Direct competition results from strong competition for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka–Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur in, Theor Popul Biol 1:1–11, 1970). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional.     

Competition-similarity relationships and the nonlinearity of competitive effects in consumer-resource systems

Much previous ecological and evolutionary theory about exploitative competition for a continuous spectrum of resources has used the Lotka-Volterra model with competition coefficients given by a Gaussian function of niche separation. Using explicit consumer-resource models, we show that the Lotka-Volterra model and the assumption of a Gaussian competition-similarity relationship both fail to reflect the impact of strong resource depletion, which typically reduces the influence of the most heavily used resources on the competitive interaction. Taking proper account of resource depletion reveals that strong exploitative competition between efficient consumers is usually a highly nonlinear interaction, implying that a single measure is no longer sufficient to characterize the process. The nonlinearity usually entails weak coupling of competing species when their abundances are high and equal. Rare invaders are likely to have effects on abundant residents much larger than those of the resident on the invader. Asymmetrical utilization curves often produce asymmetrical competition coefficients. Competition coefficients are typically non-Gaussian and are often nonmonotonic functions of niche separation. Utilization curve shape and resource growth functions can have major effects on competition-similarity relationships. A variety of previous theoretical findings need to be reassessed in light of these results.     

Limiting similarity revisited

We reinvestigate the validity of the limiting similarity principle via numerical simulations of the Lotka–Volterra model. A Gaussian competition kernel is employed to describe decreasing competition with increasing difference in a one-dimensional phenotype variable. The simulations are initiated by a large number of species, evenly distributed along the phenotype axis. Exceptionally, the Gaussian carrying capacity supports coexistence of all species, initially present. In case of any other, distinctly different, carrying capacity functions, competition resulted in extinction of all, but a few species. A comprehensive study of classes of fractal-like carrying capacity functions with different fractal exponents was carried out. The average phenotype differences between surviving species were found to be roughly equal to the competition width. We conclude that, despite the existence of exceptional cases, the classical picture of limiting similarity and niche segregation is a good rule of thumb for practical purposes.     

Species coexistence in resource-limited patterned ecosystems is facilitated by the interplay of spatial self-organisation and intraspecific competition

The exploration of mechanisms that enable species coexistence under competition for a sole limiting resource is widespread across ecology. Two examples of such facilitative processes are intraspecific competition and spatial self-organisation. These processes determine the outcome of competitive dynamics in many resource-limited patterned ecosystems, classical examples of which include dryland vegetation patterns, intertidal mussel beds and subalpine ribbon forests. Previous theoretical investigations have explained coexistence within patterned ecosystems by making strong assumptions on the differences between species (e.g. contrasting dispersal behaviours or different functional responses to resource availability). In this paper, I show that the interplay between the detrimental effects of intraspecific competition and the facilitative nature of self-organisation forms a coexistence mechanism that does not rely on species-specific assumptions and captures coexistence across a wide range of the environmental stress gradient. I use a theoretical model that captures the interactions of two generic consumer species with an explicitly modelled resource to show that coexistence relies on a balance between species' colonisation abilities and their local competitiveness, provided intraspecific competition is sufficiently strong. Crucially, the requirements on species' self-limitation for coexistence to occur differ on opposite ends of the resource input spectrum. For low resource levels, coexistence is facilitated by strong intraspecific dynamics of the species superior in its colonisation abilities, but for larger volumes of resource input, strong intraspecific competition of the locally superior species enables coexistence. Results presented in this paper also highlight the importance of hysteresis in understanding tipping points, in particular extinction events. Finally, the theoretical framework provides insights into spatial species distributions within single patches, supporting verbal hypotheses on coexistence of herbaceous and woody species in dryland vegetation patterns and suggesting potential empirical tests in the context of other patterned ecosystems.     

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.     

