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。     

Approximate reduction of multiregional models with environmental stochasticity

In this work we extend previous results regarding the use of approximate aggregation techniques to simplify the study of discrete time models for populations that live in an environment that changes randomly with time. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter. We present the reduction of a stochastic multiregional model in which the population, structured by age and spatial location, lives in a random environment and in which migration is fast with respect to demography. However, the technique works in much more general settings as, for example, those of stage-structured populations living in a multipatch environment. By manipulating the original system and appropriately defining the global variables we obtain a simpler system. The paper concentrates on establishing relationships between the original and the reduced systems for a given separation of time scales between the two processes. In particular, we relate the original state variables and the global variables and, in the case the pattern of temporal variation is Markovian, we relate the presence of strong stochastic ergodicity for the original and reduced systems. Moreover, we relate different measures of asymptotic population growth for these systems.     

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.     

Incorporating environmental stochasticity within a biological population model

The birth and death transition rates for a population are modelled as functions of both the population size and the environmental condition. An assortment of important theoretical results and techniques that can be utilized to analyze such a population’s behaviour is covered. Consequently, these results and techniques are used to study two examples. Firstly, we study a population with a stable equilibrium state, whose per capita birth and death rates are linearly related to the environmental condition. (The environmental condition in turn is modelled as an Ornstein–Uhlenbeck process.) Secondly, we study a population affected by two interdependent environmental factors.     

Derivatives of the stochastic growth rate

We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a-the “stochastic elasticities”-with respect to changes in the demographic parameters were derived by Tuljapurkar (1990). These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and old formulas.     

Recent exposure to environmental stochasticity does not determine the demographic resilience of natural populations

Escalating climatic and anthropogenic pressures expose ecosystems worldwide to increasingly stochastic environments. Yet, our ability to forecast the responses of natural populations to this increased environmental stochasticity is impeded by a limited understanding of how exposure to stochastic environments shapes demographic resilience. Here, we test the association between local environmental stochasticity and the resilience attributes (e.g. resistance, recovery) of 2242 natural populations across 369 animal and plant species. Contrary to the assumption that past exposure to frequent environmental shifts confers a greater ability to cope with current and future global change, we illustrate how recent environmental stochasticity regimes from the past 50 years do not predict the inherent resistance or recovery potential of natural populations. Instead, demographic resilience is strongly predicted by the phylogenetic relatedness among species, with survival and developmental investments shaping their responses to environmental stochasticity. Accordingly, our findings suggest that demographic resilience is a consequence of evolutionary processes and/or deep-time environmental regimes, rather than recent-past experiences.     

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.     

Long-term demographic analysis in goshawk <Emphasis Type="Italic">Accipiter gentilis</Emphasis>: the role of density dependence and stochasticity

Density dependence and environmental stochasticity are both potentially important processes influencing population demography and long-term population growth. Quantifying the importance of these two processes for population growth requires both long-term population as well as individual-based data. I use a 30-year data set on a goshawk Accipiter gentilis population from Eastern Westphalia, Germany, to describe the key vital rate elements to which the growth rate is most sensitive and test how environmental stochasticity and density dependence affect long-term population growth. The asymptotic growth rate of the fully age-structured mean matrix model was very similar to the observed one (0.7% vs. 0.3% per annum), and population growth was most elastic to changes in survival rate at age classes 1-3. Environmental stochasticity led only to a small change in the projected population growth rate (between -0.16% and 0.67%) and did not change the elasticities qualitatively, suggesting that the goshawk life history of early reproduction coupled with high annual fertility buffers against a variable environment. Age classes most crucial to population growth were those in which density dependence seemed to act most strongly. This emphasises the importance of density dependence as a regulatory mechanism in this goshawk population. It also provides a mechanism that might enable the population to recover from population lows, because a mean matrix model incorporating observed functional responses of both vital rates to population density coupled with environmental stochasticity reduced long-term extinction risk of 30% under density-independent environmental stochasticity and 60% under demographic stochasticity to zero.     

