Consumer functional response and competition in consumer-resource systems

This study investigates the effect of the functional response of resource consumers on the relationship between resource overlap and competition for some two-consumer, two-resource models. Two measures of competition are examined: α, the competition coefficient, and β, an index of the ease of invasion by the second consumer species when the first is at its carrying capacity. A comparison of systems with linear (type-1) and decelerating (type-2) functional responses shows that: (1) Competition coefficients are functions of the population densities of consumers or resources in systems with type-2 responses. (2) Competition coefficients may differ substantially in magnitude between systems with type-1 and type-2 functional responses. (3) The relative handling time of different resources is important in determining the relationship between overlap and competition. Positive correlations between capture rates (per unit resource) and handling times cause the system with type-2 functional responses to exhibit a higher level of competition for a given level of overlap than for the case of negative correlation. (4) If the functional response is type-2 it may be possible to obtain a priority effect in which either consumer species can exclude the other. (5) Invasion may be easier in a system with type-1 functional responses than in a similar system with type-2 functional responses, even when competition coefficients are larger in the former. Accelerating functional responses also affect the relationship between overlap and competition, but realistic models of such responses are likely to be very complex. Several currently accepted ideas in competition theory depend upon the assumption of a linear functional response, and are unlikely to be generally valid.     

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.     

Does competition between resources change the competition between their consumers to mutualism? Variations on two themes by Vandermeer

How does competition between resources affect the interaction between consumer species that share those resources? Existing theory suggests that high resource competition can lead to mutualism. However, this is based on an analysis that need only apply near equilibrium, and experimental demonstrations of such mutualism are rare. Two alternative approaches to measuring food web mutualism are examined here. These are based on the population-level effects of adding or removing a consumer species or on the amount of additional mortality that can be applied to one consumer without excluding it. Both measures suggest that mutualism is likely to be confined to two situations: when overlap in resource use by the consumers is very low and when the consumers are inefficient users of their resources. Competition between resources is also likely to increase the occurrence and magnitude of "hypercompetition" between consumers, where the reduction in population size caused by the introduced consumer is greater than that caused by a consumer that is identical to the resident species. Competition between resources can also increase the negative interaction between consumers by destabilizing the dynamics of the system. Such destabilization can cause negative indirect interactions between specialist consumers having no overlap in resource use.     

The effect of the Holling type II functional response on apparent competition

This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics.     

The evolution of traits affecting resource acquisition and predator vulnerability: character displacement under real and apparent competition

This article investigates some simple models of the evolutionary interaction between two prey species that share a common resource and a common predator. Each prey species is characterized by a trait that determines both the rate of resource capture and vulnerability to a predator. In a simple model of a three-species food chain, such traits usually increase in response to an imposed reduction in resource density. When the per capita growth rates of each of two prey species depend linearly on resource density, such traits will change in opposite directions when the two prey come into sympatry. In addition, the ratio of the effect of the predator on prey fitness to the effect of the resource on prey fitness will diverge from the corresponding ratio in a second prey species when those species coexist in sympatry. These simple predictions need not hold under several alternative assumptions, which may be more common in biological systems. Parallel changes in sympatry may occur if the relationship between resource consumption and prey growth is nonlinear, if the prey species have partial overlap in the set of resources used or in the set of predators that consume them, or if prey experience direct intraspecific competition. The responses to a second prey can also differ significantly from those predicted by the simplest model if separate traits affect vulnerability to predators and resource acquisition rate. It is important to determine whether examples of character displacement previously interpreted as responses to competition for resources might also reflect responses to altered predation risks in sympatry.     

Niche shift and the minimisation of competition

An analysis by MacArthur (1969) of the dynamics of competing species has been extended to allow for the possibility that the species may change their pattern of resource utilisation in order to reduce the effect of competition. Minimising the same Q function as MacArthur it is shown that such readjustment of utilisation (segregation of the species between resources) would be advantageous to the species. Competition equations so derived are in general nonlinear and will give smaller competition coefficients than the widely used ones given by MacArthur's analysis. The results have implications regarding the limits of similarity of competing species, colonisation, and niche shift in response to competition.     

