied species should focus on maintaining higher population abundances as a priority.

     

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.     

Human overexploitation and extinction risk correlates of Chinese snakes

China is one of the countries with the richest snake biodiversity in the world. However, about one‐third of all 236 species are now considered threatened, partially due to the intense human overexploitation. Despite that, to date, no study has explicitly investigated the patterns and processes of extinction and threats of Chinese snakes, or between human exploited and unexploited snake subgroups. We addressed the following three questions: 1) which snake families proportionally include more human exploited species than expected by chance? 2) Which species traits and extrinsic factors are correlated with their extinction risk? 3) Are there differences between human exploited and unexploited species in terms of patterns and processes of extinction? We found that the family Elapidae contained a significantly higher number of exploited species. Considering eight species traits and four extrinsic factors, we performed phylogenetic correlation tests, finding that small geographic range size, large body length, oviparous reproduction, diurnal activity and high human exploitation were important in determining the extinction risk of all Chinese snakes. Moreover, human exploited snakes had a higher percentage of threatened species and large‐bodied species than unexploited snakes. Extinction risk of human exploited species was related to body length, reproduction mode and activity period, whereas that of human unexploited species were associated with geographic range size, microhabitat and annual temperature. Overall, we highlight the phylogenetic non‐random exploitation of snakes, and different factors underlying species response to human overexploitation. We suggest that conservation priority should be given to exploitation‐prone families and species with extinction‐prone traits, as identified in this study. Moreover, human exploited and unexploited species should be managed considering different strategies since their extinction risk was associated with different ecological traits. Conservation actions should also focus on preventing human threats, such as human overexploitation and habitat loss, for the effective preservation of Chinese snakes.     

区域生态系统风险管理的EVR模型及其应用研究

系统探讨了生态风险的成因、内涵;结合当前国际上流行的VaR风险管理模型,在生态风险理论有关研究的基础上．建立了一类新颖而实用的区域生态系统风险管理模型-EVR。并对模型的特点、性质、建模思想、参数选取的进一步完善和改进工作进行了详细的阐述。最后,以干旱风险为例,对EVR模型进行了应用研究。     

Effects of environmental variation on extinction and establishment

Theoretical models predict that increasing environmental variation increases the probability of extinction, decreases the probability of establishment, and influences the distribution of times to extinction or establishment. We conducted an experiment with 281 independent populations of Daphnia magna under controlled laboratory conditions to test these predictions. Consistent with the theory, the fraction of populations going extinct increased and the fraction of populations establishing self‐sustaining populations decreased under higher levels of environmental variation compared with controls. Time to extinction decreased under higher levels of environmental variation, but we found no effect on time to establishment. These results are consistent with theoretical predictions from models of extinction. They therefore support the use of stochastic population models to predict the fates of introductions of non‐indigenous species or native endangered species based on historic fluctuations and/or expected future conditions.     

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.     

A toxicological basis to derive generic interspecies uncertainty factors for application in human and ecological risk assessment

A new method is proposed to derive the size of the interspecies uncertainty factor (UF) that is toxicologically and statistically based. The method is based on the biological/evolutionary assumption that similarity in susceptibility to toxic substances is a function of phylogenetic relatedness. This assumption is assessed via a large and highly structured aquatic database with over 500 agents tested in specific binary toxicity comparison (i.e., when two species have been tested with the same chemical under identical conditions) for dozens of species of wide phylogenetic relatedness. The methodology takes into account the generic need to estimate a response in any species (not just human) and the need to predict responses for new chemical agents. The method involves quantifying interspecies variation in susceptibility to numerous toxic substances via the use of binary interspecies comparisons that are converted to a 95% UF. This interspecies UF represents an estimate of the upper 95% of the population of 95% prediction intervals (PI) for binary interspecies comparisons within four categories of phylogenetic relatedness (species‐within‐genus, genera‐within‐family, families‐within‐order, orders‐within‐class). The 95% interspecies UFs range from a low of 10 for species‐within‐genus up to 65 for orders‐within‐class. Most mammalian toxicology studies involving mice, rats, cats, dogs, gerbils, and rabbits are orders‐within‐class categories for human risk assessment and would be provided a 65‐fold UF. Larger or smaller interspecies UF values could be selected based on the level of protection desired. The procedures described have application to both human and ecological risk assessment.     

外来植物的入侵机制及其生态风险评价

外来植物入侵已成为严重威胁生态系统健康发展的全球性问题,预防优于治理,对外来植物进行生态风险评价可有效地防御和降低入侵风险。本文基于生态风险评价理论,通过对外来植物入侵特性和过程的分析,探讨了外来植物入侵生态风险的评价方法。将评价程序分为风险源分析、风险受体评价、暴露与危害评价、风险综合评价和风险管理对策5部分,初步建立了风险源评价指标体系,以及度量生态损失和生态风险的指标和公式,进而得出外来植物入侵综合生态风险评价的方法。     

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).     

Extinction risk of a meta-population: aggregation approach

Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.     

