Related Experiment Video
Updated: Apr 27, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
A stochastic Pella Tomlinson model and its maximum sustainable yield
Charles Bordet1, Louis-Paul Rivest1
1Department of Mathematics and Statistics, Université Laval, 1045 rue de la médecine, Québec, QC, Canada G1V 0A6.
Abstract:
This paper investigates the biological reference points, such as the maximum sustainable yield (MSY), for the Pella Tomlinson and the Fox surplus production models (SPM) in the presence of a multiplicative environmental noise. These models are used in fisheries stock assessment as a firsthand tool for the elaboration of harvesting strategies. We derive conditions on the environmental noise distribution that insure that the biomass process for an SPM has a stationary distribution, so that extinction is avoided. Explicit results about the stationary behavior of the biomass distribution are provided for a particular specification of the noise. The consideration of random noise in the MSY calculations leads to more conservative harvesting target than deterministic models. The derivations account for a possible noise autocorrelation that represents the occurrence of spells of good and bad years. The impact of the noise is found to be more severe on Pella Tomlinson model for which the asymmetry parameter p is large while it is less important for Fox model.
Related Concept Videos
Population Growth
Modeling with Differential Equations
Growth Models with Integration: Problem Solving
Optimal Foraging
Exponential Equations for Modeling Growth
Conservation of Declining Populations