Question

You are trying to save a mainland-island population of Furbish’s lousewort. Prior to conducting a survey of the islands to see which ones are occupied, you collected some preliminary data. You found that the probability of extinction is 75%, the probability of immigration is 25%, and the lousewort produces 75 seeds on average. If you have 100 island populations, what number of islands would you expect to be occupied?

Answer 1

Let pi be the probability of immigration and f be the fraction of sites already occupied.

Immigration rate = pi(1-f)

Extinction rate = pef where pe is probability of extinction.

Rate of change of f with time = df/dt = pi (1-f) - pef

let df/dt = 0 , pef = pi (1-f)

0.75 f = 0.25 (1 - f)

0.75 f + 0.25 f = 0.25

f = 0.25.

Fraction of occupied sites is 0.25 and there are 100 island populations hence 25 islands would be expected to be occupied.