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emery_lecture_15

emery_lecture_15 - Lecture 15 from last time prove that the...

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Lecture 15 - from last time: prove that the decline of a population above its carrying capacity is faster than the corresponding increase below K Review of terms - competition: use or defense of a resource that reduces availability of that resource for another individual 2 types: 1. exploitation 2. interference Lotka-Volterra models of competition - mathematical derivation Species 1 Species 2 dN 1 /dt = r 1 N 1 (K 1 -N 1 /K 1 ) dN 2 /dt = r 2 N 2 (K 2 -N 2 /K 2 ) 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 ) α 12 and α 21 are competition coefficients α 12 = per capita effect of species 2 on species 1, measured relative to effect of species 1 on itself α 21 = per capita effect of species 1 on species 2, measured relative to effective of species 2 on itself if 1 and 2 are equal, adding another species of 2 will have same effect of adding a species 1 let species 1 = wildebeest dN w /dt = r w N w (K w -N w - α wb N b /K w ) α wb = effect of one buffalo on one wildebeest if α wb = 1, intraspecific competition = interspecific competition if α wb > 1, interspecific competition> intraspecific competition

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if α wb < 1, interspecific competition < intraspecific competition
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