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Home > Art, Film & Photography > Population Models: Competitive Lotka-Volterra Equations, Lotka-Volterra Equation, Ecosystem Model, Population Modeling
Population Models: Competitive Lotka-Volterra Equations, Lotka-Volterra Equation, Ecosystem Model, Population Modeling

Population Models: Competitive Lotka-Volterra Equations, Lotka-Volterra Equation, Ecosystem Model, Population Modeling


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Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Competitive Lotka-volterra Equations, Lotka-volterra Equation, Ecosystem Model, Population Modeling, Matrix Population Models, General Selection Model, Nicholson-bailey Model, Logistic Model of Population Growth. Excerpt: The competitive Lotka Volterra equations are a simple model of the population dynamics of species competing for some common resource . Overview The form is similar to the Lotka Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential . For the competition equations, the logistic equation is the basis. The logistic population model, when used by ecologists often takes the following form: Here x is the size of the population at a given time, r is inherent per-capita growth rate, and K is the carrying capacity . Two species Given two populations, x 1 and x 2, with logistic dynamics, the Lotka Volterra formulation adds an additional term to account for the species' interactions . Thus the competitive Lotka Volterra equations are: Here, 12 represents the effect species 2 has on the population of species 1 and 21 represents the effect species 1 has on the population of species 2. These values do not have to be equal. Because this is the competitive version of the model, all interactions must be harmful (competition ) and therefore all -values are positive. Also, note that each species can have its own growth rate and carrying capacity . N species This model can be generalized to any number of species competing against each other. One can think of the populations and growth rates as vectors and the interaction ' s as a matrix . Then the equation for any species i becomes or, if the carrying capac...


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Product Details
  • ISBN-13: 9781155579788
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Competitive Lotka-Volterra Equations, Lotka-Volterra Equation, Ecosystem Model, Population Modeling
  • Width: 229 mm
  • ISBN-10: 115557978X
  • Publisher Date: 05 May 2010
  • Binding: Paperback
  • Spine Width: 3 mm
  • Weight: 86 gr


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