MadonnaModel Arial!D(.2> B 6:4( = {Two-region migration model} {Simulation control information} METHOD RK4 STARTTIME = 0 STOPTIME=10 DT = 0.02 {Initial values of population} INIT N1 = 100 INIT N2 = 100 {Parameters} r1 = .10 r2 = .10 {net reproduction fraction in unlimited environment} k1 = 50 k2 = 100 {carrying capacity, in persons} c1 = .10 c2 = .10 {normal outmigration fraction} {Model} N1(t) = N1(t - dt) + (dN1dt - dM1dt) * dt N2(t) = N2(t - dt) + (dN2dt - dM2dt) * dt {level of population is past population plus net change minus out-migration} dN1dt = ((r1*(N1-dM1dt)*(1-N1/k1))+dM2dt) dN2dt = (r2*(N2-dM2dt))*(1-(N2/k2)^2)+dM1dt {change in population is a logistic function of the size of the current population net of outmigration, plus in-migration from the other region} dM1dt = MIN(N1,c1*N1*((N1/k1)^2)) dM2dt = MIN(N2,c2*N2*((N2/k2)^2)) {outmigration is the lesser of the current population or an exponential function of the ratio of current population to carrying capacity}9@rk4MbP?MbP?MbP?   DHL &,2^.Fjnr z  Uv1) $&(*,9.M