An Approach to the Management of Orchards that are Vulnerable to Attack by Invasive Species

Orchards are vulnerable to the damaging effects of attacks by invasive species. Therefore, in this paper, we focus on a representative tree in a stylized orchard and show how the theory of discrete time Markov chains can be used to construct a model of this tree that is to be managed in the possible presence of one or more injurious invasive species. Specifically, we accomplish three orchard management related tasks. First, we specify an apposite discrete time Markov chain theoretic model for our representative tree and then we define its one step transition probabilities. Next, given a particular decision rule, we determine the long run fraction of time that the tree under study is unhealthy. Finally, we ascertain the long run fraction of mandatory replacements that occur when the tree under consideration is dead