INCREASED PROBABILITY OF EXTINCTION DUE TO DECREASED GENETIC EFFECTIVE POPULATION SIZE: EXPERIMENTAL POPULATIONS OF CLARKIA PULCHELLA

We established replicated experimental populations of the annual plant Clarkia pulchella to evaluate the existence of a causal relationship between loss of genetic variation and population survival probability. Two treatments differing in the relatedness of the founders, and thus in the genetic effective population size (N_e), were maintained as isolated populations in a natural environment. After three generations, the low N_e treatment had significantly lower germination and survival rates than did the high N_e treatment. These lower germination and survival rates led to decreased mean fitness in the low N_e populations: estimated mean fitness in the low N_e populations was only 21% of the estimated mean fitness in the high N_e populations. This inbreeding depression led to a reduction in population survival: at the conclusion of the experiment, 75% of the high N_e populations were still extant, whereas only 31% of the low N_e populations had survived. Decreased genetic effective population size, which leads to both inbreeding and the loss of alleles by genetic drift, increased the probability of population extinction over that expected from demographic and environmental stochasticity alone. This demonstrates that the genetic effective population size can strongly affect the probability of population persistence.     

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。     

Demography_Lab,an educational application to evaluate population growth: Unstructured and matrix models

Training in Population Ecology asks for scalable applications capable of embarking students on a trip from basic concepts to the projection of populations under the various effects of density dependence and stochasticity. Demography_Lab is an educational tool for teaching Population Ecology aspiring to cover such a wide range of objectives. The application uses stochastic models to evaluate the future of populations. Demography_Lab may accommodate a wide range of life cycles and can construct models for populations with and without an age or stage structure. Difference equations are used for unstructured populations and matrix models for structured populations. Both types of models operate in discrete time. Models can be very simple, constructed with very limited demographic information or parameter‐rich, with a complex density‐dependence structure and detailed effects of the different sources of stochasticity. Demography_Lab allows for deterministic projections, asymptotic analysis, the extraction of confidence intervals for demographic parameters, and stochastic projections. Stochastic population growth is evaluated using up to three sources of stochasticity: environmental and demographic stochasticity and sampling error in obtaining the projection matrix. The user has full control on the effect of stochasticity on vital rates. The effect of the three sources of stochasticity may be evaluated independently for each vital rate. The user has also full control on density dependence. It may be included as a ceiling population size controlling the number of individuals in the population or it may be evaluated independently for each vital rate. Sensitivity analysis can be done for the asymptotic population growth rate or for the probability of extinction. Elasticity of the probability of extinction may be evaluated in response to changes in vital rates, and in response to changes in the intensity of density dependence and environmental stochasticity.     

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.     

Naturally rare versus newly rare: demographic inferences on two timescales inform conservation of Galápagos giant tortoises

Long‐term population history can influence the genetic effects of recent bottlenecks. Therefore, for threatened or endangered species, an understanding of the past is relevant when formulating conservation strategies. Levels of variation at neutral markers have been useful for estimating local effective population sizes (N_e) and inferring whether population sizes increased or decreased over time. Furthermore, analyses of genotypic, allelic frequency, and phylogenetic information can potentially be used to separate historical from recent demographic changes. For 15 populations of Galápagos giant tortoises (Chelonoidis sp.), we used 12 microsatellite loci and DNA sequences from the mitochondrial control region and a nuclear intron, to reconstruct demographic history on shallow (past ~100 generations, ~2500 years) and deep (pre‐Holocene, >10 thousand years ago) timescales. At the deep timescale, three populations showed strong signals of growth, but with different magnitudes and timing, indicating different underlying causes. Furthermore, estimated historical N_e of populations across the archipelago showed no correlation with island age or size, underscoring the complexity of predicting demographic history a priori. At the shallow timescale, all populations carried some signature of a genetic bottleneck, and for 12 populations, point estimates of contemporary N_e were very small (i.e., < 50). On the basis of the comparison of these genetic estimates with published census size data, N_e generally represented ~0.16 of the census size. However, the variance in this ratio across populations was considerable. Overall, our data suggest that idiosyncratic and geographically localized forces shaped the demographic history of tortoise populations. Furthermore, from a conservation perspective, the separation of demographic events occurring on shallow versus deep timescales permits the identification of naturally rare versus newly rare populations; this distinction should facilitate prioritization of management action.     