Clutch-size behavior and coexistence in ephemeral-patch competition models

Systems of patchy, ephemeral resources often support surprisingly diverse assemblages of consumer insects. Aggregation of consumer individuals over the landscape of patches has been suggested as one mechanism that can stabilize competition among consumer species. One mechanism for larval aggregation is the laying of eggs in clutches by females traveling among patches to distribute their total fecundity. We use simulation models to explore the consequences, for coexistence of competitors, of larval aggregation that arises from clutch laying. Contrary to some previous treatments, we find that clutch laying can be strongly stabilizing and under certain conditions can be sufficient to allow competitors to coexist stably. We extend these models by considering clutch size as a variable that responds to the abundance of resource patches. Such a relationship might be expected because females should lay their eggs in fewer but larger clutches when the cost of travel among patches is high (because patches are rare). When females adjust clutch size in response to resource abundance, coexistence can be easiest when resource patches are scarce and most difficult when resources are abundant.     

Coupled oscillations in food webs: balancing competition and mutualism in simple ecological models

As in other oscillating systems, oscillations of consumer resource pairs in ecological systems may be coupled such that complex behavior results. The form of that coupling may determine the nature and extent of this behavior. Two biologically significant forms of coupling are here investigated: first, where consumers consume each other's resources (CR coupling, representing competition between the two consumers), and second, where the resources are in competition with one another (RR coupling, potentially representing indirect mutualism between the two consumers). Interestingly, CR coupling leads to in-phase synchrony of the oscillations, whereas RR coupling leads to antiphase synchrony. With either form of coupling, if the coupling remains weak, synchronous behavior is generated in the two systems. At strong levels of coupling, when the two forms act simultaneously, a balance between competition and mutualism is generated, which is manifest differently at different levels of resource coupling.     

Evolutionarily stable range limits set by interspecific competition

A combination of abiotic and biotic factors probably restricts the range of many species. Recent evolutionary models and tests of those models have asked how a gradual change in environmental conditions can set the range limit, with a prominent idea being that gene flow disrupts local adaptation. We investigate how biotic factors, explicitly competition for limited resources, result in evolutionarily stable range limits even in the absence of the disruptive effect of gene flow. We model two competing species occupying different segments of the resource spectrum. If one segment of the resource spectrum declines across space, a species that specializes on that segment can be driven to extinction, even though in the absence of competition it would evolve to exploit other abundant resources and so be saved. The result is that a species range limit is set in both evolutionary and ecological time, as the resources associated with its niche decline. Factors promoting this outcome include: (i) inherent gaps in the resource distribution, (ii) relatively high fitness of the species when in its own niche, and low fitness in the alternative niche, even when resource abundances are similar in each niche, (iii) strong interspecific competition, and (iv) asymmetric interspecific competition. We suggest that these features are likely to be common in multispecies communities, thereby setting evolutionarily stable range limits.     

病原体感染对物种间资源竞争的影响——基于资源竞争理论

病原体感染对种间竞争的影响可能是因为改变了宿主的资源利用过程,然而竞争模型（Lotka-Volterra）由于参数化竞争系数而忽略了资源的动态变化过程,因此基于此类模型的研究无法揭示病原体对宿主资源利用的影响。基于Tilman的资源竞争理论构建了病原体感染一个物种的资源竞争模型,通过分析宿主物种资源利用效率的变化探讨了病原体对种间竞争的影响。结果表明：（1）病原体降低了宿主对资源的消耗率（消费矢量变短）,抬高了对资源的最低需求（零等倾线上移）,这意味着宿主的竞争力减弱;（2）虽然感染影响了竞争物种的密度,但不会改变共存物种的共存状态;（3）病原体可以使宿主物种的竞争对手更容易入侵,形成共存局面,极大地扩大了竞争物种共存的参数范围,本质上促进了物种多样性维持;（4）病原体的传播率和毒性也复杂地影响了竞争物种共存,传播率越大越能促进物种共存,而中等强度毒性最能促进物种共存。研究结果明确了病原体对物种资源利用模式的潜在改变,强调了病原体在物种共存和生物多样性维持中的重要性。     

Biodiversity,habitat area,resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.     

A graphical theory of competition on spatial resource gradients

Resource competition is a fundamental interaction in natural communities. However, little remains known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyse the competition of two consumers for two resources in a one-dimensional habitat in which the resources are supplied from opposite sides. We show that the success of an invading species crucially depends on the slope of the resource gradients shaped by the resident. Our analysis reveals that parameter combinations, which lead to coexistence in a uniform environment, may favour alternative stable states in a spatial system, and vice versa. Furthermore, differences in growth rate, mortality or dispersal abilities allow a consumer to coexist stationarily with - or even outcompete - a competitor with lower resource requirements. Applying our theory to a phytoplankton model, we explain shifts in the community structure that are induced by environmental changes.     

