The spatial scale of population fluctuations and quasi-extinction risk

Using a spatially homogeneous population model with migration (random individual dispersal) and spatially autocorrelated environmental noise, we show how migration and local density regulation affect the spatial scale of fluctuations in the log of population sizes as well as the 1-yr differences in these. The difference between the squares of these two spatial scales of population fluctuations does not depend on the spatial scale of the noise but only on migration rate and strength of local density regulation. We also show how migration, local density regulation, and spatially correlated environmental noise affect the realized population process at a specific location. As the migration increases, the realized local density regulation and the expected population size increase, while the realized environmental noise decreases. This approach also enables us to analyze the dynamics of the total population size within quadrats of different sizes. The risk of local quasi extinction is strongly reduced by increasing quadrat size or migration rate, while an increase in environmental stochasticity or spatial correlation in the environmental noise increases the risk of quasi extinction.     

Spatial and temporal population genetic structure of the butterfly aglais urticae L. (Lepidoptera, nymphalidae)

The genetic diversity and the temporal and spatial genetic population structure of the butterfly Aglais urticae, a highly mobile species, were studied by allozyme electrophoresis. High levels of allozyme diversity were found. Most of the total genetic diversity occurred at the within-population scale rather than at the between-population scale. This variation could not be accounted for by Wright's model of 'isolation by distance'. No significant temporal variation was observed for those populations that were sampled in different years. A process combining high movement rate between neighbouring patches, long-distance migration and rare extinction/recolonization is suggested to explain the observed genetic structure. This hypothesis is favoured over an island model of population structure because migration in A. urticae is uniform neither with distance nor with time.     

Local extinction and recolonization, species effective population size, and modern human origins

A primary objection from a population genetics perspective to a multiregional model of modern human origins is that the model posits a large census size, whereas genetic data suggest a small effective population size. The relationship between census size and effective size is complex, but arguments based on an island model of migration show that if the effective population size reflects the number of breeding individuals and the effects of population subdivision, then an effective population size of 10,000 is inconsistent with the census size of 500,000 to 1,000,000 that has been suggested by archeological evidence. However, these models have ignored the effects of population extinction and recolonization, which increase the expected variance among demes and reduce the inbreeding effective population size. Using models developed for population extinction and recolonization, we show that a large census size consistent with the multiregional model can be reconciled with an effective population size of 10,000, but genetic variation among demes must be high, reflecting low interdeme migration rates and a colonization process that involves a small number of colonists or kin-structured colonization. Ethnographic and archeological evidence is insufficient to determine whether such demographic conditions existed among Pleistocene human populations, and further work needs to be done. More realistic models that incorporate isolation by distance and heterogeneity in extinction rates and effective deme sizes also need to be developed. However, if true, a process of population extinction and recolonization has interesting implications for human demographic history.     

Genetic and phylogenetic consequences of island biogeography

Abstract.— Island biogeography theory predicts that the number of species on an island should increase with island size and decrease with island distance to the mainland. These predictions are generally well supported in comparative and experimental studies. These ecological, equilibrium predictions arise as a result of colonization and extinction processes. Because colonization and extinction are also important processes in evolution, we develop methods to test evolutionary predictions of island biogeography. We derive a population genetic model of island biogeography that incorporates island colonization, migration of individuals from the mainland, and extinction of island populations. The model provides a means of estimating the rates of migration and extinction from population genetic data. This model predicts that within an island population the distribution of genetic divergences with respect to the mainland source population should be bimodal, with much of the divergence dating to the colonization event. Across islands, this model predicts that populations on large islands should be on average more genetically divergent from mainland source populations than those on small islands. Likewise, populations on distant islands should be more divergent than those on close islands. Published observations of a larger proportion of endemic species on large and distant islands support these predictions.     

Chaotic dynamics may determine the effect of inter-patch migration on metapopulation survival

A simple, strategic model of a system of habitat fragments connected by conservation corridors is presented. The intrinsic dynamics of the population on each fragment are stochastic. In addition, at each generation there is a probability of a catastrophic event occurring which affects all the habitat fragments by greatly reducing the size of the population on each. Global extinction is considered to occur when all the populations simultaneously fall below a threshold value. If the intrinsic dynamics on each fragment are simple cycles or a stable equilibrium, then the addition of conservation corridors does not reduce the frequency of global extinction. This is because migration between fragments induces their populations to have values which are similar to each other. However, if the intrinsic population dynamics are chaotic then the probability of global extinction is greatly reduced by the introduction of conservation corridors. Although local extinction is likely, the chaos acts to oppose the synchronising effect of migration. Often a subset of the populations survive a catastrophe and can recolonize the other patches.     

