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Title: Laws of Spatially Structured Population Dynamics on a Lattice
We consider spatial population dynamics on a lattice, following a type of a contact (birth–death) stochastic process. We show that simple mathematical approximations for the density of cells can be obtained in a variety of scenarios. In the case of a homogeneous cell population, we derive the cellular density for a two-dimensional (2D) spatial lattice with an arbitrary number of neighbors, including the von Neumann, Moore, and hexagonal lattice. We then turn our attention to evolutionary dynamics, where mutant cells of different properties can be generated. For disadvantageous mutants, we derive an approximation for the equilibrium density representing the selection–mutation balance. For neutral and advantageous mutants, we show that simple scaling (power) laws for the numbers of mutants in expanding populations hold in 2D and 3D, under both flat (planar) and range population expansion. These models have relevance for studies in ecology and evolutionary biology, as well as biomedical applications including the dynamics of drug-resistant mutants in cancer and bacterial biofilms.  more » « less
Award ID(s):
1815406 2152155 2141651
NSF-PAR ID:
10385352
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Physics
Volume:
4
Issue:
3
ISSN:
2624-8174
Page Range / eLocation ID:
812 to 832
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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