Nonlinear Effect of Dispersal Rate on Spatial Synchrony of Predator-Prey Cycles

Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous.     

Microevolution of S-allele frequencies in wild cherry populations: respective impacts of negative frequency dependent selection and genetic drift

Negative frequency dependent selection (NFDS) is supposed to be the main force controlling allele evolution at the gametophytic self-incompatibility locus (S-locus) in strictly outcrossing species. Genetic drift also influences S-allele evolution. In perennial sessile organisms, evolution of allelic frequencies over two generations is mainly shaped by individual fecundities and spatial processes. Using wild cherry populations between two successive generations, we tested whether S-alleles evolved following NFDS qualitative and quantitative predictions. We showed that allelic variation was negatively correlated with parental allelic frequency as expected under NFDS. However, NFDS predictions in finite population failed to predict more than half S-allele quantitative evolution. We developed a spatially explicit mating model that included the S-locus. We studied the effects of self-incompatibility and local drift within populations due to pollen dispersal in spatially distributed individuals, and variation in male fecundity on male mating success and allelic frequency evolution. Male mating success was negatively related to male allelic frequency as expected under NFDS. Spatial genetic structure combined with self-incompatibility resulted in higher effective pollen dispersal. Limited pollen dispersal in structured distributions of individuals and genotypes and unequal pollen production significantly contributed to S-allele frequency evolution by creating local drift effects strong enough to counteract the NFDS effect on some alleles.     

Determinants of extinction in fragmented plant populations: Crepis sancta (asteraceae) in urban environments

Local populations are subject to recurrent extinctions, and small populations are particularly prone to extinction. Both demographic (stochasticity and the Allee effect) and genetic factors (drift load and inbreeding depression) potentially affect extinction. In fragmented populations, regular dispersal may boost population sizes (demographic rescue effect) or/and reduce the local inbreeding level and genetic drift (genetic rescue effect), which can affect extinction risks. We studied extinction processes in highly fragmented populations of the common species Crepis sancta (Asteraceae) in urban habitats exhibiting a rapid turnover of patches. A four-year demographic monitoring survey and microsatellite genotyping of individuals allowed us to study the determinants of extinction. We documented a low genetic structure and an absence of inbreeding (estimated by multilocus heterozygosity), which suggest that genetic factors were not a major cause of patch extinction. On the contrary, local population size was the main factor in extinction, whereas connectivity was shown to decrease patch extinction, which we interpreted as a demographic rescue effect that was likely due to better pollination services for reproduction. This coupling of demographic and genetic tools highlighted the importance of dispersal in local patch extinctions of small fragmented populations connected by gene flow.     

Which traits promote persistence of feral GM crops? Part 2: implications of metapopulation structure

Transgenes may spread from crops into the environment via the establishment of feral populations, often initiated by seed spill from transport lorries or farm machinery. Locally, such populations are often subject to large environmental variability and usually do not persist longer than a few years. Because secondary feral populations may arise from seed dispersal to adjacent sites, the dynamics of such populations should be studied in a metapopulation context. We study a structured metapopulation model with local dispersal, mimicking a string of roadside subpopulations of a feral crop. Population growth is assumed to be subject to local disturbances, introducing spatially random environmental stochasticity. Our aim is to understand the role of dispersal and environmental variability in the dynamics of such ephemeral populations. We determine the effect of dispersal on the extinction boundary and on the distribution of persistence times, and investigate the influence of spatially correlated disturbances as opposed to spatially random disturbances. We find that, given spatially random disturbances, dispersal slows down the decline of the metapopulation and results in the occurrence of long-lasting local populations which remain more or less static in space. We identify which life history traits, if changed by genetic modification, have the largest impact on the population growth rate and persistence times. For oilseed rape, these are seed bank survival and dormancy. Combining our findings with literature data on transgene-induced life history changes, we predict that persistence is promoted by transgenes for oil-modifications (high stearate or high laurate) and, possibly, for insect resistence (Bt). Transgenic tolerance to glufosinate herbicide is predicted to reduce persistence.     

