Establishment versus population growth in spatio-temporally varying environments

We consider situations where repeated invasion attempts occur from a source population into a receptor population over extended periods of time. The receptor population contains two locations that provide different expected offspring numbers to invaders. There is demographic stochasticity in offspring numbers. In addition, temporal variation causes local invader fitnesses to vary. We show that effects of environmental autocorrelation on establishment success depend on spatial covariance of the receptor subpopulations. In situations with a low spatial covariance this effect is positive, whereas high spatial covariance and/or high migration probabilities between the subpopulations causes the effect to be negative. This result reconciles seemingly contradictory results from the literature concerning effects of temporal variation on population dynamics with demographic stochasticity. We study an example in the context of genetic introgression, where invasions of cultivar plant genes occur through pollen flow from a source population into wild-type receptor populations, but our results have implications in a wider range of contexts, such as the spread of exotic species, metapopulation dynamics and epidemics.     

Quantifying stochastic introgression processes with hazard rates

Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It can have large environmental consequences, such as the spread of insecticide or herbicide resistant genes, the escape of transgenes from genetically modified crops, and the invasion of exotic genes into new habitats. Introgression usually involves strong random components, such as rare hybridization and backcrossing events, and demographic variation in reproduction and survival. Most introgression studies ignore these random effects, and consequently fail to accurately assess the risk of introgression. This paper presents a methodology for quantifying stochastic introgression processes, based on multitype branching process models. We derive a quantity called the hazard rate, which can be used to investigate how the risk of introgression depends on crop management and life history.     

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。     

How well can the exponential-growth coalescent approximate constant-rate birth–death population dynamics?

One of the central objectives in the field of phylodynamics is the quantification of population dynamic processes using genetic sequence data or in some cases phenotypic data. Phylodynamics has been successfully applied to many different processes, such as the spread of infectious diseases, within-host evolution of a pathogen, macroevolution and even language evolution. Phylodynamic analysis requires a probability distribution on phylogenetic trees spanned by the genetic data. Because such a probability distribution is not available for many common stochastic population dynamic processes, coalescent-based approximations assuming deterministic population size changes are widely employed. Key to many population dynamic models, in particular epidemiological models, is a period of exponential population growth during the initial phase. Here, we show that the coalescent does not well approximate stochastic exponential population growth, which is typically modelled by a birth–death process. We demonstrate that introducing demographic stochasticity into the population size function of the coalescent improves the approximation for values of R₀ close to 1, but substantial differences remain for large R₀. In addition, the computational advantage of using an approximation over exact models vanishes when introducing such demographic stochasticity. These results highlight that we need to increase efforts to develop phylodynamic tools that correctly account for the stochasticity of population dynamic models for inference.     

Introgressive hybridization as a mechanism for species rescue

Rapid evolution on ecological time scales can play a key role in species responses to environmental change. One dynamic that has the potential to generate the diversity necessary for evolution rapid enough to allow response to sudden environmental shifts is introgressive hybridization. However, if distinct sub-species exist before an environmental shift, mechanisms that impede hybridization, such as assortative mating and hybrid inferiority, are likely to be present. Here we explore the theoretical potential for introgressive hybridization to play a role in response to environmental change. In particular, we incorporate assortative mating, hybrid inferiority, and demographic stochasticity into a two-locus, two-allele population genetic model of two interacting species where one locus identifies the species and the other determines how fitness depends on the changing environment. Simulation results indicate that moderately high values for the strength of assortative mating will allow enough hybridization events to outweigh demographic stochasticity but not so many that continued hybridization outweighs backcrossing and introgression. Successful introgressive hybridization also requires intermediate relative fitness at the allele negatively affected by environmental change such that hybrid survivorship outweighs demographic stochasticity but selection remains strong enough to affect the genetic dynamics. The potential for successful introgression instead of extinction with greater environmental change is larger with monogamous rather than promiscuous mating due to lower stochasticity in mating events. These results suggest species characteristics (e.g., intermediate assortative mating and mating systems with low variation in mating likelihood) which indicate a potential for rapid evolution in response to environmental change via introgressive hybridization.     

