Ecosystem engineering in predator-prey interactions
by
Kim Cuddington
Ohio University (University of Waterloo as of August 2008)
Coauthors: Alan Hastings (UCDavis) Theresa Talley (UCDavis)

Predator-prey interactions are described as having a negative impact on the prey species and a positive impact on the predator species. We develop a general model to describe how ecosystem engineering may alter the net effect of trophic species interactions. We modify a standard predator (P) - prey (N) population model to include the effects of an environmental state (E). We describe the modification of the environmental state as a linear function of predator or prey density. The environment has a normal state, E₀, to which it will return in the absence of environmental modification by either of the two species, and either or both of these species can move the environment away from this state. Throughout we make the simple assumption that the modified environmental state could linearly modify all population parameters as:

dN/dt=[(a₀ + a₁ E) - (b₀ + b₁ E)N - (c₀+c₁E)P]N

dP/dt = [(f₀+f₁E)-(g₀+g₁E)P+(h₀+h₁E)N]P

dE/dt = -k(E-E₀)+mP+nN.

We apply this model to a conservation problem in a crayfish-dragonfly system. We derive the conditions where the crayfish predator may benefit the endangered dragonfly species through the building of burrows. The net impact of the crayfish on the dragonfly will be positive where the product of the environmental modification rate and the benefit of the burrow to the dragonfly species is greater than the product of the rate at which the environment returns to its unmodified state and the predation rate (a₁ m > c₀ k). As a result, we predict that the relationship between the predator and prey species could swing back and forth between a net positive and a net negative interaction with environmental variation.

Date received: May 15, 2008