ESPM-EEP%202010%20Lecture%2015

ESPM-EEP%202010%20Lecture%2015 - ESPM 104/EEP 115 Fall 2010...

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ESPM 104/EEP 115 Fall 2010: Lecture 15 1. Competition: Direct vs Indirect 2. Lotka-Volterra competion model: http://www.utm.edu/departments/cens/biology/rirwin/441_442/LVComp.htm See various texts including Rockwood, 2006, Chapt 7 ( download pages 159- 176 at bspace ). x : density of species 1 y : density of species 2 a.) Absence of species 2, species 1 grows logistically b.) Absence of species 1, species 2 grows logistically c.) The impact of interspecific competition on the growth of species 1 is α times the per capita impact of intraspecific competition d.) The impact of interspecific competition on the growth of species 2 is β times the per capita impact of intraspecific competition dx dt = ax 1 x + α y s dy dt = ry 1 y + β x k 3. Nullclines and Equilibria x -nullclines : x =0 and y = s / α x / α y -nullclines : y =0 and y = k β x Equilibria: ( ˆ x , ˆ y ) a.) Trivial: (0,0) b.) Isolation: ( s ,0), (0, k ) c.) Coexistence: Solve ˆ x / α s / α = β ˆ x k ˆ x = α k s αβ 1 and ˆ y = β s k
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  • Fall '10
  • WayneM.Getz
  • per capita, Interspecific competition, intraspecific competition, Biological interactions, capita impact, coexistence equilibrium

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