Please answer 8.) a-e (a) If the population in 1970 was (A, B) (150, 100), what

Question

Please answer 8.) a-e (a) If the population in 1970 was (A, B) (150, 100), what was the population in 1960? 8. Consider the vegetation dynamics of an area com land, and 4-Grazed. The transition matrix for this system is sed of: n iBog,2-Heath, 3-wood 0.65 0.3 0 0 0.29 0.33 0.28 0.4 0.06 0.30 0.69 0.2 0 0.07 0.03 0.4 (a) What is the sum of each column? Why does this mean biologically? (b) What does the 0.07 in the bottom row means? (c) What do the numbers in the main diagonal represent biologically? (d) What does the following matrix represent with respect to the model? 0.26 0.26 0.26 0.26 0.30 0.30 0.30 0.30 0.38 0.38 0.38 0.38 0.06 0.06 0.06 0.06 P22 (e) What does this means biologically?

Explanation / Answer

a)
sum of each column is 1
it means the sum of probability of transition from any state to all state is 1

b)
0.02 is transition probability from state 2 to state 4.
that is from heath to grazed

c)
main diagonal represent transitional probability of one state being in same state after next transition

d)
this matrix gives the 22- step transition probabilities

e)
this is limiting probability of transtion matrix P
here probability of going to any state remain same irrespective from which state it is coming

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