Derivation of SDEs for a macroevolutionary process (Q379015)

Systems of ordinary stochastic differential equations (SDEs) are derived and studied.NEWLINENEWLINEFrom the introduction: ``In the present investigation, two stochastic differential equation models for phylogenetic tree development are derived and studied. The first SDE model is developed applying Yule's assumptions while the second SDE model is derived using somewhat different but also biologically reasonable assumptions. In Model I, the rate of change of the number of genera is assumed to be proportional to the number of genera in the family.'' ``In Model II, a different assumption is made. In particular, the rate of change of the number of genera is assumed to be proportional to the number of species in the family.'' An important fact to highlight is computational results for the derived systems of SDE's agree well with the observed results for several species and genera. About Yule's assumptions, this article refers to [\textit{G. U. Yule}, Phil. Trans. Roy. Soc London 213, 21--87 (1925)].