Quantitative genetic variation in an ecological setting

The machinery was developed to investigate the behavior of quantitative genetic variation in an ecological model of a finite number of islands of finite size, with migration rate m and extinction rate e, for a quantitative genetic model general for numbers of alleles and loci and additive, dominance, and additive by additive epistatic effects. It was necessary to reckon with seven quadratic genetic components, whose coefficients in the genotypic variance components within demes, sigma Gw2, between demes within populations, sigma s2, and between replicate populations, sigma r2, are given by descent measures. The descent measures at any time are calculated with the use of transition equations which are determined by the parameters of the ecological model. Numerical results were obtained for the coefficients of the quadratic genetic components in each of the three genotypic variance components in the early phase of differentiation. The general effect of extinction is to speed up the time course leading to fixation, to increase sigma r2, and to decrease sigma s2 (with a few exceptions) in comparison with no extinction. The general effect of migration is to slow down the time course leading to fixation, to increase sigma Gw2, at least in the later generations, and to decrease sigma s2 (with a few exceptions) in comparison with no migration. Except for these, the effects of migration and extinction on the variance components are complex, depending on the genetic model, and sometimes involve interaction of migration and extinction. Sufficient details are given for an investigator to evaluate numerically the results for variations in the quantitative genetic and ecological models.     

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.     

Determinants of Genetic Structure in a Nonequilibrium Metapopulation of the Plant Silene latifolia

Population genetic differentiation will be influenced by the demographic history of populations, opportunities for migration among neighboring demes and founder effects associated with repeated extinction and recolonization. In natural populations, these factors are expected to interact with each other and their magnitudes will vary depending on the spatial distribution and age structure of local demes. Although each of these effects has been individually identified as important in structuring genetic variance, their relative magnitude is seldom estimated in nature. We conducted a population genetic analysis in a metapopulation of the angiosperm, Silene latifolia, from which we had more than 20 years of data on the spatial distribution, demographic history, and extinction and colonization of demes. We used hierarchical Bayesian methods to disentangle which features of the populations contributed to among population variation in allele frequencies, including the magnitude and direction of their effects. We show that population age, long-term size and degree of connectivity all combine to affect the distribution of genetic variance; small, recently-founded, isolated populations contributed most to increase F _ST in the metapopulation. However, the effects of population size and population age are best understood as being modulated through the effects of connectivity to other extant populations, i.e. F _ST diminishes as populations age, but at a rate that depends how isolated the population is. These spatial and temporal correlates of population structure give insight into how migration, founder effect and within-deme genetic drift have combined to enhance and restrict genetic divergence in a natural metapopulation.     

Effect of changes in population size on genetic microdifferentiation

Changes in local population size are expected to have an effect on the degree of genetic microdifferentiation. A decrease in population size is expected to lead to an increase in microdifferentiation, and an increase in population size to a decrease in microdifferentiation. These expectations are routinely used with historical and/or demographic data to evaluate changes in estimates of microdifferentiation obtained over time for human populations. Here I look more closely at these expectations by using simple mathematical models that relate a change in average effective population size to the degree of microdifferentiation. The direction of change in microdifferentiation is influenced by the migration structure of the populations and the proximity of the region to an equilibrium state. A change in population size always leads to a new equilibrium, but the speed at which this new equilibrium is reached depends on migration and time depth. A decline in population size in one generation always leads to an immediate increase in the degree of microdifferentiation. An increase in population size in one generation could lead to an initial decrease or increase in the degree of microdifferentiation or to no change at all. Consideration of the parameters of the models shows under what conditions such changes occur. The relevance of these models is explored using summary data from a number of human populations.     

On density and extinction in continuous population models

Survival analyses, investigations of extinction and persistence, are executed for populations represented by a nonautonomous differential equation model. The population is assumed governed by density dependent and time varying density independent demographic parameters. While traditional approaches to extinction postulate extinction on an infinite time horizon and at zero abundance level, survival analysis is developed not only for this traditional setting but also on a finite time horizon and at a nonzero threshold level. A main conclusion is that extinction of a temporally stressed population is determined by a totality of density independent and density dependent factors.     

