Analytical characterization of the restricted-mating overlap distribution

Characterize analytically the evolving empirical overlap distribution of the thresholded sexual Derrida–Higgs species formation model under restricted mating.

Background

The paper derives the critical genome length from a transient variance criterion based on the unrestricted homogeneous population model. This criterion evaluates the overlap variance at the deterministic time when the unrestricted mean overlap reaches the mating threshold, but it does not derive the dynamics of the overlap distribution in the restricted species formation model itself.

Under restricted mating, parent selection depends on the evolving compatibility graph, making the dynamics nonlinear and allowing the empirical overlap distribution to develop multiple within-species and between-species components. A full analytical description would therefore go beyond the moment-based approximation used to predict the onset of fragmentation and could characterize the subsequent evolution and separation of reproductive groups.