Time-dependent subpopulation induction in heterogeneous tumors

Time-dependent induction of clonal heterogeneity in the neoplastic micro-environment is analysed within the context of a competitive ecology. A model that describes a constant source for clonal emergence was analysed by Michelsonet al. (1987) as an extension of a model proposed by Jansson and Revesz (1974). The extended model has been termed the JRE Model. This paper extends these analyses to time-dependent emergence rates which may represent induction in the presence of a cytotoxic agent. If the analysis is constrained to the tumor micro-environment, and if the emergent subpopulation is drug resistant, then the model may describe the induction and emergence of drug resistant subclones in a growing neoplasm. Asymptotic closed form solutions are derived for a class of emergence rate functions which decay asymptotically to a constant mutation rate. This underlying mutation rate may represent spontaneous mutation to the resistant phenotype, and has been analysed stochastically (Coldmanet al., 1985). The asymptotic solutions to the time-dependent model approach the steady state solution for the JRE Model which represents the dynamics observed in the presence of a constant, spontaneous mutation rate. The clinical and biological implications of these results are discussed. Research support provided in part by Hungarian National Foundation for Scientific Research Grant No. 6032/6319 and ACS Grant IN45-Z and ACS PDT 243B.     

Using exclusion rate to unify niche and neutral perspectives on coexistence

The competitive exclusion principle is one of the most influential concepts in ecology. The classical formulation suggests a correlation between competitor species similarity and competition severity, leading to rapid competitive exclusion where species are very similar; yet neutral models show that identical species can persist in competition for long periods. Here, we resolve the conflict by examining two components of similarity – niche overlap and competitive similarity – and modeling the effects of each on exclusion rate (defined as the inverse of time to exclusion). Studying exclusion rate, rather than the traditional focus on binary outcomes (coexistence versus exclusion), allows us to examine classical niche and neutral perspectives using the same currency. High niche overlap speeds exclusion, but high similarity in competitive ability slows it. These predictions are confirmed by a well‐known model of two species competing for two resources. Under ecologically plausible scenarios of correlation between these two factors, the strongest exclusion rates may be among moderately similar species, while very similar and highly dissimilar competitors have very low exclusion rates. Adding even small amounts of demographic stochasticity to the model blurs the line between deterministic and probabilistic coexistence still further. Thus, focusing on exclusion rate, instead of on the binary outcome of coexistence versus exclusion, allows a variety of outcomes to result from competitive interactions. This approach may help explain species coexistence in diverse competitive communities and raises novel issues for future work.     

Frequency-dependence stabilizes competitive interactions among four annual plants

It is the combination of large fitness differences and strong stabilizing mechanisms that often constitute niche-based explanations for species abundance patterns. Despite the importance of this assumption to much of community ecology, empirical evidence is surprisingly limited. Empirical tests are critical because many abundance patterns are also consistent with neutral-based alternatives (that assume no fitness differences or stabilization). We quantified interactions of four annual grassland species in two-species mixtures at varying frequencies. We found evidence of strong negative frequency-dependent stabilization, where scaled population growth rates increased with decreasing frequency for all four species. There was also a consistent competitive hierarchy among these species indicative of strong fitness differences that, in most cases, suggested potential competitive exclusion despite the observed strong stabilization.     

Evolutionary stability in Lotka-Volterra systems

The Lotka-Volterra model of population ecology, which assumes all individuals in each species behave identically, is combined with the behavioral evolution model of evolutionary game theory. In the resultant monomorphic situation, conditions for the stability of the resident Lotka-Volterra system, when perturbed by a mutant phenotype in each species, are analysed. We develop an evolutionary ecology stability concept, called a monomorphic evolutionarily stable ecological equilibrium, which contains as a special case the original definition by Maynard Smith of an evolutionarily stable strategy for a single species. Heuristically, the concept asserts that the resident ecological system must be stable as well as the phenotypic evolution on the "stationary density surface". The conditions are also shown to be central to analyse stability issues in the polymorphic model that allows arbitrarily many phenotypes in each species, especially when the number of species is small. The mathematical techniques are from the theory of dynamical systems, including linearization, centre manifolds and Molchanov's Theorem.     

