Solving the stochastic dynamics of population growth

Area of Science:

• Ecology
• Evolutionary Biology
• Mathematical Biology

Background:

• Population growth dynamics are crucial in ecology and evolution.
• Deterministic kinetic models are commonly used to describe population size changes.
• Stochasticity in population dynamics is often overlooked in traditional models.

Purpose of the Study:

• To compare deterministic predictions with simulated stochastic population growth.
• To identify the reasons for discrepancies between deterministic and stochastic models.
• To develop a universally applicable stochastic model for population dynamics.

Main Methods:

• Simulation of various population growth models.
• Analysis of average population size across multiple stochastic realizations.
• Derivation of an exact solution for stochastic population growth dynamics.
• Application of moment-closure approximations.

Main Results:

• Deterministic models consistently overestimate population sizes, particularly for small initial populations.
• The discrepancy arises from unclosed-moment dynamics and the neglect of birth time variability.
• Moment-closure approximations offer partial improvement but are model-specific and not fully satisfactory.
• The derived stochastic solution accurately models community dynamics and predicts fixation probabilities.

Conclusions:

• Deterministic models are inadequate for accurately predicting average stochastic population dynamics.
• A novel, exact stochastic solution provides a more faithful representation of population growth.
• This work enables more accurate analysis of experimental data and parameter inference in ecological and evolutionary studies.