Breeding pond dispersal of interacting California red-legged frogs (Rana draytonii) and American Bullfrogs (Lithobates catesbeianus) of California : a mathematical model with management strategies

The invasion of American Bullfrogs (Lithobates catesbeianus) in the western United States has had a direct negative effect on the persistence of many native fauna. Native ranid frogs, in particular, face threats to their populations due to the competition and predation imposed by this behaviorally similar invader. The California Red-legged Frog (Rana draytonii) has been listed as a threatened species since 1996 due in part to the introduction of American Bullfrogs. A stage-based modeling effort has been developed for interacting American Bullfrogs and California Red-legged Frogs within a single pond (Doubledee et al., 2003). We modified and expanded this model to encompass several ponds by implementing juvenile dispersal between them. Movement rules were created using assumptions based in part on dispersal data collected for a California Red-legged Frog population within eight specific ponds in the Marin County area. They incorporate the probability of the juvenile population being able to disperse a given distance and the probability of choosing to move to a specific pond when several possibilities are present. We performed parameter studies for three unknown parameters: predation of tadpole and juvenile California Red-legged Frogs by adult American Bullfrogs and predation/competition of overwintered Bullfrog tadpoles on/with California Red-legged Frog eggs. This study provides combinations of these rates which facilitate coexistence between these species over a specified duration within the study ponds. Given a specific duration of coexistence (60 years) we explored the effect of bullfrog tadpole, metamorph, and juvenile/adult focused eradication efforts as management strategies. The optimal rates of eradication associated with each of these tactics benefiting California Red-legged Frog persistence were established. We determined that seasonal ponds need not be managed, as they act as a refuge to the California Red-legged Frog, and thus aid in its long term survival. We found that removing at least 75% of the American Bullfrog tadpole population every year or draining ponds (100% Bullfrog tadpole eradication) at least every two years are sufficient strategies for managing all permanent ponds to achieve population levels exhibited by seasonal ponds. However, our model showed that without management permanent ponds connected (within a predetermined dispersal range) to seasonal ponds were able to harbor some population of California Red-legged frog beyond our assumed value of 60 years. Furthermore, we outline the areas in which further research could be implemented to enhance our model.