sGD: software for estimating spatially explicit indices of genetic diversity

Anthropogenic landscape changes have greatly reduced the population size, range and migration rates of many terrestrial species. The small local effective population size of remnant populations favours loss of genetic diversity leading to reduced fitness and adaptive potential, and thus ultimately greater extinction risk. Accurately quantifying genetic diversity is therefore crucial to assessing the viability of small populations. Diversity indices are typically calculated from the multilocus genotypes of all individuals sampled within discretely defined habitat patches or larger regional extents. Importantly, discrete population approaches do not capture the clinal nature of populations genetically isolated by distance or landscape resistance. Here, we introduce spatial Genetic Diversity (sGD), a new spatially explicit tool to estimate genetic diversity based on grouping individuals into potentially overlapping genetic neighbourhoods that match the population structure, whether discrete or clinal. We compared the estimates and patterns of genetic diversity using patch or regional sampling and sGD on both simulated and empirical populations. When the population did not meet the assumptions of an island model, we found that patch and regional sampling generally overestimated local heterozygosity, inbreeding and allelic diversity. Moreover, sGD revealed fine-scale spatial heterogeneity in genetic diversity that was not evident with patch or regional sampling. These advantages should provide a more robust means to evaluate the potential for genetic factors to influence the viability of clinal populations and guide appropriate conservation plans.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

Autocorrelated environmental variation and the establishment of invasive species

Environmental parameters such as temperature and rainfall have a positively autocorrelated variance structure which makes it likely that runs of good or bad conditions will occur. It has previously been demonstrated that such autocorrelated environmental variance can increase the probability of extinction in small populations, in much the same way that increased variance without autocorrelation can increase extinction risk. As a result, it has also been suggested that positive autocorrelation will decrease the probability that a species will establish in a novel location. We suggest that describing the probability of invasion success as the probability of indefinite persistence may be an inappropriate definition of risk. Economic or ecological damage may be associated with a population that initially reaches high densities before going extinct in the new location. In addition, such populations may spread to new locations before extirpation. We use a modeling approach to examine the effect of positively autocorrelated conditions on the probability that small populations will reach large size before extinction. We find that where variance is high and the geometric mean of the population growth rate is low, autocorrelation increases the risk that a population will pass a an upper threshold density, even when extinction probability is unaffected. Therefore species classified as having low probability of invasion risk on the basis of population growth rates measured in low variance environments may actually have quite a substantial probability of establishing a large population for a period of time. The mechanism behind the effect is the disproportionate influence of short runs of good conditions initially following introduction.     

Detecting Isolation by Distance Using Phylogenies of Genes

We introduce a method for analyzing phylogenies of genes sampled from a geographically structured population. A parsimony method can be used to compute s, the minimum number of migration events between pairs of populations sampled, and the value of s can be used to estimate the effective migration rate M, the value of Nm in an island model with local populations of size N and a migration rate m that would yield the same value of s. Extensive simulations show that there is a simple relationship between M and the geographic distance between pairs of samples in one- and two-dimensional models of isolation by distance. Both stepping-stone and lattice models were simulated. If two demes k steps apart are sampled, then, s, the average value of s, is a function only of k/(Nm) in a one-dimensional model and is a function only of k/(Nm)2 in a two-dimensional model. Furthermore, log(M) is approximately a linear function of log(k). In a one-dimensional model, the regression coefficient is approximately -1 and in a two-dimensional model the regression coefficient is approximately -0.5. Using data from several locations, the regression of log(M) on log(distance) may indicate whether there is isolation by distance in a population at equilibrium and may allow an estimate of the effective migration rate between adjacent sampling locations. Alternative methods for analyzing DNA sequence data from a geographically structured population are discussed. An application of our method to the data of R. L. Cann, M. Stoneking and A. C. Wilson on human mitochondrial DNA is presented.     

Environment,but not migration rate,influences extinction risk in experimental metapopulations

Ecological theory suggests that several demographic factors influence metapopulation extinction risk, including synchrony in population size between subpopulations, metapopulation size and the magnitude of fluctuations in population size. Theoretically, each of these is influenced by the rate of migration between subpopulations. Here we report on an experiment where we manipulated migration rate within metapopulations of the freshwater zooplankton Daphnia magna to examine how migration influenced each of these demographic variables, and subsequent effects on metapopulation extinction. In addition, our experimental procedures introduced unplanned but controlled differences between metapopulations in light intensity, enabling us to examine the relative influences of environmental and demographic factors. We found that increasing migration rate increased subpopulation synchrony. We failed to detect effects of migration on population size and fluctuations in population size at the metapopulation or subpopulation level, however. In contrast, light intensity did not influence synchrony, but was positively correlated with population size and negatively correlated with population fluctuation. Finally, synchrony did not influence time to extinction, while population size and the magnitude of fluctuations did. We conclude that environmental factors had a greater influence on extinction risk than demographic factors, and that metapopulation size and fluctuation were more important to extinction risk than metapopulation synchrony.     

