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。     

Predicting the process of extinction in experimental microcosms and accounting for interspecific interactions in single‐species time series

Predicting population extinction risk is a fundamental application of ecological theory to the practice of conservation biology. Here, we compared the prediction performance of a wide array of stochastic, population dynamics models against direct observations of the extinction process from an extensive experimental data set. By varying a series of biological and statistical assumptions in the proposed models, we were able to identify the assumptions that affected predictions about population extinction. We also show how certain autocorrelation structures can emerge due to interspecific interactions, and that accounting for the stochastic effect of these interactions can improve predictions of the extinction process. We conclude that it is possible to account for the stochastic effects of community interactions on extinction when using single‐species time series.     

The route to extinction in variable environments

Estimating the extinction risk of natural populations is not only an urgent problem in conservation biology but also involves some profound aspects of population dynamics. Apart from the obvious case of a continuous decrease in a population's carrying capacity, understanding the extinction process necessarily includes environmental and demographic stochasticity. Here, we build from first principles two stochastic, single-population models that can account for various routes to extinction via demographic and environmental variability. The Ricker model of population dynamics generates extinctions from either low or high (around or above carrying capacity) population densities, primarily depending on the growth parameter r . Since extinctions from high densities seem 'unnatural', there is either something wrong with the model or with our intuition. Suitable data are scarce. Environmental variability has its strongest influence on extinction risk via per capita birth rates and is only marginally influencing that risk via per capita death rates if the growth parameter is high. The distribution of the environmental noise and the stochastic structure of the model have quantitative, but not qualitative effects on the estimates of extinction risks. We conclude that to determine the route to extinction and to estimate the extinction risk require a careful choice of both the deterministic component of the population model (e.g., under- or over-compensation) and the structure of the demographic and environmental variabilities.     

Incorporating the temporal autocorrelation of demographic rates into structured population models

Population dynamics are typically temporally autocorrelated: population sizes are positively or negatively correlated with past population sizes. Previous studies have found that positive temporal autocorrelation increases the risk of extinction due to ‘inertia’ that prolongs downward fluctuations in population size. However, temporal autocorrelation has not yet been analyzed at the level of life cycle transitions. We developed an R package, colorednoise, which creates stochastic matrix population projections with distinct temporal autocorrelation values for each matrix element. We used it to analyze long-term demographic data on 25 populations from the COMADRE and COMPADRE databases and simulate their stochastic dynamics. We found a broad range of temporal autocorrelation across species, populations and life cycle stages. The number of stage-classes in the matrix strongly affected the temporal autocorrelation of the growth rate. In the plant populations, reproduction transitions had more negative temporal autocorrelation than survival transitions, and matrices dominated by positive temporal autocorrelation had higher extinction risk, while in animal populations transition type was not associated with noise color. Our results indicate that temporal autocorrelation varies across life cycle transitions, even among populations of the same species. We present the colorednoise package for researchers to analyze the temporal autocorrelation of structured demographic rates.     

Demographic stochasticity, allee effects, and extinction: the influence of mating system and sex ratio

Demographic stochasticity has a substantial influence on the growth of small populations and consequently on their extinction risk. Mating system is one of several population characteristics that may affect this. We use a stochastic pair-formation model to investigate the combined effects of mating system, sex ratio, and population size on demographic stochasticity and thus on extinction risk. Our model is designed to accommodate a continuous range of mating systems and sex ratios as well as several levels of stochasticity. We show that it is not mating system alone but combinations of mating system and sex ratio that are important in shaping the stochastic dynamics of populations. Specifically, polygyny has the potential to give a high demographic variance and to lower the stochastic population growth rate substantially, thus also shortening the time to extinction, but the outcome is highly dependent on the sex ratio. In addition, population size is shown to be important. We find a stochastic Allee effect that is amplified by polygyny. Our results demonstrate that both mating system and sex ratio must be considered in conservation planning and that appreciating the role of stochasticity is key to understanding their effects.     

Estimating the time to extinction in an island population of song sparrows

We estimated and modelled how uncertainties in stochastic population dynamics and biases in parameter estimates affect the accuracy of the projections of a small island population of song sparrows which was enumerated every spring for 24 years. The estimate of the density regulation in a theta-logistic model (theta = 1.09 suggests that the dynamics are nearly logistic, with specific growth rate r1 = 0.99 and carrying capacity K = 41.54. The song sparrow population was strongly influenced by demographic (ŝigma2(d) = 0.66) and environmental (ŝigma2(d) = 0.41) stochasticity. Bootstrap replicates of the different parameters revealed that the uncertainties in the estimates of the specific growth rate r1 and the density regulation theta were larger than the uncertainties in the environmental variance sigma2(e) and the carrying capacity K. We introduce the concept of the population prediction interval (PPI), which is a stochastic interval which includes the unknown population size with probability (1 - alpha). The width of the PPI increased rapidly with time because of uncertainties in the estimates of density regulation as well as demographic and environmental variance in the stochastic population dynamics. Accepting a 10% probability of extinction within 100 years, neglecting uncertainties in the parameters will lead to a 33% overestimation of the time it takes for the extinction barrier (population size X = 1) to be included into the PPI. This study shows that ignoring uncertainties in population dynamics produces a substantial underestimation of the extinction risk.     