Phenological spread in plants: A result of adaptations to environmental stochasticity?

Summary Plant species co-inhabiting a given geographical region often have distinetly different times of flowering. It is shown that such phenological spread, duc to short-term stochastic variation in weather variables, relaxes competition for empty sites to be colonized by diaspores. For sufficiently large spreads stable coexistence becomes possible. The applicability of the proposed hypothesis to the observed instances of phenological spread is discussed and shown to extend beyond that of other current theories.We thank L.-E. Liljelund, C. Solbreck and C. Wiklund for helpful comments. This work was carried out within the Swedish Coniferous Forest Project, supported by the Swedish Natural Science Research Council, the Swedish Environmental Protection Board, the Swedish Council of Forestry and Agricultural Research, and the Wallenberg foundation.     

Evolution of dispersal in metapopulations with local density dependence and demographic stochasticity

In this paper, we predict the outcome of dispersal evolution in metapopulations based on the following assumptions: (i) population dynamics within patches are density-regulated by realistic growth functions; (ii) demographic stochasticity resulting from finite population sizes within patches is accounted for; and (iii) the transition of individuals between patches is explicitly modelled by a disperser pool. We show, first, that evolutionarily stable dispersal rates do not necessarily increase with rates for the local extinction of populations due to external disturbances in habitable patches. Second, we describe how demographic stochasticity affects the evolution of dispersal rates: evolutionarily stable dispersal rates remain high even when disturbance-related rates of local extinction are low, and a variety of qualitatively different responses of adapted dispersal rates to varied levels of disturbance become possible. This paper shows, for the first time, that evolution of dispersal rates may give rise to monotonically increasing or decreasing responses, as well as to intermediate maxima or minima.     

Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates

1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5.1%. 4. Significant density regulation was present in 53.6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.     

Stability of discrete age-structured and aggregated delay-difference population models

Sufficiency conditions for local stability are derived for a class of density dependent Leslie matrix models. Four of the recruitment functions in common use in fisheries management are then considered. In two of these oscillating instability can never occur (Beverton and Holt and Cushing forms). In the other two (Deriso-Schnute and Shepherd forms) undamped oscillations are possible within the region of parameter space described here. An algorithm is developed for calculating necessary and sufficient local stability conditions for a simplified form of the general age-structured model. The complete spectrum of stability states (monotonic stability; monotonic instability; oscillating-stable; oscillating-unstable) and the bifurcation periods are given for selected examples of this model. The examples cover a large portion of the parameter space of interest in resource management. It is shown that in perfectly deterministic systems which are observed with error, oscillating instabilities may be missed, and such systems could be erroneously assumed to be stable.     

An integrated modeling approach to estimating Gunnison sage‐grouse population dynamics: combining index and demographic data

Evaluation of population dynamics for rare and declining species is often limited to data that are sparse and/or of poor quality. Frequently, the best data available for rare bird species are based on large‐scale, population count data. These data are commonly based on sampling methods that lack consistent sampling effort, do not account for detectability, and are complicated by observer bias. For some species, short‐term studies of demographic rates have been conducted as well, but the data from such studies are typically analyzed separately. To utilize the strengths and minimize the weaknesses of these two data types, we developed a novel Bayesian integrated model that links population count data and population demographic data through population growth rate (λ) for Gunnison sage‐grouse (Centrocercus minimus). The long‐term population index data available for Gunnison sage‐grouse are annual (years 1953–2012) male lek counts. An intensive demographic study was also conducted from years 2005 to 2010. We were able to reduce the variability in expected population growth rates across time, while correcting for potential small sample size bias in the demographic data. We found the population of Gunnison sage‐grouse to be variable and slightly declining over the past 16 years.     

