Nested species interactions promote feasibility over stability during the assembly of a pollinator community

The foundational concepts behind the persistence of ecological communities have been based on two ecological properties: dynamical stability and feasibility. The former is typically regarded as the capacity of a community to return to an original equilibrium state after a perturbation in species abundances and is usually linked to the strength of interspecific interactions. The latter is the capacity to sustain positive abundances on all its constituent species and is linked to both interspecific interactions and species demographic characteristics. Over the last 40 years, theoretical research in ecology has emphasized the search for conditions leading to the dynamical stability of ecological communities, while the conditions leading to feasibility have been overlooked. However, thus far, we have no evidence of whether species interactions are more conditioned by the community''s need to be stable or feasible. Here, we introduce novel quantitative methods and use empirical data to investigate the consequences of species interactions on the dynamical stability and feasibility of mutualistic communities. First, we demonstrate that the more nested the species interactions in a community are, the lower the mutualistic strength that the community can tolerate without losing dynamical stability. Second, we show that high feasibility in a community can be reached either with high mutualistic strength or with highly nested species interactions. Third, we find that during the assembly process of a seasonal pollinator community located at The Zackenberg Research Station (northeastern Greenland), a high feasibility is reached through the nested species interactions established between newcomer and resident species. Our findings imply that nested mutualistic communities promote feasibility over stability, which may suggest that the former can be key for community persistence.     

Interference and the persistence of vertically transmitted parasites

Given their ubiquity in nature, understanding the factors that allow the persistence of multiple enemies and in particular vertically transmitted parasites (VTPs) is of considerable importance. Here a model that allows a virulent VTP to be maintained in a system containing a host and a horizontally transmitted parasite (HTP) is analysed. The method of persistence relies on the VTP offering the host a level of protection from the HTP. The VTP is assumed to reduce the HTPs ability to transmit to the host through ecological interference. We show that VTPs are more likely to persist with HTPs that prevent host reproduction than with those that allow it. The VTP persists more easily in r-selected hosts and with highly transmittable HTPs. As the level of protection through interference increases the densities of the host also increase. We also show that VTPs when they do persist tend to stabilise the host population cycles produced by free-living HTPs. The study raised questions about persistence of diseases through interactions with others, and also the stabilising effects of VTPs on dynamical systems in a biological control context.     

Extinctions in simple and complex communities

Disagreement exists between the results of theoretical and empirical exploration into the effect of increasing community complexity on the stability of multispecies ecosystems. A recent return to interest in this area suggests previous results should be re-assessed, from both experimental studies and models, to understand where this discrepancy arises from. Here we propose various simple extensions to a standard multispecies community model that each increase the complexity of the system in a different way. We find that increasing the number of species in a community leads to a decrease in community persistence after the system is perturbed, and go on to show that increasing the dynamical diversity of the community members leads to an increase in stability through a reduction in extinction events, relative to the less complex form of the model. Our results suggest that different forms of complexity lead to different outcomes in the stability properties of the community. While aspects of this work agree with previous empirical findings that more complex communities are more robust to perturbation, we stress that the type of complexity included and the measure of stability used in community models must be properly defined, to allow objective comparisons to be made with previous and future work.     

Habitat loss and the structure of plant-animal mutualistic networks

Recent papers have described the structure of plant–animal mutualistic networks. However, no study has yet explored the dynamical implications of network structure for the persistence of such mutualistic communities. Here, we develop a patch-model of a whole plant–animal community and explore its persistence. To assess the role of network structure, we build three versions of the model. In the first version, we use the exact network of interactions of two real mutualistic communities. In the other versions, we randomize the observed network of interactions using two different null models. We show that the community response to habitat loss is affected by network structure. Real communities start to decay sooner than random communities, but persist for higher destruction levels. There is a destruction threshold at which the community collapses. Our model is the first attempt to describe the dynamics of whole mutualistic metacommunities interacting in realistic ways.     

Seasonality and the persistence and invasion of measles

The critical community size (CCS) for measles, which separates persistent from extinction-prone populations, is arguably the best understood stochastic threshold in ecology. Using simple models, we explore a relatively neglected relationship of how the CCS scales with birth rate. A predominantly positive relationship of persistence with birth rate is complicated by the accompanying dynamical transitions of the underlying deterministic process. We show that these transitions imply a lower CCS for high birth rate less developed countries and contrary to the experience in lower birth rate, industrial countries, the CCS may increase after vaccination. We also consider the evolutionary implications of the CCS for the origin of measles; this analysis explores how the deterministic and stochastic thresholds for invasion and persistence set limits on the mechanism by which this highly infectious pathogen could have successfully colonized its human host.     

