For two sub-populations sharing one resource pool, an equilibrium ratio exists only when their reproduction-weighted claim survival probabilities at the common threshold are equal and at least 1.
(2016), The Bruss-Robertson Inequality: Elaborations, Extension s, and Applications, Math
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Interactions between resource dependent branching processes and equilibria
For two sub-populations sharing one resource pool, an equilibrium ratio exists only when their reproduction-weighted claim survival probabilities at the common threshold are equal and at least 1.