Weak trophic interactions and the balance of enriched metacommunities

Weak trophic interactions have been shown to promote the stability of ecological food webs characterized by perfect mixing. However, their importance at the landscape level and response to enrichment has not been extensively examined. In this paper we examine the food-web model explored by McCann et al. [1998. Weak trophic interactions and the balance of nature. Nature 395, 794-798]. The model is expanded into a metacommunity construct where local communities are coupled through global or local dispersal. We analyze global and local stability, as well as spatial synchrony in relation to trophic interaction strength and dispersal regimes. Results reveal that weak interactions can operate through two scale-dependent mechanisms: (i) under low local dispersal regimes, local stabilization of each community under weak interactions directly scales-up to global stability. (ii) Under high local dispersal, asynchronous local destabilization associated with weak interactions proves the driver behind global stability. In the face of enrichment, weak trophic interactions are shown to be instrumental in promoting global stability when dispersal is local. These results demonstrate how the importance of weak trophic interactions can be generalized at the landscape level despite contrary local predictions.     

The long-term evolution of multilocus traits under frequency-dependent disruptive selection

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.     

Habitat destruction in mutualistic metacommunities

We investigate a mutualistic metacommunity where the strength of the mutualistic interaction between species is measured by the extent to which the presence of one species on a patch either reduces the extinction rate of the others present on the same patch or increases their ability to colonize other patches. In both cases, a strong enough mutualism enables all species to persist at habitat densities where they would all be extinct in the absence of the interaction. However, a mutualistic interaction that enhances colonization enables the species to persist at lower habitat density than one that suppresses extinction. All species abruptly go extinct (catastrophe) when the habitat density is decreased infinitesimally below a critical value. A comparison of the mean field or spatially implicit case with unrestricted dispersal and colonization to all patches in the system with a spatially explicit case where dispersal is restricted to the immediate neighbours of the original patch leads to the intriguing conclusion that restricted dispersal can be favourable for species that have a beneficial effect on each other when habitat conditions are adverse. When the mutualistic interaction is strong enough, the extinction threshold or critical amount of habitat required for the persistence of all species is lower when the dispersal is locally restricted than when unrestricted ! The persistence advantage for all species created by the mutualistic interaction increases substantially with the number of species in the metacommunity, as does the advantage for restricted dispersal over global dispersal.     

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.     

The evolution of social learning rules: Payoff-biased and frequency-dependent biased transmission

Humans and other animals do not use social learning indiscriminately, rather, natural selection has favoured the evolution of social learning rules that make selective use of social learning to acquire relevant information in a changing environment. We present a gene-culture coevolutionary analysis of a small selection of such rules (unbiased social learning, payoff-biased social learning and frequency-dependent biased social learning, including conformism and anti-conformism) in a population of asocial learners where the environment is subject to a constant probability of change to a novel state. We define conditions under which each rule evolves to a genetically polymorphic equilibrium. We find that payoff-biased social learning may evolve under high levels of environmental variation if the fitness benefit associated with the acquired behaviour is either high or low but not of intermediate value. In contrast, both conformist and anti-conformist biases can become fixed when environment variation is low, whereupon the mean fitness in the population is higher than for a population of asocial learners. Our examination of the population dynamics reveals stable limit cycles under conformist and anti-conformist biases and some highly complex dynamics including chaos. Anti-conformists can out-compete conformists when conditions favour a low equilibrium frequency of the learned behaviour. We conclude that evolution, punctuated by the repeated successful invasion of different social learning rules, should continuously favour a reduction in the equilibrium frequency of asocial learning, and propose that, among competing social learning rules, the dominant rule will be the one that can persist with the lowest frequency of asocial learning.     

Modelling the morphological response to nutrient availability in the clonal plant Trientalis europaea L.

