Birth-and-death Processes in Python: The BirDePy Package

TL;DR

BirDePy is a Python package designed for estimating parameters, simulating, and forecasting population-size-dependent birth-and-death processes, demonstrated through case studies on endangered bird populations.

Contribution

The paper introduces BirDePy, a comprehensive Python toolkit for analyzing PSDBDPs, including parameter estimation, simulation, and forecasting functionalities.

Findings

Effective parameter estimation demonstrated on real population data

Sample path simulation and transition probability approximation validated

Case studies show practical applicability to endangered species populations

Abstract

Birth-and-death processes (BDPs) form a class of continuous-time Markov chains that are particularly suited to describing the changes in the size of a population over time. Population-size-dependent BDPs (PSDBDPs) allow the rate at which a population grows to depend on the current population size. The main purpose of our new Python package BirDePy is to provide easy-to-use functions that allow the parameters of discretely-observed PSDBDPs to be estimated. The package can also be used to estimate parameters of continuously-observed PSDBDPs, simulate sample paths, approximate transition probabilities, and generate forecasts. We describe in detail several methods which have been incorporated into BirDePy to achieve each of these tasks. The usage and effectiveness of the package is demonstrated through a variety of examples of PSDBDPs, as well as case studies involving annual population count data of two endangered bird species.