Periodic Matrix Population Models: Growth Rate, Basic Reproduction Number, and Entropy

This article considers three different aspects of periodic matrix population models. First, a formula for the sensitivity analysis of the growth rate lambda is obtained that is simpler than the one obtained by Caswell and Trevisan. Secondly, the formula for the basic reproduction number a>(0) in a constant environment is generalized to the case of a periodic environment. Some inequalities between lambda and a>(0) proved by Cushing and Zhou are also generalized to the periodic case. Finally, we add some remarks on Demetrius' notion of evolutionary entropy H and its relationship to the growth rate lambda in the periodic case.