Does quasi-local competition lead to pattern formation in metapopulations? An explicit resource competition model

In metapopulations, competitive interactions may extend beyond the confines of the local population such that members of neighbouring habitat patches affect each other adversely (quasi-local competition). We derive a model for quasi-local competition from first principles, assuming that individuals compete for shared resources and members of a population spend a certain fraction of their foraging time in the adjacent populations. Contrary to the results of Doebeli and Killingback [2003. Theor. Popul. Biol. 64, 397-416], our model does not produce spatial patterns of population densities in homogeneous environments. Quasi-local competition nevertheless contributes to pattern formation by amplifying the effect of heterogeneities in the external environment, and this amplification can be extremely strong when dispersal is absent. We discuss why apparently similar models lead to contrasting results.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

Joint Effects of Habitat Heterogeneity and Species’ Life-History Traits on Population Dynamics in Spatially Structured Landscapes

Both habitat heterogeneity and species’ life-history traits play important roles in driving population dynamics, yet there is little scientific consensus around the combined effect of these two factors on populations in complex landscapes. Using a spatially explicit agent-based model, we explored how interactions between habitat spatial structure (defined here as the scale of spatial autocorrelation in habitat quality) and species life-history strategies (defined here by species environmental tolerance and movement capacity) affect population dynamics in spatially heterogeneous landscapes. We compared the responses of four hypothetical species with different life-history traits to four landscape scenarios differing in the scale of spatial autocorrelation in habitat quality. The results showed that the population size of all hypothetical species exhibited a substantial increase as the scale of spatial autocorrelation in habitat quality increased, yet the pattern of population increase was shaped by species’ movement capacity. The increasing scale of spatial autocorrelation in habitat quality promoted the resource share of individuals, but had little effect on the mean mortality rate of individuals. Species’ movement capacity also determined the proportion of individuals in high-quality cells as well as the proportion of individuals experiencing competition in response to increased spatial autocorrelation in habitat quality. Positive correlations between the resource share of individuals and the proportion of individuals experiencing competition indicate that large-scale spatial autocorrelation in habitat quality may mask the density-dependent effect on populations through increasing the resource share of individuals, especially for species with low mobility. These findings suggest that low-mobility species may be more sensitive to habitat spatial heterogeneity in spatially structured landscapes. In addition, localized movement in combination with spatial autocorrelation may increase the population size, despite increased density effects.     

Population dynamical consequences of gregariousness in a size-structured consumer-resource interaction

Many animal species live in groups. Group living may increase exploitation competition within the group, and variation among groups in intra-group competition intensity could induce life-history variability among groups. Models of physiologically structured populations generally predict single generation cycles, driven by exploitation competition within and between generations. We expect that life-history variability and habitat heterogeneity induced by group living may affect such competition-driven population dynamics. In this study, we vary the gregariousness (the tendency to aggregate in groups) of a size-structured consumer population in a spatially explicit environment. The consumer has limited mobility, and moves according to a probabilistic movement process. We study the effects on the population dynamics, as mediated through the resource and the life-history of the consumer. We find that high gregariousness leads to large spatial resource variation, and highly variable individual life-history, resulting in highly stochastic population dynamics. At reduced gregariousness, life-history of consumers synchronizes, habitat heterogeneity is reduced, and single generation cycles appear. We expect this pattern to occur for any group living organism with limited mobility. Our results indicate that constraints set by population dynamical feedback may be an important aspect in understanding group living in nature.     

Competitive exclusion through reproductive interference

A simple differential equation model was developed to describe the competitive interaction that may occur between species through reproductive interference. The model has the form comparable to Volterra's competition equations, and the graphical analysis of the outcome of the two-species interaction based on its zero-growth isoclines proved that: (1) The possible outcome in this model, as in usual models of resource competition, is either stable coexistence of both species or gradual exclusion of one species by the other, depending critically upon the values of the activity overlapping coefficient c_ij; (2) but, for the same c_ij-values, competitive exclusion is much more ready to occur here than in resource competition; (3) and moreover, the final result of the competition is always dependent on the initial-condition due to its non-linear isoclines, i.e., even under the parameter condition that generally allows both species to coexist, an extreme bias in intial density to one species can readily cause subsequent complete exclusion of its counterparts. Thus, it may follow that the reproductive interference is likely to be working in nature as an efficient mechanism to bring about habitat partitioning in either time or space between some closely related species in insect communities, even though they inhabit heterogeneous habitats where resource competition rarely occurs so that they could otherwise attain steady coexistence.     