Adaptive dynamics of competition for nutritionally complementary resources: character convergence, displacement, and parallelism

Consumers acquire essential nutrients by ingesting the tissues of resource species. When these tissues contain essential nutrients in a suboptimal ratio, consumers may benefit from ingesting a mixture of nutritionally complementary resource species. We investigate the joint ecological and evolutionary consequences of competition for complementary resources, using an adaptive dynamics model of two consumers and two resources that differ in their relative content of two essential nutrients. In the absence of competition, a nutritionally balanced diet rarely maximizes fitness because of the dynamic feedbacks between uptake rate and resource density, whereas in sympatry, nutritionally balanced diets maximize fitness because competing consumers with different nutritional requirements tend to equalize the relative abundances of the two resources. Adaptation from allopatric to sympatric fitness optima can generate character convergence, divergence, and parallel shifts, depending not on the degree of diet overlap but on the match between resource nutrient content and consumer nutrient requirements. Contrary to previous verbal arguments that suggest that character convergence leads to neutral stability, coadaptation of competing consumers always leads to stable coexistence. Furthermore, we show that incorporating costs of consuming or excreting excess nonlimiting nutrients selects for nutritionally balanced diets and so promotes character convergence. This article demonstrates that resource-use overlap has little bearing on coexistence when resources are nutritionally complementary, and it highlights the importance of using mathematical models to infer the stability of ecoevolutionary dynamics.     

Interference competition and species coexistence

Interference competition is ubiquitous in nature. Yet its effects on resource exploitation remain largely unexplored for species that compete for dynamic resources. Here, I present a model of exploitative and interference competition with explicit resource dynamics. The model incorporates both biotic and abiotic resources. It considers interference competition both in the classical sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, and interference on, the other species) and in the broad sense (i.e. each species suffers a net reduction in per capita growth rate via interference from, but can experience an increase in growth rate via interference on, the other species). Coexistence cannot occur under classical interference competition even when the species inferior at resource exploitation is superior at interference. Such a trade-off can, however, change the mechanism of competitive exclusion from dominance by the superior resource exploiter to a priority effect. Now the inferior resource exploiter can exclude the superior resource exploiter provided it has a higher initial abundance. By contrast, when interference is beneficial to the interacting species, coexistence is possible via a trade-off between exploitation and interference. These results hold regardless of whether the resource is biotic or abiotic, indicating that the outcome of exploitative and interference competition does not depend on the exact nature of resource dynamics. The model makes two key predictions. First, species that engage in costly interference mechanisms (e.g. territoriality, overgrowth or undercutting, allelopathy and other forms of chemical competition) should not be able to coexist unless they also engage in beneficial interference mechanisms (e.g. predation or parasitism). Second, exotic invasive species that displace native biota should be superior resource exploiters that have strong interference effects on native species with little or negative cost. The first prediction provides a potential explanation for patterns observed in several natural systems, including plants, aquatic invertebrates and insects. The second prediction is supported by data on invasive plants and vertebrates.     

Convergence in a resource-based competition system

A resource-based competition model of two consumer species and one resource species is formulated in the form of a Lotka-Volterra system. The competition involves both exploitation and interference. By a method of asymptotic estimates, sufficient conditions are derived for the three species system to converge ast→∞ to an equilibrium point with all three species present; a generalization of the result forn≥2 and single resource species is indicated. The strong form of equilibrium perisistence of the three species consumer-resource system is achieved by the ability of each of the consumer species to exploit the resource and interfere with others in such a way which will avoid exclusion by the other.     

Testing a simple rule for dominance in resource competition

Competition for limiting resources long has been considered an important factor generating community structure. A minimal model of resource competition predicts that the species that reduces the limiting resource R to the lowest level ([Formula: see text]) will exclude its competitors. Whether this "[Formula: see text] rule" is robust to violations of model assumptions remains largely unknown. I conducted a competition experiment with four species of bacterivorous protists in laboratory microcosms and predicted the outcome from each species' [Formula: see text] value. I also examined how the outcome of competition, species abundances, and the effect of protists on bacterial density varied with productivity. Microcosms were unstirred batch cultures containing a variety of bacteria, challenging the robustness of the simplest competition models. Protists with low [Formula: see text] values were less affected by competition, although competing protists often coexisted. The values of [Formula: see text] can predict competitive dominance, even in the absence of competitive exclusion. Other model predictions were less robust. Contrary to expectation, densities of grazed bacteria increased with productivity, and the effect of some protists on bacterial density did not vary with productivity. Bacterial heterogeneity may account for deviations from model predictions. Further experiments should examine the conditions under which simple rules can be expected to identify dominant species.     

