A membership society whose goal is to advance and to diffuse knowledge of organic evolution and other broad biological principles so as to enhance the conceptual unification of the biological sciences.
Posted on
by
Jawad Sakarchi and Rachel M. Germain: Read the article
Sakarchi & Germain break down MacArthur’s consumer resource model with insights on the mechanistic understanding and biological intuition of how competition and coexistence operate
B iologists have two wolves inside of them – one that craves tractability and simplicity, and another that hungers for complexity and biological realism. Striking a balance between these two desires has proven to be difficult across all fields of biology, and competition theory is no exception. Competition theory assesses how ecological mechanisms mediate coexistence outcomes of two species competing for limited resources. In a recent American Naturalist article, Sakarchi and Germain argue that MacArthur’s consumer-resource model offers a rare middle ground: a biologically rich framework with the tractability and accessibility of simpler competition models. By presenting the model, synthesizing over 40 years of research, linking it to recent theoretical advances, and highlighting its empirical implications and relevance, Sakarchi and Germain demonstrate that this historical model continues to offer valuable insights for competition theory and for ecology and evolution more broadly.
Sakarchi and Germain begin by outlining the structure of the model. MacArthur’s Consumer-Resource Model organizes species into two trophic levels: resources and consumers. For instance, in the classic moose-wolf predator-prey example, moose correspond to resource dynamics while wolves correspond to consumer dynamics. Resource and consumer species exhibit antithetical dynamics. In monoculture, resource species grow toward their carrying capacity, whereas consumer species decay to extinction in the absence of resources. When both are present, the growth rate of the resource species decreases proportionally with consumer density, whereas the growth rate of consumer species increases proportionally with resource density. Sakarchi and Germain ground the mathematical form of the model in biological terms, explaining assumptions made that inform how the model’s results should be interpreted.
Sakarchi and Germain demonstrate how this mechanistic, yet tractable model can be used to understand key processes in community ecology. For instance, they derive the community utilization function – a function that, when minimized, allows for optimal community assembly patterns by ensuring maximized efficiency of resource utilization by consumers. Such metrics help extend ideas from coexistence theory into other areas of community ecology such as assembly theory, demonstrating the flexibility and utility of MacArthur’s consumer-resource model.
By performing a mathematical magic trick, Sakarchi and Germain demonstrate that the mechanistic MacArthur’s consumer-resource model is dynamically equivalent to a classic model in community ecology – Lotka-Volterra. Lotka-Volterra is often considered a phenomenological model, wherein biologically meaningful parameters are sacrificed for simplicity to understand general patterns. Despite this, a redefining of parameters transforms MacArthur’s consumer-resource model into the Lotka-Volterra model. In doing so, Sakarchi and Germain synthesize two seemingly distinct areas of theoretical ecology and demonstrate that a phenomenological, biologically-simplified model can be equivalent to a mechanistic, biologically-detailed one—sometimes, the two wolves take different paths to the same destination. They leverage this connection between models to guide the design of competition experiments, enabling parameterization based on mechanistic rather than traditionally parameterized phenomenological parameters. Such parameterizations can help experimentalists better understand biological mechanisms underpinning outcomes of competition experiments.
Concluding with empirical recommendations, Sakarchi and Germain demonstrate how these theoretical insights can be used to inform empirical studies on consumer-resource dynamics. By compiling 40 years’ worth of research into one concise piece, they highlight both the rich legacy of MacArthur’s consumer-resource model and its ongoing relevance for competition studies. By embracing the complexity associated with the model and highlighting simplifying assumptions, Sakarchi and Germain demonstrate how MacArthur’s consumer-resource model situates itself uniquely in competition theory—offering both mathematical tractability for analytical exploration and the biological complexity and realism to inform empirical work. In striking this delicate balance between simplicity and complexity, MacArthur’s model exemplifies how biologists can indeed satisfy the two wolves within us.
Joe Brennan is a Ph.D. candidate in the Population Biology Graduate Group at the University of California, Davis. Joe's research addresses how ecological communities change over time in response to species invasion and extinction using mathematical and computational models. Outside of the lab, you can find Joe listening to electronic and pop music, appreciating surrealist art, and trying his best at trivia night.
