mathmatical modeling 32 Ecological succession in this projec

mathmatical modeling

3.2 Ecological succession

in this project we consider modeling the ecological succession of barren dunes to an oak community using a Markov chain. in this simple model, it is assumed that there are three states for a specific ecological region. these states are bare dunes, which will be labeled BD; a grass community, which is labeled G; and an oak community, labeled O. Table is

1. Using this information, construct the state diagram representing the ecological succession from bare dunes to oak community.

2. Construct the transition matrix T.

3. suppose initially 10% of the regions are bare dunes, 10% are grass communities, and 80% are oak communities. Determine the distribution of states after 2 time steps and after 10 time steps. Interpret the meaning of these results.

4. Determine the limiting matrix L and the steady-state distribution for this ecological succession interpret the meaning of these results.

Solution