Productivity, dispersal and the coexistence of intraguild predators and prey

A great deal is known about the influence of dispersal on species that interact via competition or predation, but very little is known about the influence of dispersal on species that interact via both competition and predation. Here, I investigate the influence of dispersal on the coexistence and abundance-productivity relationships of species that engage in intraguild predation (IGP: competing species that prey on each other). I report two key findings. First, dispersal enhances coexistence when a trade-off between resource competition and IGP is strong and/or when the Intraguild Prey has an overall advantage, and impedes coexistence when the trade-off is weak and/or when the Intraguild Predator has an overall advantage. Second, the Intraguild Prey's abundance-productivity relationship depends crucially on the dispersal rate of the Intraguild Predator, but the Intraguild Predator's abundance-productivity relationship is unaffected by its own dispersal rate or that of the Intraguild Prey. This difference arises because the two species engage in both a competitive interaction as well as an antagonistic (predator-prey) interaction. The Intraguild Prey, being the intermediate consumer, has to balance the conflicting demands of resource acquisition and predator avoidance, while the Intraguild Predator has to contend only with resource acquisition. Thus, the Intraguild Predator's abundance increases monotonically with resource productivity regardless of either species' dispersal rate, while the Intraguild Prey's abundance-productivity relationship can increase, decrease, or become hump-shaped with increasing productivity depending on the Intraguild Predator's dispersal rate. The important implication is that a species' trophic position determines the effectiveness of dispersal in sampling spatial environmental heterogeneity. The dispersal behavior of a top predator is likely to have a stronger effect on coexistence and spatial patterns of abundance than the dispersal behavior of an intermediate consumer.     

A shift from exploitation to interference competition with increasing density affects population and community dynamics

Intraspecific competition influences population and community dynamics and occurs via two mechanisms. Exploitative competition is an indirect effect that occurs through use of a shared resource and depends on resource availability. Interference competition occurs by obstructing access to a resource and may not depend on resource availability. Our study tested whether the strength of interference competition changes with protozoa population density. We grew experimental microcosms of protozoa and bacteria under different combinations of protozoan density and basal resource availability. We then solved a dynamic predator–prey model for parameters of the functional response using population growth rates measured in our experiment. As population density increased, competition shifted from exploitation to interference, and competition was less dependent on resource levels. Surprisingly, the effect of resources was weakest when competition was the most intense. We found that at low population densities, competition was largely exploitative and resource availability had a large effect on population growth rates, but the effect of resources was much weaker at high densities. This shift in competitive mechanism could have implications for interspecific competition, trophic interactions, community diversity, and natural selection. We also tested whether this shift in the mechanism of competition with protozoa density affected the structure of the bacterial prey community. We found that both resources and protozoa density affected the structure of the bacterial prey community, suggesting that competitive mechanism may also affect trophic interactions.     

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.     

Determinants of the strength of disruptive and/or divergent selection arising from resource competition

We investigate how the intensity of competition for resources affects the strength of disruptive selection on a resource acquisition trait. This is done by analyzing several consumer–resource models in which consumers use a linear array of resources. We show that disruptive selection can be diminished under both strong and weak competition, making disruptive selection a unimodal function of the strength of competition. Weak selection under strong competition arises when competition causes the extinction (for self-reproducing resources) or depletion (for abiotic resources) of the most rapidly caught resources. Weak selection under weak competition is a consequence of minimal effects of consumers on resources. The precise relationship between intensity of competition and strength of disruptive selection is sensitive to the shape of the consumer's resource utilization curve and the nature of resource growth. The most strongly unimodal competition–selection relationships result from utilization curves with long tails. Our results show that a simple comparison of the width of the resource abundance distribution and the consumer's utilization function is not sufficient to determine whether selection is disruptive. The results may explain some contradictory experimental findings regarding the effect of consumer mortality on the strength of disruptive selection.