An explicit solution for calculating optimum spawning stock size from Ricker's stock recruitment model

Area of Science:

• Fisheries Science
• Population Dynamics
• Ecosystem Management

Background:

• Stock-recruitment models are crucial for fisheries management, predicting offspring numbers based on parent stock.
• Ricker's stock-recruitment model is widely adopted for its adaptability and parameter estimation ease.
• Maximum Sustainable Yield (MSY) reference points (S MSY and U MSY) are vital for sustainable fisheries but lack explicit solutions.

Purpose of the Study:

• To derive explicit analytical solutions for S MSY and U MSY within Ricker's stock-recruitment model.
• To offer precise calculations for fisheries managers, replacing traditional approximations.

Main Methods:

• Analytical derivation of explicit formulae for S MSY and U MSY.
• Utilizing the productivity and density-dependent parameters of the Ricker model.

Main Results:

• Explicit formulae for S MSY and U MSY are presented, directly calculable from Ricker model parameters.
• These formulae eliminate the need for numerical or statistical approximations previously used for over 30 years.

Conclusions:

• The derived explicit formulae provide accurate and direct methods for calculating critical fisheries management reference points.
• This advancement simplifies and enhances the precision of fisheries stock assessment and management strategies.