A cenain colony of squirrels has a life span of less than

Chapter , Problem 15

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A cenain colony of squirrels has a life span of less than 3 years. Suppose that the females arc divided into three age group>: those under age I. those of age I. and those of age 2. Suppo'e funhcr that the proponion of newborn females that urvivcs until age I is .2 and that the proponion of one-year-old females th:u survives until age 2 is .5. Assume also that females under age I do not give birth. thO>C of age I have, on average. 2 female offspring. and tho'e of age 2 have, on averuge. h female offspring. Suppose there arc initi:tlly 240 females of age less than one, 400 of age one. :md 320 of age two. (a) Write a Leslie mmrix II for this colony of 1uirrcls. (b) If b = 3. what will happen to the population in 50 years? (c) If b = 9. what will happen to the population in 50 year'? (d) Find by trial and error a value of b for which the >quirrel popul:ttion rcachc> a nontero >table di>tribution. What ts this stable distribution? (e) For the value of b found in (d). what happens to an initial population of 100 females of age less than one. 280 of age one. and 400 of age two? (f) For what value of b does (A - / 3)x = 0 have a nonzero solutton' (g) Let P = ~~l be an arbitrary population vector. and let b ha\c 1 c value found in (f). O'er time, p approaches a stable population vector q. Express q in terms of I' fl! and fiJ.