Constraints on the evolution of attractive traits: genetic (co)variance of zebra finch bill colour

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Abstract
We estimated the heritability and genetic correlation between male and female bill colour in a laboratory population of zebra finches (Taeniopygia guttata) in order to examine the potential genetic constraints on the evolution of a sexually dimorphic trait. The heritability estimates of bill colour from regressions of offspring on single parents ranged from h2 = 0.34 to 0.73 and all but one of these estimates were significantly greater than zero. The restricted maximum likelihood heritability estimates for full- and half-siblings were significant for females (h2 = 0.48) but not significant for males (h2 = 0.45). The maximum likelihood estimates indicate that there is little dominance genetic variance for bill colour. The large genetic correlation between male and female bill colour (rg = 0.91) combined with opposing selection on male and female bill colour indicates that the evolution to sex-specific optima may proceed very slowly.