Species packing in nonsmooth competition models

Despite the potential for competition to generate equilibrium coexistence of infinitely tightly packed species along a trait axis, prior work has shown that the classical expectation of system-specific limits to the similarity of stably coexisting species is sound. A key reason is that known instances of continuous coexistence are fragile, requiring fine-tuning of parameters: A small alteration of the parameters leads back to the classical limiting similarity predictions. Here we present, but then cast aside, a new theoretical challenge to the expectation of limiting similarity. Robust continuous coexistence can arise if competition between species is modeled as a nonsmooth function of their differences—specifically, if the competition kernel (differential response of species’ growth rates to changes in the density of other species along the trait axis) has a nondifferentiable sharp peak at zero trait difference. We will say that these kernels possess a “kink.” The difference in predicted behavior stems from the fact that smooth kernels do not change to a first-order approximation around their maxima, creating strong competitive interactions between similar species. “Kinked” kernels, on the other hand, decrease linearly even for small species differences, reducing interspecific competition compared with intraspecific competition for arbitrarily small species differences. We investigate what mechanisms would lead to kinked kernels in the first place. It turns out that discontinuities in resource utilization generate them. We argue that such sudden jumps in the utilization of resources are unrealistic, and therefore, one should expect kernels to be smooth in reality.     

Departures from neutrality induced by niche and relative fitness differences

Breaking the core assumption of ecological equivalence in Hubbell’s “neutral theory of biodiversity” requires a theory of species differences. In one framework for characterizing differences between competing species, non-neutral interactions are said to involve both niche differences, which promote stable coexistence, and relative fitness differences, which promote competitive exclusion. We include both in a stochastic community model in order to determine if relative fitness differences compensate for changes in community structure and dynamics induced by niche differences, possibly explaining neutral theory’s apparent success. We show that species abundance distributions are sensitive to both niche and relative fitness differences, but that certain combinations of differences result in abundance distributions that are indistinguishable from the neutral case. In contrast, the distribution of species’ lifetimes, or the time between speciation and extinction, differs under all combinations of niche and relative fitness differences. The results from our model experiment are inconsistent with the hypothesis of “emergent neutrality” and support instead a hypothesis that relative fitness differences counteract effects of niche differences on distributions of abundance. However, an even more developed theory of interspecific variation appears necessary to explain the diversity and structure of non-neutral communities.     

Species packing and the competition function with illustrations from coral reef fish

This paper concerns the contrast between guilds whose species show resource partitioning and those that show extensive overlap. Using a Lotka-Volterra model, the ease of invasion by a third species into a guild already containing two species is examined for various shapes of resource utilization curves. I show that (a) a guild is more easily invasible and allows tighter packing if its member species have leptokurtic (thick-tailed) resource utilization curves than if they have platykurtic (thin-tailed) curves; (b) the distribution of niche separation distances is bimodal in a “thin-tailed” guild and is unimodal in a “thick-tailed” guild; (c) there are three-species guilds such that removal of one particular species leaves a two-species system in which one of the remaining species excludes the other. In this context, competition pressure is a force maintaining species diversity.Groupers (Serranidae) appear to be a thin-tailed guild, and Parrotfish (Scaridae) and Surgeonfish (Acanthuridae) together appear to be a thick-tailed guild, and these guilds show many properties predicted by the model. I conjecture that thick-tailed guilds form when the constituent species are selected to be generalists and apply this idea to tropical fruit- and flower-feeding birds.     

Using Malmquist Indices to evaluate environmental impacts of alternative land development scenarios

The degree to which regions can produce desirable socioeconomic and environmental outcomes while consuming fewer resources and producing fewer undesirable outcomes can be viewed as measure of productivity. Economists have frequently used Malmquist Indices to evaluate intertemporal productivity changes of economic entities, such as firms and countries. We use Malmquist Indices to evaluate the predicted environmental performance of the rapidly growing Charlotte, NC, metropolitan area under alternative future land use scenarios. These scenarios project population, urban development, and environmental impacts from the base year 2000 to the year 2030 within the region's 184 watersheds. The first scenario is based on a continuation of current growth trends and patterns (“Business as Usual” or BAU). The second scenario uses compact “smart growth” development (“Compact Centers” or CC). We use data envelopment analysis (DEA) to estimate Malmquist Indices, which in this case, combine multiple variables into a single indicator that measures the relative impact of different development patterns on the consumption of natural resources. The results predict that the CC scenario maintains the region's current productivity, while the BAU scenario results in lower productivity. As watersheds in the study area are about the same size, weighting the results by area makes little difference. Watershed populations, however, vary greatly, and our results predict that watersheds with higher population densities also have higher Malmquist Index efficiencies. The model also predicts that low population watersheds will benefit more from the CC scenario. While the application of these analytical techniques in this case study is limited in scope, the results demonstrate that the Malmquist Index is a potentially powerful tool for interdisciplinary environmental impact analysis     