Competition between microorganisms for a single limiting resource with cell quota structure and spatial variation

Microbial populations compete for nutrient resources, and the simplest mathematical models of competition neglect differences in the nutrient content of individuals. The simplest models also assume a spatially uniform habitat. Here both of these assumptions are relaxed. Nutrient content of individuals is assumed proportional to cell size, which varies for populations that reproduce by division, and the habitat is taken to be an unstirred chemostat where organisms and nutrients move by simple diffusion. In a spatially uniform habitat, the size-structured model predicts competitive exclusion, such that only the species with lowest break-even concentration persists. In the unstirred chemostat, coexistence of two competitors is possible, if one has a lower break-even concentration and the other can grow more rapidly. In all habitats, the calculation of competitive outcomes depends on a principal eigenvalue that summarizes relationships among cell growth, cell division, and cell size.     

Two-species asymmetric competition: effects of age structure on intra- and interspecific interactions

1. The patterns of density-dependent resource competition and the mechanisms leading to competitive exclusion in an experimental two-species insect age-structured interaction were investigated. 2. The modes of competition (scramble or contest) and strength of competition (under- to overcompensatory) operating within and between the stages of the two species was found to be influenced by total competitor density, the age structure of the competitor community and whether competition is between stages of single or two species. 3. The effect of imposed resource limitation on survival was found to be asymmetric between stages and species. Environments supporting both dominant and subordinate competitors were found to increase survival of subordinate competitors at lower total competitor densities. Competitive environments during development within individual stage cohorts (i.e. small or large larvae), differed from the competitive environment in lumped age classes (i.e. development from egg-->pupae). 4. Competition within mixed-age, stage or species cohorts, when compared with uniform-aged or species cohorts, altered the position of a competitive environment on the scramble-contest spectrum. In some cases the competitive environment switched from undercompensatory contest to overcompensatory scramble competition. 5. Such switching modes of competition suggest that the relative importance of the mechanisms regulating single-species population dynamics (i.e. resource competition) may change when organisms are embedded within a wider community.     

Spatial separation without territoriality in shark communities

Spatial separation within predator communities can arise via territoriality but also from competitive interactions among and within species. However, linking competitive interactions to predator distribution patterns is difficult and theoretical models predict different habitat selection patterns dependent on habitat quality and how competition manifests itself. While models generally consider competitors to be either equal in ability, or for one phenotype to have a fixed advantage over the other, few studies consider that an animal may only have a competitive advantage in specific habitats. We used  10 years of telemetry data, habitat surveys and behavioral experiments, to show spatial partitioning between and within two species of reef shark (grey reef Carcharhinus amblyrhinchos and blacktip reef sharks C. melanopterus) at an unfished Pacific atoll. Within a species, sharks remained within small ‘sub‐habitats’ with very few movements of individuals between sub‐habitats, which previous models have suggested could be caused by intra‐specific competition. Blacktip reef sharks were more broadly distributed across habitat types but a greater proportion used lagoon and backreef habitats, while grey reef sharks preferred forereef habitats. Grey reef sharks at a nearby atoll where blacktip reef sharks are absent, were distributed more broadly between habitat types than when both species were present. A series of individual‐based models predict that habitat separation would only arise if there are competitive interactions between species that are habitat‐specific, with grey reefs having a competitive advantage on the forereefs and blacktips in the lagoons and backreef. We provide compelling evidence that competition helps drive distribution patterns and spatial separation of a marine predator community, and highlight that competitive advantages may not be constant but rather dependent on habitats.     

Competition in variable environments: experiments with planktonic rotifers

1. In a constant environment, competition often tends to reduce species diversity. However, several theories predict that temporal variation in the environment can slow competitive exclusion and allow competing species to coexist. This study reports on laboratory competition experiments in which two pairs of planktonic rotifer species competed for a phytoplankton resource under different conditions of temporal variability in resource supply.
2. For both species pairs, Keratella cochlearis dominated under all conditions of temporal variability, and the other species ( Brachionus calyciflorus or Synchaeta sp.) almost always went extinct. Increasing temporal variation in resource supply slowed competitive exclusion but did not change competitive outcome or allow coexistence.
3. Rotifers show a gleaner–opportunist trade-off, because gleaner species have low threshold resource levels ( R *) and low maximum population growth rates, while opportunist species have the opposite characteristics. In the competition experiments, the gleaner always won and the opportunists always lost. Thus, a gleaner–opportunist trade-off was not sufficient to facilitate coexistence under conditions of resource variability. Instead, the winning species had both the lowest R * and the greatest ability to store resources and ration their use during times of extreme resource scarcity.     