Ecological paradoxes*

Two controversial areas of ecology are examined critically to ascertain the limits of some current theories. In the field of population ecology it is argued that no general theory can explain the regulation of animal numbers. Existing theories are considered inadequate because either (1) evidence points to multiple causes rather than a single cause, (2) propositions lose scientific appeal by accumulating qualifiers, or (3) conflicting theories are irrefutable in scientific inquiry. Different research strategies are required to discover generalities in population regulation. In the field of community organization it is pointed out that too much emphasis on the competitive exclusion principle has blinded ecologists from the clustering of resources and of species populations. Conditions of co-existence as well as segregation are considered important in the organization of communities, which allow elements of chance in small scale distribution. The ecological world is likened to the physical world in which small scale disorder leads to order on a large scale. For the development of a global ecology the acceleration of studies in the tropics and the southern hemisphere is urged.     

Habitat selection,interspecific interactions and landscape composition

Summary I argue here that, from the perspective of any individual, most landscapes are composed of only three basic types of habitats. These are: (1) source habitat in which reproduction exceeds mortality and the expected per capita growth rate is greater than one; (2) sink habitat, in which limited, reproduction is possible but will not on average, compensate for mortality and the per capita rate of growth is between zero and one; and (3) unusable habitat, which comprises the matrix of all habitats that are never exploited by the species in question, and in which patches of source and sink habitats are embedded. Unlike earlier source-sink models, this model explicitly considers the effects that substituting one type of habitat for another has on the equilibrium size of a population and the interactions between species which can use both source and sink habitats. The model demonstrates that the equilibrium size of a species' population can sometimes be increased by substituting unusable habitat for sink habitat. Thus, even though the average patch quality in the landscape may be decreased, the overall quality of the landscape can increase. For two species with distinct habitat preferences, interactions between species can vary qualitatively as well as quantitatively as a function of the relative abundances of each of the habitat types. The model also shows that the interactions between species are particularly sensitive to the relative costs of moving between patches and sampling patches to determine their quality. Recent fragmentation of natural landscapes may increase the cost of searching for usable (source or sink) patches. Under some conditions, the interspecific interactions may be substantially more negative (competitive) than the interactions that evolved in the original natural landscape, further reducing population sizes and increasing the likelihood of competitive exclusion in fragmented modern landscapes.     

Dynamical modeling of viral spread in spatially distributed populations: stochastic origins of oscillations and density dependence

In order to understand the spatio-temporal structure of epidemics beyond that permitted with classical SIR (susceptible-infective-recovered)-type models, a new mathematical model for the spread of a viral disease in a population of spatially distributed hosts is described. The positions of the hosts are randomly generated in a rectangular habitat. Encounters between any pair of individuals are according to a Poisson process with a mean rate that declines exponentially as the distance between them increases. The contact rate allows the mean rates to be set at a certain number of encounters per day on average. The relevant state variables for each individual at any time are given by the solution of a pair of coupled differential equations for the viral load and the quantity of general immune system effectors which reduce the viral load. The parameters describing within-host viral-immune system dynamics are generated randomly to reflect variability across a population. Transmission is assumed to depend on the viral loads in donors and occurs with a probability ptrans. The initial conditions are such that one randomly chosen individual carries a randomly chosen amount of the virus, whereas the rest of the population is uninfected. Simulations reveal local or whole-population responses. Whole-population disease spread may be in the form of isolated or multiple occurrences, the latter often being approximately periodic. The mechanisms of this oscillatory behaviour are analyzed in terms of several parameters and the distribution of critical points in the host dynamical systems. Increased contact rate, increased probability of transmission and decreased threshold for viral transmission, decreased immune strength and increased viral growth rate all increase the probability of multiple outbreaks and the distribution of the critical points also plays a role.     

Coexistence in a competitive parasitoid-host system

The main objective of this work is to determine the conditions for coexistence and competitive exclusion in a discrete model for a community of three species: a stage-structured host and two competing parasitoids sharing the same host developmental stage. Coexistence of the community of the species is found to depend on the host life history parameters in the first place, and on competitive ability and parasitoid efficiency in the second place. In particular, parasitoids equilibrium densities are defined by the size of the refuge. Extinction is expected with low growth rate and with low adult survival. Host life histories are also associated with oscillations in population density, and depending on the combination of host adult survival from one generation to the next and host growth rate, the minimum of fluctuations approaches zero, implying a higher potential risk of extinction because of stochastic factors. Our results suggest that equally reduced survival of parasitoids in hosts parasitized by both species determines extinction of the parasitoid with lower population density, in contrast to the case when both parasitoids benefit with 50% of all doubly parasitized hosts, leading to the hypothesis that a community where competitors in multiparasitized hosts die, easily becomes extinct. Competitive exclusion is expected for highly asymmetric competitive interactions, independent of population densities, allowing us to hypothesize that coexistence of competitors in systems with limited resources and refuges is associated with a clearly defined competitive hierarchy.     

