Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models

Area of Science:

• Ecology
• Statistics
• Population Dynamics

Background:

• Mark-recapture-recovery studies are crucial for estimating survival probabilities in animal populations.
• Traditional analyses often use fixed or mixed-effects parametric models to link covariates with survival parameters.
• These parametric models can limit the flexibility in capturing complex relationships between covariates and survival.

Purpose of the Study:

• To develop and apply a unified inferential framework for semiparametric mark-recapture-recovery models for open populations.
• To enhance the flexibility of modeling the relationship between survival probabilities and covariates using penalized splines.
• To investigate underlying ecological dynamics by comparing semiparametric models with standard parametric approaches.

Main Methods:

• Utilized penalized splines to model covariate-parameter relationships, allowing for flexible functional forms.
• Employed numerical maximum penalized likelihood estimation for model fitting.
• Used cross-validation for data-driven selection of smoothing parameters.
• Applied the semiparametric approach to mark-recapture-recovery data from gray herons and Soay sheep.

Main Results:

• The semiparametric models revealed novel ecological dynamics in survival probabilities for both gray herons and Soay sheep.
• Survival probability in gray herons was modeled as a function of environmental condition (time-varying global covariate).
• Survival probability in Soay sheep was modeled as a function of individual weight (time-varying individual-specific covariate).
• Comparison with standard parametric logistic regression highlighted the advantages of the flexible semiparametric approach.

Conclusions:

• The proposed semiparametric modeling framework offers a more flexible and powerful tool for analyzing mark-recapture-recovery data.
• This approach provides deeper insights into population dynamics by uncovering complex covariate-survival relationships.
• The method is effective for estimating survival probabilities in open populations and understanding ecological drivers of survival.