Ecology and evolution of symbiosis in metapopulations

We present a model for symbionts in plant host metapopulation. Symbionts are assumed not only to form a systemic infection throughout the host and pass into the host seeds, but also to reproduce and infect new plants by spores. Thus, we study a metapopulation of qualitatively identical patches coupled through seeds and spores dispersal. Symbionts that are only vertically inherited cannot persist in such a uniform environment if they lower the host's fitness. They have to be beneficial in order to coexist with the host if they are not perfectly transmitted to the seeds; but evolution selects for 100% fidelity of infection inheritance. In this model we want to see how mixed strategies (both vertical and horizontal infection) affect the coexistence of uninfected and infected plants at equilibrium; also, what would evolution do for the host, for the symbionts and for their association. We present a detailed classification of the possible equilibria with examples. The stability of the steady states is rigorously proved for the first time in a metapopulation set-up.     

集合种群模拟模型及其在竞争共存机制与物种多样性研究中的应用

以荒漠区人工植被的恢复与重建为背景,从宏观尺度研究了很集合种群的空间分布新模式,建立了基于Levins集合种群模型的数值模拟方法。对两物种的模拟结果表明：在适当选择参数下,模拟植被区的集合种群可以形成“海藻式”稳定的时空分布结构,在理论上表明相同生态特征的物种在空间生境中可以达成共存。为了达到物种丰富度和生产力最佳,实现持续发展,对多物种集合种群进行了模拟。模拟结果显示当物种的种数为5时,空间上随机播种的模拟种群覆盖率达到最大,因而可发挥最大的治沙作用。另外,模拟还显示在播种时应采取集聚式的空间播种模式,以使种群具有较高的防沙能力。该结果可为生物防沙治沙领域提供理论依据。     

Density-dependent migration and synchronism in metapopulations

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.     

Joint evolution of specialization and dispersal in structured metapopulations

We study the joint evolution of dispersal and specialization concerning resource usage in a mechanistically underpinned structured discrete-time metapopulation model. We show that dispersal significantly affects the evolution of specialization and that specialization is a key factor that determines the possibility of evolutionary branching in dispersal propensity. Allowing both dispersal propensity and specialization to evolve as a consequence of natural selection is necessary in order to understand the evolutionary dynamics. The joint evolution of dispersal and specialization forms a natural evolutionary path leading to the coexistence of generalists and specialists. We show that in this process, the number of different patch types and the resource distribution are essential.     

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.     

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.     

Experimental demonstration of accelerated extinction in source‐sink metapopulations

Population extinction is a fundamental ecological process which may be aggravated by the exchange of organisms between productive (source) and unproductive (sink) habitat patches. The extent to which such source‐sink exchange affects extinction rates is unknown. We conducted an experiment in which metapopulation effects could be distinguished from source‐sink effects in laboratory populations of Daphnia magna. Time‐to‐extinction in this experiment was maximized at intermediate levels of habitat fragmentation, which is consistent with a minority of theoretical models. These results provided a baseline for comparison with experimental treatments designed to detect effects of concentrating resources in source patches. These treatments showed that source‐sink configurations increased population variability (the coefficient of variation in abundance) and extinction hazard compared with homogeneous environments. These results suggest that where environments are spatially heterogeneous, accurate assessments of extinction risk will require understanding the exchange of organisms among population sources and sinks. Such heterogeneity may be the norm rather than the exception because of both the intrinsic heterogeneity naturally exhibited by ecosystems and increasing habitat fragmentation by human activity.     

Modelling and analysing evolution of dispersal in populations at expanding range boundaries

Abstract 1. Species would be expected to shift northwards in response to current climate warming, but many are failing to do so because of fragmentation of breeding habitats. Dispersal is important for colonisation and an individual‐based spatially explicit model was developed to investigate impacts of habitat availability on the evolution of dispersal in expanding populations. Model output was compared with field data from the speckled wood butterfly Pararge aegeria, which currently is expanding its range in Britain. 2. During range expansion, models simulated positive linear relationships between dispersal and distance from the seed location. This pattern was observed regardless of quantity (100% to 10% habitat availability) or distribution (random vs. gradient distribution) of habitat, although higher dispersal evolved at expanding range margins in landscapes with greater quantity of habitat and in gradient landscapes. Increased dispersal was no longer evident in any landscape once populations had reached equilibrium; dispersal values returned to those of seed populations. However, in landscapes with the least quantity of habitat, reduced dispersal (below that of seed populations) was observed at equilibrium. 3. Evolutionary changes in adult flight morphology were examined in six populations of P. aegeria along a transect from the distribution core to an expanding range margin in England (spanning a latitudinal distance of >200 km). Empirical data were in agreement with model output and showed increased dispersal ability (larger and broader thoraxes, smaller abdomens, higher wing aspect ratios) with increasing distance from the distribution core. Increased dispersal ability was evident in populations from areas colonised >30 years previously, although dispersal changes were generally evident only in females. 4. Evolutionary increases in dispersal ability in expanding populations may help species track future climate changes and counteract impacts of habitat fragmentation by promoting colonisation. However, at the highest levels of habitat loss, increased dispersal was less evident during expansion and reduced dispersal was observed at equilibrium indicating that, for many species, continued habitat fragmentation is likely to outweigh any benefits from dispersal.     