Adaptation of timing of life history traits and population dynamic responses to climate change in spatially structured populations

Changes in the seasonal timing of life history events are documented effects of climate change. We used a general model to study how dispersal and competitive interactions affect eco-evolutionary responses to changes in the temporal distribution of resources over the season. Specifically, we modeled adaptation of the timing of reproduction and population dynamic responses in two competing populations that disperse between two habitats characterized by an early and late resource peak. We investigated three scenarios of environmental change: (1) food peaks advance in both habitats, (2) in the late habitat only and (3) in the early habitat only. At low dispersal rates the evolutionarily stable timing of reproduction closely matched the local resource peak and the environmental change typically caused population decline. Larger dispersal rates rendered less intuitive eco-evolutionary population responses. First, dispersal caused mismatch between evolutionarily stable timing of reproduction and local resource peaks and as a result, reproductive output for subpopulations could increase as well as decrease when resource availability underwent temporal shifts. Second, population responses were contingent on competition between populations. This could accelerate population declines and cause extinctions or even reverse population trends from negative to positive compared to the low dispersal case. When dispersal rate was large and the early resource peak was advanced available niche space was reduced. Hence, even when a population survived the environmental change and obtained positive equilibrium population density, subsequent adaptation of competing populations could drive it to extinction due to convergent evolution and competitive exclusion. These results shed new light on the role of competition and dispersal for the evolution of timing of life history events and provide guidelines for understanding short and long-term population response to climate change.     

Parallel evolution and ecological selection: replicated character displacement in spadefoot toads

Ecological character displacement—trait evolution stemming from selection to lessen resource competition between species—is most often inferred from a pattern in which species differ in resource-use traits in sympatry but not in allopatry, and in which sympatric populations within each species differ from conspecific allopatric populations. Yet, without information on population history, the presence of a divergent phenotype in multiple sympatric populations does not necessarily imply that there has been repeated evolution of character displacement. Instead, such a pattern may arise if there has been character displacement in a single ancestral population, followed by gene flow carrying the divergent phenotype into multiple, derived, sympatric populations. Here, we evaluate the likelihood of such historical events versus ongoing ecological selection in generating divergence in trophic morphology between multiple populations of spadefoot toad (Spea multiplicata) tadpoles that are in sympatry with a heterospecific and those that are in allopatry. We present both phylogenetic and population genetic evidence indicating that the same divergent trait, which minimizes resource competition with the heterospecific, has arisen independently in multiple sympatric populations. These data, therefore, provide strong indirect support for competition''s role in divergent trait evolution.     

Differential effect of inter- and intraspecific competition on the performance of invasive and native Taraxacum species

Inter- and intraspecific competitive abilities are significant determinants of invasive success and the ecological impact of non-native plants. We tested two major hypotheses on the competitive ability of invasive species using invasive (Taraxacum officinale) and native (T. platycarpum) dandelions: differential interspecific competitive ability between invasive and native species and the kin recognition of invasive species. We collected seeds from two field sites where the two dandelion species occurred nearby. Plants were grown alone, with kin (plants from the same maternal genotype) or strangers (plants from different populations) of the same species, or with different species in a growth chamber, and the performance at the early developmental stage between species and treatments was compared. The invasive dandelions outcompeted the native dandelions when competing against each other, although no difference between species was detected without competition or with intraspecific competition. Populations of native species responded to interspecific competition differently. The effect of kinship on plant performance differed between the tested populations in both species. A population produced more biomass than the other populations when grown with a stranger, and this trend was manifested more in native species. Our results support the hypothesis that invasive plants have better competitive ability than native plants, which potentially contributes to the establishment and the range expansion of T. officinale in the introduced range. Although kin recognition is expected to evolve in invasive species, the competitive ability of populations rather than kinship seems to affect plant growth of invasive T. officinale under intraspecific competition.     

