Not Just a Theory--The Utility of Mathematical Models in Evolutionary Biology: e1002017

An important purpose of mathematical models in evolutionary research, as in many other fields, is to act as "proof-of-concept" tests of the logic in verbal explanations, paralleling the way in which empirical data are used to test hypotheses. Because not all subfields of biology use mathematics for this purpose, misunderstandings of the function of proof-of-concept modeling are common. Speciation models in general have made it clear that the devil is in the details; there are many important biological conditions that combine to determine whether speciation is more or less likely to occur. Because speciation is exceedingly difficult to replicate experimentally, theoretical developments such as these have been particularly valuable.