Coexistence and displacement in consumer-resource systems with local and shared resources

Competition for local and shared resources is widespread. For example, colonial waterbirds consume local prey in the immediate vicinity of their colony, as well as shared prey across multiple colonies. However, there is little understanding of conditions facilitating coexistence vs. displacement in such systems. Extending traditional models based on type I and type II functional responses, we simulate consumer-resource systems in which resources are “substitutable,” “essential,” or “complementary.” It is shown that when resources are complementary or essential, a small increase in carrying capacity or decrease in handling time of a local resource may displace a spatially separate consumer species, even when the effect on shared resources is small. This work underscores the importance of determining both the nature of resource competition (substitutable, essential, or complementary) and appropriate scale-dependencies when studying metacommunities. We discuss model applicability to complex systems, e.g., urban wildlife that consume natural and anthropogenic resources which may displace rural competitors by depleting shared prey.     

No species is an island: testing the effects of biotic interactions on models of avian niche occupation

Traditionally, the niche of a species is described as a hypothetical 3D space, constituted by well‐known biotic interactions (e.g. predation, competition, trophic relationships, resource–consumer interactions, etc.) and various abiotic environmental factors. Species distribution models (SDMs), also called “niche models” and often used to predict wildlife distribution at landscape scale, are typically constructed using abiotic factors with biotic interactions generally been ignored. Here, we compared the goodness of fit of SDMs for red‐backed shrike Lanius collurio in farmlands of Western Poland, using both the classical approach (modeled only on environmental variables) and the approach which included also other potentially associated bird species. The potential associations among species were derived from the relevant ecological literature and by a correlation matrix of occurrences. Our findings highlight the importance of including heterospecific interactions in improving our understanding of niche occupation for bird species. We suggest that suite of measures currently used to quantify realized species niches could be improved by also considering the occurrence of certain associated species. Then, an hypothetical “species 1” can use the occurrence of a successfully established individual of “species 2” as indicator or “trace” of the location of available suitable habitat to breed. We hypothesize this kind of biotic interaction as the “heterospecific trace effect” (HTE): an interaction based on the availability and use of “public information” provided by individuals from different species. Finally, we discuss about the incomes of biotic interactions for enhancing the predictive capacities on species distribution models.     

Aggregation pattern of individuals and the outcomes of competition within and between species: Differential equation models

The influence of spatial distribution pattern on the outcomes of intra- and interspecific competition is studied theoretically. The models developed are the generalized logistic andVolterra equations, whereLloyd 's indices of intra- and interspecies mean crowding were incorporated with their assumed linear relationship to mean density in order to express the intensity of crowding which is really effective to the existing individuals. It is shown that while the increasing patchiness of distribution has a pronounced effect of promoting the intraspecific competition and lowering the equilibrium density for individual populations, it generally relaxes the interspecific competition, making it easy for different species sharing the same niche, which would otherwise be incompatible, to coexist stably. These models thus provide a simplest theoretical basis to explain why many insect populations in nature are kept relatively rare in number and why a number of allied species often coexist freely sharing the same resource, against the “competitive exclusion principle” deduced from the originalVolterra equations.     

A new method for describing predator-prey relations in discontinous environments

I propose a new method for anlysing predatorprey interactive systems in discontinuous environments. The basic index used here is a generalized version ofLloyd 's (1967) “interspecies mean crowding”, which is defined as the number of individuals of one species existing in a given patch per that of the other species in either the same or different patches at either the same or different times. Four indices are derived from different combinations of the numbers of the prey and the predator in habitat patches. Then, the correlation coefficients between the numbers of individuals in patches in both different locations and times are derived by modifying the above new indices. Using this technique, dynamical changes of the joint distributions of the numbers of predators and prey which reflect variation in local conditions, can readily be described. As an example, this method was applied to an analysis of the outcomes of a multi-patch version of theLotka-Volterra model of predator-prey interactions.     