Modelling single nucleotide effects in phosphoglucose isomerase on dispersal in the Glanville fritillary butterfly: coupling of ecological and evolutionary dynamics

Dispersal comprises a complex life-history syndrome that influences the demographic dynamics of especially those species that live in fragmented landscapes, the structure of which may in turn be expected to impose selection on dispersal. We have constructed an individual-based evolutionary sexual model of dispersal for species occurring as metapopulations in habitat patch networks. The model assumes correlated random walk dispersal with edge-mediated behaviour (habitat selection) and spatially correlated stochastic local dynamics. The model is parametrized with extensive data for the Glanville fritillary butterfly. Based on empirical results for a single nucleotide polymorphism (SNP) in the phosphoglucose isomerase (Pgi) gene, we assume that dispersal rate in the landscape matrix, fecundity and survival are affected by a locus with two alleles, A and C, individuals with the C allele being more mobile. The model was successfully tested with two independent empirical datasets on spatial variation in Pgi allele frequency. First, at the level of local populations, the frequency of the C allele is the highest in newly established isolated populations and the lowest in old isolated populations. Second, at the level of sub-networks with dissimilar numbers and connectivities of patches, the frequency of C increases with decreasing network size and hence with decreasing average metapopulation size. The frequency of C is the highest in landscapes where local extinction risk is high and where there are abundant opportunities to establish new populations. Our results indicate that the strength of the coupling of the ecological and evolutionary dynamics depends on the spatial scale and is asymmetric, demographic dynamics having a greater immediate impact on genetic dynamics than vice versa.     

How do sessile dioecious species cope with their males?

In terrestrial plants the segregation of male and female reproductions on different individuals results in the seed-shadow handicap: males do not disperse any seed so that the number of local patches reached by seeds is potentially reduced in dioecious populations in comparison to hermaphrodite populations. An analytical model, incorporating a lottery-based recruitment and dispersal stochasticity, was built. The spatially mediated cost of the seed-shadow handicap has been assessed considering the criterions for the invasion of a resident hermaphrodite species by a dioecious species and the reverse invasion, both species having the same demographic parameters but assuming a likely higher fecundity for dioecious females. The reciprocal invasion of a dioecious and hermaphrodite species differing only by their fecundity is never possible. The seed-shadow handicap disappears when the dispersal or survival rate is high enough. This latter point is due to dispersal stochasticity, which allows for the existence of empty patches. A low fecundity and an aggregated seed distribution increase dispersal stochasticity and increase the positive impact of a low mortality rate on the relative competitivity of dioecy and hermaphroditism. Adding a dispersal cost has a comparable effect but also requires higher dispersal rates for the dioecious invasion.     

demoniche – an R‐package for simulating spatially‐explicit population dynamics

demoniche is a freely available R‐package which simulates stochastic population dynamics in multiple populations of a species. A demographic model projects population sizes utilizing several transition matrices that can represent impacts on species growth. The demoniche model offers options for setting demographic stochasticity, carrying capacity, and dispersal. The demographic projection in each population is linked to spatially‐explicit niche values, which affect the species growth. With the demoniche package it is possible to compare the influence of scenarios of environmental changes on future population sizes, extinction probabilities, and range shifts of species.     

The highs and lows of dispersal: how connectivity and initial population size jointly shape establishment dynamics in discrete landscapes

Identifying the main factors driving introduced populations to establishment is a major challenge of invasion biology. Due to their small initial size, introduced populations are most vulnerable to extinction because of demographic stochasticity or Allee effects. While an increase in initial population size is known to increase establishment success, much remains to be understood regarding its interplay with connectivity in spatially structured environments. In order to better understand how demographic mechanisms interact at such spatial scale, we developed a stochastic model of population dynamics in discrete space to investigate the effect of connectivity and initial population size on establishment. The predictions derived from the model were then tested using experimental introductions of an insect parasitoid (Trichogramma chilonis) in spatially structured laboratory microcosms. Both theoretical and experimental results demonstrated that the connectivity of the introduction site had 1) a deleterious effect in the first generation when the introduced population was small and 2) a beneficial impact brought about by metapopulation effects in the subsequent generations. Interestingly, populations displayed a weakly pushed invasion pattern promoting early establishment, which was mainly underpinned by dispersal stochasticity and the discrete nature of the landscape. These results shed light on the critical influence of landscape connectivity on establishment dynamics.     

