Question

10. Mountain Gorilla Conservation You are trying to build a mathematical model for the size of the population of mountain gorillas in a national park in Uganda. The data in this question are taken from Robbins et al. (2009) a. You start by writing a word equation relating the population of gorillas t years after the study begins, N, to the population Nt+1 in the next year: number of gorillas number of gorillas +1 born in one year that die in one year We will derive together formulas for the number of births and the number of deaths i. Around half of gorillas are female, 75% of females are of reproductive age, and in a given year 22% of the females of reproductive age will give birth. Explain why the number of births is equal to: 0.5 - 0.75 - 0.22 - Nt-0.0825 Nt In a given year 4.5% of gorillas will die. Write down a formula for the number of deaths ii. Write down a recurrence equation for the number of gorillas in the national park. Assuming that there are 300 gorillas initially (that is No- 300), derive an explicit formula for the number of gorillas after t years iv. Calculate the population size after 1, 2, 5, and 10 years. v. According to the model, how long will it take for population size to double to 600 gorillas?

Answer 1

1 O a) The numbUT c on ohure N+I ) and ucd 2 trn year (75%) X No.a tomou

No300. i v) 1.0375×300 = 311.2s N 2 3 23 Ns 36 (1037s) T 2 T In (1.6375)二1n/2) en(8.82 837 4n (1 037S Yen