Stochastic von Bertalanffy models, with applications to fish recruitment

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Organism growth is influenced by environmental factors.
• Stochasticity in environments can affect population dynamics.
• Understanding fish growth and mortality is crucial for fisheries management.

Purpose of the Study:

• To model organism growth in stochastic environments using stochastic differential equations (SDEs).
• To analyze the impact of different stochasticity patterns on growth and survival.
• To evaluate the effects of stochasticity on fish recruitment and population growth rates.

Main Methods:

• Formulation of three individual-based models using SDEs with von Bertalanffy growth functions.
• Analysis of stochastic terms that decrease, remain constant, or increase with organism size.
• Evaluation of probability density functions for hitting times to assess growth and mortality dynamics.

Main Results:

• Stochasticity can substantially increase fish recruitment probability.
• The mean growth rate of surviving individuals consistently exceeds the mean population growth rate.
• The mean population growth rate surpasses the growth rate predicted by deterministic models.

Conclusions:

• Stochastic environments can lead to enhanced population recruitment and individual growth.
• The findings have implications for understanding biological processes in variable environments.
• This study provides insights into the adaptive significance of growth responses to environmental fluctuations.