On estimating critical population size for an endangered species in the presence of environmental stochasticity

A stationary second order autoregressive process with Gaussian noise, which was linked to survivorship and reproductive success by logistic transformations, was used as a model for an environmental process. Computer experiments in Monte Carlo integration, with the objective of exploring the sensitivity of estimates of mean critical population size to variations in the parameters of the environmental process, were then conducted. These experiments suggest that estimates of mean critical population size are very sensitive to the form of the autocorrelation function of the stationary environmental process. For the most part, those experiments in which the autocorrelation function was strictly positive not only resulted in the largest estimates of mean critical population size but also led to the highest levels of environmental stochasticity as measured by its coefficient of variation. As in previous work, these experiments suggest that concerted efforts should be made to model those environmental factors that are critical to the survivability of an endangered species in assessing its chances for continued existence.     

Estimating rates of local extinction and colonization in colonial species and an extension to the metapopulation and community levels

Coloniality has mainly been studied from an evolutionary perspective, but relatively few studies have developed methods for modelling colony dynamics. Changes in number of colonies over time provide a useful tool for predicting and evaluating the responses of colonial species to management and to environmental disturbance. Probabilistic Markov process models have been recently used to estimate colony site dynamics using presence–absence data when all colonies are detected in sampling efforts. Here, we define and develop two general approaches for the modelling and analysis of colony dynamics for sampling situations in which all colonies are, and are not, detected. For both approaches, we develop a general probabilistic model for the data and then constrain model parameters based on various hypotheses about colony dynamics. We use Akaike's Information Criterion (AIC) to assess the adequacy of the constrained models. The models are parameterised with conditional probabilities of local colony site extinction and colonization. Presence–absence data arising from Pollock's robust capture–recapture design provide the basis for obtaining unbiased estimates of extinction, colonization, and detection probabilities when not all colonies are detected. This second approach should be particularly useful in situations where detection probabilities are heterogeneous among colony sites. The general methodology is illustrated using presence–absence data on two species of herons. Estimates of the extinction and colonization rates showed interspecific differences and strong temporal and spatial variations. We were also able to test specific predictions about colony dynamics based on ideas about habitat change and metapopulation dynamics. We recommend estimators based on probabilistic modelling for future work on colony dynamics. We also believe that this methodological framework has wide application to problems in animal ecology concerning metapopulation and community dynamics.     

Rules of thumb for conservation of metapopulations based on a stochastic winking-patch model

From a theoretical viewpoint, nature management basically has two options to prolong metapopulation persistence: decreasing local extinction probabilities and increasing colonization probabilities. This article focuses on those options with a stochastic, single-species metapopulation model. We found that for most combinations of local extinction probabilities and colonization probabilities, decreasing the former increases metapopulation extinction time more than does increasing the latter by the same amount. Only for relatively low colonization probabilities is an effort to increase these probabilities more beneficial, but even then, decreasing extinction probabilities does not seem much less effective. Furthermore, we found the following rules of thumb. First, if one focuses on extinction, one should preferably decrease the lowest local extinction probability. Only if the extinction probabilities are (almost) equal should one prioritize decreases in the local extinction probability of the patch with the best direct connections to and from other patches. Second, if one focuses on colonization, one should preferably increase the colonization probability between the patches with the lowest local extinction probability. Only if the local extinction probabilities are (almost) equal should one instead prioritize increases in the highest colonization probability (unless extinction probabilities and colonization probabilities are very low). The rules of thumb have an important common denominator: the local extinction process has a greater bearing on metapopulation extinction time than colonization.     

