Competition-colonization models The metapopulation model from Exercise 15 can be extended to include two species, where one is a superior competitor. The equations are dp1dt c1p1s1 2 p1d 2 m1p1 dp2dt c2p2s1 2 p12 p2d 2 m2p22 c1p1p2 where p1 and p2 are the fractions of patches occupied by species 1 and 2, respectively. These equations model a process in which any patch has at most one species, and where species 2 patches can be taken over by species 1, but not vice versa. (a) Explain how the terms in the equations reflect the assumption that species 1 is the superior competitor. (b) Suppose that m1 m2 3, c1 5, and c2 30. Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane. Show that, despite species 1 being a better competitor, the two species are predicted to coexist.