Metapopulation dynamics Rate at which subpopulations go extinct Probability of each subpopulation...
Transcript of Metapopulation dynamics Rate at which subpopulations go extinct Probability of each subpopulation...
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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
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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
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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
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dN1
dt=r1N1
K1 −N1 −αN2
K1
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
dN2
dt=r2 N2
K2 −N2 −βN1
K2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
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N1 + αN2 = K1
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N1 + N2 = K2
For species 1
For species 2
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N1 =K2 /β
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N2 =K1 /α
>> species 1 can’t grow
>> species 2 can’t grow
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Competition between two diatoms, Asterionella formosa and Synedra ulna for silica.
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