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best-investigated models of linked selection is the recurrent full-sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies rapidly achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way toward providing a more flexible framework to describe genomic patterns of diversity than is currently available.     

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

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

Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.     

Effects of population size and metapopulation dynamics on a mating-system polymorphism

The evolutionary dynamics of neutral alleles under the Wright-Fisher model are well understood. Similarly, the effect of population turnover on neutral genetic diversity in a metapopulation has attracted recent attention in theoretical studies. Here we present the results of computer simulations of a simple model that considers the effects of finite population size and metapopulation dynamics on a mating-system polymorphism involving selfing and outcrossing morphs. The details of the model are based on empirical data from dimorphic populations of the annual plant Eichhornia paniculata, but the results are also of relevance to species with density-dependent selfing rates in general. In our model, the prior selfing rate is determined by two alleles segregating at a single diploid locus. After prior selfing occurs, some remaining ovules are selfed through competing self-fertilisation in finite populations as a result of random mating among gametes. Fitness differences between the mating-system morphs were determined by inbreeding depression and pollen discounting in a context-dependent manner. Simulation results showed evidence of frequency dependence in the action of pollen discounting and inbreeding depression in finite populations. In particular, as a result of selfing in outcrossers through random mating among gametes, selfers experienced a "fixation bias" through drift, even when the mating-system locus was selectively neutral. In a metapopulation, high colony turnover generally favoured the fixation of the outcrossing morph, because inbreeding depression reduced opportunities for colony establishment by selfers through seed dispersal. Our results thus demonstrate that population size and metapopulation processes can lead to evolutionary dynamics involving pollen and seed dispersal that are not predicted for large populations with stable demography.     

Effects of local interactions and local migration on stability

Mathematical models can help to resolve the longstanding question of whether more diverse communities are more stable. Here, I focus on how local dispersal and local interactions--hallmarks of spatial communities--affect stability in a spatially implicit model with demographic stochasticity. The results are based on a novel way to analyze moment equations. The main conclusion is that the type and strength of density-dependent factors, such as fecundity and competition, determine whether local dispersal and local interactions increase or decrease stability. Local dispersal has a stabilizing effect when fecundity is high, interspecific competition is either low or high, and the number of species is small. Effects of local migration on stability are amplified when space is explicit.     

Fixation in haploid populations exhibiting density dependence I: The non-neutral case

We extend the one-locus two allele Moran model of fixation in a haploid population to the case where the total size of the population is not fixed. The model is defined as a two-dimensional birth-and-death process for allele number. Changes in allele number occur through density-independent death events and birth events whose per capita rate decreases linearly with the total population density. Uniquely for models of this type, the latter is determined by these same birth-and-death events. This provides a framework for investigating both the effects of fluctuation in total population number through demographic stochasticity, and deterministic density-dependent changes in mean density, on allele fixation. We analyze this model using a combination of asymptotic analytic approximations supported by numerics. We find that for advantageous mutants demographic stochasticity of the resident population does not affect the fixation probability, but that deterministic changes in total density do. In contrast, for deleterious mutants, the fixation probability increases with increasing resident population fluctuation size, but is relatively insensitive to initial density. These phenomena cannot be described by simply using a harmonic mean effective population size.     

The evolution of dispersal under demographic stochasticity

Temporal and spatial variations of the environment are important factors favoring the evolution of dispersal. With few exceptions, these variations have been considered to be exclusively fluctuations of habitat quality. However, since the presence of conspecifics forms part of an individual's environment, demographic stochasticity may be a component of this variability as well, in particular when local populations are small. To study this effect, we analyzed the evolution of juvenile dispersal in a metapopulation model in which habitat quality is constant in space and time but occupancy fluctuates because of demographic stochasticity. Our analysis extends previous studies in that it includes competition of resources and competition for space. Also, juvenile dispersal is not given by a fixed probability but is made conditional on the presence of free territories in a patch, whereas individuals born in full patches will always disperse. Using a combination of analytical and numerical approaches, we show that demographic stochasticity in itself may provide enough variability to favor dispersal even from patches that are not fully occupied. However, there is no simple relationship between the evolution of dispersal and various indicators of demographic stochasticity. Selected dispersal depends on all aspects of the life-history profile, including kin selection.     

