Question

In a model of demographic stochasticity, the probability of a birth or a death depends on the relative magnitudes of b and d: Pbirth = b/((b+d) ) and Pdeath = d/((b+d) ) The probability of extinction depends not only on the relative births and death rates but also on the starting population size No: Pextinction = (d/b)No Suppose that following the discovery of 100 individuals of an endangered mammal, b was estimated as 0.0175 births per individual per year, and d was estimated as 0.0160 deaths per individual per year. Subsequently, disease reduced the population to only 15 individuals. What would the probability of extinction at the time of the discovery, and how would the disease have altered the probability of extinction for this species? Show your answers (3 pts)

Answer 1

Hi,
The species is discovered with 100 individuals ; hence No = 100
b = 0.0175 births per year
d = 0.0160 deaths per year

After the disease the No has changed to 15;hence Nt = 15
b and d rates are unchanged.

Pextinction = (d/b) ^ No
P extinction@discovery = (0.0160/0.0175) ^ 100 = converting the value to percentage (multiply by 100) = 0.008%

P extinction @disease = ((0.0160/0.0175) * 15 = converting to percentage (multiply by 100) = 24%.
The disease has significantly increased the probability of extinction from 0.008% to 24%.