H abitat destruction The model of Exercise 23 can be extended to include the effects of habitat destruction.

Suppose that only a fraction h of the patches are habitable (0 , h , 1). The equations become dp1 dt

− c1p1sh 2 p1d 2 m1p1 dp2 dt

− c2p2sh 2 p1 2 p2d 2 m2p2 2 c1p1p2 Suppose that m1 − m2 − 3, c1 − 5, and c2 − 30.

(a) Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane when 35

, h , 1.

(b) Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane when 1 10 , h , 35

.

(c) Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane when 0 , h , 1 10.

(d) From your results to parts (a), (b), and (c), determine how habitat destruction is expected to affect the coexistence of the two species.

Source: Adapted from S. Nee et al., “Dynamics of Metapopulations: Habitat Destruction and Competitive Coexistence,” Journal of Animal Ecology 61

(1992): 37–40.