The probability of extinction depends not only on the relative births and death

Question

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

Explanation / Answer

Given that, Pextinction = (d/b)No

Also given that d = 0.0160, b = 0.0175, initial No = 100 and later No' = 15.

Thus, at the time of discovery, Pextinction = (d/b)No = [(0.0160/0.0175)100] = 91.42%,

and later, Pextinction = (d/b)No' = [(0.0160/0.0175)15] = 13.71%.

Hence, the disease has decreased the probability of extinction of the species.

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