Macroecology and extinction risk correlates of frogs

Aim  Our aim was to test whether extinction risk of frog species could be predicted from their body size, fecundity or geographical range size. Because small geographical range size is a correlate of extinction risk in many taxa, we also tested hypotheses about correlates of range size in frogs.
Location  Global.
Methods  Using a large comparative data set ( n  = 527 species) compiled from the literature, we performed bivariate and multiple regressions through the origin of independent contrasts to test proposed macroecological patterns and correlates of extinction risk in frogs. We also created minimum adequate models to predict snout–vent length, clutch size, geographical range size and IUCN Red List status in frogs. Parallel non-phylogenetic analyses were also conducted. We verified the results of the phylogenetic analyses using gridded data accounting for spatial autocorrelation.
Results  The most threatened frog species tend to have small geographical ranges, although the relationship between range and extinction risk is not linear. In addition, tropical frogs with small clutches have the smallest ranges. Clutch size was strongly positively correlated with geographical range size ( r ² = 0.22) and body size ( r ² = 0.28).
Main conclusions  Our results suggest that body size and fecundity only affect extinction risk indirectly through their effect on geographical range size. Thus, although large frogs with small clutches tend to be endangered, there is no comparative evidence that this relationship is direct. If correct, this inference has consequences for conservation strategy: it would be inefficient to allocate conservation resources on the basis of low fecundity or large body size; instead it would be better to protect areas that contain many frog species with small geographical ranges.     

Reconstructing past species assemblages reveals the changing patterns and drivers of extinction through time

Predicting future species extinctions from patterns of past extinctions or current threat status relies on the assumption that the taxonomic and biological selectivity of extinction is consistent through time. If the driving forces of extinction change through time, this assumption may be unrealistic. Testing the consistency of extinction patterns between the past and the present has been difficult, because the phylogenetically explicit methods used to model present-day extinction risk typically cannot be applied to the data from the fossil record. However, the detailed historical and fossil records of the New Zealand avifauna provide a unique opportunity to reconstruct a complete, large faunal assemblage for different periods in the past. Using the first complete phylogeny of all known native New Zealand bird species, both extant and extinct, we show how the taxonomic and phylogenetic selectivity of extinction, and biological correlates of extinction, change from the pre-human period through Polynesian and European occupation, to the present. These changes can be explained both by changes in primary threatening processes, and by the operation of extinction filter effects. The variable patterns of extinction through time may confound attempts to identify risk factors that apply across time periods, and to infer future species declines from past extinction patterns and current threat status.     

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。     

Primate extinction risk and historical patterns of speciation and extinction in relation to body mass

Body mass is thought to influence diversification rates, but previous studies have produced ambiguous results. We investigated patterns of diversification across 100 trees obtained from a new Bayesian inference of primate phylogeny that sampled trees in proportion to their posterior probabilities. First, we used simulations to assess the validity of previous studies that used linear models to investigate the links between IUCN Red List status and body mass. These analyses support the use of linear models for ordinal ranked data on threat status, and phylogenetic generalized linear models revealed a significant positive correlation between current extinction risk and body mass across our tree block. We then investigated historical patterns of speciation and extinction rates using a recently developed maximum-likelihood method. Specifically, we predicted that body mass correlates positively with extinction rate because larger bodied organisms reproduce more slowly, and body mass correlates negatively with speciation rate because smaller bodied organisms are better able to partition niche space. We failed to find evidence that extinction rates covary with body mass across primate phylogeny. Similarly, the speciation rate was generally unrelated to body mass, except in some tests that indicated an increase in the speciation rate with increasing body mass. Importantly, we discovered that our data violated a key assumption of sample randomness with respect to body mass. After correcting for this bias, we found no association between diversification rates and mass.     

Phylogenetic,spatial and environmental components of extinction risk in carnivores

Aim Extinction risk is non‐randomly distributed across phylogeny and space and is influenced by environmental conditions. We quantified the relative contribution of these factors to extinction risk to unveil the underlying macroecological processes and derive predictive models. Location Global. Methods Based on the IUCN global assessments, we divided 192 carnivore species into two dichotomous classes representing different levels of extinction risk. We used spatial proximity, phylogenetic relationship and environmental variables together with phylogenetic eigenvector regression and spatial eigenvector filters to model and predict threat status. Results Our full models explained between 57% and 96% of the variance in extinction risk. Phylogeny and spatial proximity roughly explained between 21% and 70% of the total variation in all analyses, while the explanatory power of environmental conditions was relatively weaker (up to 15%). Phylogeny and spatial proximity contributed equally to the explained variance in the lower threat level, while spatial proximity was the most important factor in the models of the higher threat level. Prediction of threat status achieved 97% correct assignments. Main conclusions Our approach differs fundamentally from current studies of extinction risk because it does not necessarily rely on life‐history information. We clearly show that instead of treating phylogenetic inertia and spatial signal as statistical nuisances, space and phylogeny should be viewed as very useful in explaining a wide range of phenomena in comparative studies.