Competition and coexistence in regional habitats

Habitat heterogeneity plays a key role in the dynamics and structures of communities. In this article, a two-species metapopulation model that includes local competitive dynamics is analyzed to study the population dynamics of two competing species in spatially structured habitats. When local stochastic extinction can be ignored, there are, as in Lotka-Volterra equations, four outcomes of interspecific competition in this model. The outcomes of competition depend on the competitive intensity between the competing pairs. An inferior competitor and a superior competitor, or two strongly competing species, can never stably coexist, whereas two weak competitors (even if they are very similar species) may coexist over the long term in such environments. Local stochastic extinction may greatly affect the outcomes of interspecific competition. Two competing species can or cannot stably coexist depending not only on the competitive intensity between the competing pairs but also on their precompetitive distributions. Two weak competitors that have similar precompetitive distributions can always regionally coexist. Two strongly competing species that competitively exclude each other in more stable habitats may be able to stably coexist in highly heterogenous environments if they have similar precompetitive distributions. There is also a chance for an inferior competitor to coexist regionally or even to exclude a superior competitor when the superior competitor has a narrow precompetitive distribution and the inferior competitor has a wide precompetitive distribution.     

Classical and resource-based competition: a unifying graphical approach

A graphical technique is given for determining the outcome of two species competition for two resources. This method is unifying in the sense that the graphical criterion leading to the various outcomes of competition are consistent across most of the spectrum of resource types (from those that fulfill the same growth needs to those that fulfill different needs) regardless of the classification method used, and the resulting graphs bear a striking resemblance to the well-known phase portraits for two species Lotka–Volterra competition. Our graphical method complements that of Tilman. Both include zero net growth isoclines. However, instead of using the consumption vectors at potential coexistence equilibria to determine input resource concentrations leading to specific competitive outcomes, we introduce curves bounding the feasible set (the set where the resource concentrations of any equilibrium solution must be located). The washout equilibrium (corresponding to the supply point) occurs at an intersection of curves defining the feasible set boundary. The resource concentrations of all other equilibria are found where zero net growth isoclines either intersect each other inside the feasible set or they intersect the feasible set boundary. A species has positive biomass at such an equilibrium only if its zero net growth isocline is involved in such an intersection. The competitive outcomes are then determined from the position of the single species equilibria, just as in the phase portrait analysis for classical competition (rather than from information at potential coexistence equilibria as in Tilman’s method).     

The role of competition in creating multiple steady states and favouring evolution of prebiotic polymers

In a prebiotic context the assumption is made that a mutation leads to the formation of a new polymer displaying autocatalytic and cross-catalytic properties. By the use of a simple chemical model it is shown that, despite these favourable attributes, the new species either remains at low concentration or accumulates, unless a competition is imposed between the new polymer and its precursor. In the latter case, the well-known situation of multiple steady states and hysteresis is established and the new “improved” species, under specific conditions, may become the dominant one. The need of competition suggests an early compartmentation of the system.     

Multivariate measures of similarity and niche overlap

Niche overlap measures are used to assess the similarity in resource use by two species. Recently researchers have used niche overlap measures as summary measures and for making inferences, typically about competition for resources. The problem of estimating niche overlap when the niches are multivariate normal distributions with equal covariance matrices has previously been studied. In this work, the assumption of equal covariance matrices is relaxed. Two general measures of similarity are evaluated assuming general multivariate normal distributions. Commonly used measures of overlap are given as special cases of these two general measures. The question of bias in estimating these measures is discussed and shown to be a potential problem, especially when there are many redundant variables or if sample sizes are small.     

