Stabilization of chaotic and non-permanent food-web dynamics

Several decades of dynamical analyses of food-web networks [1–6] have led to important insights into the effects of complexity, omnivory and interaction strength on food-web stability [6–8]. Several recent insights [7,8] are based on nonlinear bioenergetic consumer-resource models [9] that display chaotic behavior in three species food chains [10,11] which can be stabilized by omnivory [7] and weak interaction of a fourth species [8]. We slightly relax feeding on low-density prey in these models by modifying standard food-web interactions known as “type II” functional responses [12]. This change drastically alters the dynamics of realistic systems containing up to ten species. Our modification stabilizes chaotic dynamics in three species systems and reduces or eliminates extinctions and non-persistent chaos [11] in ten species systems. This increased stability allows analysis of systems with greater biodiversity than in earlier work and suggests that dynamic stability is not as severe a constraint on the structure of large food webs as previously thought. The sensitivity of dynamical models to small changes in the predator-prey functional response well within the range of what is empirically observed suggests that functional response is a crucial aspect of species interactions that must be more precisely addressed in empirical studies. PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 05.45.Jn High-dimensional chaos – 05.45.Pq Numerical simulations of chaotic systems – 87.23.-n Ecology and evolution