An application of Markov models to the dynamics of Minnesota's forests

Markov models are matrices of transition probabilities between states and are used to project a vector of state distribution forward in time. Traditionally, Markov models of landscapes assume that the transition probabilities are independent of age for all pixels in a given cover type. But harvesting practices vary the probability of harvesting within cover types by stand age, and so the transition probabilities between older age-classes or into other cover types depend not only on the cover type but also on the age-class within a cover type or successional stage. We used satellite imagery and stand inventory data for northern Minnesota to parameterize and set initial conditions for both age-class independent and age-class dependent Markov models. The assumptions of an age-class independent Markov model are not satisfied by current landscape dynamics in northern Minnesota. Making the probability of harvest depend on age within a cover type results in different landscape dynamics than making the harvest independent of age. Decreasing the nominal rotation age and increasing the spread of harvest ages around the nominal rotation age results in greater abundance of land in regeneration stages, even if the amount of land harvested annually is held constant. Forest landscape models should consider age-dependent as well as cover type-dependent transitions.