Fitting Models to Data
In Chapter 8, we studied a model of sustainable harvesting of renewable resources. The model was a quadratic curve relating the sustainable yield Y to the amount of harvest effort E:
Y hE gE= − 2 .
Here, h and g are constants with values that will be different from resource to resource and situation to situation. The constants ultimately depend on the rate of growth of the biological resource, that is, the rate at which the resource is replenished. However, the data we had in hand for the example, shrimp in the Gulf of Mexico (Table 8.1), only provided information about Y under varying values of E. No information about the biology or population growth rates of shrimp were provided toward determining the constants h and g.