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October 22 , 2012 Biology 2F03: Fundamental and Applied Ecology Competition (2) Logistic growth - recall: in finite environment populations follow a growth pattern where Question - what happens when two species must share a limiting resource (one that defines K)? - would growth of one affect K of the other: yes, carrying capacities depend on each other Two species - take a finite resource and two species ‘consuming’ it. With one species and no competition - 13 individuals would use all the resource - the red species could fit 65 individuals - a green could replace 5 red individuals. The red thus=1/5 of the green and the green=5 red (or 1 green affects negatively 5 reds) - we know that increase in N limits further growth - if you increase green there will be less growth for red and vice versa - what happens when another species also has some growth and N? Species 1 Explanation Species 2 N 1 Abundance N 2 K 1 Carrying capacity K 2 r1 Net rate of growth (per capita) r2 α12 Inhibitory effect of species 2 on species 1 or vice versa α21 - α is called competition coefficient; measure the per capita Two species equations - two species logistic growth function for species 1: - read: increase in population size of species 1 is a function of its r, N, and numbers of species 2, N .2Similarly: - useful? Not yet. Question - do you want to do the calculations using the two population growth equations? - No! Analysis - these equations can either be solved or examined visually - let’s see what happens when both species stop growing (say, all space is filled) due to competition - mathematically, this means that the rate of population change is 0 for each of them: - could be r is 0: sleep or population does not reproduce - N is zero: there is no population - Then,
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