Competitive asymmetry, foraging area size and coexistence of annuals

Individuals allocate resources to the expansion of their foraging area and those resources are no longer available for the traits that determine how well those individuals are able to protect their foraging area against competitors. The resulting trade‐off between foraging area size and the traits associated with the ability to compete for the resources within the foraging area applies to ecological scenarios as different as territorial defence by individuals and colonies, and light competition in plants. Whether the trade‐off affects species performance in competition for resources at the area of overlap between foraging areas depends on the symmetry of resource division. In symmetric competition resources are divided equally between the competitors, while in asymmetric competition the individual with the smallest foraging area, and consequently the greatest competitive ability, gains all the resources. Competition may also be a combination of the symmetric and asymmetric processes. I studied the effects of competitive asymmetry on population dynamics and coexistence of two annual species with different sized foraging areas using an individual‐based spatially explicit simulation model. Symmetric competition favoured the species with the larger foraging area and did not allow coexistence. Competitive asymmetry favoured the species with smaller foraging area and allowed coexistence, which was due to the consequences of losing an asymmetric competition being more severe than losing a symmetric competition. The mechanism of coexistence is the larger foraging area's superiority in low population densities (little competition) and the smaller foraging area's ability to win a large foraging area when competition was intense. Competitive asymmetry and small size of both foraging areas led to population dynamics dominated by long‐term fluctuations of small intensity. Symmetric competition and large size of the foraging areas led to large short‐term fluctuations, which often resulted in the extinction of one or both of the species due to demographic stochasticity.     

The effects of stochastic population dynamics on food web structure

We develop a stochastic, individual-based model for food web simulation which in the large-population limit reduces to the well-studied Webworld model, which has been used to successfully construct model food webs with several realistic features. We demonstrate that an almost exact match is found between the population dynamics in fixed food webs, and that the demographic fluctuations have systematic effects when the new model is used to construct food webs due to the presence of species with small populations.     

Trophic interactions affect the population dynamics and risk of extinction of basal species in food webs

This paper addresses effects of trophic complexity on basal species, in a Lotka–Volterra model with stochasticity. We use simple food web modules, with three trophic levels, and expose every species to random environmental stochasticity and analyze (1) the effect of the position of strong trophic interactions on temporal fluctuations in basal species’ abundances and (2) the relationship between fluctuation patterns and extinction risk. First, the numerical simulations showed that basal species do not simply track the environment, i.e. species dynamics do not simply mirror the characteristics of the applied environmental stochasticity. Second, the extinction risk of species was related to the fluctuation patterns of the species.More specifically, we show (i) that despite being forced by random stochasticity without temporal autocorrelation (i.e. white noise), there is significant temporal autocorrelation in the time series of all basal species’ abundances (i.e. the spectra of basal species are red-shifted), (ii) the degree of temporal autocorrelation in basal species time series is affected by food web structure and (iii) the degree of temporal autocorrelation tend to be correlated to the extinction risks of basal species.Our results emphasize the role of food web structure and species interactions in modifying the response of species to environmental variability. To shed some light on the mechanisms we compare the observed pattern in abundances of basal species with analytically predicted patterns and show that the change in the predicted pattern due to the addition of strong trophic interactions is correlated to the extinction risk of the basal species. We conclude that much remain to be understood about the mechanisms behind the interaction among environmental variability, species interactions, population dynamics and vulnerability before we quantitatively can predict, for example, effects of climate change on species and ecological communities. Here, however, we point out a new possible approach for identifying species that are vulnerable to environmental stochasticity by checking the degree of temporal autocorrelation in the time series of species. Increased autocorrelation in population fluctuations can be an indication of increased extinction risk.     

From local interactions to population dynamics in site-based models of ecology

A central problem in ecology is relating the interactions of individuals-described in terms of competition, predation, interference, etc.-to the dynamics of the populations of these individuals-in terms of change in numbers of individuals over time. Here, we address this problem for a class of site-based ecological models, where local interactions between individuals take place at a finite number of discrete resource sites over non-overlapping generations and, between generations, individuals move randomly between sites over the entire system. Such site-based models have previously been applied to a wide range of ecological systems: from those involving contest or scramble competition for resources to host-parasite interactions and meta-populations. We show how the population dynamics of site-based models can be accurately approximated by and understood through deterministic and stochastic difference equations. Conversely, we use the inverse of this approximation to show what implicit assumptions are made about individual interactions by modelling of population dynamics in terms of difference equations. To this end, we prove a useful and general theorem: that any model in our class of site-based models has a corresponding stochastic difference equation population model, by which it can be approximated. This theorem allows us to calculate long-term population dynamics, evolutionary stable strategies and, by extending our theory to account for large deviations, extinction probabilities for a wide range of site-based systems. Our methodology is then illustrated to various examples of between species competition, predator-prey interactions and co-operation.     

