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We consider the dynamics of spatially-distributed, diffusing populations oforganisms with antagonistic interactions. These interactions are found on manylength scales, ranging from kilometer-scale animal range dynamics withselection against hybrids to micron-scale interactions between poison-secretingmicrobial populations. We find that the dynamical line tension at the interfacebetween antagonistic organisms suppresses survival probabilities of smallclonal clusters: the line tension introduces a critical cluster size that anorganism with a selective advantage must achieve before deterministicallyspreading through the population. We calculate the survival probability as afunction of selective advantage $\delta$ and antagonistic interaction strength$\sigma$. Unlike a simple Darwinian selective advantage, the survivalprobability depends strongly on the spatial diffusion constant $D_s$ of thestrains when $\sigma>0$, with suppressed survival when both species are moremotile. Finally, we study the survival probability of a single mutant cell atthe frontier of a growing spherical cluster of cells, such as the surface of anavascular spherical tumor. Both the inflation and curvature of the frontiersignificantly enhance the survival probability by changing the critical size ofthe nucleating cell cluster.

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