Seascape origin of Richards growth

Area of Science:

• Ecology
• Mathematical Biology
• Statistical Physics

Background:

• The Richards growth equation is a widely used empirical model in population dynamics and forecasting.
• Its fractional exponent is typically determined by data fitting, lacking a clear theoretical foundation.
• Understanding the origins of this fractional exponent is key to refining population modeling.

Purpose of the Study:

• To provide a theoretical justification for the Richards growth equation's fractional exponent.
• To connect the empirical Richards model to underlying mechanisms in distributed populations.
• To explore how spatial diffusion and growth rate stochasticity influence population dynamics.

Main Methods:

• Developed a theoretical framework for population growth in distributed systems.
• Incorporated migration (spatial diffusion) and stochasticity ('seascape noise') into analytical growth rules.
• Analyzed the emergent properties of the population model, focusing on the growth law.

Main Results:

• Demonstrated that Richards-like growth laws naturally arise from generic analytical growth rules.
• Showed that the inclusion of migration and stochasticity leads to a fractional exponent in the overall population growth.
• Identified a power-law distribution in local population numbers as a key factor.

Conclusions:

• The study provides a theoretical underpinning for the empirical Richards growth equation.
• Migration and stochasticity are identified as crucial factors generating fractional growth laws.
• This work offers a testable link between population distribution and the Richards growth model.