Resident-invader dynamics of similar strategies in fluctuating environments

Journal of Mathematical Biology - We study resident-invader dynamics in fluctuating environments when the invader and the resident have close but distinct strategies. First we focus on a class of...     

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.     

Species coexistence of communities with intraguild predation: The role of refuges used by the resource and the intraguild prey

In this paper, we develop a three-species intraguild predation model which incorporates refuges used by the resource and the intraguild prey, and focus on the effects of refuges on the three species coexistence. The invasion condition and parameter region for coexistence are obtained using invasion analysis. The new invasion condition requires that all boundary states with one missing species can be invaded by the missing species. Numerical simulations show that refuges have a major influence on species coexistence of intraguild predation system, and the results strongly depend on the types of refuges introduced into the model. Our study also shows that prey's refuges are detrimental to species coexistence except the resource using refuges. In contrast to previous research, we find that spatial structure may play an important role in effects of refuges on species coexistence of intraguild predation systems. Our results may shed new light on understanding the mechanisms and the persistence of multi-species predators-prey system.     

Stabilizing factors interact in promoting host-parasite coexistence

Understanding the mechanisms that promote coexistence among species is a fundamental problem in evolutionary ecology. Such mechanisms include environmental noise, spatial population structure, density dependence, and genetic variation. In natural populations such factors may exert combined effects on coexistence. Thus, to disentangle the contribution of several factors to coexistence, their effects have to be considered simultaneously. Here we investigate the effects of Ricker-type density dependence, genetic variation, and the frequency of sex on host-parasite coexistence, using Nicholson-Bailey models with and without host density dependence. Interestingly, a low frequency of sex (and the genetic variation induced by sex) is the most important factor in explaining the stability of the host-parasite interaction. However, the carrying capacity K and the frequency of sex interact in affecting coexistence. If K is low (strong density regulation), coexistence is easily attained in the density-dependent model, independently of the frequency of sex. In contrast, for high values of K (weak density regulation), low frequencies of sex considerably improve coexistence. Thus, our results suggest that coexistence among species may strongly depend on interactions among several stabilizing factors. These results seem to be robust since they remain qualitatively unchanged if one assumes (1) Beverton-Holt-type or genotype-specific rather than Ricker-type density dependence in the host, or (2) different genotype-specific susceptibilities of hosts to their parasites, or if one adds (3) moderate levels of environmental stochasticity.     

Bioaugmentation and coexistence of two functionally similar bacterial strains in aerobic granules

The survival of the inoculated microbial culture is critical for successful bioaugmentation but impossible to predict precisely. As an alternative strategy, bioaugmentation of a group of microorganisms may improve reliability of bioaugmentation. This study evaluated simultaneous bioaugmentation of two functionally similar bacterial strains in aerobic granules. The two strains, Pandoraea sp. PG-01 and Rhodococcus erythropolis PG-03, showed high phenol degradation and growth rates in phenol medium, but they were characterized as having a poor aggregation activity and weak bioflocculant-producing and biofilm-forming abilities. In the spatially homogeneous batch conditions, strain PG-01 with higher growth rates outcompeted strain PG-03. However, the two strains could stably coexist in the spatially heterogeneous conditions. Then the two strains were mixed and bioaugmented into activated sludge in two sequencing batch reactors, which were operated with the different settling times of 5 and 30 min, respectively. Aerobic granules were developed only in the reactor with a settling time of 5 min. Fluorescence in situ hybridization and denaturing gradient gel electrophoresis showed that the two strains could coexist in aerobic granules but not in activated sludge. These findings suggested that the compact structure of aerobic granules provided spatial isolation for coexistence of competitively superior and inferior strains with similar functions.     

