Maximum likelihood estimation for model Mt,α for capture-recapture data with misidentification

Area of Science:

• Ecology
• Population Biology
• Statistical Modeling

Background:

• Capture-recapture studies are vital for estimating population abundance.
• Natural marks like DNA or photos are used for individual identification.
• Classical models assume perfect identification, which is often unrealistic.

Purpose of the Study:

• To investigate the Mt,α model for abundance estimation in closed populations with identification errors.
• To derive and efficiently compute a closed-form likelihood for the Mt,α model.
• To assess the statistical properties of maximum likelihood estimates under this model.

Main Methods:

• Developed an exact closed-form expression for the likelihood of the Mt,α model.
• Employed efficient computation of the likelihood.
• Analyzed statistical properties (precision, bias) of abundance estimates.

Main Results:

• The Mt,α model's indirect error estimation requires substantial data richness.
• High capture probabilities or many capture occasions are needed for precise and unbiased estimates.
• Under data limitations, ignoring misidentification errors can yield better results than the Mt,α model.

Conclusions:

• The Mt,α model should be used cautiously due to its data demands.
• Alternative strategies for handling misidentification errors should be explored.
• Illustrative application to southern right whale (Eubalaena australis) population surveys.