不同栖息地状态下物种竞争模式及模拟研究与应用

物种竞争是影响生态系统演化的重要生态过程之一.而物种在受人类影响出现不同程度毁坏的栖息地上的演化又是非常复杂的,因此研究物种演化对栖息地毁坏的响应是非常必要的.在Tilman研究工作的基础上,将竞争系数引入集合种群动力模式,建立了多物种集合种群竞争共存的数学模型,并对5-物种集合种群在不同栖息地状态下的竞争动态进行了计算机模拟研究.结果表明：（1）不同结构的群落（q值不同）,物种之间的竞争排斥作用强度不同,优势物种明显的群落,物种之间的排斥强度大;（2）随着栖息地毁坏程度的增加,对优势物种的负面影响逐渐减小,而对弱势物种的负面影响逐渐增加;（3）随着栖息地恢复幅度的增加,优势物种和弱势物种之间的竞争越强烈,优势物种受到的竞争排斥加大,而弱势物种逐渐变强,出现了强者变弱、弱者变强的格局;（4）物种竞争排斥与共存受迁移扩散能力和竞争能力影响很大,竞争共存的条件是其竞争能力与扩散能力呈非线性负相关关系;（5）竞争共存的物种的强弱序列发生了变化.     

Resource competition and adaptive radiation in a microbial microcosm

Theory predicts that competition for shared resources in a monomorphic population generates divergent selection for adaptation to alternative resources. Experimental tests of this hypothesis are scarce. We selected populations of the bacterium Pseudomonas fluorescens in spatially homogeneous microcosms containing a complex mixture of resources. Initially, all populations consisted of two isogenic clones. The outcome of selection was the evolution of a diverse community of genotypes within each population. Sympatric genotypes exhibited differentiation in metabolic traits related to resource acquisition and frequency‐dependent trade‐offs in competitive ability, as we would expect if different genotypes consumed different resources. These results are consistent with the hypothesis of adaptive radiation driven by resource competition. Reconciling the results of this study with those of earlier experiments provides a new interpretation of the ecological causes of adaptive radiation in microbial microcosms.     

Competition between near and far dispersers in spatially structured habitats

Competitive interactions and invasibility between short- and long-distance dispersal was investigated in a population on a heterogeneous landscape with spatial correlations in habitat types, and where the driving interaction between individuals is competition for space. Stochastic spatially explicit simulations were used, along with differential equation models based on pair approximations. Conditions under which either dispersal strategy can successfully invade the other were determined, as a function of the amount and clustering of suitable habitat and the relative costs involved in the two dispersal strategies. Long-distance dispersal, which reduces intraspecific competition, is sometimes advantageous even where aggregation of suitable habitat would otherwise favor short-distance dispersal, although certain habitat distributions can lead to either strategy being dominant. Coexistence is also possible on some landscapes, where the spatial structure of the populations partitions suitable sites according to the number of suitable neighboring sites. Mutual competitive exclusion, where whichever strategy is established first cannot be invaded, is also possible. All of these results are observed even when there is no intrinsic difference in the two strategies' costs, such as mortality or competitive abilities.     

Which population density affects home ranges of co-occurring rodents?

Animal space use patterns can be affected by the intra- and interspecific density of individuals competing for resources, with home ranges generally decreasing with increasing population density. By applying spatially explicit capture–recapture models implemented in the R package secr, we study whether home ranges of co-occurring yellow-necked mice, Apodemus flavicollis, and bank voles, Myodes glareolus, are related to population density of (a) conspecifics (intraspecific density), (b) the other sympatric species, A. flavicollis or M. glareolus (interspecific density), or (c) total rodent density (A. flavicollis plus M. glareolus). Home ranges of both species were negatively related to intraspecific population density, and were not related to interspecific density or total rodent density. Given that rodents tend to reduce home ranges if resources are abundant, this pattern may merely result from the higher abundance of resources generally associated with high density populations, if the two species were responding to different subsets of resources. However, intraspecific density could directly reduce home ranges, because conspecifics are more likely to interfere with each other due to the overlapping of space use patterns. Therefore, results suggest complementary space or resource use patterns between species, with consequent weak competition and niche differentiation. Across several years and population densities, home ranges of the two co-occurring rodents thus appear to be affected by conspecifics only, suggesting that the two species may coexist in the study area owing to limited space or resource use overlap.     