The morphological responses to changes in environmental quality shown by many clonal plants have been interpreted as an expression of foraging behaviour, as they allow the ramets to become concentrated in more favourable microhabitats. The morphological response to increased nutrient availability in the pseudoannual plant Trientalis europaea was studied in a field experiment. The response was largely size-dependent and consistent with enhanced clonal growth. Fertilized ramets produced more tubers and a larger main tuber. In contrast, stolon length was not affected by the treatment. A spatially explicit simulation model calibrated with data from the field experiment examined the population dynamics of T. europaea ramets in a spatially hetereogeneous, temporally constant, environment. The model showed that T. europaea was effective at concentrating its ramets in favourable patches, but this process was strongly influenced by patch size. The analysis of this response at the clone level showed that ramet aggregation was mainly due to the enhanced performance of clones located initially in the favourable patches, or clones that located a favourable patch by chance. In these clones, the simultaneous increase of ramet size and survival accelerated the production of ramets. The temporal and spatial scale at which the aggregation of ramets in favourable patches was manifested suggests that the effectiveness of the morphological response in T. europaea is favoured by a high spatio-temporal predictability in the environment. Overall, the model emphasized the important role of population dynamics in understanding the nature of the foraging response.     

Long-term evolution of polygenic traits under frequency-dependent intraspecific competition

We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive selection induced by intraspecific competition and frequency-independent stabilizing selection. Moreover, the trait is restricted to a finite range by constraints on the particular loci. Our investigations are based on explicit analytical results (provided by Bürger [2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50, 355-396]; Schneider [2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52, 483-523]) on the short-term dynamics under the assumption of linkage equilibrium. We show that the population always reaches a long-term equilibrium (LTE), i.e., an equilibrium that is resistant against perturbations of mutations of sufficiently small effect. In general, several LTEs can coexist. They can be calculated explicitly, and we provide necessary and sufficient conditions for their existence. In the case that more than one LTE exists, we exemplify numerically that the evolutionary outcome depends crucially on the initial genetic architecture, on the joint distribution of mutational effects across loci, and on the particular realization of the mutation process. Therefore, long-term evolution cannot be predicted from the ecology alone. We further show that a partial order exists for the LTEs. The set of LTEs has a 'largest' element, an LTE which is reached during long-term evolution if the effects of the occurring mutant alleles are sufficiently large.     

Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

The importance of dispersal in determining seed versus safe site limitation of plant populations

The traditional dichotomy of seed versus safe site limitation of plant populations is an oversimplification. While most plant models implicitly assume that the number of safe sites colonized will increase directly with increased seed production by each plant, the number of sites colonized may also strongly depend on patterns of seed dispersal relative to the parent plant, since the majority of a plant’s seeds are deposited very close to it and so not all safe sites are equally accessible. I created a series of spatially explicit individual based plant population models exploring how seed versus safe site limitation is jointly affected by the number of seeds produced per plant and mean dispersal distances. While increased dispersal distance led to reduced seed limitation (more saturation of available safe sites) when a parent plant’s site was temporarily unsuitable following its death, increased dispersal distances could increase seed limitation, especially at low per-plant fecundities, if safe sites did not turn over through time. Models comparing localized to global seed dispersal indicated substantially different degrees of seed limitation for constant per-plant fecundities. Thus seed addition experiments need to be designed to add seeds in realistic spatial patterns to yield meaningful results.     

Effect of systemic diseases on clonal integration: modelling approach

Systemic disease spread has been suggested as a possible disadvantage of clonal plant integration. As connected ramets have higher risk of being infected, disease should cause a selective pressure against clonality. Since experimental tests of this hypothesis are not easy to perform, we chose a modelling approach, by which we could easily separate different factors influencing the process. We used a spatially explicit model of clonal growth with disease spread implemented and we tested the hypothesis that systemic disease decreases the competitive ability of highly integrated clonal plants when compared to less integrated plants with the same parameters. In contrast to our expectations, the integrator was competitively stronger than the splitter in most cases and it lost only when the disease severity and infection rates were very high. We think that the larger the integrated network is, the better the plant utilises its translocation ability. Even a very small amount of resource sharing greatly increased the relative success of the integrator and larger integrators were competitively stronger than the smaller ones. Our results also indicate that although the same infection rate caused more systemic disease in the integrator than in the splitter population, the disease has only a limited potential to select for the splitter strategy. This is caused not only by the advantages of the clonal integration but also by the fact that there is only a small range of infection rates at which there is sufficient difference in disease impact between the strategies.     

