Predator-Prey Dynamics and the Red Queen Hypothesis: Putting Limits on the Evolutionary Arms Race

Abstract

Computer simulations of complex food-webs are an important tool for deepening our understanding of these systems. Yet most computer models assume, rather than generate, key system-level patterns, or use mathematical modeling approaches that make it difficult to account fully for non-linear dynamics. In this article we present a computer simulation model that addresses these concerns by focusing on assumptions of agent attributes rather than agent outcomes. Our model utilizes the techniques of Complex Adaptive Systems and Agent-Based Modeling so that system-level patterns of a general ecosystem emerge from the interactions of thousands of individual simulated agents. This methodology has been validated in previous work by using this general simulation model to replicate fundamental properties of an ecosystem, including: (1) the predator-prey oscillations found in Lotka-Volterra; (2) the “stepped pattern” of biomass accrual from resource enrichment; (3) the Paradox of Enrichment; and (4) Gause’s Law. In this work we explore further the fundamental properties of this generative model in the context of the Red Queen Hypothesis, also referred to as the “arms race” between antagonistic species, e.g. predators and prey. We find that improvements in the competitive landscape for a single entity in a predator species does not generally confer a benefit on the predator species as a whole, and may even be detrimental to the predator population. This non-intuitive result is shown through two methods of adjusting the predators effectiveness in consuming prey. We further explore this idea by explicitly accounting for individual entity's energy requirements, and also allowing evolutionary adaptation for an effectiveness / energy trade-off. 1.0 Overview The literature on marine and terrestrial ecosystems is long and varied, encompassing both theoretical models (e.g.: Grimm, 1999; DeAngelis & Mooij, 2005) and empirical surveys (e.g.: Christensen et al., 2003; Frank et al., 2005). Some significant differences between model results and real-world surveys have persisted for years, and it has been difficult identifying fundamental principles relative to the many complicating factors that can be found in existent ecosystems. For example, in the early 1980s Oksanen et al. examined multiple trophic levels in a predator-prey system using mathematical models, in order to determine whether species population (bio-mass) is fundamentally controlled by resources – as was the conventional wisdom at the time – or dominated by predation (Oksanen et al., 1981). In describing this work, Power states that these models produce “a stepped pattern of biomass accrual” (Power, 1992); Brett and Goldman further characterize the Oksanen et al. results, saying that “In food webs with an odd number of trophic levels, increases in primary production should lead to increased biomass for odd-numbered trophic levels and no change in biomass for even-numbered trophic levels. Conversely, in food webs with an even number of trophic levels, increases in primary production should lead to increased biomass for even-numbered trophic levels and no change in biomass for odd-numbered trophic levels” (Brett & Goldman,