Resident-invader dynamics and the coexistence of similar strategies

We study the resident-invader dynamics for a given class of models of unstructured populations of finite-dimensional strategies. We prove various results on the existence and uniqueness of -limit sets in the interior of the resident-invader population state space, and we classify the generically possible types of dynamics in terms of the invasion conditions when the resident and invader strategies are similar to one another.This work was supported by the Academy of Finland     

Practical coexistence of two species in the chemostat - A slow-fast characterization

We show that the chemostat model with two species having different but close break-even concentrations exhibits a slow-fast dynamics. Considering small perturbations about the dilution rate for which break-even concentrations are identical, we use the Fenichel theory to show the coexistence of species for large times. Then we determine the reduced dynamics, which is non-trivial and characterized by the slopes of the growth functions about their break-even concentrations.     

Evolution of the maturation rate collapses competitive coexistence

Most theoretical studies on character displacement and the coexistence of competing species have focused attention on the evolution of competitive traits driven by inter-specific competition. We investigated the evolution of the maturation rate which is not directly related to competition and trades off with the birth rate and how it influences competitive outcomes. Evolution may result in the superior competitor becoming extinct if, initially, the inferior competitor has a lower, and the superior one a higher, maturation rate at the coexistence equilibrium. This counterintuitive result is explained by an explosive increase in the adult population of the inferior competitor as a result of the more rapid evolution of its maturation rate, which is caused by differences in the intensity and direction of selection on the maturation rates of the two species and in their adult densities, which are related to differences in their life histories. Thus, a life history trait trade-off with a competitive trait may cause a competitive ecological coexistence to collapse.     

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host’s intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.     

A host-parasite model yielding heterogeneous parasite loads

Many models of parasitic infections lead to an approximately Poisson distribution of parasites among hosts, in stark contrast to the highly over-dispersed distributions that are usually encountered in practice. In this paper, a model is analyzed which, while assuming all individuals to be alike, can still lead to a very heterogeneous distribution of parasites among the host population. The model can be viewed as a very simple mean field interacting particle system, with the particles corresponding to the individual hosts, which behaves like an associated deterministic system when the number of hosts is large. The deterministic system describes the evolution over time of the proportions of the population with different parasite loads, and its equilibria are interpreted as typical distributions of parasites among hosts. Despite its simplicity, the model is complicated enough mathematically to leave a number of open problems.This work was supported in part by Schweiz. Nationalfonds Grants Nos 21-25579.88 and 20-31262.91, and by NSF Grant DMS 90-05833     

Stabilizing effects in spatial parasitoid-host and predator-prey models: a review

We review the literature on spatial host-parasitoid and predator-prey models. Dispersal on its own is not stabilizing and can destabilize a stable local equilibrium. We identify three mechanisms whereby limited dispersal of hosts and parasitoids combined with other features, such as spatial and temporal heterogeneity, can promote increased persistence and stability. The first mechanisms, "statistical stabilization", is simply the statistical effect that summing a number of out-of-phase population trajectories results in a relatively constant total population density. The second mechanism involves decoupling of immigration from local density, such that limited dispersal between asynchronous patches results in an effect that mimics density-dependence at the local patch level. The third mechanism involves altering spatially averaged parameter values resulting from spatial heterogeneity in density combined with non-linear responses to density. Persistence in spatially explicit models with local dispersal frequently associated with self-organized spatial patterning.     

Leishmania donovani flagellum-specific epitopes mediating host-parasite interactions

Abstract Monoclonal antibodies were developed against flagellar components of promastigotes of Leishmania donovani . The monoclonal antibody produced by clone A₁₁ (mAb A₁₁) recognised epitopes in the polypeptides with molecular weights of 86, 66 and weakly 53 kDa. These epitopes were found to be distributed along the flagellum and at the anterior end of promastigotes. The mAb A₁₁ of IgG₁ isotype strongly agglutinated the promastigotes of L. donovani . The prior treatment of promastigotes of L. donovani with mAb A₁₁ resulted in a significant ( P < 0.001) reduction in the attachment of promastigotes to cultured mouse peritoneal macrophages of line J774G8. The affinity-purified epitopes identified by mAb A₁₁ were recognised by human sera of cases of visceral leishmaniasis. The present study suggest that flagellar-specific epitopes mediate host-parasite interactions and, therefore, the role of these epitopes in the disease process is speculated.     