Scaling of the mean and variance of population dynamics under fluctuating regimes

Theoretical ecologists have long sought to understand how the persistence of populations depends on the interactions between exogenous (biotic and abiotic) and endogenous (e.g., demographic and genetic) drivers of population dynamics. Recent work focuses on the autocorrelation structure of environmental perturbations and its effects on the persistence of populations. Accurate estimation of extinction times and especially determination of the mechanisms affecting extinction times is important for biodiversity conservation. Here we examine the interaction between environmental fluctuations and the scaling effect of the mean population size with its variance. We investigate how interactions between environmental and demographic stochasticity can affect the mean time to extinction, change optimal patch size dynamics, and how it can alter the often-assumed linear relationship between the census size and the effective population size. The importance of the correlation between environmental and demographic variation depends on the relative importance of the two types of variation. We found the correlation to be important when the two types of variation were approximately equal; however, the importance of the correlation diminishes as one source of variation dominates. The implications of these findings are discussed from a conservation and eco-evolutionary point of view.     

Effective size of density‐dependent two‐sex populations: the effect of mating systems

Density dependence in vital rates is a key feature affecting temporal fluctuations of natural populations. This has important implications for the rate of random genetic drift. Mating systems also greatly affect effective population sizes, but knowledge of how mating system and density regulation interact to affect random genetic drift is poor. Using theoretical models and simulations, we compare N_e in short‐lived, density‐dependent animal populations with different mating systems. We study the impact of a fluctuating, density‐dependent sex ratio and consider both a stable and a fluctuating environment. We find a negative relationship between annual N_e/N and adult population size N due to density dependence, suggesting that loss of genetic variation is reduced at small densities. The magnitude of this decrease was affected by mating system and life history. A male‐biased, density‐dependent sex ratio reduces the rate of genetic drift compared to an equal, density‐independent sex ratio, but a stochastic change towards male bias reduces the N_e/N ratio. Environmental stochasticity amplifies temporal fluctuations in population size and is thus vital to consider in estimation of effective population sizes over longer time periods. Our results on the reduced loss of genetic variation at small densities, particularly in polygamous populations, indicate that density regulation may facilitate adaptive evolution at small population sizes.     

Demographic variance in heterogeneous populations: matrix models and sensitivity analysis

The demographic consequences of stochasticity in processes such as survival and reproduction are modulated by the heterogeneity within the population. Therefore, to study effects of stochasticity on population growth and extinction risk, it is critical to use structured population models in which the most important sources of heterogeneity (e.g. age, size, developmental stage) are incorporated as i‐state variables. Demographic stochasticity in heterogeneous populations has often been studied using one of two approaches: multitype branching processes and diffusion approximations. Here, we link these approaches, through the demographic stochasticity in age‐ or stage‐structured matrix population models. We derive the demographic variance, σ²_d, which measures the per capita contribution to the variance in population growth increment, and we show how it can be decomposed into contributions from transition probabilities and fertility across ages or stages. Furthermore, using matrix calculus we derive the sensitivity of σ²_d to age‐ or stage‐specific mortality and fertility. We apply the methods to an extensive set of data from age‐classified human populations (long‐term time‐series for Sweden, Japan and the Netherlands; two hunter–gatherer populations, and the high‐fertility Hutterites), and to a size‐classified population of the herbaceous plant Calathea ovandensis. For the human populations our analysis reveals substantial temporal changes in the demographic variance as well as its main components across age. These new methods provide a powerful approach for calculating the demographic variance for any structured model, and for analyzing its main components and sensitivities. This will make possible new analyses of demographic variance across different kinds of heterogeneity in different life cycles, which will in turn improve our understanding of mechanisms underpinning extinction risk and other important biological outcomes.     

Ongoing localized extinctions of stream-dwelling white-spotted charr populations in small dammed-off habitats of Hokkaido Island,Japan

Habitat fragmentation caused by damming can greatly reduce the population viability of aquatic organisms, with smaller fragmented populations at higher risk of extinction due to increased demographic, genetic, and environmental stochasticity. However, empirical evidence demonstrating that smaller natural populations are more vulnerable to extinction is limited. We studied the vulnerability to extinction of white-spotted charr (Salvelinus leucomaenis) populations in 30 dammed-off streams in Oshima Peninsula, southwestern Hokkaido Island, Japan, by comparing the incidence of charr populations in streams between 1999 and 2014. Using electrofishing and environmental DNA surveys, we identified three localized extinctions, with the probability of extinction increasing with decreasing watershed area (our surrogate for habitat size). We also found a new population in one dammed-off stream in which white-spotted charr were previously unknown, after installation of a fish ladder, indicating the capacity of white-spotted charr to recolonize reconnected habitat in a short period. Our results suggest that localized extinction of white-spotted charr in small dammed-off streams is ongoing, but that appropriate fish migration corridors can reduce localized extinction risk and increase the probability of species persistence.