Self-thinning and community persistence in a simple size-structured dynamical model of plant growth

This paper presents a size-structured dynamical model of plant growth. The model takes the form of a partial differential-integral equation and includes the effects of self- shading by leaves. Closed form solutions are presented for the equilibrium size density distribution. Analytic conditions are derived for community persistence, and the self-thinning exponent is obtained as a function of species characteristics and environmental conditions.     

Persistence of pollination mutualisms in plant-pollinator-robber systems

Interactions between pollinators, nectar robbers, defensive plants and non-defensive plants are characterized by evolutionary games, where payoffs for the four species are represented by population densities at steady states in the corresponding dynamical systems. The plant-robber system is described by a predator-prey model with the Holling II functional response, while the plant-pollinator system is described by a cooperative model with the Beddington-DeAngelis functional response. By combining dynamics of the models with properties of the evolutionary games, we show mechanisms by which pollination mutualisms could persist in the presence of nectar robbers. The analysis leads to an explanation for persistence of plant-pollinator-robber systems in real situations.     

Dynamical entropy via entropy of non-random matrices: Application to stability and complexity in modelling ecosystems

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems.     

Allee效应对具有生境恢复的集合种群的影响

Allee效应与种群的灭绝密切相关,其研究对生态保护和管理至关重要。Allee效应对物种续存是潜在的干扰因素,濒危物种更容易受其影响,可能会增加生存于生境破碎化斑块的濒危物种的死亡风险,因此研究Allee效应对种群的动态和续存的影响是必要的。从包含由生物有机体对环境的修复产生的Allee效应的集合种群模型出发,引入由其他机制形成的Allee效应,建立了常微分动力系统模型和基于网格模型的元胞自动机模型。通过理论分析和计算机模拟表明:(1)强Allee效应不利于具有生境恢复的集合种群的续存;(2)生境恢复有利于种群续存;(3)局部扩散影响了集合种群的空间结构、动态行为和稳定性,生境斑块之间的局部作用将会减缓或消除集合种群的Allee效应,有利于集合种群的续存。     

Nutrient- and density-dependent effects in a producer-consumer model

A class of models of a nutrient-producer-consumer community is studied analytically and numerically. The analytical study focuses upon the role of total system nutrient and consumer density dependence in governing system behavior and especially, on the persistence and extinction of the population. The numerical study demonstrates that the relationship between consumer density dependence, total system nutrient, and dynamic system behavior can be complicated. Features of the model system include behavior determined solely by total system nutrient, behavior where the relationship between total system nutrient and density dependence governs system dynamics, and behavior where nutrient enrichment or deplation cannot modify ultimate system structure. A conclusion, robust for the model consumer density dependent formulation, indicates that, in the case of ample total nutrient, persistence of the community is independent of consumer density dependence.     

Competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

A model of competition in the chemostat with an inhibitor is combined with a model of competition in the chemostat between plasmid-bearing and plasmid-free organism to produce a model that more closely approximates the way chemostat-like devices are used in biotechnology. The asymptotic behavior of the solutions of the resulting system of nonlinear differential equations is analyzed as a function of the relevant parameters. The techniques are those of dynamical systems although perturbation techniques are used when the parameter reflecting plasmid-loss is small.Research Supported by National Council of Science, Republic of ChinaResearch Supported by National Science Foundation Grant MCS 9204490     

Critical patch size generated by Allee effect in gypsy moth, Lymantria dispar (L.)

Allee effects are important dynamical mechanisms in small-density populations in which per capita population growth rate increases with density. When positive density dependence is sufficiently severe (a 'strong' Allee effect), a critical density arises below which populations do not persist. For spatially distributed populations subject to dispersal, theory predicts that the occupied area also exhibits a critical threshold for population persistence, but this result has not been confirmed in nature. We tested this prediction in patterns of population persistence across the invasion front of the European gypsy moth (Lymantria dispar) in the United States in data collected between 1996 and 2008. Our analysis consistently provided evidence for effects of both population area and density on persistence, as predicted by the general theory, and confirmed here using a mechanistic model developed for the gypsy moth system. We believe this study to be the first empirical documentation of critical patch size induced by an Allee effect.     