Migration, coherence and persistence in a fragmented landscape

The chance of local extinction is high during periods of small population size. Accordingly, a metapopulation made of local communities that support internal population cycling may face the threat of regional extinction if the local dynamics is coherent (synchronized). These systems achieve maximum sustainability at an intermediate level of migration that allows recolonization but prevents synchronization. Here we implement an individual-based simulation technique to examine the maximum persistence condition for a system of patch habitats connected by passive migration. The models discussed in this paper take into consideration realistic elements of metapopulations, such as migration cost, disordered spatial structure, frustration and environmental noise. It turns out that the state with maximum anti-correlation between neighboring patches is the most sustainable one, even in the presence of these complications. The results suggest, at least for small systems, a model independent conservation strategy: coherence between neighboring local communities has, in general, a negative impact, and population will benefit from intervention that increases anti-correlations.     

Metapopulation processes and persistence in remnant water vole populations

We examined the spatial distribution of water vole populations in four consecutive years and investigated whether the regional population processes of extinction, recolonisation and migration influence distribution and persistence. We examined how such regional processes are influenced by spatial variation in habitat quality. In addition, we assessed the relevance of metapopulation concepts for understanding the dynamics of species that deviate from classical metapopulation assumptions and developing conservation measures for them. Populations were patchy and discrete, and the patchy distribution was not static between years. Population turnover occurred even in the absence of predatory mink, which only influenced the network of populations at the end of the study. Most populations were clustered close together in the upper tributaries. Local population persistence was predominantly influenced by population size: large populations were more persistent. Recolonisation rates were influenced by isolation and habitat quality. The isolation estimates which best explained the distribution of water vole populations incorporated straight‐line distances, suggesting water voles disperse overland. The distribution of recolonised sites indicated that dispersing voles actively selected habitat on the basis of its quality. Water voles depart from some of the assumptions made by frequently used metapopulation models. In particular there is no clear binary distinction between suitable and non‐suitable habitat. Accounting for variation in habitat quality before investigating temporal changes in population distribution allowed us to demonstrate that the key metapopulation processes were important. The significance of regional population processes relative to local population processes may have increased in declining, fragmented populations compared to pristine regional populations. We hypothesise that although mink predation is likely to eventually cause regional extinction in many areas, metapopulation processes have delayed this decline. Consequently, conservation measures should take into account mink predation rates and regional population processes, before considering aspects of habitat quality.     

Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

Rapid increase in southern elephant seal genetic diversity after a founder event

Genetic diversity provides the raw material for populations to respond to changing environmental conditions. The evolution of diversity within populations is based on the accumulation of mutations and their retention or loss through selection and genetic drift, while migration can also introduce new variation. However, the extent to which population growth and sustained large population size can lead to rapid and significant increases in diversity has not been widely investigated. Here, we assess this empirically by applying approximate Bayesian computation to a novel ancient DNA dataset that spans the life of a southern elephant seal (Mirounga leonina) population, from initial founding approximately 7000 years ago to eventual extinction within the past millennium. We find that rapid population growth and sustained large population size can explain substantial increases in population genetic diversity over a period of several hundred generations, subsequently lost when the population went to extinction. Results suggest that the impact of diversity introduced through migration was relatively minor. We thus demonstrate, by examining genetic diversity across the life of a population, that environmental change could generate the raw material for adaptive evolution over a very short evolutionary time scale through rapid establishment of a large, stable population.     

Genetic structure and seed-mediated dispersal rates of an endangered shrub in a fragmented landscape: a case study for Juniperus communis in northwestern Europe

Background

Population extinction risk in a fragmented landscape is related to the differential ability of the species to spread its genes across the landscape. The impact of landscape fragmentation on plant population dynamics will therefore vary across different spatial scales. We quantified successful seed-mediated dispersal of the dioecious shrub Juniperus communis in a fragmented landscape across northwestern Europe by using amplified fragment length polymorphism (AFLP) markers. Furthermore we investigated the genetic diversity and structure on two spatial scales: across northwestern Europe and across Flanders (northern Belgium). We also studied whether seed viability and populations size were correlated with genetic diversity.

Results

Unexpectedly, estimated seed-mediated dispersal rates were quite high and ranged between 3% and 14%. No population differentiation and no spatial genetic structure were detected on the local, Flemish scale. A significant low to moderate genetic differentiation between populations was detected at the regional, northwest European scale (PhiPT = 0.10). In general, geographically nearby populations were also genetically related. High levels of within-population genetic diversity were detected but no correlation was found between any genetic diversity parameter and population size or seed viability.

Conclusions

In northwestern Europe, landscape fragmentation has lead to a weak isolation-by-distance pattern but not to genetic impoverishment of common juniper. Substantial rates of successful migration by seed-mediated gene flow indicate a high dispersal ability which could enable Juniperus communis to naturally colonize suitable habitats. However, it is not clear whether the observed levels of migration will suffice to counterbalance the effects of genetic drift in small populations on the long run.