Absorption and fixation times for neutral and quasi-neutral populations with density dependence

We study a generalisation of Moran’s population-genetic model that incorporates density dependence. Rather than assuming fixed population size, we allow the number of individuals to vary stochastically with the same events that change allele number, according to a logistic growth process with density dependent mortality. We analyse the expected time to absorption and fixation in the ‘quasi-neutral’ case: both types have the same carrying capacity, achieved through a trade-off of birth and death rates. Such types would be competitively neutral in a classical, fixed-population Wright-Fisher model. Nonetheless, we find that absorption times are skewed compared to the Wright-Fisher model. The absorption time is longer than the Wright-Fisher prediction when the initial proportion of the type with higher birth rate is large, and shorter when it is small. By contrast, demographic stochasticity has no effect on the fixation or absorption times of truly neutral alleles in a large population. Our calculations provide the first analytic results on hitting times in a two-allele model, when the population size varies stochastically.     

Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance

To a first order of approximation, selection is frequency independent in a wide range of family structured models and in populations following an island model of dispersal, provided the number of families or demes is large and the population is haploid or diploid but allelic effects on phenotype are semidominant. This result underlies the way the evolutionary stability of traits is computed in games with continuous strategy sets. In this paper similar results are derived under isolation by distance. The first-order effect on expected change in allele frequency is given in terms of a measure of local genetic diversity, and of measures of genetic structure which are almost independent of allele frequency in the total population when the number of demes is large. Hence, when the number of demes increases the response to selection becomes of constant sign. This result holds because the relevant neutral measures of population structure converge to equilibrium at a rate faster than the rate of allele frequency changes in the total population. In the same conditions and in the absence of demographic fluctuations, the results also provide a simple way to compute the fixation probability of mutants affecting various ecological traits, such as sex ratio, dispersal, life-history, or cooperation, under isolation by distance. This result is illustrated and tested against simulations for mutants affecting the dispersal probability under a stepping-stone model.     

Separation of time scales, fixation probabilities and convergence to evolutionary stable states under isolation by distance

To a first order of approximation, selection is frequency independent in a wide range of family structured models and in populations following an island model of dispersal, provided the number of families or demes is large and the population is haploid or diploid but allelic effects on phenotype are semidominant. This result underlies the way the evolutionary stability of traits is computed in games with continuous strategy sets. In this paper similar results are derived under isolation by distance. The first-order effect on expected change in allele frequency is given in terms of a measure of local genetic diversity, and of measures of genetic structure which are almost independent of allele frequency in the total population when the number of demes is large. Hence, when the number of demes increases the response to selection becomes of constant sign. This result holds because the relevant neutral measures of population structure converge to equilibrium at a rate faster than the rate of allele frequency changes in the total population. In the same conditions and in the absence of demographic fluctuations, the results also provide a simple way to compute the fixation probability of mutants affecting various ecological traits, such as sex ratio, dispersal, life-history, or cooperation, under isolation by distance. This result is illustrated and tested against simulations for mutants affecting the dispersal probability under a stepping-stone model.     

Absorption and fixation times for neutral and quasi-neutral populations with density dependence

We study a generalisation of Moran’s population-genetic model that incorporates density dependence. Rather than assuming fixed population size, we allow the number of individuals to vary stochastically with the same events that change allele number, according to a logistic growth process with density dependent mortality. We analyse the expected time to absorption and fixation in the ‘quasi-neutral’ case: both types have the same carrying capacity, achieved through a trade-off of birth and death rates. Such types would be competitively neutral in a classical, fixed-population Wright–Fisher model. Nonetheless, we find that absorption times are skewed compared to the Wright–Fisher model. The absorption time is longer than the Wright–Fisher prediction when the initial proportion of the type with higher birth rate is large, and shorter when it is small. By contrast, demographic stochasticity has no effect on the fixation or absorption times of truly neutral alleles in a large population. Our calculations provide the first analytic results on hitting times in a two-allele model, when the population size varies stochastically.     

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.