     

Evolutionary tracking is determined by differential selection on demographic rates and density dependence

Recent ecological forecasts predict that ~25% of species worldwide will go extinct by 2050. However, these estimates are primarily based on environmental changes alone and fail to incorporate important biological mechanisms such as genetic adaptation via evolution. Thus, environmental change can affect population dynamics in ways that classical frameworks can neither describe nor predict. Furthermore, often due to a lack of data, forecasting models commonly describe changes in population demography by summarizing changes in fecundity and survival concurrently with the intrinsic growth rate (r). This has been shown to be an oversimplification as the environment may impose selective pressure on specific demographic rates (birth and death) rather than directly on r (the difference between the birth and death rates). This differential pressure may alter population response to density, in each demographic rate, further diluting the information combined to produce r. Thus, when we consider the potential for persistence via adaptive evolution, populations with the same r can have different abilities to persist amidst environmental change. Therefore, we cannot adequately forecast population response to climate change without accounting for demography and selection on density dependence. Using a continuous‐time Markov chain model to describe the stochastic dynamics of the logistic model of population growth and allow for trait evolution via mutations arising during birth events, we find persistence via evolutionary tracking more likely when environmental change alters birth rather than the death rate. Furthermore, species that evolve responses to changes in the strength of density dependence due to environmental change are less vulnerable to extinction than species that undergo selection independent of population density. By incorporating these key demographic considerations into our predictive models, we can better understand how species will respond to climate change.     

Assessing seasonal demographic covariation to understand environmental‐change impacts on a hibernating mammal

Natural populations are exposed to seasonal variation in environmental factors that simultaneously affect several demographic rates (survival, development and reproduction). The resulting covariation in these rates determines population dynamics, but accounting for its numerous biotic and abiotic drivers is a significant challenge. Here, we use a factor‐analytic approach to capture partially unobserved drivers of seasonal population dynamics. We use 40 years of individual‐based demography from yellow‐bellied marmots (Marmota flaviventer) to fit and project population models that account for seasonal demographic covariation using a latent variable. We show that this latent variable, by producing positive covariation among winter demographic rates, depicts a measure of environmental quality. Simultaneously, negative responses of winter survival and reproductive‐status change to declining environmental quality result in a higher risk of population quasi‐extinction, regardless of summer demography where recruitment takes place. We demonstrate how complex environmental processes can be summarized to understand population persistence in seasonal environments.     

Estimate of population extinction risk and its application to ecological risk management

Environmental threats, such as habitat size reduction or environmental pollution, may not cause immediate extinction of a population but may shorten the expected time to extinction. We developed a method to estimate the mean time to extinction for a density-dependent population with environmental fluctuation and to compare the impacts of different risk factors. We first derived a formula of the mean extinction time for a population with logistic growth and environmental and demographic stochasticities expressed as a stochastic differential equation model (canonical model). The relative importance of different risk factors is evaluated by the decrease in the mean extinction time. We studied an approximated formula for the reduction in habitat size that enhances extinction risk by the same magnitude as a given decrease in survivorship caused by toxic chemical exposure. In a large population (large K) or in a slowly growing population (small r), a small decrease in survivorship can cause the extinction risk to increase, corresponding to a significant reduction in the habitat size. Finally, we studied an approximate maximum likelihood estimate of three parameters (intrinsic growth rate r, carrying capacity K, and environmental stochasticity σ ² _e ) from time series data. By Monte Carlo sampling, we can remove the bias very effectively and determine the confidence interval. We discuss here how the reliability of the estimate changes with the length of time series. If we know the intrinsic rate of population growth r, the mean extinction time is estimated quite accurately even when only a short time series is available for parameter estimation. Received: March 31, 1999 / Accepted: November 9, 1999     

A range-wide genetic bottleneck overwhelms contemporary landscape factors and local abundance in shaping genetic patterns of an alpine butterfly (Lepidoptera: Pieridae: Colias behrii)

