Michigan Department of Natural Resources
Fisheries Research Report No.1897, 1981

A General Numerical Model for Evaluating Size Limit Regulations with Application to Michigan Bluegill (Lepomis macrochirus Rafinesque)


Kelley David Smith


      Abstract.-A general numerical model was developed which can be used to study the biological response of a fishery to a variety of size limit restrictions. Effects of minimum, maximum (inverted), or slot size limits, or a catch-and-release regulation can be studied using this model. Fishing and hooking mortality are adjustable for simulating effects of different gear types and restrictions. Density-dependent growth can be used and seasonal fluctuations of growth may be assessed. It is also possible to model seasonal fluctuation in fishing mortality, including shifts in season length or time periods.

Effects of a 7.0 inch maximum size limit (i.e., all fish 7.0 inches and longer have to be returned to the water) were analyzed for slow, average, and fast growing bluegill (Lepomis macrochirus Rafinesque) populations in Michigan. Density-dependent mortality was used to estimate the number of fry surviving to age I. Density-dependent growth was simulated using a relationship between number of fry produced and total initial mean length.

Equations were developed to simulate the processes of mortality (natural, fishing, and hooking), growth, and recruitment. Number of fish in a population, number harvested, number caught and released, number lost to hooking mortality, and number of natural deaths were calculated using these equations and length-frequency information. Yield was calculated for harvested and caught and released fish using a length-weight regression.

Model simulations demonstrated that a 7.0 inch maximum size limit restriction was not effective in controlling bluegill populations. Variable and constant recruitment were modeled separately, and in neither case did the size limit regulation increase the number of bluegills 7.0 inches and larger, nor did mean length at each age change appreciably as compared to the same populations simulated under a 5.0 inch minimum size limit.

The greatest impact was observed in the fast growing population (using constant recruitment). Equilibrium numbers of 7.0 inch plus bluegills increased from 589 fish under a 5.0 inch minimum to 724 fish under the 7.0 inch maximum restriction, at a fishing mortality rate (m) of 0.40 for both. Total catch remained about equal - 2,038 and 2,089 fish per year for a 5.0 inch minimum and a 7.0 inch maximum size limit respectively, but legal harvest dropped from 1,530 under the existing conditions to 1,332 fish per year for the special regulation. As the conditional fishing mortality rate decreased, the population characteristics became virtually equal for the 5.0 inch minimum and the 7.0 inch maximum restrictions.