Modeling the density–area relationship in a dynamic landscape: an examination for the beetle Tetraopes tetraophthalmus and a generalized model

Abstract

The relationship between local population density and habitat area is an important factor in spatial population ecology. I examined how density dependence in the growth of local insect populations and their host plant patches, combined with patch birth and death, and insect dispersal affect the density–area relationship. I constructed a simulation model to examine the relationship for an insect herbivore, Tetraopes tetraophthalmus, inhabiting patches of its host plant, Asclepias syriaca. Given the observed growth of insect populations, patch growth, dispersal of insects, and change in the number of patches within the landscape, the model predicts that T. tetraophthalmus density should decrease with increasing A. syriaca patch size. The model also predicts moderate amounts of temporal variation in the relationship. A more general insect herbivore-host plant model was also developed to extend the results. The general model shows that density dependence in patch and insect population growth rates have large effects on the density–area relationship. The density–area relationship was strongly affected by density dependence in insect growth. Increasing density dependence in insect growth caused insect density to decrease with increasing patch size. Temporal variation in the relationship was most strongly affected by density dependence in patch growth. Variation in the density–area relationship increased as density dependence in patch growth increased. The results of this study show that density–area relationships can be variable and are not necessarily a species-specific trait. Application of density–area relationships, especially in dynamic landscapes, need to be aware of and account for factors that affect the size and number of patches as well as growth and dispersal of the target populations.