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Chinese Journal of Applied Ecology ›› 1990, Vol. 1 ›› Issue (1): 31-39.

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A new mathematical model of interspecific competition: an expansion of Lotka-Volterra competition equations

Sun Guowei, Cui Qiwu   

  1. Institute of Applied Ecology, Academia Sinica, Shenyang 110015
  • Received:1989-07-03 Online:1990-01-25 Published:1990-01-25

Abstract: The classical Lotka-Volterra competition equations are the direct extension of the classical Logistic equation of single population growth. Because they have no necessary theoretical basis and oversimplify the process of interspecific competition, it is not suitable for Lotka Volterra competition equations to be a general theoretical model of interspecific competition. Based upon the theory of nutrition kinetics, a new kind of competition model is constructed as follows: dX1/dt=μc1*X1 * 1-(X1+a12X2)/Xm1*/1-(X1+a12X2)/Xm1 dX2/dt=μc2*X2 * 1-(X2+a21X1)/Xm2*/1-(X2+a21X1)/Xm2 They are the extension of Cui-Lawson model of single population growth which is as follows: dX/dt=μc*X * 1-X/Xm*/1-X/Xm The new competition model has more complex and extensive behaviours than Lotka Volterra competition equations, and under specific condition, it turns into Lotka-Volterra competition equations. Therefore, the new competition equations are more general, and are the expansion of classical Lotka-Volterra competition equations.

Key words: Modelling, Nutrition kinetics, Competition, Lotka-Volterra equations, Functional response