Genetic estimates of contemporary effective population size: what can they tell us about the importance of genetic stochasticity for wild population persistence?

Genetic stochasticity due to small population size contributes to population extinction, especially when population fragmentation disrupts gene flow. Estimates of effective population size ( N _e) can therefore be informative about population persistence, but there is a need for an assessment of their consistency and informative relevance. Here we review the body of empirical estimates of N _e for wild populations obtained with the temporal genetic method and published since Frankham's (1995 ) review. Theoretical considerations have identified important sources of bias for this analytical approach, and we use empirical data to investigate the extent of these biases. We find that particularly model selection and sampling require more attention in future studies.
We report a median unbiased N _e estimate of 260 (among 83 studies) and find that this median estimate tends to be smaller for populations of conservation concern, which may therefore be more sensitive to genetic stochasticity. Furthermore, we report a median N _e/ N ratio of 0.14, and find that this ratio may actually be higher for small populations, suggesting changes in biological interactions at low population abundances. We confirm the role of gene flow in countering genetic stochasticity by finding that N _e correlates strongest with neutral genetic metrics when populations can be considered isolated. This underlines the importance of gene flow for the estimation of N _e, and of population connectivity for conservation in general. Reductions in contemporary gene flow due to ongoing habitat fragmentation will likely increase the prevalence of genetic stochasticity, which should therefore remain a focal point in the conservation of biodiversity.     

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。     

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.     

Molecular systematics and population genetics of biological invasions: towards a better understanding of invasive species management

The study of population genetics of invasive species offers opportunities to investigate rapid evolutionary processes at work, and while the ecology of biological invasions has enjoyed extensive attention in the past, the recentness of molecular techniques makes their application in invasion ecology a fairly new approach. Despite this, molecular biology has already proved powerful in inferring aspects not only relevant to the evolutionary biologist but also to those concerned with invasive species management. Here, we review the different molecular markers routinely used in such studies and their application(s) in addressing different questions in invasion ecology. We then review the current literature on molecular genetic studies aimed at improving management and the understanding of invasive species by resolving of taxonomic issues, elucidating geographical sources of invaders, detecting hybridisation and introgression, tracking dispersal and spread and assessing the importance of genetic diversity in invasion success. Finally, we make some suggestions for future research efforts in molecular ecology of biological invasions.     

Whole‐genome sequencing reveals small genomic regions of introgression in an introduced crater lake population of threespine stickleback

Invasive species pose a major threat to biological diversity. Although introduced populations often experience population bottlenecks, some invasive species are thought to be originated from hybridization between multiple populations or species, which can contribute to the maintenance of high genetic diversity. Recent advances in genome sequencing enable us to trace the evolutionary history of invasive species even at whole‐genome level and may help to identify the history of past hybridization that may be overlooked by traditional marker‐based analysis. Here, we conducted whole‐genome sequencing of eight threespine stickleback (Gasterosteus aculeatus) individuals, four from a recently introduced crater lake population and four of the putative source population. We found that both populations have several small genomic regions with high genetic diversity, which resulted from introgression from a closely related species (Gasterosteus nipponicus). The sizes of the regions were too small to be detected with traditional marker‐based analysis or even some reduced‐representation sequencing methods. Further amplicon sequencing revealed linkage disequilibrium around an introgression site, which suggests the possibility of selective sweep at the introgression site. Thus, interspecies introgression might predate introduction and increase genetic variation in the source population. Whole‐genome sequencing of even a small number of individuals can therefore provide higher resolution inference of history of introduced populations.     