Population biology of multispecies helminth infection: competition and coexistence

The role that interspecific interactions play in shaping parasite communities is uncertain. To date, models of competition between helminth species have assumed that interaction occurs through parasite-induced host death. To our knowledge, there has been no theoretical exploration of other forms of competition. We examine models in which competition acts at the point of establishment within the host, and at the time of egg production by the adult worm. The models used are stochastic and we allow hosts to vary in their rate of exposure to infective larvae. We derive the Lotka-Volterra model of competition when exposure is homogenous and thus demonstrate that two helminth species cannot coexist on a single limiting resource. We show that coexistence of species is promoted by heterogeneity in host exposure provided that the rates of exposure to the two species are not perfectly correlated, and, if they are positively correlated, provided that the degree of heterogeneity in host exposure is similar for the two competing helminth species. These results are robust to the mechanism of competition.     

Evidence for constraint on species coexistence in vegetation of the Park Grass experiment

Repeated patterns, of a type that would be expected to result from limitations to species coexistence (i.e. assembly rules) were sought in the Park Grass experiment. This classical grassland experiment was sampled in two years, using replicated biomass samples. Variance in a number of measures was examined, and compared to the variance expected under appropriate null models, the latter based on assumptions of no interactions between species. In each case, an assembly rule would result in low variance. Examining variance in species richness between quadrats within a treatment, there was no indication of constraint on species co-occurrences; variance in richness was actually greater than expected under the null model, attributable to environmental variation or perhaps positive interactions between species. However, there was control on biomass, evidenced by variance in total biomass (i.e. over all species) within a treatment being significantly lower than expected under the null model. There was no indication of community structure based on guilds (i.e. functional types). Although there was in 1991 some, non-significant, indication of a constant proportion of species from the legume guild, there was no sign of such an effect in 1992. Searches for intrinsic guilds failed to converge. There was no indication at all of constancy in the proportional representation of guilds by biomass. Thus, there is good evidence for competitive control on plant growth, but none for control of species occurrences. There is no convincing evidence for guild structure in this community at the scale sampled. Possible conflict is discussed between the existence of evidence for temporal stability but the absence of evidence for spatial uniformity. It is concluded that most of the mechanisms proposed for temporal stability will not necessarily lead to control on spatial variation. For many mechanisms, this would depend on the spatial scale examined.     

高寒草甸常见雀形目鸟类共存机制的生态形态学解释

生态形态学特征是生物在选择压力下长期进化的结果,对生物的生存和繁衍具重要影响。为使种间竞争最小化,同质环境中关系密切的物种一般具有不同的生态形态学特征,以实现对有限资源的分割。1983—2012年,对高寒草甸生态系统中常见的9种雀形目鸟类的生态形态学特征所进行的研究结果表明:9种雀形目鸟类的各个生态形态学特征指标均具有显著差异;～92.0%的个体被正确归类,除小云雀(Eremophila alpestris,79.2%)外,其余各物种判别正确率均较高(84.5%~100%),9个物种被分成5个集团(guild)。各集团独特的生态形态学特征与集团内物种的栖息地环境和取食行为相关,最终解释了各个物种如何在高寒草甸生态系统中实现共存。     