Spatial patterns and coexistence mechanisms in systems with unidirectional flow

River ecosystems are the prime example of environments where unidirectional flow influences the dispersal of individuals. Spatial patterns of community composition and species replacement emerge from complex interplays of hydrological, geochemical, biological, and ecological factors. Local processes affecting algal dynamics are well understood, but a mechanistic basis for large scale emerging patterns is lacking. To understand how these patterns could emerge in rivers, we analyze a reaction-advection-diffusion model for two competitors in heterogeneous environments. The model supports waves that invade upstream up to a well-defined "upstream invasion limit". We discuss how these waves are produced and present their key properties. We suggest that patterns of species replacement and coexistence along spatial axes reflect stalled waves, produced from diffusion, advection, and species interactions. Emergent spatial scales are plausible given parameter estimates for periphyton. Our results apply to other systems with unidirectional flow such as prevailing winds or climate-change scenarios.     

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.     

Niche invasion,competition and coexistence amongst wild and domestic Bolivian populations of Chagas vector Triatoma infestans (Hemiptera,Reduviidae, Triatominae)

The model developed for human parasites by Bottomley et al. (2007) [52] has been adapted to the dynamics of triatomines to better understand the processes of niche invasion, competition among species and coexistence. In Bolivia, both wild and domestic populations of Triatoma infestans exist. Their ecological niches are normally separated and the two populations do not interbreed, behaving as two distinct species. However, it has been suggested that the two populations may compete, highlighting therefore the potential risk of wild populations invading human dwellings. The model revealed the importance of the basic reproduction rates R₀ of triatomine colonies for the risk of invasion. This depends not only on life traits such as survival and fecundity, but also on (1) the density-dependence phenomenon that limits triatomine establishment, (2) on house exposure to infection and (3) on the correlation between house susceptibility to domestic T. infestans and house susceptibility to wild T. infestans. Competition and coexistence amongst the two groups of T. infestans may occur under particular conditions, but are very unlikely.     

Alternate plant life history strategies and coexistence in randomly varying environments

Environmental fluctuations can in theory allow the coexistence ofecologically similar species by time-sharing a niche, as envisioned by Hutchinson. The evolution of this situation is studied in a competition model, using as an example the evolution of seed germination strategies. Coexistence occurs via the evolution of low-risk and high-risk strategies for dealing with the variability by different species. Coexistence is promoted by intermediate levels of variability or disturbance, and by a trade-off between seed yield and seed survivorship. These results may be applicable also to other low vs. high risk life history options in unpredictably varying environments, such as: stress resistance vs. potentially rapid growth, high adult survivorship vs. high reproductive output. The model's predictions differ from those obtained without consideration of life history evolution in response to environmental variability, and are consistent with some recent studies of plant strategies in intermittently stressed communities.I thank A. Shmida for many discussions on this topic, D. Cohen and I. Noy-Meir for comments after a seminar presentation of this paper, and H. de Kroon, H. During, and E. Van der Maarel for decreasing my ignorance of the empirical literature.Research conducted while the author was recipient of a Sir Charles Clore Postdoctoral Fellowship in the Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel.     

Seasonal dynamics and interspecific competition in Oneida Lake Daphnia

I investigated the population dynamics and competitive interactions of two species of the suspension-feeding crustacean Daphnia in Oneida Lake, N.Y. Both species have persisted in the lake for decades, but their water-column densities are negatively correlated. The larger Daphnia pulicaria dominates in some years, the smaller D. galeata mendotae in others, and in some years one species replaces the other seasonally. Although this pattern results in part from annual variation in vertebrate predation pressure, predation alone cannot explain the irregular daphnid dynamics. In 1992–1995, I examined the water-column abundances, birth and death rates of both species. D. pulicaria dominated in two years, D. galeata mendotae was replaced by D. pulicaria in one year and in 1994, both species persisted in low numbers. To test the effect of temporal changes on the strength of intra- and interspecific competition on both juvenile and adult daphnids, I manipulated a series of field enclosures in 1994 and 1995. The outcome of competition varied within and between years, and its effects were most evident at the highest densities and lowest resource levels. For adults of both species, the effects of interspecific competition were detected more often than those of intraspecific competition. Lipid reserves (a metric of fitness) among juveniles were generally low, with those of D. galeata mendotae often being less than those of D. pulicaria. Contrary to the results of other studies examining competition in daphnids, spatial segregation and predictable within-year reversals in competitive dominance most likely do not play a large role in fostering coexistence of the Oneida Lake daphnids. Instead, coexistence of these competitors is promoted by interannual variation and long-lived diapausing eggs. Received: 20 July 1997 / Accepted: 21 November 1997     