Stochastic population theory faces reality in the laboratory

Understanding the factors that affect most severely the extinction risk of populations is crucial for maintaining biodiversity. An important general pattern derived from stochastic population theory is that time to extinction should decrease with increasing environmental stochasticity. Drake and Lodge recently provided one of the first pieces of experimental support for this simple prediction by artificially manipulating the dynamics of populations of Daphnia. A future challenge will be to include both demographic stochasticity and environmental stochasticity in such studies.     

Impact of natural enemies on obligately cooperative breeders

Obligately cooperative breeders (cooperators) display a negative growth rate once they fall below a minimum density. Constraints imposed by natural enemies, such as predators or competitors, may push cooperator groups closer to this threshold, thus increasing the risk that stochastic fluctuations will drive them below it. This may indirectly drive these groups to extinction, thereby increasing the risk of population extinction. In this paper, we construct mathematical models of the dynamics of groups of cooperators and non-cooperators in the presence of two types of enemies: enemies whose dynamics do not depend on the dynamics of their victim (e.g., amensal competitor, generalist predator) and those whose dynamics do. In the latter case, we distinguish positive (e.g., specialist predator) and negative (e.g., bilateral competitor) reciprocal effects. These models correspond to the classical amensal, predation and competition models, in the presence of an Allee effect. We then develop the models to study consequences at the population level. By comparing models with or without an Allee effect, we show that enemies decrease the group size of cooperators more than that of non-cooperators, and this increases their group extinction risk. We also demonstrate how an Allee effect at a lower dynamical level can have consequences at a higher level: inverse density dependence at the group level generated lower population sizes and higher risks of population extinction. Our results also suggest that demographic compensation can be achieved by cooperators through an increased intrinsic growth rate, or by decreasing the enemy constraint. Both of these types of compensation have been observed in empirical studies of cooperators.     

Population viability analysis of the butterfly Lopinga achine in a changing landscape in Sweden

Metapopulation theory has generally focused only on the stochastic turn-over rate among populations and assumed that the number and location of suitable habitat patches will remain constant through time. This study combines in a PVA both the deterministic landscape dynamics and the stochastic colonisations and extinctions of populations for the butterfly Lopinga achine in Sweden. With data on occupancy pattern and the rate of habitat change, we built a simulation model and examined five different scenarios with different assumptions of landscape changes for L. achine . If no landscape changes would be expected, around 80 populations are predicted to persist during the next 100 yr. Adding the knowledge that many of the sites are unmanaged and that the host plant will slowly deteriorate as canopies close over, and adding environmental variation and synchrony, showed that the number of populations will decrease to around of 4.3 and 2.8 respectively, with an extinction risk of 34% – quite different from the first scenario based only on the metapopulation model. This study has shown the importance of incorporating both deterministic and stochastic events when making a reliable population viability analysis. Even though one can not expect that the long-term predictions of either occupied patches or extinction risks will be accurate quantitatively, the qualitative implications are correct. The extinction risk will be high if grazing is not applied to more patches than is the case today. The simulations indicate that an absolute minimum of 10–30 top-ranked patches needs to be managed for the persistence of the metapopulation of L. achine in the long term. The same problem of abandoned and overgrowing habitats affects many other threatened species in the European landscape and a similar approach could also be applied to them.     

Using population viability analysis to predict the effect of fire on the extinction risk of an endangered shrub <Emphasis Type="Italic">Verticordia fimbrilepis</Emphasis> subsp. <Emphasis Type="Italic">fimbrilepis</Emphasis> in a fragmented landscape

The fragmentation of mediterranean climate landscapes where fire is an important landscape process may lead to unsuitable fire regimes for many species, particularly rare species that occur as small isolated populations. We investigate the influence of fire interval on the persistence of population fragments of the endangered shrub Verticordia fimbrilepis Turcz. subsp. fimbrilepis in mediterranean climate south-west of Western Australia. We studied the population biology of the species over 5 years. While the species does recruit sporadically without fire this occurs only in years with above average rainfall, so fire seems to be the main environmental factor producing extensive recruitment. Transition matrix models were constructed to describe the shrub’s population dynamics. As the species is killed by fire and relies on a seed bank stimulated to germinate by smoke, stochastic simulations to compare different fire frequencies on population viability were completed. Extinction risk increased with increasing average fire interval. Initial population size was also important, with the lowest extinction risk in the largest population. For populations in small reserves where fire is generally excluded, inevitable plant senescence will lead to local extirpation unless fires of suitable frequency can be used to stimulate regeneration. While a suitable fire regime reduces extinction risk small populations are still prone to extinction due to stochastic influences, and this will be exacerbated by a projected drying climate increasing rates of adult mortality and also seedling mortality in the post-fire environment.     

