On the meaning and existence of an effective population size

Per Sjodin, Ingemar Kaj, Stephen M. Krone, Martin Lascoux, and Magnus Nordborg


We investigate conditions under which a model with stochastic demography or population structure converges to the coalescent with a linear change in time scale. We argue that this is a necessary condition for the existence of a meaningful effective population size. We find that such a linear time scale change is obtained when demographic fluctuations and coalescence events occur on different time scales. Simple models of population structure and randomly fluctuating population size are used to exemplify the ideas and provide an intuitive feel for the meaning of the conditions.