Extinctions in competitive communities forced by coloured environmental variation

Understanding the relationships between environmental fluctuations, population dynamics and species interactions in natural communities is of vital theoretical and practical importance. This knowledge is essential in assessing extinction risks in communities that are, for example, pressed by changing environmental conditions and increasing exploitation. We developed a model of density dependent population renewal, in a Lotka–Volterra competitive community context, to explore the significance of interspecific interactions, demographic stochasticity, population growth rate and species abundance on extinction risk in populations under various autocorrelation (colour) regimes of environmental forcing. These factors were evaluated in two cases, where either a single species or the whole community was affected by the external forcing. Species' susceptibility to environmental noise with different autocorrelation structure depended markedly on population dynamics, species' position in the abundance hierarchy and how similarly community members responded to external forcing. We also found interactions between demographic stochasticity and environmental noise leading to a reversal in extinction probabilities from under- to overcompensatory dynamics. We compare our results with studies of single species populations and contrast possible mechanisms leading to extinctions. Our findings indicate that abundance rank, the form of population dynamics, and the colour of environmental variation interact in affecting species extinction risk. These interactions are further modified by interspecific interactions within competitive communities as the interactions filter and modulate the environmental noise.     

Interactions within and between clades shaped the diversification of terrestrial carnivores

A longstanding debate in evolutionary biology and paleontology is whether ecological interactions such as competition impose diversity dependence on speciation and extinction rates. Here, we analyze the fossil record of terrestrial mammalian carnivores in North America and Eurasia using a Bayesian framework to assess whether their diversity dynamics were affected by diversity dependence within and between families (12 in Eurasia, 10 in North America). We found eight instances of within‐clade diversity dependence suppressing speciation rates and detected between‐clade effects increasing extinction rates in six instances. Diversity dependence often involved lineages that migrated between continents and we found that speciation was more responsive to diversity changes within the clade, whereas extinction responded to diversity of taxa in other clades. The analysis of the fossil record of Carnivora suggests that interactions within and between clades are associated with different speciation and extinction regimes, opening room for a broader theory of diversity dependence.     

Frequency-dependent selection on information-transfer strategies at breeding colonies: a simulation study

Through computer simulations, we model three different foodfinding strategies: searcher, no information transfer, watcher,limited information transfer; follower, full information transfer.The aim of this article was to study how frequency-dependentselection affects the proportion of these strategies at a simulatedcolony under different patterns of food distribution. Furthermore,we determined how information transfer in a population witha mixed evolutionarily stable strategy (ESS) modified the averageforaging efficiency of an individual compared to that of anindividual in a population with mutual information exchange.We found that the proportion of information gaining strategiesincreases as the food resources become more clumped. The improvementin foraging efficiency through the operation of an informationcenter need not require mutuality in information exchange. Onthe basis of the presented study, at the ESS only a small percentageof colony members need discover food patches, yet the foragingefficiency may be high because of the operation of an informationcenter.     

Adaptive foraging behaviour of individual pollinators and the coexistence of co-flowering plants

Although pollinators can play a central role in determining the structure and stability of plant communities, little is known about how their adaptive foraging behaviours at the individual level, e.g. flower constancy, structure these interactions. Here, we construct a mathematical model that integrates individual adaptive foraging behaviour and population dynamics of a community consisting of two plant species and a pollinator species. We find that adaptive foraging at the individual level, as a complementary mechanism to adaptive foraging at the species level, can further enhance the coexistence of plant species through niche partitioning between conspecific pollinators. The stabilizing effect is stronger than that of unbiased generalists when there is also strong competition between plant species over other resources, but less so than that of multiple specialist species. This suggests that adaptive foraging in mutualistic interactions can have a very different impact on the plant community structure from that in predator–prey interactions. In addition, the adaptive behaviour of individual pollinators may cause a sharp regime shift for invading plant species. These results indicate the importance of integrating individual adaptive behaviour and population dynamics for the conservation of native plant communities.     

Stochastic hybrid delay population dynamics: well-posed models and extinction

Nonlinear differential equations have been used for decades for studying fluctuations in the populations of species, interactions of species with the environment, and competition and symbiosis between species. Over the years, the original non-linear models have been embellished with delay terms, stochastic terms and more recently discrete dynamics. In this paper, we investigate stochastic hybrid delay population dynamics (SHDPD), a very general class of population dynamics that comprises all of these phenomena. For this class of systems, we provide sufficient conditions to ensure that SHDPD have global positive, ultimately bounded solutions, a minimum requirement for a realistic, well-posed model. We then study the question of extinction and establish conditions under which an ecosystem modelled by SHDPD is doomed.     