Optimization and Phenotype Allocation

We study the phenotype allocation problem for the stochastic evolution of a multitype population in a random environment. Our underlying model is a multitype Galton–Watson branching process in a random environment. In the multitype branching model, different types denote different phenotypes of offspring, and offspring distributions denote the allocation strategies. Two possible optimization targets are considered: the long-term growth rate of the population conditioned on nonextinction, and the extinction probability of the lineage. In a simple and biologically motivated case, we derive an explicit formula for the long-term growth rate using the random Perron–Frobenius theorem, and we give an approximation to the extinction probability by a method similar to that developed by Wilkinson. Then we obtain the optimal strategies that maximize the long-term growth rate or minimize the approximate extinction probability, respectively, in a numerical example. It turns out that different optimality criteria can lead to different strategies.     

Stochastic population dynamics of clonal plants: Numerical experiments with ramet and genet models

Dynamics of ramer and genet populations were analyzed by use of stochastic matrix models. Based on field data, population development and extinction rates during 50 simulated years were estimated for ramet populations of three speciesPotentilla anserina, Rubus saxatilis andLinnaea borealis. Only small initial populations (below 125–250 ramets), experienced a detectable risk of extinction within this time interval. ForP. anserina andR. saxatilis, population increase occurred in some simulations despite negative average growth rates. A model for stochastic genet dynamics was constructed by combining field data and hypothesized parameter values. Growth rate and population structure were insensitive to variation in disturbance intensity and frequency, whereas variation in recruitment affected population structure but only to a minor extent growth rate. Decreasing recruitment causes extinction of genet populations, but the time-scale for the decline is in the magnitude of centuries for initial genet populations of about 1000 individuals. Dynamics of genets in clonal plants thus incorporate processes occurring on widely different scales. Some implications of the results for models of population dynamics in long-lived clonal plants are discussed.     

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.     

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.     

Partitioning the effects of deterministic and stochastic processes on species extinction risk

Species populations are subjected to deterministic and stochastic processes, both of which contribute to their risk of extinction. However, current understanding of the relative contributions of these processes to species extinction risk is far from complete. Here, we address this knowledge gap by analyzing a suite of models representing species populations with negative intrinsic growth rates, to partition extinction risk according to deterministic processes and two broad classes of stochastic processes – demographic and environmental variance. Demographic variance refers to random variations in population abundance arising from random sampling of events given a particular set of intrinsic demographic rates, whereas environmental variance refers to random abundance variations arising from random changes in intrinsic demographic rates over time. When the intrinsic growth rate was not close to zero, we found that deterministic growth was the main driver of mean time to extinction, even when population size was small. This contradicts the intuition that demographic variance is always an important determinant of extinction risk for small populations. In contrast, when the intrinsic growth rate was close to zero, stochastic processes exerted substantial negative effects on the mean time to extinction. Demographic variance had a greater effect than environmental variance at low abundances, with the reverse occurring at higher abundances. In addition, we found that the combined effects of demographic and environmental variance were often substantially lower than the sum of their effects in isolation from each other. This sub-additivity indicates redundancy in the way the two stochastic processes increase extinction risk, and probably arises because both processes ultimately increase extinction risk by boosting variation in abundance over time.     

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.     

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。     

Harvest reserves reduce extinction risk in an experimental microcosm

Overharvesting by humans threatens a substantial fraction of endangered species. Reserves have recently received enormous attention as a means of better conserving harvested resources, despite limited empirical evidence of their efficacy. We used manipulated microcosms to test whether reserves reduce extinction risk in mobile populations of harvested Tetrahymena thermophila , a ciliate. Here we show that patterns of population distribution inside and outside reserves can be accurately predicted on the basis of simple models of diffusion coupled with logistic controls on local population growth. No extinctions occurred in eight experimental trials with reserves, whereas extinction occurred in seven of eight trials without reserves, as predicted by population viability models based on stochastic population processes. These results suggest that marine reserves may be an effective means of improving long-term viability in heavily harvested fish species.     

How inbreeding and outbreeding influence the risk of extinction--a genetically explicit model

We have developed a stochastic model to explore the common effect which genetics and demography have on the extinction risk of endangered populations. The dynamics is formulated as a MARKOVian birth and death process (in continuous time), whereby selection acts through different mortalities of each genotype. With the help of this model we are able to show how inbreeding and outbreeding can influence the genetic variability and the survival of a population. Whether inbreeding or outbreeding takes place depends on the specific mating system. In our model we consider positive assortative as well as disassortative mating. In the case of additive fitness we show that inbreeding reduces the extinction risk and the genetic variability.