Accounting for stochasticity in demographic compensation along the elevational range of an alpine plant

Demographic compensation arises when vital rates change in opposite directions across populations, buffering the variation in population growth rates, and is a mechanism often invoked to explain the stability of species geographic ranges. However, studies on demographic compensation have disregarded the effects of temporal variation in vital rates and their temporal correlations, despite theoretical evidence that stochastic dynamics can affect population persistence in temporally varying environments. We carried out a seven‐year‐long demographic study on the perennial plant Arabis alpina (L.) across six populations encompassing most of its elevational range. We discovered demographic compensation in the form of negative correlations between the means of plant vital rates, but also between their temporal coefficients of variation, correlations and elasticities. Even if their contribution to demographic compensation was small, this highlights a previously overlooked, but potentially important, role of stochastic processes in stabilising population dynamics at range margins.     

Estimating fluctuating selection in age-structured populations

In age-structured populations, viability and fecundity selection of varying strength may occur in different age classes. On the basis of an original idea by Fisher of weighting individuals by their reproductive value, we show that the combined effect of selection on traits at different ages acts through the individual reproductive value defined as the stochastic contribution of an individual to the total reproductive value of the population the following year. The selection differential is a weighted sum of age-specific differentials that are the covariances between the phenotype and the age-specific relative fitness defined by the individual reproductive value. This enables estimation of weak selection on a multivariate quantitative character in populations with no density regulation by combinations of age-specific linear regressions of individual reproductive values on the traits. Demographic stochasticity produces random variation in fitness components in finite samples of individuals and affects the statistical inference of the temporal average directional selection as well as the magnitude of fluctuating selection. Uncertainties in parameter estimates and test power depend strongly on the demographic stochasticity. Large demographic variance results in large uncertainties in yearly estimates of selection that complicates detection of significant fluctuating selection. The method is illustrated by an analysis of age-specific selection in house sparrows on a fitness-related two-dimensional morphological trait, tarsus length and body mass of fledglings.     

A neutral theory with environmental stochasticity explains static and dynamic properties of ecological communities

Understanding the forces shaping ecological communities is crucial to basic science and conservation. Neutral theory has made considerable progress in explaining static properties of communities, like species abundance distributions (SADs), with a simple and generic model, but was criticised for making unrealistic predictions of fundamental dynamic patterns and for being sensitive to interspecific differences in fitness. Here, we show that a generalised neutral theory incorporating environmental stochasticity may resolve these limitations. We apply the theory to real data (the tropical forest of Barro Colorado Island) and demonstrate that it much better explains the properties of short‐term population fluctuations and the decay of compositional similarity with time, while retaining the ability to explain SADs. Furthermore, the predictions are considerably more robust to interspecific fitness differences. Our results suggest that this integration of niches and stochasticity may serve as a minimalistic framework explaining fundamental static and dynamic characteristics of ecological communities.     

Integral projection models perform better for small demographic data sets than matrix population models: a case study of two perennial herbs

1. Matrix population models are widely used to describe population dynamics, conduct population viability analyses and derive management recommendations for plant populations. For endangered or invasive species, management decisions are often based on small demographic data sets. Hence, there is a need for population models which accurately assess population performance from such small data sets.
2. We used demographic data on two perennial herbs with different life histories to compare the accuracy and precision of the traditional matrix population model and the recently developed integral projection model (IPM) in relation to the amount of data.
3. For large data sets both matrix models and IPMs produced identical estimates of population growth rate (λ). However, for small data sets containing fewer than 300 individuals, IPMs often produced smaller bias and variance for λ than matrix models despite different matrix structures and sampling techniques used to construct the matrix population models.
4. Synthesis and applications . Our results suggest that the smaller bias and variance of λ estimates make IPMs preferable to matrix population models for small demographic data sets with a few hundred individuals. These results are likely to be applicable to a wide range of herbaceous, perennial plant species where demographic fate can be modelled as a function of a continuous state variable such as size. We recommend the use of IPMs to assess population performance and management strategies particularly for endangered or invasive perennial herbs where little demographic data are available.