Life-history models of extinction: a test with island spiders

This study analyzes extinction patterns for two species of orb spiders monitored annually on 77 islands over a continuous 20-yr period. One species, Argiope argentata, has large populations sometimes crashing quickly to extinction and a much weaker relation of extinction likelihood to population size than does the other species, Metepeira datona. Demographic models were built for both species and matched against observations. Differences between the species in life-history traits-estimated with measurements from the field-together with incorporation of demographic stochasticity, a population ceiling, and environmental stochasticity, were necessary to fit the observed extinction curves. As predicted from life-history patterns, long-term population growth rates (and hence predicted extinction probabilities) are relatively very sensitive to values of juvenile survivorship. Models are also sensitive to variation in the population ceiling and environmental noise, which tend to act in a complementary manner. A simple model with no age structure was able to fit the data on large initial population sizes but not on small initial population sizes, showing that life cycle characteristics interact with the various sources of stochasticity and hence have to be taken into account to produce a precise model of the extinction process.     

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.     

Viability of the Endangered Little Bustard <Emphasis Type="Italic">Tetrax tetrax</Emphasis> Population of Western France

Stochastic computer simulations are used to evaluate the sensitivity of Little bustard population parameters, estimating the survival probabilities of the seven endangered Little bustard populations of central-western France for which conservation actions are currentlybeing or have been implemented. Different scenarios of parameter compensation for those nuclei to establish parameter levels assuring population viability are discussed. Adult survival, productivity per female, initial population size and carrying capacity were the most sensitive parameters in a hypothetical, isolated population. Juvenile survival also affected population survival, although its sensitivity was lower. Sex ratio did not have a linear effect on population survival, but probability of extinction increased for extreme values. Productivity per female and initial population size, varied strongly among the populations studied, determining their average time of extinction and growth rate. When a metapopulation scenario was simulated, the survival probabilities of each population and the metapopulations stayed close to 1.0 if no mortality was associated to migration. When mortality during migration was included in the simulations, the metapopulation's probability of survival significantly decreased under 90%. This approach may help managers to correctly address conservation measures and design effective strategies, which should be directed mainly to improve productivity, enhance female survival, and minimise mortality during migration (e.g. promoting insect-rich nesting substrates, avoiding female killing and nest destruction at harvesting, reducing the risk of collision with powerlines, or controlling poaching).     

Timing of reproduction in a Darwin''s finch: temporal opportunism under spatial constraints

We investigated whether predation by the minor grison ( Galictis cuja , a small mustelid) played a key role in limiting a wild cavy population ( Cavia magna ), ultimately leading to its local extinction. Radio-telemetry and capture-mark-recapture techniques were used to estimate grison predation rates (kill rates), time-specific probabilities of apparent mortality (population loss rate), overall mortality and grison predation for the cavy population. Additionally, we present data on alternative prey species, grison diet and reproduction to show potential proximate mechanisms of grison predation on wild cavies. The predictions specified were mostly confirmed: (1) grison predation was responsible for almost 80% of the cavies killed by known predators; (2) grison predation probabilities paralleled those of overall mortality of cavies over time; and (3) also those of the apparent mortality of the population. Thus, the population dynamics and the local extinction of the cavy population were not due to emigration processes. (4) Grison predation rates were not density-dependent, but showed pronounced peaks during the austral summer. The grison mainly preyed on small mammals: two water-rat species and the wild cavies. When the availability of alternative prey decreased in summer, the grison appeared to specialise on cavies. The onset of grison reproduction was somewhat delayed in relation to the onset of cavy reproduction. The lack of alternative prey coincided with high grison food demands due to reproduction, leading to a very high predation pressure ultimately resulting in the local extinction of the cavy population. We conclude that grison predation was indeed the main factor driving changes of the cavy population studied and speculate why caviomorph rodents might be especially susceptible to local extinction processes.     