A multiparent advanced generation inter-cross population for genetic analysis in wheat

We present the first results from a novel multiparent advanced generation inter-cross (MAGIC) population derived from four elite wheat cultivars. The large size of this MAGIC population (1579 progeny), its diverse genetic composition and high levels of recombination all contribute to its value as a genetic resource. Applications of this resource include interrogation of the wheat genome and the analysis of gene-trait association in agronomically important wheat phenotypes. Here, we report the utilization of a MAGIC population for the first time for linkage map construction. We have constructed a linkage map with 1162 DArT, single nucleotide polymorphism and simple sequence repeat markers distributed across all 21 chromosomes. We benchmark this map against a high-density DArT consensus map created by integrating more than 100 biparental populations. The linkage map forms the basis for further exploration of the genetic architecture within the population, including characterization of linkage disequilibrium, founder contribution and inclusion of an alien introgression into the genetic map. Finally, we demonstrate the application of the resource for quantitative trait loci mapping using the complex traits plant height and hectolitre weight as a proof of principle.     

The Impact of Accelerating Faster than Exponential Population Growth on Genetic Variation

Current human sequencing projects observe an abundance of extremely rare genetic variation, suggesting recent acceleration of population growth. To better understand the impact of such accelerating growth on the quantity and nature of genetic variation, we present a new class of models capable of incorporating faster than exponential growth in a coalescent framework. Our work shows that such accelerated growth affects only the population size in the recent past and thus large samples are required to detect the models’ effects on patterns of variation. When we compare models with fixed initial growth rate, models with accelerating growth achieve very large current population sizes and large samples from these populations contain more variation than samples from populations with constant growth. This increase is driven almost entirely by an increase in singleton variation. Moreover, linkage disequilibrium decays faster in populations with accelerating growth. When we instead condition on current population size, models with accelerating growth result in less overall variation and slower linkage disequilibrium decay compared to models with exponential growth. We also find that pairwise linkage disequilibrium of very rare variants contains information about growth rates in the recent past. Finally, we demonstrate that models of accelerating growth may substantially change estimates of present-day effective population sizes and growth times.     

Can genetic data confirm or refute historical records? The island invasion of the small Indian mongoose (Herpestes auropunctatus)

Many studies aimed at reconstructing the invasion history of a species rely, in part, on inferences based on patterns of genetic variation. These inferences warrant careful interpretation, however. In particular, given the time scale of most invasions, the typical demography of invasive species in their invaded range, and the available molecular tools, the underlying assumptions of population genetic models will often be violated. Given this fact, we examined the potential of population genetic data for reconstructing the history of serial introductions of the small Indian mongoose, Herpestes auropunctatus. We used simulations to test the power of existing microsatellite data for testing the credibility of historical introduction records. Although our results are generally consistent with most historical records for H. auropunctatus, the existing data have low power to reject alternative historical hypotheses. Simulations of a wide range of founder population sizes show broadly overlapping results, making rather different historical scenarios of introductions difficult to rule out with typical datasets. We advocate caution in the use of molecular population genetics to infer the history of invasive species, and we suggest extensive simulations as a tool to evaluate, in advance, this approach for addressing important research questions.     

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.     

Testing an hypothesis of hybrid zone movement for toads in France

Hybrid zone movement may result in substantial unidirectional introgression of selectively neutral material from the local to the advancing species, leaving a genetic footprint. This genetic footprint is represented by a trail of asymmetric tails and displaced cline centres in the wake of the moving hybrid zone. A peak of admixture linkage disequilibrium is predicted to exist ahead of the centre of the moving hybrid zone. We test these predictions of the movement hypothesis in a hybrid zone between common (Bufo bufo) and spined toads (B. spinosus), using 31 nuclear and one mtDNA SNPs along a transect in the northwest of France. Average effective selection in Bufo hybrids is low and clines vary in shape and centre. A weak pattern of asymmetric introgression is inferred from cline discordance of seven nuclear markers. The dominant direction of gene flow is from B. spinosus to B. bufo and is in support of southward movement of the hybrid zone. Conversely, a peak of admixture linkage disequilibrium north of the hybrid zone suggests northward movement. These contrasting results can be explained by reproductive isolation of the B. spinosus and B. bufo gene pools at the southern (B. spinosus) side of the hybrid zone. The joint occurrence of asymmetric introgression and admixture linkage disequilibrium can also be explained by the combination of low dispersal and random genetic drift due to low effective population sizes.     

