The Markov structure of population growth (Q1119513)

The paper consists of a beautifully written and largely non-technical description of the general Markovian theory of population growth developed by B. Chauvin, the author and O. Nerman during the past decade. The fundamental idea is that, to reconcile reasonably realistic population dynamics with the Markov property, time should not be taken to be chronological linear time, but should instead be associated with a partial order on sets of individuals, determined by descent. An analogue with respect to this ``time'' of the classical exponentially normed martingale can be constructed, and \(L_ 1\)-convergence to a stable population regime can be proved under very general conditions.