In today’s news, NJ & NYfishermen are understandably upset because the allowed number offlukepermitted to becaughtin the upcoming season has been reduced by 28%. Just as the number of deer is regulated, with certain numbers of permits issued during deer season, several fish species, and spawning and feeding areas are tightly controlled. Both of these "game" speciesare subjectto three often irreconcilable forces: scientific predictions in the form of regulatory commissions, local needs of those relying on the game for a livelihood, and the contingencies ofpolitics.

The amount of any species permitted to be caught ("harvested" in the parlance of population minders and modelers) is chosen with one of two possible goals:

1. to keep the overall population in a steady state, i.e. the harvesting rate is basically the net birth rate (absolute birth rate - death rate)
2. to increase the overall population - i.e. the harvesting rate is greater than the net birth rate

Presumably the 3rd option - harvesting faster than the series can regenerate, is not a consideration in game or food species, or there soon would be no species left.

Population modeling has a long tradition, and especially within Chaos Theory. As shown byworld-famouspopulation modeler Robert May, the standard Logistic Map model of population growth undergoes period doubling and ultimate chaotic dynamics (population swings) as the net growth rate parameter increases through critical values. (And of course this is the same mapping made famous by Feigenbaum in his historic study of period doubling.)

Often times, a logistic differential equation (or system of differential equations with one or more logistically-modelled species) is used instead of a logistic map to model the population. In this case, chaotic dynamics are usually not observed, unless the system has at least three species and is suitably non-linear and coupled.

There are many more models than logistic, certainly, but all modelsthat can lead to a steady-state population contain a parameter known as the carrying capacity of the population. The carrying capacity is a single number that represents a lot of hidden detail;basically, however, it effectively the equilibrium value of species that the particular eco-nichecan sustain. Once this value is obtained, as well as the netgrowth rate- bothempirical determinations- the other main parameter, the harvesting rate, is adjusted until the overall population dynamics follow one of the two options listed above.

Game commissions use these model predictions then to issue mandates on allowed catch tonnage, number of hunting licenses, etc.

The fluke situation is more complex than most because three agencies are involved in setting limits - presumably they may all be using different models.

Now, back to theNortheast Atlantic coastsituation. Because of extreme over harvesting years ago, a number of agencies have been setting the harvest limits on a yearly basisin order to meet Goal #2 above. Even with increasing numbers of fluke (a number that fluke fisherman claim to be the highest in over 10 years), the total weight of fluke permitted to be fished is being cut by over 6 million pounds from this past year’s allowed catch of 23.6 million pounds. This new limithas been setbecause the available fluke count is not increasing fast enough, i.e. whatever model(s) are being used, the predictions are not coming true.

When a model’s prediction don’t pan out, the question isfairly simple- is the model wrong, or are the parameter(s) used in the model incorrect? Presumably the model equation(s) are OK; modeling fish dynamics has a pretty robust and successful history. Interestingly, the parameter that may be incorrect here is the carrying capacity. The carrying capacity may in fact be lower than the value being used in the models, which would mean that the fluke population cannot reach the value chosen that will allow full levels of fishing. In other words, the mandated bottom-line population can’t be met, implying that the fishermen will never fish for fluke at the same levels again.

That is unless the regulatory agencies revisit their models and assumptions There is enouogh of an outcry from affected fishermen that this hopefully will happen.

I find this story interesting and important because it points out some of the difficulties of setting policy based on mathematical models whose predictions are not accurate. It is imperative that we always know when decisions are being made using predictive models - and especially if the models don’t seem to be working!