Spatial and environmental heterogeneity are major factors in structuring species distributions in alpine landscapes. These landscapes have also been affected by glacial advances and retreats, causing alpine taxa to undergo range shifts and demographic changes. These nonequilibrium population dynamics have the potential to obscure the effects of environmental factors on the distribution of genetic variation. Here, we investigate how demographic change and environmental factors influence genetic variation in the alpine butterfly Colias behrii. Data from 14 microsatellite loci provide evidence of bottlenecks in all population samples. We test several alternative models of demography using approximate Bayesian computation (ABC), with the results favouring a model in which a recent bottleneck precedes rapid population growth. Applying independent calibrations to microsatellite loci and a nuclear gene, we estimate that this bottleneck affected both northern and southern populations 531–281 years ago, coinciding with a period of global cooling. Using regression approaches, we attempt to separate the effects of population structure, geographical distance and landscape on patterns of population genetic differentiation. Only 40% of the variation in F_ST is explained by these models, with geographical distance and least‐cost distance among meadow patches selected as the best predictors. Various measures of genetic diversity within populations are also decoupled from estimates of local abundance and habitat patch characteristics. Our results demonstrate that demographic change can have a disproportionate influence on genetic diversity in alpine species, contrasting with other studies that suggest landscape features control contemporary demographic processes in high‐elevation environments.     

Effects of habitat size and quality on equilibrium density and extinction time of Sorex araneus populations

1. The effects of changes in habitat size and quality on the expected population density and the expected time to extinction of Sorex araneus are studied by means of mathematical models that incorporate demographic stochasticity.
2. Habitat size is characterized by the number of territories, while habitat quality is represented by the expected number of offspring produced during the lifetime of an individual.
3. The expected population density of S. araneus is shown to be mainly influenced by the habitat size. The expected time to extinction of S. araneus populations due to demographic stochasticity, on the other hand, is much more affected by the habitat quality.
4. In a more general setting we demonstrate that, irrespective of the actual species under consideration, the likelihood of extinction as a consequence of demographic stochasticity is more effectively countered by increasing the reproductive success and survival of individuals then by increasing total population size.     

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。     

PHENOTYPIC DIFFERENTIATION AT SOUTHERN LIMIT BORDERS: THE CASE STUDY OF TWO FUCOID MACROALGAL SPECIES WITH DIFFERENT LIFE‐HISTORY TRAITS1

Marginal populations are often geographically isolated, smaller, and more fragmented than central populations and may frequently have to face suboptimal local environmental conditions. Persistence of these populations frequently involves the development of adaptive traits at phenotypic and genetic levels. We compared population structure and demographic variables in two fucoid macroalgal species contrasting in patterns of genetic diversity and phenotypic plasticity at their southern distribution limit with a more central location. Models were Ascophyllum nodosum (L.) Le Jol. (whose extreme longevity and generation overlap may buffer genetic loss by drift) and Fucus serratus L. (with low genetic diversity at southern margins). At edge locations, both species exhibited trends in life‐history traits compatible with population persistence but by using different mechanisms. Marginal populations of A. nodosum had higher reproductive output in spite of similar mortality rates at all life stages, making edge populations denser and with smaller individuals. In F. serratus, rather than demographic changes, marginal populations differed in habitat, occurring restricted to a narrower vertical habitat range. We conclude that persistence of both A. nodosum and F. serratus at the southern‐edge locations depends on different strategies. Marginal population persistence in A. nodosum relies on a differentiation in life‐history traits, whereas F. serratus, putatively poorer in evolvability potential, is restricted to a narrower vertical range at border locations. These results contribute to the general understanding of mechanisms that lead to population persistence at distributional limits and to predict population resilience under a scenario of environmental change.     

Genetic diversity shaped by historical and recent factors in the live‐bearing twoline skiffia Neotoca bilineata

The endangered twoline skiffia Neotoca bilineata, a viviparous fish of the subfamily Goodeinae, endemic to central Mexico (inhabiting two basins, Cuitzeo and Lerma‐Santiago) was evaluated using genetic and habitat information. The genetic variation of all remaining populations of the species was analysed using both mitochondrial and microsatellite markers and their habitat conditions were assessed using a water quality index (I_WQ). An 80% local extinction was found across the distribution of N. bilineata. The species was found in three of the 16 historical localities plus one previously unreported site. Most areas inhabited by the remaining populations had I_WQ scores unsuitable for the conservation of freshwater biodiversity. Populations showed low but significant genetic differentiation with both markers (mtDNA φ_ST = 0·076, P < 0·001; microsatellite F_ST = 0·314, P < 0·001). Borbollon, in the Cuitzeo Basin, showed the highest level of differentiation and was identified as a single genetic unit by Bayesian assignment methods. Rio Grande de Morelia and Salamanca populations showed the highest genetic diversity and also a high migration rate facilitated by an artificial channel that connected the two basins. Overall, high genetic diversity values were observed compared with other freshwater fishes (average N_a = 16 alleles and loci and mean ±s.d . H_o = 0·63 ± 0·10 and nucleotide diversity π = 0·006). This suggests that the observed genetic diversity has not diminished as rapidly as the species' habitat destruction. No evidence of correlation between habitat conditions and genetic diversity was found. The current pattern of genetic diversity may be the result of both historical factors and recent modifications of the hydrological system. The main threat to the species may be the rapid habitat deterioration and associated demographic stochasticity rather than genetic factors.     

