Nucleation of antagonistic organisms and cellular competitions on curved, inflating substrates

Abstract

We consider the dynamics of spatially-distributed, diffusing populations of organisms with antagonistic interactions. These interactions are found on many length scales, ranging from kilometer-scale animal range dynamics with selection against hybrids to micron-scale interactions between poison-secreting microbial populations. We find that the dynamical line tension at the interface between antagonistic organisms suppresses survival probabilities of small clonal clusters: the line tension introduces a critical cluster size that an organism with a selective advantage must achieve before deterministically spreading through the population. We calculate the survival probability as a function of selective advantage $\delta$ and antagonistic interaction strength $\sigma$. Unlike a simple Darwinian selective advantage, the survival probability depends strongly on the spatial diffusion constant $D_s$ of the strains when $\sigma >0$, with suppressed survival when both species are more motile. Finally, we study the survival probability of a single mutant cell at the frontier of a growing spherical cluster of cells, such as the surface of an avascular spherical tumor. Both the inflation and curvature of the frontier significantly enhance the survival probability by changing the critical size of the nucleating cell cluster.

arXiv comment15 pages, 10 figures, final version

References in corpus (13)

• Genetic drift at expanding frontiers promotes gene segregation
• Genetic Demixing and Evolutionary Forces in the One-Dimensional Stepping Stone Model
• Genetic drift opposes mutualism during spatial population expansion
• Effects of Fluctuations on Propagating Fronts
• Fisher waves in the strong noise limit
• Spatial gene drives and pushed genetic waves
• Phase nucleation in curved space
• Competition and cooperation in one-dimensional stepping stone models
• Growth, competition and cooperation in spatial population genetics
• Asymmetric Mutualism in Two- and Three-Dimensional Range Expansions
• Survival Probabilities at Spherical Frontiers
• Universality and Scaling for the Structure Factor in Dynamic Order-Disorder Transitions
• Aspects of nucleation on curved and flat surfaces

Cited by in corpus (2)

• Spatial population genetics with fluid flow
• Turbulent mixing controls fixation of growing antagonistic populations