Mathematical model of faunal spreading in benthic palaeobiogeography (applied to Cenozoic Tethyan molluscs)

Abstract

A mathematical model has been developed to relate the amount of benthic mollusc species shared between interconnected sea basins and the interbasinal distance. The resulting equation is of exponential type d N/ N = − kd L and its intergration gives N = N oe − kl where N = number of shared species; L = distance; N 0 = N( L = 0) = migrating stock inside the total fauna at the origin; k is a constant, with the dimension of an inverse of a length, and accounts for the ease of mollusc spreading. The factos opposing to spreading are fo a biological and a physical type. When the linkage between the basins ceases, N drops down quickly to zero. The model could represent as useful tool for palaeogeographic study. L 1 2 is the “ half-value distance”, that is the distance at which the number of diffusing species becomes haft with respcet to the origin, and is considered a good indicator of the mollusc spreading possibility. As applied to Cenozoic Tethyan belt (inclunding Paratethys) for the various epoch L 1 2 and N 0 show a cycle of easier or more diffcult mollusc migration of about 25 m.y. The cycle seems to be related to astronomical factors regarding the whole solar system.