A hunter-gatherer-farmer population model: Lie symmetries, exact solutions and their interpretation
Roman Cherniha, Vasyl' Davydovych
TL;DR
This paper classifies Lie symmetries of a reaction-diffusion model for farmer and hunter-gatherer populations, deriving exact solutions and interpreting their biological significance.
Contribution
It provides a Lie symmetry classification for a three-component population model and constructs exact solutions with biological insights.
Findings
Several traveling front solutions identified
Exact solutions help interpret population spread dynamics
Symmetry analysis simplifies complex reaction-diffusion systems
Abstract
The Lie symmetry classification of the known three-component reaction-diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived. The Lie symmetries obtained for reducing the system in question to systems of ODEs and constructing exact solutions are applied. Several exact solutions of traveling front type are found, their properties are identified and biological interpretation is discussed.
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