interactions[1]

interactions[1] - Populations at Play ! The study of...

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Populations at Play The study of Interactions remember me? dN dt = rN ( K N ) K
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Interactions- Competition Predator/Prey Host/Parasite All are complex All are generally Modeled as two interacting species
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Lotka-Volterra Competition Equations dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1 dN 2 dt = r 2 N 2 ( K 2 N 2 −α 21 N 1 ) K 2
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dN dt = rN ( K N ) K dN 2 dt = r 2 N 2 ( K 2 N 2 −α 21 N 1 ) K 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1
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dN dt = rN ( K N ) K dN 2 dt = r 2 N 2 ( K 2 N 2 −α 21 N 1 ) K 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1
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dN dt = rN ( K N ) K dN 2 dt = r 2 N 2 ( K 2 N 2 −α 21 N 1 ) K 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1
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dN dt = rN ( K N ) K dN 2 dt = r 2 N 2 ( K 2 N 2 −α 21 N 1 ) K 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1
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dN 2 dt = r 2 N 2 ( K 2 N 2 −α 21 N 1 ) K 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1 dN dt = rN ( K N ) K
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We are left with: Interaction coefFcients “the effect of population 1 on population 2” “the effect of population 2 on population 1” What is the effect? Enhance population size- Decrease population size-
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If interaction coefFcient negative: Effect of 1 on 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1 The effect of Each 2 on 1 total number of 2’s
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If interaction coefFcient negative: Effect of 1 on 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1 The effect of Each 2 on 1 Positive effect for 2 -- neg for 1 (+) + (-) = -
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If interaction coefFcient negative: Effect of 1 on 2 dN 1 dt = r 1 N 1 ( K 1 N 1 −α 12 N 2 ) K 1 The effect of Each 2 on 1 Negative effect for 2 -- pos for 1 (-) + (-) = +
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interactions[1] - Populations at Play ! The study of...

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