The metapopulation fitness criterion: Proof and perspectives

Metapopulation theory has recently been stirred by the development of a metapopulation persistence criterion (RmRm) quantifying the “lifetime dispersal success” of a newly colonized deme in a sparsely occupied metapopulation. No rigorous proof of this criterion in continuous time has been available so far. Here, we show that this criterion can be mathematically justified from standard Jacobian arguments. A summary of the key elements of this proof emphasizes the assumptions under which this criterion is valid. Examples illustrate how to generally compute metapopulation fitness in continuous time models. The underlying assumptions behind the criterion are discussed, as well as theoretical puzzles surrounding the concept of metapopulation fitness.