 Mating assortment contrast

For observed pairings between two labels $A,B$, let $N_{\mathrm{same}}=N_{AA}+N_{BB}$ and $N_{\mathrm{cross}}=N_{AB}+N_{BA}$, where the first label denotes the female's group and the second the male's. A mating assortment contrast isIt lies between $-1$ and $1$. Positive $I$ describes an excess of same-label pairings over cross-label pairings; whether that is evidence of assortative mating depends on the null mathematical model and the assay. The four counts form a contingency table.

Here is an original scope check. Suppose independently paired females and males have probabilities $p_f,p_m$ of carrying label $A$. ThenWith $p_f=p_m=1/2$, the expected value is zero. With $p_f=p_m=4/5$, it is $9/25=0.36$, despite pairing being independent of label. This counterexample concerns unequal pool composition; it does not replace the group introductions and contingency table tests in the dietary divergence and mating isolation in Drosophila pseudoobscura experiment. Even with balanced pools, finite observed samples fluctuate: a positive $I$ alone is not a hypothesis test, much less a universal species boundary.