Parasite transmission modes and the evolution of virulence

A mathematical model is presented that explores the relationship between transmission patterns and the evolution of virulence for horizontally transmitted parasites when only a single parasite strain can infect each host. The model is constructed by decomposing parasite transmission into two processes, the rate of contact between hosts and the probability of transmission per contact. These transmission rate components, as well as the total parasite mortality rate, are allowed to vary over the course of an infection. A general evolutionarily stable condition is presented that partitions the effects of virulence on parasite fitness into three components: fecundity benefits, mortality costs, and morbidity costs. This extension of previous theory allows us to explore the evolutionary consequences of a variety of transmission patterns. I then focus attention on a special case in which the parasite density remains approximately constant during an infection, and I demonstrate two important ways in which transmission modes can affect virulence evolution: by imposing different morbidity costs on the parasite and by altering the scheduling of parasite reproduction during an infection. Both are illustrated with examples, including one that examines the hypothesis that vector-borne parasites should be more virulent than non-vector-borne parasites (Ewald 1994). The validity of this hypothesis depends upon the way in which these two effects interact, and it need not hold in general.     

Dealing with Uncertainty in Spatially Explicit Population Models

It has been argued that spatially explicit population models (SEPMs) cannot provide reliable guidance for conservation biology because of the difficulty of obtaining direct estimates for their demographic and dispersal parameters and because of error propagation. We argue that appropriate model calibration procedures can access additional sources of information, compensating the lack of direct parameter estimates. Our objective is to show how model calibration using population-level data can facilitate the construction of SEPMs that produce reliable predictions for conservation even when direct parameter estimates are inadequate. We constructed a spatially explicit and individual-based population model for the dynamics of brown bears (Ursus arctos) after a reintroduction program in Austria. To calibrate the model we developed a procedure that compared the simulated population dynamics with distinct features of the known population dynamics (=patterns). This procedure detected model parameterizations that did not reproduce the known dynamics. Global sensitivity analysis of the uncalibrated model revealed high uncertainty in most model predictions due to large parameter uncertainties (coefficients of variation CV 0.8). However, the calibrated model yielded predictions with considerably reduced uncertainty (CV 0.2). A pattern or a combination of various patterns that embed information on the entire model dynamics can reduce the uncertainty in model predictions, and the application of different patterns with high information content yields the same model predictions. In contrast, a pattern that does not embed information on the entire population dynamics (e.g., bear observations taken from sub-areas of the study area) does not reduce uncertainty in model predictions. Because population-level data for defining (multiple) patterns are often available, our approach could be applied widely.     

The evolution of parasite virulence and transmission rate in a spatially structured population

If the transmission occurs through local contact of the individuals in a spatially structured population, the evolutionarily stable (ESS) traits of parasite might be quite different from what the classical theory with complete mixing predicts. In this paper, we theoretically study the ESS virulence and transmission rate of a parasite in a lattice-structured host population, in which the host can send progeny only to its neighboring vacant site, and the transmission occurs only in between the infected and the susceptible in the nearest-neighbor sites. Infected host is assumed to be infertile. The analysis based on the pair approximation and the Monte Carlo simulation reveal that the ESS transmission rate and virulence in a lattice-structured population are greatly reduced from those in completely mixing population. Unlike completely mixing populations, the spread of parasite can drive the host to extinction, because the local density of the susceptible next to the infected can remain high even when the global density of host becomes very low. This demographic viscosity and group selection between self-organized spatial clusters of host individuals then leads to an intermediate ESS transmission rate even if there is no tradeoff between transmission rate and virulence. The ESS transmission rate is below the region of parasite-driven extinction by a finite amount for moderately large reproductive rate of host; whereas, the evolution of transmission rate leads to the fade out of parasite for small reproductive rate, and the extinction of host for very large reproductive rate.     

Loop analysis for pathogens: niche partitioning in the transmission graph for pathogens of the North American tick Ixodes scapularis

In population biology, loop analysis is a method of decomposing a life cycle graph into life history pathways so as to compare the relative contributions of pathways to the population growth rate across species and populations. We apply loop analysis to the transmission graph of five pathogens known to infect the black-legged tick, Ixodes scapularis. In this context loops represent repeating chains of transmission that could maintain the pathogen. They hence represent completions of the life cycle, in much the same way as loops in a life cycle graph do for plants and animals. The loop analysis suggests the five pathogens fall into two distinct groups. Borellia burgdorferi, Babesia microti and Anaplasma phagocytophilum rely almost exclusively on a single loop representing transmission to susceptible larvae feeding on vertebrate hosts that were infected by nymphs. Borellia miyamotoi, in contrast, circulates among a separate set of host types and utilizes loops that are a mix of vertical transmission and horizontal transmission. For B. miyamotoi the main loop is from vertebrate hosts to susceptible nymphs, where the vertebrate hosts were infected by larvae that were infected from birth. The results for Powassan virus are similar to B. miyamotoi. The predicted impacts of the known variation in tick phenology between populations of I. scapularis in the Midwest and Northeast of the United States are hence markedly different for the two groups. All of these pathogens benefit, though, from synchronous activity of larvae and nymphs.     

