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.


Biomass Fishing Librium 


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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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