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E = eP
C = mP(1− P)
Metapopulation dynamics
Rate at which subpopulations go extinctProbability of each subpopulation going extinct
Proportion of patches that are occupied Rate of colonization of empty patches
Rate of colonization of empty patchesProbability of colonization (constant that reflects rate of dispersal between patches)
Proportion of patches that are occupied
Metapopulation dynamics
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ΔP /Δt = C − E
ΔP /Δt = [mP(1− P)] − eP
Proportion of patches that are occupied
Rate of colonization of empty patches
Rate at which subpopulations go extinct
dNdt
=rNK −NK
⎛ ⎝ ⎜
⎞ ⎠ ⎟
Lotka-Volterra models of interspecific competition
Population growth with carrying capacity:
Competitive impact of species 2 on species 1 = N2
= Impact per individual of species 2 on 1
Competitive impact of species 1 on species 2 = N1