Abstract
We consider a continuum version of a previously introduced and numerically studied model of macroevolution [P. Sibani, M. R. Schimdt, and P. Alstr\o{}m, Phys. Rev. Lett. 75, 2055 (1995)] in which agents evolve by an optimization process in a rugged fitness landscape and die due to their competitive interactions. We first formulate dynamical equations for the fitness distribution and the survival probability. Secondly, we analytically derive the ${t}^{\ensuremath{-}2}$ law which characterizes the lifetime distribution of biological genera. Thirdly, we discuss other dynamical properties of the model as the rate of extinction and conclude with a brief discussion.
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