Quasi-Local Competition in Stage-Structured Metapopulations: A New Mechanism of Pattern Formation

A central question of ecology is what determines the presence and abundance of species at different locations. In cases of ecological pattern formation, population sizes are largely determined by spatially distributed interactions and may have very little to do with the habitat template. We find pattern formation in a single-species metapopulation model with quasi-local competition, but only if the populations have (at least) two age or stage classes. Quasi-local competition is modeled using an explicit resource competition model with fast resource dynamics, and assuming that adults, but not juveniles, spend a fraction of their foraging time in habitat patches adjacent to their home patch. Pattern formation occurs if one stage class depletes the common resource but the shortage of resource affects mostly the other stage. When the two stages are spatially separated due to quasi-local competition, this results in competitive exclusion between the populations. We find deep similarity between spatial pattern formation and population cycles due to competitive exclusion between cohorts of biennial species, and discuss the differences between the present mechanism and established ways of pattern formation such as diffusive instability and distributed competition with local Allee-effects.     

Biodiversity in model ecosystems, II: species assembly and food web structure

This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here, we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species and shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies.     

Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect

Invasion of an exotic species initiated by its local introduction is considered subject to predator-prey interactions and the Allee effect when the prey growth becomes negative for small values of the prey density. Mathematically, the system dynamics is described by two nonlinear diffusion-reaction equations in two spatial dimensions. Regimes of invasion are studied by means of extensive numerical simulations. We show that, in this system, along with well-known scenarios of species spread via propagation of continuous population fronts, there exists an essentially different invasion regime which we call a patchy invasion. In this regime, the species spreads over space via irregular motion and interaction of separate population patches without formation of any continuous front, the population density between the patches being nearly zero. We show that this type of the system dynamics corresponds to spatiotemporal chaos and calculate the dominant Lyapunov exponent. We then show that, surprisingly, in the regime of patchy invasion the spatially average prey density appears to be below the survival threshold. We also show that a variation of parameters can destroy this regime and either restore the usual invasion scenario via propagation of continuous fronts or brings the species to extinction; thus, the patchy spread can be qualified as the invasion at the edge of extinction. Finally, we discuss the implications of this phenomenon for invasive species management and control.     

Linked exploitation and interference competition drives the variable behavior of a classic predator–prey system

The potential connection between exploitation and interference competition was recognized long ago but has not been evaluated. We measured the levels of both forms of competition for the protist Didinium preying upon Paramecium. Across populations, exploitation intensity was tightly linked to interference intensity, and the form of this relationship follows from a simple model of interaction speeds. The variation in interference competition was as large across populations of Didinium as has been observed previously across species from a variety of taxa including birds, mammals, insects, crustaceans, flatworms and protists. The link between exploitation and interference competition alters our understanding of how interference competition influences population dynamics. Instead of simply stabilizing systems, variation in interference levels can shift population dynamics through qualitatively different regimes because of its association with exploitation competition. Strong interference competition pushes a system to a regime of deterministic extinction, but intermediate interference generates a system that is stable with a high competitive ability. This may help to explain why the distribution of interference values is unimodal and mostly intermediate in intensity. Synthesis Exploitation and interference competition are typically viewed as separate processes. Exploitation is described with a functional response in which the inclusion of interference competition – the effect of predator density on foraging rates – is optional. Although recent work indicates that interference competition is widespread, there is little work linking the two forms of competition. In this article we present evidence that exploitation and interference competition are linked mechanistically through movement patterns that simultaneously generate beneficial interactions of consumers with resources and detrimental interactions with other consumers. This connection alters our view of the role that interference plays in ecological dynamics.     

Apparent competition through facilitation between Melanoides tuberculata and Biomphalaria glabrata and the control of schistosomiasis

Interactions between two species that result in reduced growth rates for both and extinction of one of the species are generally considered cases of asymmetric interspecific competition. Exploitative or interference competition is the usual mechanism invoked. Here we describe another mechanism producing the same result, named apparent competition through facilitation (ACF), observed between Melanoides tuberculata and Biomphalaria glabrata populations. The superior competitor actually gives some benefit to the other species, whose population becomes unstable with progressively increasing oscillations, leading to extinction. A model of ACF using difference equations suggests initial dynamics distinct from traditional interspecific competition. The dynamics of two freshwater snails in the field and in laboratory experiments suggest ACF, and these relations should be considered in studies of schistosomiasis control. ACF could occur in natural populations, but might have gone undetected because the final result is similar to traditional interspecific competition.     

