How old is this bird? The age distribution under some phase sampling schemes

Area of Science:

• Mathematical modeling
• Population dynamics
• Ecology

Background:

• Individual lifetime can be modeled using finite-state continuous-time Markov chains.
• The time of death follows a phase-type distribution, with transient states termed phases.

Purpose of the Study:

• To determine the conditional age distribution of an individual given its current phase.
• To investigate how different phase observation schemes affect this distribution.
• To apply these findings to ecological studies, specifically age pyramid computation for the Chatham Island black robin.

Main Methods:

• Utilized a finite-state continuous-time Markov chain model with one absorbing state.
• Analyzed the conditional age distribution based on different phase observation schemes.
• Applied the derived methods to calculate the age pyramid for Petroica traversi.

Main Results:

• The conditional age distribution is dependent on the interpretation of the question and the specific phase observation scheme.
• Successfully computed the age pyramid for the Chatham Island black robin population between 2007 and 2014.

Conclusions:

• The phase-type distribution model provides a framework for understanding lifetime and age structure.
• The study highlights the importance of defining observation schemes in Markov chain applications.
• Results offer valuable insights for conservation efforts and population management of endangered species.