Predator – Prey Dynamics and the Red Queen Hypothesis
studied as complex adaptive systems ( CAS ); that is , systems that are characterized by their emergent properties , self-organization , and non-linear dynamics ( Allesina & Pascual , 2007 ; Brose & Dunne , 2010 ; Gell-Mann , 1994 ; Holland , 1992 ; Valdovinos , Ramos- Jiliberto , Garay-Narváez , Urbani , & Dunne , 2010 ). The field of CAS recognizes that these systems are generally robust and flexible , consisting of multiple negative feedbacks that produce one or more “ basin ( s ) of attraction ,” i . e ., the emergence of resilient , system-level patterns . It is the identification of the key feedbacks and their contributions to system resilience that is the ultimate goal of ecological research .
Advances in computing technology have allowed for more robust in silico simulations that can model these complex ecosystem dynamics in ways previously intractable . In order to address certain limitations of purely mathematical models , which generally simplify individual variation and spatial representation , and represent global properties in a top-down manner , we have created a general CAS model of a marine ecosystem ( DeAngelis & Mooij , 2007 ). Central to a more flexible , agent-based modeling ( ABM ) approach ( sometimes called individual-based modeling or agent-based complex systems ) is the generated outcome of the simulation in a bottom-up design process , rather than via top-down constraints ( DeAngelis & Mooij , 2007 , p . 2 ). It is important to note that the phrase “ bottom-up ” design has a somewhat different meaning in the CAS literature than the similarly worded “ bottom-up ” forces referred to in marine and terrestrial ecosystem literature . A CAS-based ABM implies that the system-level patterns , such as population growth , aggregate predation rates , etc ., are generated from the bottom up , rather than assumed as a “ top-down ” constraint on the modeled system ( Grimm et al ., 2005 ). That is , the system-level patterns are emergent properties that arise from the interactions of the autonomous agents that comprise the simulated system . Thus , the method of computer simulation relies on assumptions of agent attributes rather than agent outcomes . ( The similar phrasing in the ecosystem literature is unfortunate ; one might come across , for example , a discussion of the controlling forces in constraining a particular population : i . e ., “ bottom-up ” forces of resource availability versus “ topdown ” predation . This is a different context than “ bottom-up ” emergence in an ABM .)
Here we present a general ABM marine ecosystem with a focus on key phenomena in population dynamics in the context of the Red Queen hypothesis , also referred to as the “ arms race ” between antagonistic species , for example , predators and prey . This model has been validated in previous work by replicating fundamental properties of an ecosystem , including : the predator – prey oscillations found in Lotka – Volterra ; the “ stepped pattern ” of biomass accrual from resource enrichment found in Oksanen et al . ( 1981 ); the Paradox of Enrichment ; and Gause ’ s Law ( Epstein , 1999 ). In this work , we will extend our understanding of found in Oksanen et al . ( 1981 ), by considering how these patterns of biomass accrual change when the predator population becomes more ( or less ) efficient at catching prey . We will also consider these changing patterns in the context of the Red Queen hypothesis , as well as how evolutionary pressures align in ways that could prevent an escalating arms race between predators and prey .
II - Background and Previous Work
In the previous work we validated the
results of Oksanen et al . ( 1981 ), by showing that our agent-based model
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