Laws of Spatially Structured Population Dynamics on a Lattice

We consider spatial population dynamics on a lattice, following type of contact (birth–death) stochastic process. show that simple mathematical approximations for the density cells can be obtained in variety scenarios. In case homogeneous cell population, we derive cellular two-dimensional (2D) lattice with an arbitrary number neighbors, including von Neumann, Moore, and hexagonal lattice. then turn our attention to evolutionary dynamics, where mutant different properties generated. For disadvantageous mutants, approximation equilibrium representing selection–mutation balance. neutral advantageous scaling (power) laws numbers mutants expanding populations hold 2D 3D, under both flat (planar) range expansion. These models have relevance studies ecology biology, as well biomedical applications drug-resistant cancer bacterial biofilms.