A Two Species Model

  • Ola Flaaten
Part of the Studies in Contemporary Economics book series (CONTEMPORARY)


First we shall give a review of the two species model analysed in May et al. (1979), since our three species model will be based upon this. Suppose there is a prey, W1, on which the existence of a predator, W2, is based. W1 and W2 can be thought of as biomasses. A simple model describing the dynamics of such a system is
$$ {{\text{w}}_{\text{1}}}{\text{ = d}}{{\text{w}}_{\text{1}}}{\text{/dt = }}{{\text{r}}_{\text{1}}}{{\text{w}}_{\text{1}}}\left( {{\text{1 - }}{{\text{w}}_{\text{1}}}{\text{/k}}} \right){\text{ - a}}{{\text{w}}_{\text{1}}}{{\text{w}}_{\text{2}}} $$
$${{\dot{w}}_{2}} = d{{W}_{2}}/dt = {{r}_{2}}{{W}_{2}}\left( {1 - {{W}_{2}}/\alpha {{W}_{1}}} \right)$$
where r1 and r2 are the intrinsic growth rates of the respective species. K is the carrying capacity of the total system, at which the prey will settle in the case of no predator and no harvest.


Species Model Positive Equilibrium Stock Level Catch Rate Fishing Pressure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Ola Flaaten
    • 1
  1. 1.Norwegian School of FisheriesUniversity of TromsøGuleng, TromsøNorway

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