question archive As a plant community matures, certain plant species replace others
As a plant community matures, certain plant species replace others
Subject:MathPrice:4.87 Bought7
As a plant community matures, certain plant species replace others. Consider a forest with two types of trees, red oak and hickory. In each generation, red oak may be replaced by itself or by hickory, and hickory may be replaced by itself or red oak. Assume that the life spans of the two trees are similar and that this is a Markov process with each time epoch indicating a generation.
Suppose that when a red oak tree dies, it is equally likely to be replaced by hickory or red oak. When a hickory tree dies, it has probability 0.75 of being replaced by red oak and 0.25 of being replaced by hickory
(a) Construct a Markov chain model of how the forest population changes over time by defining the states and drawing a transition diagram (clearly identifying each state and labeling the arrows with probabilities). Then write down the transition matrix.
(b) Many thousands of years into the future, what.percentage of trees in the forest will be red oak trees?
(c) On average, how many generations will it take for a hickory tree to be replaced by another hickory tree?
(d) On average, how many times will a hickory tree be replaced by another hickory tree before being replaced by a red oak tree?,