The unavoidable costs and unexpected benefits of parasitism: population and metapopulation models of parasite-mediated competition

When faced with limited resources, organisms have to determine how to allocate their resources to maximize fitness. In the presence of parasites, hosts may be selected for their ability to balance between the two competing needs of reproduction and immunity. These decisions can have consequences not only for host fitness, but also for the ability of parasites to persist within the population, and for the competitive dynamics between different host species. We develop two mathematical models to investigate how resource allocation strategies evolve at both population and metapopulation levels. The evolutionarily stable strategy (ESS) at the population level is a balanced investment between reproduction and immunity that maintains parasites, even though the host has the capacity to eliminate parasites. The host exhibiting the ESS can always invade other host populations through parasite-mediated competition, effectively using the parasites as biological weapons. At the metapopulation level, the dominant strategy is sometimes different from the population-level ESS, and depends on the ratio of local extinction rate to host colonization rate. This study may help to explain why parasites are as common as they are, and can serve as a modeling framework for investigating parasite-mediated ecological invasions. Furthermore, this work highlights the possibility that the ‘introduction of enemies’ process may facilitate species invasion.     

Scramble competitions can rescue endangered species subject to strong Allee effects

In this article, we study population dynamics of a general two-species discrete-time competition model where each species suffers from both strong Allee effects and scramble intra-specific competitions. We focus on how the combinations of the scramble intra-specific and inter-specific competition affect the extinction and coexistence of these two competing species where each species is subject to strong Allee effects. We derive sufficient conditions on the extinction, essential-like extinction and coexistence for such models. One of the most interesting findings is that scramble competitions can promote coexistence of these two species at their high densities. This is supported by the outcome of single species models with strong Allee effects. In addition, we apply theoretical results to a symmetric competition model with strong Allee effects induced by predator saturations where we give a completed study of its possible equilibria and attractors. Numerical simulations are performed to support our results.     

Competitive speciation in quantitative genetic models

We study sympatric speciation due to competition in an environment with a broad distribution of resources. We assume that the trait under selection is a quantitative trait, and that mating is assortative with respect to this trait. Our model alternates selection according to Lotka-Volterra-type competition equations, with reproduction using the ideas of quantitative genetics. The recurrence relations defined by these equations are studied numerically and analytically. We find that when a population enters a new environment, with a broad distribution of unexploited food sources, the population distribution broadens under a variety of conditions, with peaks at the edge of the distribution indicating the formation of subpopulations. After a long enough time period, the population can split into several subpopulations with little gene flow between them.     

Evolution of unconditional dispersal in periodic environments

Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against 'unconditional' dispersal in spatially heterogeneous environments. 'Unconditional' means individuals disperse at a rate independent of their location. We prove that if within-patch fitness varies spatially and between two values temporally, then there is selection for unconditional dispersal: any evolutionarily stable strategy (ESS) or evolutionarily stable coalition (ESC) includes a dispersive phenotype. Moreover, at this ESS or ESC, there is at least one sink patch (i.e. geometric mean of fitness less than one) and no sources patches (i.e. geometric mean of fitness greater than one). These results coupled with simulations suggest that spatial-temporal heterogeneity is due to abiotic forcing result in either an ESS with a dispersive phenotype or an ESC with sedentary and dispersive phenotypes. In contrast, the spatial-temporal heterogeneity due to biotic interactions can select for higher dispersal rates that ultimately spatially synchronize population dynamics.     

The effects of spatial food distribution and group size on foraging behaviour in a benthic fish

Animals foraging in heterogeneous environments benefit from information on local resource density because it allows allocation of foraging effort to rich patches. In foraging groups, this information may be obtained by individuals through sampling or by observing the foraging behaviour of group members. We studied the foraging behaviour of goldfish (Carassius auratus) groups feeding in pools on resources distributed in patches. First, we determined if goldfish use sampling information to distinguish between patches of different qualities, and if this allowed goldfish to benefit from a heterogeneous resource distribution. Then, we tested if group size affected the time dedicated to food searching and ultimately foraging success. The decision of goldfish to leave a patch was affected by whether or not they found food, indicating that goldfish use an assessment rule. Giving-up density was higher when resources were highly heterogeneous, but overall gain was not affected by resource distribution. We did not observe any foraging benefits of larger groups, which indicate that grouping behaviour was driven by risk dilution. In larger groups the proportion searching for food was lower, which suggests interactions among group members. We conclude that competition between group members affects individual investments in food searching by introducing the possibility for alternative strategies, such as scrounging or resource monopolisation.