Seasonal Dynamics of Plant Diversity on lnselbergs in the Ivory Coast (West Africa)

Inselbergs are isolated monolithic outcrops which are characterized by large areas of exposed crystalline rock. Due to harsh edaphic and microclimatic conditions, inselbergs are completely differentiated from their surroundings. Consequently they host a very distinct vegetation which is being investigated on a global scale over a six year period. The seasonal dynamics of Selected plant communities (Afrotrilepis pilosa mat, shallow depression, ephemeral flush vegetation) on granitic inselbergs in the Comoe National Park (NE Ivory Coast) were studied during the rainy period from May to November 1991 by recording all vascular plant species at 12 intervals. For the habitats investigated, the seasonal vegetation dynamics were related to the rainfall pattern. Maximum values both in species diversity and richness were attained in the first third of the rainy period. Drought in August and September caused a decline in species number and diversity in the shallow depression and ephemeral flush vegetation, resulting in mortality of more than 20% of the species. The individual communities studied differed considerably in species diversity and richness. We conclude that ephemeral flush and shallow depression communities are more species rich than the mat community which is dominated by the highly competitive and specialized K-strategist Afrotrilepis pilosa (a poikilohydric Cyperaceae) due to stochastic climatic perturbations which allow the maintenance of species rich non-equilibrium assemblages with r-strategists as major components.     

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499-508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%-20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.     

Invasion of an intermediate predator: Fish population dynamics in a mathematical model of a trophic chain (As applied to Syamozero lake)

A mathematical model is presented for the dynamics of a spatially heterogeneous predator-prey population system; a prototype is the Syamozero lake fish community. We show that the invasion of an intermediate predator can evoke chaotic oscillations in the population densities. We also show that different dynamic regimes (stationary, nonchaotic oscillatory, and chaotic) can coexist. The “choice” of a particular regime depends on the initial invader density. Analysis of the model solutions shows that invasion of an alien species is successful only in the absence of competition between the juvenile invaders and the native species.     

A dispersal-induced paradox: synchrony and stability in stochastic metapopulations

Understanding how dispersal influences the dynamics of spatially distributed populations is a major priority of both basic and applied ecologists. Two well-known effects of dispersal are spatial synchrony (positively correlated population dynamics at different points in space) and dispersal-induced stability (the phenomenon whereby populations have simpler or less extinction-prone dynamics when they are linked by dispersal than when they are isolated). Although both these effects of dispersal should occur simultaneously, they have primarily been studied separately. Herein, I summarise evidence from the literature that these effects are expected to interact, and I use a series of models to characterise that interaction. In particular, I explore the observation that although dispersal can promote both synchrony and stability singly, it is widely held that synchrony paradoxically prevents dispersal-induced stability. I show here that in many realistic scenarios, dispersal is expected to promote both synchrony and stability at once despite this apparent destabilising influence of synchrony. This work demonstrates that studying the spatial and temporal impacts of dispersal together will be vital for the conservation and management of the many communities for which human activities are altering natural dispersal rates.     

The evolution of genetic architecture under frequency-dependent disruptive selection

We propose a model to analyze a quantitative trait under frequency-dependent disruptive selection. Selection on the trait is a combination of stabilizing selection and intraspecific competition, where competition is maximal between individuals with equal phenotypes. In addition, there is a density-dependent component induced by population regulation. The trait is determined additively by a number of biallelic loci, which can have different effects on the trait value. In contrast to most previous models, we assume that the allelic effects at the loci can evolve due to epistatic interactions with the genetic background. Using a modifier approach, we derive analytical results under the assumption of weak selection and constant population size, and we investigate the full model by numerical simulations. We find that frequency-dependent disruptive selection favors the evolution of a highly asymmetric genetic architecture, where most of the genetic variation is concentrated on a small number of loci. We show that the evolution of genetic architecture can be understood in terms of the ecological niches created by competition. The phenotypic distribution of a population with an adapted genetic architecture closely matches this niche structure. Thus, evolution of the genetic architecture seems to be a plausible way for populations to adapt to regimes of frequency-dependent disruptive selection. As such, it should be seen as a potential evolutionary pathway to discrete polymorphisms and as a potential alternative to other evolutionary responses, such as the evolution of sexual dimorphism or assortative mating.     