Cultivation Fosters Plant Naturalization by Reducing Environmental Stochasticity

A large fraction of the immigrant (or founder) populations of terrestrial plants are small (< 10⁴) and are acutely sensitive to environmental stochasticity. As a result, they undergo radical size fluctuations during a prolonged lag phase that almost always result in their extirpation. Naturalizations are those rare examples in which an immigrant population increases above a threshold size such that the consequences of environmental stochasticity are markedly lower. The likelihood that a non-indigenous population will reach this threshold size would be enhanced substantially through either deliberate or inadvertent cultivation. Cultivation (e.g. protection from predators, parasites, drought, frost) shields small immigrant populations from the extreme expressions of environmental stochasticity. In addition, cultivation can preserve through seed storage a residual non-indigenous population from which new populations can be established. As disseminules are spread locally, and even regionally, immigrant populations sample a wide variety of micro-habitats, thus increasing the likelihood that some plants will survive even without cultivation. Origins of naturalized floras in Australia and the US reveal a strong circumstantial link between cultivation and subsequent naturalization: the single largest group of naturalized species was deliberately introduced as either crops, forage spp., or ornamentals. Another group was introduced inadvertently as contaminants in crop seeds. This correspondence between cultivation and subsequent naturalization provides a common demographic explanation for non-indigenous plant persistence that largely transcends species’ attributes and the commonly ascribed features of communities that are vulnerable to the entry of non-indigenous plants. Humans have played a more profound role in fostering plant naturalizations than by acting simply as plant dispersers; their post-immigration cultivation fosters much naturalization. This revised version was published online in July 2006 with corrections to the Cover Date.     

TEMPORAL FLUCTUATIONS IN DEMOGRAPHIC PARAMETERS AND THE GENETIC VARIANCE AMONG POPULATIONS

Contrary to assumptions commonly made in the study of population genetics, the demographic properties of many populations are not always constant. Important characteristics of populations such as migration rate and population size may vary in time and space. Moreover, local populations often come and go; the rate of extinction and the properties of colonization may also vary. In this paper, the approach to equilibrium following a disturbance in the genetic variance among populations is described. The rate of migration is shown to be critical in determining the extent to which extinction and recolonization affects genetic differentiation. Perturbations and variations through time and space in demographic parameters such as population size and migration rate are shown to be important in determining the partitioning of genetic variance. Equations are given to predict the average through time of genetic differentiation among populations in the event of a single disturbance or in constant fluctuations in the pertinent demographic parameters. In general, these fluctuations increase the F_ST of a species. Spatial demographic variation affects F_STmuch more than temporal variation. These demographic properties make some species unsuitable for the empirical analysis of migration with indirect genetic measures. Demographic instability may play a large role in the evolution of genetic variation.     

Density-dependent demographic variation determines extinction rate of experimental populations

Understanding population extinctions is a chief goal of ecological theory. While stochastic theories of population growth are commonly used to forecast extinction, models used for prediction have not been adequately tested with experimental data. In a previously published experiment, variation in available food was experimentally manipulated in 281 laboratory populations of Daphnia magna to test hypothesized effects of environmental variation on population persistence. Here, half of those data were used to select and fit a stochastic model of population growth to predict extinctions of populations in the other half. When density-dependent demographic stochasticity was detected and incorporated in simple stochastic models, rates of population extinction were accurately predicted or only slightly biased. However, when density-dependent demographic stochasticity was not accounted for, as is usual when forecasting extinction of threatened and endangered species, predicted extinction rates were severely biased. Thus, an experimental demonstration shows that reliable estimates of extinction risk may be obtained for populations in variable environments if high-quality data are available for model selection and if density-dependent demographic stochasticity is accounted for. These results suggest that further consideration of density-dependent demographic stochasticity is required if predicted extinction rates are to be relied upon for conservation planning.