Demonstrating frequency-dependent transmission of sarcoptic mange in red foxes

Understanding the relationship between disease transmission and host density is essential for predicting disease spread and control. Using long-term data on sarcoptic mange in a red fox Vulpes vulpes population, we tested long-held assumptions of density- and frequency-dependent direct disease transmission. We also assessed the role of indirect transmission. Contrary to assumptions typical of epidemiological models, mange dynamics are better explained by frequency-dependent disease transmission than by density-dependent transmission in this canid. We found no support for indirect transmission. We present the first estimates of R₀ and age-specific transmission coefficients for mange in foxes. These parameters are important for managing this poorly understood but highly contagious and economically damaging disease.     

空间直观景观模型在呼中林区土壤侵蚀预测研究中的初步应用

土壤通用流失方程(USLE)已被广泛应用于大尺度的土壤侵蚀预测．在以往的土壤侵蚀研究中,由于只能获得静态的植被图,土壤通用流失方程只能用于土壤侵蚀的静态估算．空间直观景观模型能在大尺度上模拟植被动态,为土壤通用流失方程提供动态的植被因子,从而使土壤侵蚀的动态模拟成为可能．本研究结合空间直观景观模型LANDIS和土壤通用流失修正方程,以大兴安岭呼中林区为研究区。动态地模拟未来650年内有采伐和无采伐预案下的土壤侵蚀量;同时以无火无采伐预案下的土壤侵蚀为对比值．结果表明,土壤侵蚀量随时间变化呈周期性的波动,其波动程度在无火无采伐预案下最小,而在有火无采伐预案下最大;采伐对土壤侵蚀的影响没有火对土壤侵蚀的影响在空间上表现得明显,但是其累积效果则比火的影响强;降低采伐所产生的裸露土能有效降低年平均土壤侵蚀量,但是对土壤侵蚀动态变化的影响不明显;虽然采伐增加使平均土壤侵蚀量增加,但是也同时使土壤侵蚀的年际变化更趋于平稳．     

Playing by different rules: the evolution of virulence in sterilizing pathogens

We investigate the evolution of virulence of pathogens that reduce their hosts' fitness primarily by affecting host fecundity. We show that, under many conditions, such sterilizing pathogens evolve high rather than intermediate levels of virulence, and this pushes the pathogen population and sometimes the host population toward extinction. We also show that spatial population structure can reverse this evolutionary result and allow the persistence of intermediate-virulence pathogens. Thus, spatial population structure may be vital to the persistence of sterilizing pathogens in nature.     

Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion

We formulated a spatially explicit stochastic population model with an Allee effect in order to explore how invasive species may become established. In our model, we varied the degree of migration between local populations and used an Allee effect with variable birth and death rates. Because of the stochastic component, population sizes below the Allee effect threshold may still have a positive probability for successful invasion. The larger the network of populations, the greater the probability of an invasion occurring when initial population sizes are close to or above the Allee threshold. Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded.     

On the evolutionary dynamics of pathogens with direct and environmental transmission

A number of ecologically and economically important pathogens exhibit a complex transmission dynamics that involves distinct transmission modes. In this paper, we study the evolutionary dynamics of pathogens for which transmission includes direct host-to-host as well as indirect environmental transmission. Different routes of infection spread require specific adaptations of the parasite, which may result in conflicting selection pressures. Using the framework of Adaptive dynamics, we investigate how these conflicting selection pressures are resolved in the course of evolution and determine the conditions for evolutionary diversification of pathogen strains. We show that evolutionary branching and subsequent evolution of specialist strains occurs in wide parameter regions but evolutionary bistability and evolution of generalist pathogens are possible as well. Our analysis reveals that the relative contributions of direct and environmental transmission, as well as the underlying ecological dynamics, play a crucial role in shaping the course of pathogen evolution. Our findings may explain the coexistence of high and low virulence strains observed in several pathogenic organisms using different transmission modes (e.g., influenza viruses) and highlight the importance of considering ecological dynamics in virulence management.