On the nonidentifiability of population sizes

Area of Science:

• Ecology
• Biostatistics
• Wildlife population estimation

Background:

• Nonparametric mixture models are used to account for varying capture probabilities in population size estimation.
• Previous research identified nonidentifiability issues with these models, particularly concerning the population size.
• Specific conditions for identifiability within subfamilies of mixing distributions have been explored.

Discussion:

• This study addresses the nonidentifiability problem in population size estimation when using nonparametric mixture models.
• It highlights that nonidentifiability persists even across identifiable subfamilies of mixing distributions.
• The research focuses on a specific subfamily where mixing distributions are uniquely determined by their mixture.

Key Insights:

• A subfamily of mixing distributions is identified where each distribution is determined by its mixture.
• The population size is shown to have estimable lower bounds within this subfamily.
• These lower bounds are crucial for constructing lower confidence limits for population size.

Outlook:

• Developing robust methods for population size estimation in the presence of heterogeneity.
• Further investigation into the properties and applications of the identified subfamily of mixing distributions.
• Improving the precision and reliability of wildlife population estimates through advanced statistical modeling.