Stability and permanence in gender- and stage-structured models for the boreal toad

Abstract

The boreal toad Bufo boreas boreas, once common in the western USA, is listed as an endangered species in Colorado and New Mexico, and protected in Wyoming. Populations have dramatically declined due to the presence of the fungal pathogen Batrachochytrium dendrobatidis (Bd). A gender- and stage-structured model for the boreal toad is formulated which depends on its life cycle and breeding strategies. In addition, an epizootic model for the spread of Bd is formulated. Analysis of these models provides two thresholds. The first threshold, the basic reproduction number for the population, ℛ(0), determines whether the population persists and the second threshold, the basic reproduction number for the fungal disease, ℛ(F), determines whether the disease persists. If ℛ(0)>1 and ℛ(F)<1, then the population becomes disease-free. However, if both thresholds are greater than one, the population levels are severely reduced by the fungal pathogen.