Refining mortality estimates in shark demographic analyses: a Bayesian inverse matrix approach

Area of Science:

• Conservation Biology
• Population Ecology
• Demographic Modeling

Background:

• Leslie matrix models are crucial for estimating population growth (λ) using vital rates.
• Estimating vital rates from λ is challenging due to data limitations on population structure.
• Existing inverse matrix methods require detailed age or stage class information, limiting their application.

Purpose of the Study:

• To develop and apply a novel inverse matrix approach using Monte Carlo simulations and SIR algorithm to estimate vital rates without population structure data.
• To determine the demography of the grey reef shark (Carcharhinus amblyrhynchos) population in the Great Barrier Reef (GBR).
• To provide updated demographic parameters for fisheries management of grey reef sharks in Papua New Guinea (PNG).

Main Methods:

• Employed a combination of Monte Carlo simulations and the sample-importance-resampling (SIR) algorithm.
• Solved the inverse matrix problem to estimate vital rates (natural mortality (M), total mortality (Z)) from population growth rate (λ).
• Applied the method to grey reef shark data from the GBR and PNG.

Main Results:

• Demonstrated that natural mortality (M) and total mortality (Z) for grey reef sharks were previously overestimated, leading to underestimated λ.
• Generated updated distributions for Z and λ for the GBR population.
• Corrected demographic parameter errors for the PNG population, improving estimates for fisheries management.

Conclusions:

• The developed SIR-based inverse matrix approach effectively estimates vital rates and population growth (λ) without requiring population structure data.
• This method enhances the applicability of inverse matrix techniques in conservation biology and fisheries management, especially with limited data.
• Provides more accurate demographic insights for grey reef sharks, crucial for effective conservation and sustainable fisheries.