CANCELLED - Comparative dynamics of fish population models in the arctic

Background/Question/Methods

: Various mathematical models have arisen to address specific problems inherent in simulating and understanding the growth of fish populations. These include the Verhulst logistic, the Ricker, the Beverton-Holt, and the Gompertz models, and each has distinctive properties at low, medium, and high population densities. For example, it is well studied that their dynamics at low densities are key to understanding the likelihood of collapse or recovery of a threatened species. We recast each model into a common mathematical format to compare their dynamics directly, in part by representing each in its Taylor series format to clarify the dynamics as a function of population density and in Jacobian format to compare their equilibria and stability. We then fit each model to ecosystem survey data from the Barents Sea to understand how the models deemphasize or exaggerate qualitative properties of single-species dynamics, as well as how such effects are compounded when used in two- and three-species networks.

Results/Conclusions

: Perhaps surprising, the data show faster than exponential growth when fish populations recover from low population densities. Such growth is observed in this and other multi-species data but is not a property of the commonly-used models we examine here and is given little attention in the literature. We explain the range of application of each model and examine possible extensions of each model to more accurately represent dynamics suggested by the actual data. We also discuss ways to examine how the dynamics of a single species at high densities can provide clues to the structure of the multispecies-system in which it is embedded.