Brewster’s and Lawrence’s Warbler genetics
An excellent paper on this subject was presented in 1951 by Kenneth C. Parkes.
It helps to think of two genes, one for the main body color (white is dominant WW and yellow is recessive ww), and one for the black throat patch (absent black patch is dominant PP, black patch is recessive pp). Pure (homozygous) Golden-winged parent thus is WWpp, while homozygous Blue-winged is wwPP. Both parents must convey a dominate gene, so no doubly recessive (Lawrence’s) offspring can result from their pairing.
Brewster’s Warbler (WwPp) is a first generation (F1) hybrid offspring of a mating between a Golden-winged parent and a Blue-winged parent. This Brewster’s typically has yellow on the underparts. A bird displaying white underparts (WWPp) would be a second generation backcross between an F1 Brewster’s and a Golden-winged.
Lawrence’s Warbler (wwpp), with two recessive genes for each trait, can not be accounted for by a first generation pairing. Rather, it has to be the result of a pairing between either two Brewster’s (statistically possible, but exceedingly rare), or a pairing between a Brewster’s or a Lawrence’s with either a heterozygous Golden-winged (Wwpp) or a heterozygous Blue-winged (wwPp), or a pairing of any two heterozygous parents of either species. In other words, because Lawrence’s is recessive for both of two traits, it cannot have received a gene from any parent homozygous for either dominant trait.