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A diffusion model of species selection

A diffusion model of the distribution of a phenotypic character in a group of species is developed and analyzed. The model incorporates the combined effects of phyletic evolution, speciation and extinction. Directed speciation is modeled by assuming there is some bias to phenotypic changes during speciation. Species selection is modeled by assuming there is some dependence of either speciation or extinction rates on the phenotypic character. Three examples are analyzed to illustrate the use of the model. A model of completely random changes due to both phyletic evolution and speciation shows how between-species differences are established. A model of directed speciation due to multiplicative changes during speciation shows how a simple assumption about the speciation process can produce macroevolutionary trends. A model of species selection due to differences in extinction rates shows how the efficacy of species selection depends on the between-species variance produced both by speciation and by phyletic evolution.