In this lecture we discuss alternative bioeconomic modelling approaches along the following lines:
- Modifications/extensions of the Gordon-Schaefer model, including the use of other surplus production models
- Cohort models
- Multispecies modelling
Modifications/extensions of the Gordon-Schaeffer modelA bioeconomic model is made up of the following components: A biological growth model, a harvest production function including costs of input factors and a revenue function. The classical Gordon- Schaefer model includes a logistic biomass growth function, a short term catch equation linear in effort and stock biomass, constant unit cost of effort and constant unit price of harvest.
The most typical modifications are
- to exchange the biological growth functions by other surplus production functions. You may also obtain more information about other surplus production models here.
- to use a Cobb-Douglas production function to model short term harvest production
- to include harvest quantity dependent prices (representing some degrees of market power)
- to assume intra marginal rent deriving from marginal cost differences between fishing units
Cohort modelsYou may investigate the Mathematica demonstration of the well-known Beverton and Holt model by clicking at the figure. This demonstration includes however not any economic module. Beverton and Holt believed the envelope curve of the yield curves of varying t
_{c}-values (t_{c}: Age of first catch) could be used as an connection to market economy. This envelope curve (called the eumetric curve) has however some specific properties which makes it less useful (or even useless) as the biological part of a bioeconomic model.Other representations of this cohort model:
- Yield per recruit model (graphs)
- Yield per recruit functions (equations)
- Growth of cohorts
The three links above present webMathematica pages where it is possible to calculate (Evaluate) graphs and equations (including analytical equations) of different inputs.
| ## Competition## One dominantThe competitive exclusion principle proposed by Gause. The equilibrium defined by the intersection of the two isoclines is not stable, while the two equilibriums where each isocline intersect its own axis are stable.## SymbiosisTwo species benefiting from each other.You may also download a live version of Predator-Prey equations from Wolfram Demonstration Project. |

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