Temperature-mediated coexistence in temperate forest ant communities

Patterns of ant species diversity are well documented and yet the mechanisms promoting species coexistence among communities are often elusive. Two emerging hypotheses that account for coexistence in ant communities are the discovery-dominance tradeoff and the dominance-thermal tolerance tradeoff. Here we used behavioural assays and community-level sampling from ant assemblages in the southern Appalachians, USA to test for the discovery-dominance and dominance-thermal tolerance tradeoffs. Species that were behaviorally dominant during interspecific interactions tended to forage in a narrow window of generally warmer temperatures, whereas subordinate species tended to forage in a wide range of temperatures, including colder temperatures. Species that foraged at lower temperature tended to be behaviourally subordinate, suggesting that a dominance-thermal tolerance tradeoff promotes coexistence in this system. Species richness was positively related to site average annual temperature and within-site variation in ground temperature, suggesting that temperature also shapes the structure of ant communities and regulates diversity. There was no relationship between the ability of a species to discover food resources and its behavioural dominance, contrary to the predictions of the discovery-dominance tradeoff hypothesis. In sum, our results show that temperature plays numerous roles in promoting regional coexistence in this system.     

The role of epistasis on the evolution of recombination in host-parasite coevolution

Antagonistic coevolution between hosts and parasites is known to affect selection on recombination in hosts. The Red Queen Hypothesis (RQH) posits that genetic shuffling is beneficial for hosts because it quickly creates resistant genotypes. Indeed, a large body of theoretical studies have shown that for many models of the genetic interaction between host and parasite, the coevolutionary dynamics of hosts and parasites generate selection for recombination or sexual reproduction. Here we investigate models in which the effect of the host on the parasite (and vice versa) depend approximately multiplicatively on the number of matched alleles. Contrary to expectation, these models generate a dynamical behavior that strongly selects against recombination/sex. We investigate this atypical behavior analytically and numerically. Specifically we show that two complementary equilibria are responsible for generating strong linkage disequilibria of opposite sign, which in turn causes strong selection against sex. The biological relevance of this finding stems from the fact that these phenomena can also be observed if hosts are attacked by two parasites that affect host fitness independently. Hence the role of the Red Queen Hypothesis in natural host parasite systems where infection by multiple parasites is the rule rather than the exception needs to be reevaluated.     

Ecological buffering mechanisms in savannas: A unifying theory of long-term tree-grass coexistence

Plant Ecology - Despite the large spatial extent and the obvious importance of the savanna biome, not to mention several decades of savanna research, the origin, age, nature, and dynamics of...     

Effect of domain-shape on coexistence problems in a competition-diffusion system

We discuss a competition-diffusion system to study coexistence problems of two competing species in a homogeneous environment. In particular, by using invariant manifold theory, effects of domain-shape are considered on this problem.     

Spatial mechanisms for coexistence of species sharing a common natural enemy

We examine the conditions under which spatial structure can mediate coexistence of apparent competitors. We use a spatially explicit, host-parasitoid metapopulation model incorporating local dynamics of Nicholson-Bailey type and global dispersal. Depending on the model parameters, the resulting system displays a plethora of asynchronous dynamical behaviors for which permanent or transient coexistence is observed. We identify a number of spatially mediated tradeoffs which apparent competitors can utilize and demonstrate that the dynamics of spatial coexistence can typically be understood from consideration of two and three patch systems. The phase relationships of species abundances are different for our model than for some other mechanisms of spatial coexistence. We discuss the implications of our findings relative to issues of community organization and biological conservation.     

Quantifying and testing coexistence mechanisms arising from recruitment fluctuations

Temporal fluctuations in recruitment are involved in two distinct coexistence mechanisms, the storage effect and relative nonlinearity of competition, which may act simultaneously to stabilize species coexistence. It is shown that comparisons of recruitment variation between species at high versus low densities can test whether these mechanisms are responsible for stable coexistence. Moreover, under certain circumstances, these comparisons can measure the total coexistence stabilizing effect of the mechanism. These comparisons are clearest for the situation of an invader (a species perturbed to low density) in the presence of its competitors, termed residents. Then average invader-resident differences in the variances of log recruitment, potentially weighted by adult survival rates and species' sensitivities to competition, are proportional to the overall stabilizing effect of the storage effect and relative nonlinearity of competition. Less effective comparisons are available for species naturally at high and low densities or with substantial mean differences in average fitness. These developments lead also to a technique of partitioning the long-term low-density growth rate of a species into community average measures of stabilizing mechanisms, deviations from these measures, and other factors. The community average measure is argued as most appropriate for understanding the ability of a coexistence mechanism to stabilize coexistence. Individual species' deviations from the community average indicate the ways in a which a coexistence mechanism may affect average fitness differences between species either enhancing or diminishing the ability of a given set of species to coexist, depending on other factors. This approach provides a general new tool for analyzing species coexistence.     