Competing species model with behavioral adaptation

This paper studies the properties of a modified Lotka-Volterra model for two competing species, in which the coefficients of the interaction terms are time-dependent averages of the level of interaction over the entire past. For this model, it is shown that (1) competitive exclusion does not occur, (2) there are two possible stable equilibrium points, and (3) in a certain region of parameter space numerical simulations suggest the existence of interesting oscillatory solutions.     

Constrained proteome allocation affects coexistence in models of competitive microbial communities

Microbial communities are ubiquitous and play crucial roles in many natural processes. Despite their importance for the environment, industry and human health, there are still many aspects of microbial community dynamics that we do not understand quantitatively. Recent experiments have shown that the structure and composition of microbial communities are intertwined with the metabolism of the species that inhabit them, suggesting that properties at the intracellular level such as the allocation of cellular proteomic resources must be taken into account when describing microbial communities with a population dynamics approach. In this work, we reconsider one of the theoretical frameworks most commonly used to model population dynamics in competitive ecosystems, MacArthur’s consumer-resource model, in light of experimental evidence showing how proteome allocation affects microbial growth. This new framework allows us to describe community dynamics at an intermediate level of complexity between classical consumer-resource models and biochemical models of microbial metabolism, accounting for temporally-varying proteome allocation subject to constraints on growth and protein synthesis in the presence of multiple resources, while preserving analytical insight into the dynamics of the system. We first show with a simple experiment that proteome allocation needs to be accounted for to properly understand the dynamics of even the simplest microbial community, i.e. two bacterial strains competing for one common resource. Then, we study our consumer-proteome-resource model analytically and numerically to determine the conditions that allow multiple species to coexist in systems with arbitrary numbers of species and resources.Subject terms: Biodiversity, Microbial ecology, Microbial ecology, Bacterial physiology     

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.     

Competitive abilities in experimental microcosms are accurately predicted by a demographic index for R*

Resource competition theory predicts that R*, the equilibrium resource amount yielding zero growth of a consumer population, should predict species' competitive abilities for that resource. This concept has been supported for unicellular organisms, but has not been well-tested for metazoans, probably due to the difficulty of raising experimental populations to equilibrium and measuring population growth rates for species with long or complex life cycles. We developed an index (R(index)) of R* based on demography of one insect cohort, growing from egg to adult in a non-equilibrium setting, and tested whether R(index) yielded accurate predictions of competitive abilities using mosquitoes as a model system. We estimated finite rate of increase (λ') from demographic data for cohorts of three mosquito species raised with different detritus amounts, and estimated each species' R(index) using nonlinear regressions of λ' vs. initial detritus amount. All three species' R(index) differed significantly, and accurately predicted competitive hierarchy of the species determined in simultaneous pairwise competition experiments. Our R(index) could provide estimates and rigorous statistical comparisons of competitive ability for organisms for which typical chemostat methods and equilibrium population conditions are impractical.     

Switching effect of predation on competitive prey species

The fact that the predation pressure has a stabilizing effect on the community of competitive species is demonstrated by a mathematical model of two-preys and one-predator system which has the switching property of predation. By analyzing a dynamical system for these three species populations, it is shown that, in a wide range of parameter space, the system has stable coexisting equilibrium states and the manifold of stable stationary points exhibits a cusp catastrophe and there exist two stable stationary points in the cusp region in the parameter space. Thus, it has been shown that Cause's competitive exclusion is actually relaxed by the switching mechanism of predation.     

基于竞争和扩散能力的非捕食-被捕食集合种群系统的竞争机制

对于非捕食 被捕食(食饵)生态系统,强弱物种之间存在一定的竞争影响.在不考虑栖息地毁坏的情况下,引进双向竞争机制,将Tilman的单向竞争模式推广为n集合种群双向竞争模型,并对6-集合种群的竞争动态进行了计算机模拟研究.结果表明,在平衡态,种群竞争共存的条件是其竞争能力与扩散能力呈现指数型负相关关系,竞争的结果使物种的强弱序列发生变化;物种竞争排除与共存受迁移扩散能力和竞争能力影响很大,在局域斑块上竞争排斥的集合种群在广域尺度上可以竞争共存,即逃亡共存.     

