The use of Markovian metapopulation models: a comparison of three methods reducing the dimensionality of transition matrices

The use of Markovian models is an established way for deriving the complete distribution of the size of a population and the probability of extinction. However, computationally impractical transition matrices frequently result if this mathematical approach is applied to natural populations. Binning, or aggregating population sizes, has been used to permit a reduction in the dimensionality of matrices. Here, we present three deterministic binning methods and study the errors due to binning for a metapopulation model. Our results indicate that estimation errors of the investigated methods are not consistent and one cannot make generalizations about the quality of a method. For some compared output variables of populations studied, binning methods that caused a strong reduction in dimensionality of matrices resulted in better estimations than methods that produced a weaker reduction. The main problem with deterministic binning methods is that they do not properly take into account the stochastic population process itself. Straightforward usage of binning methods may lead to substantial errors in population-dynamical predictions.