Estimating the degree of compensation from fluctuations in fish biomass

Background/Question/Methods

Reliably estimating the recruitment function of fish populations is important for predicting population dynamics and the effects of specific harvest pressures. However, statistical approaches using time series are often difficult to fit, particularly when data are sparse. Here we present a new approach for estimating the recruitment function of fish populations using generalized modeling techniques. This approach permits an analysis of the system in terms of the general families of functional forms, thereby bounding the possible shapes of an unknown recruitment function. Moreover, these generalized techniques take advantage of small, short-term fluctuations in fish biomass, and are of maximal utility when access to long-term datasets is limited. We demonstrate the utility of this approach by investigating a theoretical fish population that grows in accordance to the Shepherd function, a versatile functional form that can demonstrate qualities of Ricker, Berverton-Holt, and Cushing-type functions. These functional forms differ primarily by the degree of compensation at high levels of fish biomass, and thereby assume different density-dependent population-level effects.

Results/Conclusions

We first show how general attributes of a function governing the dynamics of a population can be known even if the governing functional form is not. Specifically, we show that short-term fluctuations in fish biomass can be used to determine the general functional family that governs fish recruitment. If it is assumed that recruitment is controlled by the Shepherd function (reducing the dimensionality of the problem), we can then map the Shepherd function to our generalized analysis. Mapping the generalized and specific models permits an examination of how specific parameters that govern the Shepherd function impact the general family to which it belongs, which can impact predictions of population dynamics. Moreover, this combined approach can be used to assess the stability of the system, and is extendable to multi-species systems. Importantly, because generalized modeling does not require information regarding the structure of the functional forms governing population dynamics, it is useful for investigating the dynamics of data-limited animal populations.