On the sensitive dependence on initial conditions of the dynamics of networks of spiking neurons

We have previously formulated an abstract dynamical system for networks of spiking neurons and derived a formal result that identifies the criterion for its dynamics, without inputs, to be “sensitive to initial conditions”. Since formal results are applicable only to the extent to which their assumptions are valid, we begin this article by demonstrating that the assumptions are indeed reasonable for a wide range of networks, particularly those that lack overarching structure. A notable aspect of the criterion is the finding that sensitivity does not necessarily arise from randomness of connectivity or of connection strengths, in networks. The criterion guides us to cases that decouple these aspects: we present two instructive examples of networks, one with random connectivity and connection strengths, yet whose dynamics is insensitive, and another with structured connectivity and connection strengths, yet whose dynamics is sensitive. We then argue based on the criterion and the gross electrophysiology of the cortex that the dynamics of cortical networks ought to be almost surely sensitive under conditions typically found there. We supplement this with two examples of networks modeling cortical columns with widely differing qualitative dynamics, yet with both exhibiting sensitive dependence. Next, we use the criterion to construct a network that undergoes bifurcation from sensitive dynamics to insensitive dynamics when the value of a control parameter is varied. Finally, we extend the formal result to networks driven by stationary input spike trains, deriving a superior criterion than previously reported. Action Editor: John Rinzel     

Hydration dynamics promote bacterial coexistence on rough surfaces

Identification of mechanisms that promote and maintain the immense microbial diversity found in soil is a central challenge for contemporary microbial ecology. Quantitative tools for systematic integration of complex biophysical and trophic processes at spatial scales, relevant for individual cell interactions, are essential for making progress. We report a modeling study of competing bacterial populations cohabiting soil surfaces subjected to highly dynamic hydration conditions. The model explicitly tracks growth, motion and life histories of individual bacterial cells on surfaces spanning dynamic aqueous networks that shape heterogeneous nutrient fields. The range of hydration conditions that confer physical advantages for rapidly growing species and support competitive exclusion is surprisingly narrow. The rapid fragmentation of soil aqueous phase under most natural conditions suppresses bacterial growth and cell dispersion, thereby balancing conditions experienced by competing populations with diverse physiological traits. In addition, hydration fluctuations intensify localized interactions that promote coexistence through disproportional effects within densely populated regions during dry periods. Consequently, bacterial population dynamics is affected well beyond responses predicted from equivalent and uniform hydration conditions. New insights on hydration dynamics could be considered in future designs of soil bioremediation activities, affect longevity of dry food products, and advance basic understanding of bacterial diversity dynamics and its role in global biogeochemical cycles.     

Evolution of life-history traits collapses competitive coexistence

Trade-offs between competitive ability and the other life-history traits are considered to be a major mechanism of competitive coexistence. Many theoretical studies have demonstrated the robustness of such a coexistence mechanism ecologically; however, it is unknown whether the coexistence is robust evolutionarily. Here, we report that evolution of life-history traits not directly related to competition, such as longevity, and predator avoidance, easily collapses competitive coexistence in several competition systems: spatially structured, and predator-mediated two-species competition systems. In addition, we found that a superior competitor can be excluded by an inferior one by common mechanisms among the models. Our results suggest that ecological competitive coexistence due to a life-history trait trade-off balance may not be balanced on an evolutionary timescale, that is, it may be evolutionarily fragile.     

