Study Questions for Final

In this question, you will analyse a source-sink model.

Consider two populations of a single species, one in a good environment (population 1) and one in a poor environment (population 2). The number of individuals in the two populations is n1 and n2, respectively.

In the good environment, the population is able to grow logistically with a carrying capacity, K1, and an intrinsic rate of growth, r1. Each generation, a proportion, m, migrate to the poor environment (this is the "source" population).

In the poor environment, each individual has R offspring. R is less than one and the population is unable to replace itself (this is the "sink" population). The sink population is maintained by the constant input of migrants every generation from the source population.

Equations describing this model are:

n1[t+1] = n1[t] (1-m) + n1[t] r1 (1-n1[t]/K1)

n2[t+1] = R n2[t] + m n1[t]

What are the equilibrium population sizes for the two populations in this model (assuming that the system is not extinct)?

Under what conditions is the source-sink metapopulation stable?