Density compensation,isocline shape and single-level competition models

Criticism of the Lotka-Volterra competition model implies that the theory of competition should be based upon more general concepts. It is suggested that the shape of the competitor isoclines can provide this basis.The relationship between the total density of a competitive community and species number depends crucially upon isocline shape. This has immediate relevance to the interpretation of the excess density compensation seen in some island communities, since if isoclines are sufficiently concave (curved towards the origin) then this phenomenon is expected to be the rule rather than the exception.These observations do not depend upon any specific model, but in order to determine the shape of isoclines in natural communities a link must be made between the biological processes of competition and isocline shape. To this end three types of single-level competition model are distinguished (additive, multiplicative and temporal resource models) depending upon how gains from resources interact in determining individual fitness.The models are based upon resource availability functions (RAFs), which are decreasing functions of the level of competition and determine the availability of each resource to each species. Provided that the argument of these functions is always a weighted sum of the number of competitors then in the case of the additive resource model the shape of the RAFs determines directly the shape of the isoclines. For the multiplicative model, the shape of the logarithm of the RAFs adopts this role.Analysis of a special case of the additive resource model suggests that concave isoclines are likely to predominate, and that the degree of concavity is of an order which minimizes the tendency of total numbers to increase with species number. In some circumstances, involving “scramble”-type competition and habitat selection, the expected concavity is sufficient to cause a decrease. In any event the expected occurrence of concave competition isoclines predicts a much higher incidence of excess density compensation (due to carrying capacity differences) than expected from any model having linear isoclines.The effect of shifting from an additive to a multiplicative resource model is to make the existence of purely concave isoclines less probable and to raise the possibility of purely convex isoclines. On the other hand, shifting from an additive resource model to a temporal resource model apparently has no such simple interpretation and specific predictions must await further analysis.     

Non‐equilibrium in plant distribution models – only an issue for introduced or dispersal limited species?

Species distribution models rely on the assumption that species' distributions are at equilibrium with environmental conditions within a region – i.e. they occur in all suitable habitats. If this assumption holds, species occurrence should be predictable from measures of the environment. Introduced species may be poor candidates for distribution models due to their presumed lack of equilibrium within the landscapes they occupy, although predicting their potential distributions is often of critical importance to natural resource managers. We determined if the accuracy of species distribution models differed between 17 native and 17 introduced riparian plant species in the western United States. We also assessed if model accuracy was associated with both environmental and biological factors that can influence dispersal. We used Random Forests to model species distributions and linear regression to determine if model accuracy was associated with dispersal‐related traits. Model accuracy for introduced species was higher than that for native species. Dispersal‐related traits did not affect model accuracy or improvement, though two other traits, family affiliation and rarity on the landscape, did have an effect. Distance‐based measures of dispersal potential improved model fit equally for both native and introduced species and for species with a variety of dispersal traits, suggesting that the importance of regional propagule pressure is relatively constant across species with different dispersal opportunities. Several lines of future questioning are suggested by our results, including why introduced species may in some cases produce more accurate distribution models than native species and how species dispersal traits relate to distribution model accuracy at different spatial scales.     

Where vectors collide: the importance of mechanisms shaping the realized niche for modeling ranges of invasive <Emphasis Type="Italic">Aedes</Emphasis> mosquitoes

The vector mosquitoes Aedes aegypti (L.), native to Africa, and Aedes albopictus (Skuse), native to Asia, are widespread invasives whose spatial distributions frequently overlap. Predictive models of their distributions are typically correlative rather than mechanistic, and based on only abiotic variables describing putative environmental requirements despite extensive evidence of competitive interactions leading to displacements. Here we review putative roles of competition contributing to distribution changes where the two species meet. The strongest evidence for competitive displacements comes from multiple examples of habitat segregation where the two species co-occur and massive reductions in the range and abundance of A. aegypti attributable to A. albopictus invasions in the southeastern U.S.A. and Bermuda (U.K). We summarize evidence to support the primacy of asymmetric reproductive interference, or satyrization, and larval resource competition, both favoring A. albopictus, as displacement mechanisms. Where evidence of satyrization or interspecific resource competition is weak, differences in local environments or alternative ecologies or behaviors of these Aedes spp. may explain local variation in the outcomes of invasions. Predictive distribution modeling for both these major disease vectors needs to incorporate species interactions between them as an important process that is likely to limit their realized niches and future distributions. Experimental tests of satyrization and resource competition are needed across the broad ranges of these species, as are models that incorporate both reproductive interference and resource competition to evaluate interaction strengths and mechanisms. These vectors exemplify how fundamental principles of community ecology may influence distributions of invasive species.