Consumer-resource Model Research Articles

The nonlinearity of competitive effects in models of competition for essential resources

This paper investigates the question of whether the linear competitive effects assumed in the Lotka-Volterra model of competition hold for a class of consumer-resource models. The consumers in these models are dependent upon two resources, an adequate supply of each being required for population growth to occur. Simple differential equation models of competition between two consumers for such essential resources usually exhibit nonconstant competition coefficients whose magnitude depends on the parameters of the resource growth model. The equilibrium densities of the two consumer species are generally not linearly related. Constant competition coefficients can occur if the functional responses of a given consumer on the two resources differ by a constant factor. Differences between the conclusions reached by G. D. Tilman (1982, “Resource Competition and Community Structure,” Princeton Univ. Press, Princeton, NJ) and those described above are analyzed.

A Consumer-Resource Approach to Community Structure

Because all species are consumers and all, eventually, are consumed by other species, consumer-resource interaction is one of the most fundamental processes of ecology. Simple models that include the direct mechanisms of consumer-resource interactions may thus be the fundamental building-block for models of community structure. These models are easily extended to include such complexity as the effects of physical limiting factors, spatial heterogeneity in resource supply, fluctuating resource supply, and multiple trophic levels. Each such modification places constraints on the traits of species that can persist. Consumer-resource models make predictions about many aspects of community structure, including species richness, species composition, species dominance, population dynamics, morphological or physiological traits of species, and patterns of phenotypic variation within species. Thus, each model affords numerous opportunities to test and modify or reject it. A review of a variety of communities suggests that much of the structure of each community can be explained by a relatively simple consumer-resource model, but that different elements of complexity may be important in different communities.

Character displacement and niche shift analyzed using consumer-resource models of competition

This paper analyzes the adaptive responses to competition (both character displacement and niche shift) in a two consumer-two resource model. The model includes density dependence that is unrelated to the resources that are explicit in the model. This could be due to another resource dimension, parasites, or interference competition. Competitors adapt by changing their relative consumption rate constants on the two resource types. This model can result in mutually divergent, parallel, or mutually convergent displacement of competitors. Parallel displacement may entail net divergence, net convergence, or no net change. Parallel change with net convergence is most likely when the competitors have similar constraints on the possible values of consumption rate constants, unequal allopatric abundances, and significant intraspecific density dependence. Numerical calculations of displacements are presented for several models and the effect of a number of different possible alterations of the model are discussed. The evolution of resource handling and processing efficiency, and displacement in the presence of additional selective pressures on the character are considered in detail. The results have implications for questions about maximization of population size, the relationship of character displacement and the competition coefficient, and “null” models in the study of competition. Differences between this and previous theoretical works are discussed. It is argued that conditions allowing parallel or convergent displacement are not biologically unlikely, and possible examples are discussed. Data on resource partitioning seem to be more consistent with the results reached here than with previous theory.

