A new preprint from Stuart Johnston, with Mat Simpson (QUT), looks at a new approximation method for birth-death-movement random walks.
Normally, random walk models are approximated via an ODE (i.e. logistic growth), which predicts the population size quite well. However, because the ODE represents the number of agents as a continuum, the agent population will never actually go extinct.
Here instead we represent the random walk via an approximate state space (which includes the extinction state) and use a PDE (over time and state space) to describe how the population transitions through the state space.
This allows us to not only predict the population size accurately, but also determine the probability that the population has gone extinct by a certain time.
Read it here:
Predicting population extinction in lattice-based birth-death-movement models
S.T. Johnston, M.J. Simpson, E.J. Crampin