Habitat Partitioning in a Patchy Environment: Considering the Role of Intraspecific Competition

Coexistence of many size groups of conspecifics in habitat patches may complicate resource partitioning and increase intraspecific interactions. The objectives of my study were to determine partitioning of habitat among age groups of rainbow trout, Oncorhynchus mykiss, coexisting in pool habitat of a headwater stream, and to determine the role of intraspecific competition for such resource partitioning. The trout population showed size and age specific patterns of habitat use, and trout selected locations based on depth and longitudinal position. This habitat use pattern decreased intraspecific overlap among the trout age groups for use of pool space. I used a removal experiment to determine if two-year old trout constrained habitat use by the smaller conspecifics. Although the experimental results imply that recent intraspecific competition was not present, the absence of competitive exclusion was not clearly demonstrated because of low experimental power. While this study identified habitat partitioning among the trout age groups, it remains unclear whether biotic interactions or size specific requirements were causing the habitat use patterns.     

Competitive exclusion and persistence in models of resource and sexual competition

 We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model. Received 1 November 1995; received in revised form 13 January 1996     

Physiological Ecology Meets the Ideal-free Distribution: Predicting the Distribution of Size-structured Fish Populations Across Temperature Gradients

We describe a habitat selection model that predicts the distribution of size-structured groups of fish in a habitat where food availability and water temperature vary spatially. This model is formed by combining a physiological model of fish growth with the logic of ideal free distribution (IFD) theory. In this model we assume that individuals scramble compete for resources, that relative competitive abilities of fish vary with body size, and that individuals select patches that maximize their growth rate. This model overcomes limitations in currently existing physiological and IFD-based models of habitat selection. This is because existing physiological models do not take into account the fact that the amount of food consumed by a fish in a patch will depend on the number of competitors there (something that IFD theory addresses), while traditional IFD models do not take into account the fact that fish are likely to choose patches based on potential growth rate rather than gross food intake (something that physiological models address). Our model takes advantage of the complementary strengths of these two approaches to overcome these weaknesses. Reassuringly, our model reproduces the predictions of its two constituent models under the simple conditions where they apply. When there is no competition for resources it mimics the physiological model of habitat selection, and when there is competition but no temperature variation between patches it mimics either the simple IFD model or the IFD model for unequal competitors. However, when there are both competition and temperature differences between patches our model makes different predictions. It predicts that input-matching between the resource renewal rate and the number of fish (or competitive units) in a patch, the hallmark of IFD models, will be the exception rather than the rule. It also makes the novel prediction that temperature based size-segregation will be common, and that the strength and direction of this segregation will depend on per capita resource renewal rates and the manner in which competitive weight scales with body size. Size-segregation should become more pronounced as per capita resource abundance falls. A larger fish/cooler water pattern is predicted when competitive ability increases more slowly than maximum ration with body size, and a smaller fish/cooler water pattern is predicted when competitive ability increases more rapidly than maximum ration with body size.     

EVOLUTIONARY RESPONSES TO ENVIRONMENTAL CHANGES: HOW DOES COMPETITION AFFECT ADAPTATION?

The role and importance of ecological interactions for evolutionary responses to environmental changes is to large extent unknown. Here it is shown that interspecific competition may slow down rates of adaptation substantially and fundamentally change patterns of adaptation to long-term environmental changes. In the model investigated here, species compete for resources distributed along an ecological niche space. Environmental change is represented by a slowly moving resource maximum and evolutionary responses of single species are compared with responses of coalitions of two and three competing species. In scenarios with two and three species, species that are favored by increasing resource availability increase in equilibrium population size whereas disfavored species decline in size. Increased competition makes it less favorable for individuals of a disfavored species to occupy a niche close to the maximum and reduces the selection pressure for tracking the moving resource distribution. Individual-based simulations and an analysis using adaptive dynamics show that the combination of weaker selection pressure and reduced population size reduces the evolutionary rate of the disfavored species considerably. If the resource landscape moves stochastically, weak evolutionary responses cause large fluctuations in population size and thereby large extinction risk for competing species, whereas a single species subject to the same environmental variability may track the resource maximum closely and maintain a much more stable population size. Other studies have shown that competitive interactions may amplify changes in mean population sizes due to environmental changes and thereby increase extinction risks. This study accentuates the harmful role of competitive interactions by illustrating that they may also decrease rates of adaptation. The slowdown in evolutionary rates caused by competition may also contribute to explain low rates of morphological change in spite of large environmental fluctuations found in fossil records.