The relationship between species detection probability and local extinction probability

In community-level ecological studies, generally not all species present in sampled areas are detected. Many authors have proposed the use of estimation methods that allow detection probabilities that are <1 and that are heterogeneous among species. These methods can also be used to estimate community-dynamic parameters such as species local extinction probability and turnover rates (Nichols et al. Ecol Appl 8:1213–1225; Conserv Biol 12:1390–1398). Here, we present an ad hoc approach to estimating community-level vital rates in the presence of joint heterogeneity of detection probabilities and vital rates. The method consists of partitioning the number of species into two groups using the detection frequencies and then estimating vital rates (e.g., local extinction probabilities) for each group. Estimators from each group are combined in a weighted estimator of vital rates that accounts for the effect of heterogeneity. Using data from the North American Breeding Bird Survey, we computed such estimates and tested the hypothesis that detection probabilities and local extinction probabilities were negatively related. Our analyses support the hypothesis that species detection probability covaries negatively with local probability of extinction and turnover rates. A simulation study was conducted to assess the performance of vital parameter estimators as well as other estimators relevant to questions about heterogeneity, such as coefficient of variation of detection probabilities and proportion of species in each group. Both the weighted estimator suggested in this paper and the original unweighted estimator for local extinction probability performed fairly well and provided no basis for preferring one to the other.     

Lag time in microbe growth as an age-dependent branching process with two phase types

We study a two-type, age-dependent branching process in which the branching probabilities of one of the types may vary with time. Specifically this modification of the Bellman-Harris process starts with a Type I particle which may either die or change to a Type II particle depending upon a time varying probability. A Type II particle may either die or reproduce with fixed probabilities but may not return to a particle of Type I. In this way the process models the lag phenomenon observed in microbe growth subsequent to transfer to a new culture medium while the organism is adapting to its new environment. We show that if the mean reproduction rate of Type II particles exceeds 1, then the population size grows exponentially. Further the extinction probability for this process is related to that of the Bellman-Harris process. Finally the governing equations are solved for several choices of the growth parameters and the solutions are graphically displayed showing that a wide variety of behavior can be modeled by this process.     

Microspectrophotometric study of the crystalline inclusions in different strains of Amoeba proteus]

Using microspectrometric technique, integral extinction and extinction spectra of crystalline inclusions of two amoeba strains, C and Ct, have been studied. The analysis of extinction spectrum form allowed to suggest that the crystals seen in both amoeba strains have identical chemical composition, whereas the morphological differences between cells in their transparency may be due to different mode of the crystal package. The relative amount of the crystals was measured in both amoeba strains on the basis of the integral extinction value. The distinct differences between the strains were detected in the integral extinction value and in the extinction spectra, which allowed us to use these parameters as genetic markers in the experiments on the nuclear transplantation in amoeba.     

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 review of extinction in experimental populations

1. Population extinction is a fundamental ecological process. Recent experimental work has begun to test the large body of theory that predicts how demographic, genetic and environmental factors influence extinction risk. We review empirical studies of extinction conducted under controlled laboratory conditions. Our synthesis highlights four findings. First, extinction theory largely considers individual, isolated populations. However, species interactions frequently altered or even reversed the influence of environmental factors on population extinction as compared to single-species conditions, highlighting the need to integrate community ecology into population theory. 2. While most single-species studies qualitatively agree with theoretical predictions, studies are needed that quantitatively compare observed and predicted extinction rates. A quantitative understanding of extinction processes is needed to further advance theory and to predict population extinction resulting from human activities. 3. Many stresses leading to population extinction can be assuaged by migration between subpopulations. However, too much migration increases synchrony between subpopulations and thus increases extinction risk. Research is needed to determine how to strike a balance that maximizes the benefit of migration. 4. Results from laboratory experiments often conflict with field studies. Understanding these inconsistencies is crucial for extending extinction theory to natural populations.     