Changes in Individual Allometry Can Lead to Species Coexistence without Niche Separation

The principle of competitive exclusion is a fundamental tenet of ecology. Commonly used competition models predict that at most only one species per limiting resource can coexist in the same environment at steady state; hence, the upper limit to species diversity depends only on the number of limiting resources and not on the rates of resource supply. We demonstrate that such model behavior is the result of both the growth and biomass turnover functions being proportional to the population biomass. We argue that at least the growth function should be a nonlinear, concave downward function of biomass. This form for the growth function should arise simply because of changes in the allometry of individuals in the population. With this change in model structure, we show that any number of species can coexist at an asymptotically stable steady state, even where there is only one limiting resource. Furthermore, if growth increases nonlinearly with biomass, the steady-state resource concentration and hence the potential for biodiversity increases as the resource supply rate increases. Received 31 August 2001; accepted 10 April 2002.     

Coexistence of incompatible plasmids in a bacterial population living under a feast and famine regime

A model is formulated to examine the possibility of (co)existence of plasmids of the same incompatibility and surface exclusion group in a bacterial population living under a feast-and-famine regime. The condition is given under which a growth rate decreasing plasmid can invade a bacterial population. It appears that in case only one plasmid type is present, the frequency of plasmid bearers will tend to a stable equilibrium if the food supply at each growth site gets exhausted and if both plasmid-free and plasmid-bearing bacteria need an equal quantity of food per cell division. If these two conditions are not satisfied, the frequency of plasmid-bearers might oscillate. Two plasmids will sometimes be able to coexist, but only if they follow different survival strategies; one with a high conjugational transfer rate and a lower fitness of its host, and the other with a low transfer rate and a higher host fitness. Coexistence of three plasmids of the same surface exclusion group is impossible.     

Consumer effects on the vital rates of their resource can determine the outcome of competition between consumers

Current competition theory does not adequately address the fact that competitors may affect the survival, growth, and reproductive rates of their resources. Ecologically important interactions in which consumers affect resource vital rates range from parasitism and herbivory to mutualism. We present a general model of competition that explicitly includes consumer-dependent resource vital rates. We build on the classic MacArthur model of competition for multiple resources, allowing direct comparison with expectations from established concepts of resource-use overlap. Consumers share a stage-structured resource population but may use the different stages to different extents, as they do the different independent resources in the classic model. Here, however, the stages are dynamically linked via consumer-dependent vital rates. We show that consumers' effects on resource vital rates result in two important departures from classic results. First, consumers can coexist despite identical use of resource stages, provided each competitor shifts the resource stage distribution toward stages that benefit other species. Second, consumers specializing on different resource stages can compete strongly, possibly resulting in competitive exclusion despite a lack of resource stage-use overlap. Our model framework demonstrates the critical role that consumer-dependent resource vital rates can play in competitive dynamics in a wide range of biological systems.     

Transferable Measurements of Heredity in Models of the Origins of Life

We propose a metric which can be used to compute the amount of heritable variation enabled by a given dynamical system. A distribution of selection pressures is used such that each pressure selects a particular fixed point via competitive exclusion in order to determine the corresponding distribution of potential fixed points in the population dynamics. This metric accurately detects the number of species present in artificially prepared test systems, and furthermore can correctly determine the number of heritable sets in clustered transition matrix models in which there are no clearly defined genomes. Finally, we apply our metric to the GARD model and show that it accurately reproduces prior measurements of the model’s heritability.     

Theoretical analysis of mixed Plasmodium malariae and Plasmodium falciparum infections with partial cross-immunity

A deterministic model for assessing the dynamics of mixed species malaria infections in a human population is presented to investigate the effects of dual infection with Plasmodium malariae and Plasmodium falciparum. Qualitative analysis of the model including positivity and boundedness is performed. In addition to the disease free equilibrium, we show that there exists a boundary equilibrium corresponding to each species. The isolation reproductive number of each species is computed as well as the reproductive number of the full model. Conditions for global stability of the disease free equilibrium as well as local stability of the boundary equilibria are derived. The model has an interior equilibrium which exists if at least one of the isolation reproductive numbers is greater than unity. Among the interesting dynamical behaviours of the model, the phenomenon of backward bifurcation where a stable boundary equilibrium coexists with a stable interior equilibrium, for a certain range of the associated invasion reproductive number less than unity is observed. Results from analysis of the model show that, when cross-immunity between the two species is weak, there is a high probability of coexistence of the two species and when cross-immunity is strong, competitive exclusion is high. Further, an increase in the reproductive number of species i increases the stability of its boundary equilibrium and its ability to invade an equilibrium of species j. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.