Parameter redundancy in Jolly‐Seber tag loss models

Abstract

Capture–recapture experiments are conducted to estimate population parameters such as population size, survival rates, and capture rates. Typically, individuals are captured and given unique tags, then recaptured over several time periods with the assumption that these tags are not lost. However, for some populations, tag loss cannot be assumed negligible. The Jolly‐Seber tag loss model is used when the no‐tag‐loss assumption is invalid. Further, the model has been extended to incorporate group heterogeneity, which allows parameters to vary by group membership. Many mark–recapture models become overparameterized resulting in the inability to independently estimate parameters. This is known as parameter redundancy. We investigate parameter redundancy using symbolic methods. Because of the complex structure of some tag loss models, the methods cannot always be applied directly. Instead, we develop a simple combination of parameters that can be used to investigate parameter redundancy in tag loss models. The incorporation of tag loss and group heterogeneity into Jolly‐Seber models does not result in further parameter redundancies. Furthermore, using hybrid methods we studied the parameter redundancy caused by data through case studies and generated tag histories with different parameter values. Smaller capture and survival rates are found to cause parameter redundancy in these models. These problems resolve when applied to large populations.

On near‐redundancy and identifiability of parametric hazard regression models under censoring

“…This method has been used for different classes of models. However, for structurally complex models, computer algebra packages may not be able to calculate the required symbolic rank of the derivative matrices, due to computer memory limitations (Cole et al., 2010; Cole, 2012; Cai et al., 2021). In such cases, numerical methods have been used as an alternative.…”