Murray Bourne at ‘squareCircleZ’ has a great post on modeling fish stocks as an interesting applied example for a math class.

In addition to helping students find interest in understanding the mathematics, this can also help people to really see why when fisheries scientists say that a particular harvesting practice is probably unsustainable.

My only caution would be to note that while it makes sense to avoid what the model says is unsustainable it doesn’t necessarily go the other way, and in fact sometimes what looks like a plausible model can give undue confidence in a belief that a certain harvesting rate is sustainable when in fact it is not.

One example of a wrong assumption which might lead to a prediction of sustainability for an unsustainable harvest rate is the idea that the harvest rate at constant effort, being proportional to the population density in the fished region, is also proportional to the total population. This is reasonable if the fished region includes the entire population, but for some populations the density remains constant and the population occupies a variable depth. If fishing samples mainly near the surface, then the population may appear to be replacing those harvested by reproduction when in fact the replacement comes just from fish lower down moving up. When the bottom of the population reaches the surface region there are no more replacements and all the remaining fish get removed before people realize that the breeding rate was much smaller than supposed.