Vertical habitat segregation as a mechanism for coexistence in sympatric rodents

Coexistence has been widely studied in small mammals and frequently is assumed to be facilitated by habitat segregation. Using live trapping and spool-and-line experiments, we analyzed habitat selection and segregation across multiples scales for Peromyscus leucopus and Ochrotomys nuttalli. At the habitat scale of a forest stand (∼1–100s ha) P. leucopus co-occurred at all sites where O. nuttalli was found, and we did not detect evidence of positive or negative associations or habitat segregation. However, O. nuttalli was restricted to early successional forests, and P. leucopus had significantly lower abundances in early successional forests than in other habitats. We found similar patterns at the mesohabitat scale of the study site (400 m²). O. nuttalli abundance increased with increasing shrub and tree densities, while increases in P. leucopus abundance were associated with open understories. At the microhabitat scale of the individual movement trail, we found vertical segregation. Movement trails for O. nuttalli were at significantly higher elevation (mean height = 142.93 ± 37.10 cm) than P. leucopus trails (mean height = 15.4 ± 4.98 cm; F-value = 35.29, p < 0.001). We concluded that microhabitat segregation was driven by differential use of vertical space for movement and foraging. We suggest O. nuttalli is superior to P. leucopus in its ability to acquire food especially in shrubby subcanopies where few acorns are available. However, P. leucopus is superior in its ability to forage and avoid predators.     

Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling

We consider plankton-nutrient interaction models consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non-negative equilibria, as well as persistence are given. We also consider the zooplankton-phytoplankton-nutrient interaction models with a fluctuating nutrient input and with a periodic washout rate, respectively. It is shown that coexistence of the zooplankton and phytoplankton may arise due to positive bifurcating periodic solutions.Research has been supported in part by a University of Alberta Ph.D. Scholarship and is in part based on the author's Ph.D. thesis under the supervision of Professor H. 1. Freedman, to whom the author owes a debt of appreciation and gratitude for his kind advice, helpful comments and continuous encouragement     

On the coexistence of three predatory stonefly species in a central Japanese stream

Three large-bodied stonefly species (Paragnetina tinctipennis, Oyamia lugubris, and Kamimuria tibialis) coexist in a central Japanese stream. These species have been classified as predators. Here we study their microhabitat use while focusing on the physical environments, physiological activity, and food resources. We show that Paragnetina uses a niche with faster currents than other species throughout the year. Oyamia has seasonal flexibility in microhabitat preference, physiological activity, and food resources. Kamimuria is a rather stable species, independent of seasonal patterns.     

Strange limits of stability in host-parasitoid systems

The classical Nicholson-Bailey model for a two species host-parasitoid system with discrete generations assumes random distributions of both hosts and parasitoids, randomly searching parasitoids, and random encounters between the individuals of the two species. Although unstable, this model induced many investigations into more complex host-parasitoid systems. Local linearized stability analysis shows that equilibria of host parasitoid systems within the framework of a generalized Nicholson-Bailey model are generally unstable. Stability is only possible if host fertility does not exceede ⁴=54.5982 and if superparasitism is unsuccessful. This special situation has already been discovered by Hassell et al. (1983) in their study of the effects of variable sex ratios on host parasitoid dynamics. We discuss global behaviour of the Hassell-Waage-May model using KAM-theory and illustrate its sensitivity to small perturbations, which can give rise to radically different patterns of the population dynamics of interacting hosts and parasitoids.