Net reproductive rate and persistence in matrix population models

Net reproductive rate is lifetime reproductive output of a single individual. This biologically relevant quantity can be used to establish population persistence, determine management or control strategies, or study the evolutionary consequences of life history traits. Historically, it has been difficult to calculate the net reproductive rate for complex stage-structured models. Here we present a new graph-theoretic method for calculating the net reproductive rate. This method can be applied easily to complex stage-structured models. The resulting net reproductive rate formula expresses reproductive rate contributions grouped according to fecundity pathways. We compare this application with a recently proposed condition for determining persistence in matrix population models (Hastings-Botsford persistence condition) and argue that our graph-theoretic approach can be simpler to apply and yield additional biological insight. Furthermore, based on the net reproductive rate formula, we derived a new method for calculating mean generation time and generation time variance, for complex stage-structure.