天然杂交与遗传渐渗对植物入侵性的影响

生物入侵给全球生态环境与社会经济都带来了严重危害, 对其入侵机制的研究非常重要。生物入侵是一个适应性进化的过程, 天然杂交与遗传渐渗可以改变外来物种对环境的适应性并提高其入侵能力, 使其进化成为入侵种。因此了解杂交-渐渗在促进生物入侵过程中的遗传作用, 将有助于我们采取有效措施来控制生物入侵及其危害。本文从杂交-渐渗对生物适应性进化和物种形成影响的角度, 阐明外来种如何通过杂交-渐渗在新的生境中改变其适应性、生存竞争能力和入侵能力。杂交-渐渗可以导致物种发生多倍体水平和同倍体水平的进化, 虽然二者的进化过程不尽相同, 但均能使杂种群体在遗传上产生较大变化, 进而影响杂种群体的适合度, 这一过程可能促使外来种在新的生境中的成功入侵进而转变为入侵种。随着转基因生物技术的迅速发展, 大量转基因作物进入环境释放和商品化种植, 具有特定功能的转基因可能通过杂交-渐渗进入野生近缘种群体, 也可能使之成为入侵性强的农田杂草, 带来难以预测的生态后果。总之, 生物入侵是一个复杂的进化和生态过程, 利用杂交-渐渗的理论来解释植物的入侵性, 仅从一个方面反映了入侵生物学的研究, 杂交-渐渗与其他理论的结合, 将从更深的层次来解释外来种的入侵机制。     

Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

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.     

Genomic regions with a history of divergent selection affect fitness of hybrids between two butterfly species

Speciation is the process by which reproductively isolated lineages arise, and is one of the fundamental means by which the diversity of life increases. Whereas numerous studies have documented an association between ecological divergence and reproductive isolation, relatively little is known about the role of natural selection in genome divergence during the process of speciation. Here, we use genome-wide DNA sequences and Bayesian models to test the hypothesis that loci under divergent selection between two butterfly species (Lycaeides idas and L. melissa) also affect fitness in an admixed population. Locus-specific measures of genetic differentiation between L. idas and L. melissa and genomic introgression in hybrids varied across the genome. The most differentiated genetic regions were characterized by elevated L. idas ancestry in the admixed population, which occurs in L. idas-like habitat, consistent with the hypothesis that local adaptation contributes to speciation. Moreover, locus-specific measures of genetic differentiation (a metric of divergent selection) were positively associated with extreme genomic introgression (a metric of hybrid fitness). Interestingly, concordance of differentiation and introgression was only partial. We discuss multiple, complementary explanations for this partial concordance.     

Genome scan linkage results for longitudinal systolic blood pressure phenotypes in subjects from the Framingham Heart Study

The relationship between elevated blood pressure and cardiovascular and cerebrovascular disease risk is well accepted. Both systolic and diastolic hypertension are associated with this risk increase, but systolic blood pressure appears to be a more important determinant of cardiovascular risk than diastolic blood pressure. Subjects for this study are derived from the Framingham Heart Study data set. Each subject had five records of clinical data of which systolic blood pressure, age, height, gender, weight, and hypertension treatment were selected to characterize the phenotype in this analysis. We modeled systolic blood pressure as a function of age using a mixed modeling methodology that enabled us to characterize the phenotype for each individual as the individual's deviation from the population average rate of change in systolic blood pressure for each year of age while controlling for gender, body mass index, and hypertension treatment. Significant (p = 0.00002) evidence for linkage was found between this normalized phenotype and a region on chromosome 1. Similar linkage results were obtained when we estimated the phenotype while excluding values obtained during hypertension treatment. The use of linear mixed models to define phenotypes is a methodology that allows for the adjustment of the main factor by covariates. Future work should be done in the area of combining this phenotype estimation directly with the linkage analysis so that the error in estimating the phenotype can be properly incorporated into the genetic analysis, which, at present, assumes that the phenotype is measured (or estimated) without error.