Dynamical modeling of drug effect using hybrid systems

Drug discovery today is a complex, expensive, and time-consuming process with high attrition rate. A more systematic approach is needed to combine innovative approaches in order to lead to more effective and efficient drug development. This article provides systematic mathematical analysis and dynamical modeling of drug effect under gene regulatory network contexts. A hybrid systems model, which merges together discrete and continuous dynamics into a single dynamical model, is proposed to study dynamics of the underlying regulatory network under drug perturbations. The major goal is to understand how the system changes when perturbed by drugs and give suggestions for better therapeutic interventions. A realistic periodic drug intake scenario is considered, drug pharmacokinetics and pharmacodynamics information being taken into account in the proposed hybrid systems model. Simulations are performed using MATLAB/SIMULINK to corroborate the analytical results.     

Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems

When searching for hosts, parasitoids are observed to aggregate in response to chemical signalling cues emitted by plants during host feeding. In this paper we model aggregative parasitoid behaviour in a multi-species host-parasitoid community using a system of reaction-diffusion-chemotaxis equations. The stability properties of the steady-states of the model system are studied using linear stability analysis which highlights the possibility of interesting dynamical behaviour when the chemotactic response is above a certain threshold. We observe quasi-chaotic dynamic heterogeneous spatio-temporal patterns, quasi-stationary heterogeneous patterns and a destabilisation of the steady-states of the system. The generation of heterogeneous spatio-temporal patterns and destabilisation of the steady state are due to parasitoid chemotactic response to hosts. The dynamical behaviour of our system has both mathematical and ecological implications and the concepts of chemotaxis-driven instability and coexistence and ecological change are discussed. I. G. Pearce gratefully acknowledges the financial support of the NERC.     

Spatiotemporal behavior of a prey–predator system with a group defense for prey

Group defense is a strategy widely employed by various species. We consider the effect of grouping on population persistence when animals join together in herds in order to provide a self-defense from predators. In literature, group defense is usually addressed in terms of individual behavioral responses. In this paper, we consider an alternative ‘mean-field’ approach which uses prey and predator densities as the dynamical variables. The model is essentially a predator–prey system but with an unconventional parametrization for the predation term. We discuss the outcomes of the ecosystem dynamics in terms of persistence and prey survival. In the spatially distributed model some specific spatio-temporal features are discovered.     

Global stability, local stability and permanence in model food webs

The dynamical theory of food webs has been based typically on local stability analysis. The relevance of local stability to food web properties has been questioned because local stability holds only in the immediate vicinity of the equilibrium and provides no information about the size of the basin of attraction. Local stability does not guarantee persistence of food webs in stochastic environments. Moreover, local stability excludes more complex dynamics such as periodic and chaotic behaviors, which may allow persistence. Global stability and permanence could be better criteria of community persistence. Our simulation analysis suggests that these three stability measures are qualitatively consistent in that all three predict decreasing stability with increasing complexity. Some new predictions on how stability depends on food web configurations are generated here: a consumer-victim link has a smaller effect on the probabilities of stability, as measured by all three stability criteria, than a pair of recipient-controlled and donor-controlled links; a recipient-controlled link has a larger effect on the probabilities of local stability and permanence than a donor-controlled link, while they have the same effect on the probability of global stability; food webs with equal proportions of donor-controlled and recipient-controlled links are less stable than those with different proportions.     

The effects of interference competition on stability,structure and invasion of a multi-species system

Summary An interference competition model for a many species system is presented, based on Lotka-Volterra equations in which some restrictions are imposed on the parameters. The competition coefficients of the Lotka-Volterra equations are assumed to be expressed as products of two factors: the intrinsic interference to other individuals and the defensive ability against such interference. All the equilibrium points of the model are obtained explicitly in terms of its parameters, and these equilibria are classified according to the concept of sector stability. Thus survival or extinction of species at a stable equilibrium point can be determined analytically.The result of the analysis is extended to the successional processes of a community. A criterion for invasion of a new species is obtained and it is also shown that there are some characteristic quantities which show directional changes as succession proceeds.     

Global dynamics of a selection model for the growth of a population with genotypic fertility differences

A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-8130Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-4823Research supported by NSF Grant MCS 7901069. A portion of the work was carried out while the author was a Visiting Professor at the University of Utah, Salt Lake City, Utah     

Models of competition in the chemostat with instantaneous and delayed nutrient recycling

Two models for competition of two populations in a chemostat environment with nutrient recycling are considered. In the first model, the recycling is instantaneous, whereas in the second, the recycling is delayed. For each model an equilibrium analysis is carried out, and persistence criteria are obtained. This paper extends the work done by Beretta et al. (1990) for a single species.Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant NSERC A4823Research carried out at the University of Alberta while on a Canada-China Scholarly Exchange Program