When the patch occupancy rate (c) equals the patch extinction rate (e), patch occupancy (P) is

a. 1.5

b. 1

c. 2.0

d. 0

When the patch occupancy rate (c) equals the patch extinction rate (e), patch occupancy (P) is 0

Explanation:

According to Levin's model (1969):

dP/dt = c - e

where P represents the proportion of occupied patches.

c and e are the local immigration and extinction probabilities per patch.

Thus, the rate of change of P, written as dP/dt, tells you whether P will increase, decrease or stay the same:

if dP/dt >0, then P is increasing with time if dP/dt <0, then P is decreasing with time if dP/dt = 0, then P is remaining the same with time.

The rate dP/dt is calculated by the difference between colonization or occupancy rate (c) and extinction rate (e).

c is then calculated as the number of successful colonizations of unoccupied patches as a proportion of all available patches, while e is the proportion of patches becoming empty. Notice that P can range between 0 and 1.

As a result, if the patch occupancy rate (c) equals the patch extinction rate (e), then patch occupancy P equals to 0.