Oscillatory dynamics in evolutionary games are suppressed by heterogeneous adaptation rates of players

Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in oscillatory dynamics of densities of individual strategists. In finite-size populations, it is known that oscillations blow up until all but one strategies are eradicated if without mutation. In the present paper, we formalize replicator dynamics with players who have different adaptation rates. We show analytically and numerically that the heterogeneous adaptation rate suppresses the oscillation amplitude. In social dilemma games with cyclically competing strategies and homogeneous adaptation rates, altruistic strategies are often relatively weak and cannot survive in finite-size populations. In such situations, heterogeneous adaptation rates save coexistence of different strategies and hence promote altruism. When one strategy dominates the others without cyclic competition, fast adaptors earn more than slow adaptors. When not, mixture of fast and slow adaptors stabilizes population dynamics, and slow adaptation does not imply inefficiency for a player.     

Evolutionary dynamics of predator-prey systems: an ecological perspective

 Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals – the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator–prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator–prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species. Received 10 November 1993; received in revised form 25 July 1994     

A mathematical model for progression and heterogeneity in colorectal cancer dynamics

This paper deals with the development of a mathematical model that describes cancer dynamics at the cellular scale.The selected case study concerns colon and rectum cancer, which originates in colorectal crypts. Cells inside the crypts are assumed to be organized according to a compartmental-like arrangement and to be homogeneously mixing. A mathematical model for cancer progression is proposed here. This model describes the generation of multiple clonal sub-populations of cells at different progression stages in a single crypt.Asymptotic analysis and simulations are developed with an exploratory aim. The obtained results offer some insights into the role played by mutation, proliferation and differentiation phenomena on cancer dynamics. In particular, the acquisition of an additional growing power and a reduction for cellular differentiation seem more likely to be the driving force behind carcinogenesis rather than an increase in the mutation rate. The mutation rate instead seems to affect progression dynamics and intra-tumor heterogeneity. The role played by cells, at different differentiation stages, in the onset and progression of colorectal cancer is highlighted. The results support the fact that stem cells play a key role in cancer development and the idea that transit-amplifying cells could also take on an active role in carcinogenesis.     

Scaling coexistence and assemblage patterns of desert small mammals

Scaling biodiversity patterns has been recognized lately as a very important issue in the search of global processes; however coexistence and assemblage patterns are typically approached at a single spatial scale. Here, we examined coexistence and co-occurrence patterns of desert small mammal communities across different spatial scales in the search of general community patterns. We sampled small mammals in Monte desert (Argentina, South America) for small spatial scales and reviewed published papers from other worldwide deserts for large spatial scale analyses. We used classic community estimators (Shannon, Richness), rank abundance curves and fitting distributions to analyze species coexistence and co-occurrence patterns. Assemblage patterns were analyzed evaluating nestedness across spatial scales and among deserts. Worldwide desert small mammal assemblages are characterized mainly by low species richness and high variation in species composition. The central Monte desert of Argentina showed a consistent assemblage pattern across spatial scales, with a generalist species being the most abundant and widely distributed, accompanied by other subordinate and more narrowly distributed species. All Monte desert communities were significantly nested, with nestedness increasing with scale from patch to regional. Assemblage and coexistence patterns were similar when comparing worldwide deserts despite differences in total richness and faunal singularity. The degree of nestedness varied among worldwide deserts; however all of them showed a consistent nested pattern. Differences in the degree of nestedness could be a result of different regulating factors depending on the desert and scale. These results highlight the importance of including multiscale approaches when dealing with processes that structure desert communities.     

Mechanisms of succession on fallow lands

Vegetation changes during succession can be regarded as plant-to-plant replacement processes. For deeper insight into the nature of these process we need to investigate the mechanisms involved. Therefore two experiments with herbaceous plant communities were analyzed. The data confirm the view that all three types of interaction: competition, coexistence by niche separation, and cooperation, act together. Likewise it can be concluded that the three models of succession proposed by Connell & Slatyer (1977) are not exclusive but describe mechanisms acting together in the same succession process. Evidence is given that seasonal events can act like a switch and influence the successional trend at a later time. It is, therefore, not meaningful to differentiate between fluctuations in the sense of yearly oscillations and the successional trend itself.Dedicated to Prof. Dr Dr h.c. Heinrich Walter on the occasion of the 90th anniversary of his birthday.     

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.