MacArthur's Minimization Principle: A Footnote

Previous articleNext article No AccessNotes and CommentsMacArthur's Minimization Principle: A FootnoteTed J. CaseTed J. Case Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The American Naturalist Volume 115, Number 1Jan., 1980 Published for The American Society of Naturalists Article DOIhttps://doi.org/10.1086/283550 Views: 10Total views on this site Citations: 10Citations are reported from Crossref Copyright 1979 The University of ChicagoPDF download Crossref reports the following articles citing this article:Robert Marsland III, Wenping Cui, and Pankaj Mehta The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory, The American Naturalist 196, no.33 (Jul 2020): 291–305.https://doi.org/10.1086/710093 Peter A. Abrams High Competition with Low Similarity and Low Competition with High Similarity: Exploitative and Apparent Competition in Consumer‐Resource Systems Abrams, The American Naturalist 152, no.11 (Jul 2015): 114–128.https://doi.org/10.1086/286153M. Gatto A general minimum principle for competing populations: Some ecological and evolutionary consequences, Theoretical Population Biology 37, no.33 (Jun 1990): 369–388.https://doi.org/10.1016/0040-5809(90)90044-VPeter Chesson MacArthur's consumer-resource model, Theoretical Population Biology 37, no.11 (Feb 1990): 26–38.https://doi.org/10.1016/0040-5809(90)90025-QMartin L. Cody Bird diversity and density in south african forests, Oecologia 59, no.2-32-3 (Sep 1983): 201–215.https://doi.org/10.1007/BF00378838J.S. Brew Niche shift and the minimisation of competition, Theoretical Population Biology 22, no.33 (Dec 1982): 367–381.https://doi.org/10.1016/0040-5809(82)90050-8Ted J. Case Coevolution in resource-limited competition communities, Theoretical Population Biology 21, no.11 (Feb 1982): 69–91.https://doi.org/10.1016/0040-5809(82)90007-7John R. Beaumont Towards a conceptualization of evolution in environmental systems, International Journal of Man-Machine Studies 16, no.22 (Feb 1982): 113–145.https://doi.org/10.1016/S0020-7373(82)80053-9 Marino Gatto Comments on "Macarthur's Minimization Principle: A Footnote", The American Naturalist 119, no.11 (Oct 2015): 140–144.https://doi.org/10.1086/283900Bruce Winterhalder Hominid paleoecology and competitive exclusion: Limits to similarity, niche differentiation, and the effects of cultural behavior, American Journal of Physical Anthropology 24, no.S2S2 (Jan 1981): 101–121.https://doi.org/10.1002/ajpa.1330240505

Resource Competition and an Analytical Model of Zooplankton Feeding on Phytoplankton

In this paper we have developed a new consumer-resource model, with specific reference to zooplankton feeding on phytoplankton. In principle, the model can be extended to any terrestrial or aquatic community in which the consumers graze nearly randomly (as described by the grazing rate parameter fi) on food which has relatively little mobile escape capability. In contrast with the intuitive or phenomenological approaches often used in constructing competition models, we have tried to derive the consumer-resource interaction term from first principles as much as possible. We developed a general form with clearly defined parameters that represent fundamental system processes such as consumer filtering rate. We particularized the model parameters to describe two known forms of feeding: (1) saturation feeding in which the rate remains constant above a given food density while the filtering rate decreases, and (2) inhibited feeding in which a decline appears at high food density. From an examination of the model's equilibrium equations for strongly similar zooplankton species feeding on similar phytoplankton species, we have drawn the following conclusions: (1) The competitive exclusion principle has only limited validity. For a community in which the consumers exhibit no intraspecific competition and have identical assimilation efficiency to death-rate ratios, ē/d, any number of consumer species may, in fact, coexist and compete for the same food. Communities in which the consumer species have identical ē/d are probably rare. However, in a community with intraspecific competition (a common occurrence) any number of consumer species, with a wide spectrum of ē/d ratios, may coexist and compete for the same food. (2) The equations for a complex community composed of many consumer and food species can be reduced to a single equation whose form is identical with that of a single-consumer, single-food system. This implies that, at equilibrium, structurally complex communities may behave functionally like simple ones. (3) The standard competition coefficient, α, of the Volterra equation is a poor measure of competition in nonlinear systems. It exhibits incongruous variations with changes in system parameters. We have proposed a new definition of competition coefficient, Cin, which is based on derivatives of state variables evaluated at the system operating point and which eliminates the incongruities exhibited by α. In a community with no intraspecific competition, all Cin are unity. In a community with intraspecific competition, the Cin tend to equalize as the number of food species increases, resulting in equal competitive strength of all consumer species in systems of the type studied here.

A Model for Tropic Interaction

A nonlinear function general enough to include the effects of feeding saturation and intraspecific consumer interference is used to represent the transfer of material or energy from one trophic level to another. The function agrees with some recent experimental data on feeding rates. A model using this feeding rate function is subjected to equilibrium and stability analyses to ascertain its mathematical implications. The anaylses lead to several observations; for example, increases in maximum feeding rate may, under certain circumstances; result in decreases in consumer population and mutal interference between consumers is a major stabilizing factor in a nonlinear system. The analyses also suggest that realistic classes of consumer—resource models exist which do not obey Kolmogorov's Criteria but are nevertheless globally stable.