Modelling population redistribution in a leaf beetle: an evaluation of alternative dispersal functions

1. Dispersal is a fundamental ecological process, so spatial models require realistic dispersal kernels. We compare five different forms for the dispersal kernel of the tansy beetle Chrysolina graminis moving between patches of its host-plant (tansy Tanacetum vulgare) in a riparian landscape. 2. Multi-patch mark-recapture data were collected every 2 weeks over 2 years within a large network of patches and from 2226 beetles. Dispersal was common (28.4% of 880 recaptures after a fortnight) and was more likely over longer intervals, out of small patches, for females and during flooding. Interpatch movement rates did not differ between years and exhibited no density dependence. Dispersal distances were similar for males and females, in both years and over all intervals, with a median dispersal distance of just 9.8 m, although a maximum of 856 m was recorded. 3. A model of dispersal, where patches competed for dispersers based on their size and distance from the beetle's source patch (scaled by the dispersal kernel) was fitted to the field data with a maximum likelihood procedure and each of five alternative kernels. The best fitting had relatively extended tails of long-distance dispersal, while Gaussian and negative exponential kernels performed worst. 4. The model suggests that females disperse more commonly than males and that both are strongly attracted to large patches but do not differ between years, which are consistent with the empirical results. Model-predicted emigration and immigration rates and dispersal phenologies match those observed, suggesting that the model captured the major drivers of tansy beetle dispersal. 5. Although negative exponential and Gaussian kernels are widely used for their simplicity, we suggest that these should not be the models of automatic choice, and that fat-tailed kernels with relatively higher proportions of long-distance dispersal may be more realistic.     

On the evolution of specialization with a mechanistic underpinning in structured metapopulations

We analyze the evolution of specialization in resource utilization in a discrete-time metapopulation model using the adaptive dynamics approach. The local dynamics in the metapopulation are based on the Beverton-Holt model with mechanistic underpinnings. The consumer faces a trade-off in the abilities to consume two resources that are spatially heterogeneously distributed to patches that are prone to local catastrophes. We explore the factors favoring the spread of generalist or specialist strategies. Increasing fecundity or decreasing catastrophe probability favors the spread of the generalist strategy and increasing environmental heterogeneity enlarges the parameter domain where the evolutionary branching is possible. When there are no catastrophes, increasing emigration diminishes the parameter domain where the evolutionary branching may occur. Otherwise, the effect of emigration on evolutionary dynamics is non-monotonous: both small and large values of emigration probability favor the spread of the specialist strategies whereas the parameter domain where evolutionary branching may occur is largest when the emigration probability has intermediate values. We compare how different forms of spatial heterogeneity and different models of local growth affect the evolutionary dynamics. We show that even small changes in the resource dynamics may have outstanding evolutionary effects to the consumers.     

Impacts of dispersal on rapid adaptation and dynamic stability of Daphnia in fluctuating environments

Prior ecological research has shown that spatial processes can enhance the temporal stability of populations in fluctuating environments. Less explored is the effect of dispersal on rapid adaptation and its concomitant impact on population dynamics. For asexually reproducing populations, theory predicts that dispersal in fluctuating environments can facilitate asynchrony among clones and enhance stability by reducing temporal variability of total population abundance. This effect is predicted when clones exhibit heritable variation in environmental optima and when fluctuations occur asynchronously among patches. We tested this in the field using artificial ponds and metapopulations composed of a diverse assemblage of Daphnia pulex clones. We directly manipulated dispersal presence/absence and environmental fluctuations in the form of nutrient pulses. Consistent with predictions, dispersal enhanced temporal asynchrony among clones in the presence of nutrient pulses; this in turn stabilized population dynamics. This effect only emerged when patches experienced spatially asynchronous nutrient pulses (dispersal had no effect when patches were synchronously pulsed). Clonal asynchrony was driven by strong positive selection for a single clone that exhibited a performance advantage under conditions of low resource availability. Our work highlights the importance of dispersal as a driver of eco-evolutionary dynamics and population stability in variable environments.     

Permanent coexistence in general models of three interacting species

We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x _i = X _i f _i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f _i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.