Extinctions in competitive communities forced by coloured environmental variation

Understanding the relationships between environmental fluctuations, population dynamics and species interactions in natural communities is of vital theoretical and practical importance. This knowledge is essential in assessing extinction risks in communities that are, for example, pressed by changing environmental conditions and increasing exploitation. We developed a model of density dependent population renewal, in a Lotka–Volterra competitive community context, to explore the significance of interspecific interactions, demographic stochasticity, population growth rate and species abundance on extinction risk in populations under various autocorrelation (colour) regimes of environmental forcing. These factors were evaluated in two cases, where either a single species or the whole community was affected by the external forcing. Species' susceptibility to environmental noise with different autocorrelation structure depended markedly on population dynamics, species' position in the abundance hierarchy and how similarly community members responded to external forcing. We also found interactions between demographic stochasticity and environmental noise leading to a reversal in extinction probabilities from under- to overcompensatory dynamics. We compare our results with studies of single species populations and contrast possible mechanisms leading to extinctions. Our findings indicate that abundance rank, the form of population dynamics, and the colour of environmental variation interact in affecting species extinction risk. These interactions are further modified by interspecific interactions within competitive communities as the interactions filter and modulate the environmental noise.     

Test of mathematical assumptions behind the 'incidence function' estimation process of metapopulations' dynamic parameters.

I question Hanski's [I. Hanski, A practical model of metapopulation dynamics, J. Animal Ecol. 63 (1994) 151] assumption that incidence functions are relevant approximations of the equilibrium dynamics of stochastic metapopulation models to estimate models' parameters based on snapshot data. Based on ten different metapopulation models, this assumption is found to be at least partly unjustified when referring to the asymptotic behaviour of the models. This leads me to recommend the use of explicit extinction-colonisation transition probabilities and process data (rather than snapshot data) in the estimation process of metapopulation models.     

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。     

基于遗传算法的渔情预报HSI建模与智能优化

鱼类栖息地适宜性指数模型(HSI)基于鱼类分布与海洋环境之间存在的非线性关系而构建。然而,海洋环境因子之间存在着传统方法无法消除的相关性,导致获取的HSI参数较难准确表达环境因子与渔场之间的复杂关系。基于遗传算法(GA),自动消除海洋环境因子之间的相关性,构建了一种通用的鱼类HSI建模与智能优化框架(GeneHSI)。GeneHSI框架的核心是HSI建模空间向遗传算法空间的映射以及GA适应度函数的构建。该函数构建的思想是HSI预测的渔场概率与商业捕捞获取的渔场概率之间的累计误差值达到最小化。GeneHSI由待解问题构建、GA初始化和GA优化策略3部分组成。利用随机生成的标准化海洋环境数据与渔场概率数据,验证了GeneHSI模型框架的有效性。研究表明,GeneHSI能够有效优化HSI的建模并能自动获取HSI参数。不同限制条件下,遗传算法获取的HSI具有较大的差异,其中一般优化策略下获取的HSI参数最差;不等式、等式和上下界条件下,GeneHSI优化过程显著地更加合理,因此获取的HSI参数也更准确。此外,100、1000、5000和10000样本量下的优化建模表明,GeneHSI具有处理海量样本数据的能力。     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

Emergence and loss of assortative mating in sympatric speciation

We have studied an agent model which presents the emergence of sexual barriers through the onset of assortative mating, a condition that might lead to sympatric speciation. In the model, individuals are characterized by two traits, each determined by a single locus A or B. Heterozygotes on A are penalized by introducing an adaptive difference from homozygotes. Two niches are available. Each A homozygote is adapted to one of the niches. The second trait, called the marker trait has no bearing on the fitness. The model includes mating preferences, which are inherited from the mother and subject to random variations. A parameter controlling recombination probabilities of the two loci is also introduced. We study the phase diagram by means of simulations, in the space of parameters (adaptive difference, carrying capacity, recombination probability). Three phases are found, characterized by (i) assortative mating, (ii) extinction of one of the A alleles and (iii) Hardy-Weinberg like equilibrium. We also make perturbations of these phases to see how robust they are. Assortative mating can be gained or lost with changes that present hysteresis loops, showing the resulting equilibrium to have partial memory of the initial state and that the process of going from a polymorphic panmictic phase to a phase where assortative mating acts as sexual barrier can be described as a first-order transition.     

Modeling the dynamics of natural rotifer populations: Phase-parametric analysis

A model of the dynamics of natural rotifer populations is described as a discrete non-linear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes.