Correllated traits

# Correllated traits - L567 Evolution C Lively 2008 Problem...

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L567 Evolution. C. Lively 2008 Problem: convert the breeder’s equation into the form used in the QG of correlated traits. R = h 2 S The breeder’s equation ! z 1 = h 1 2 S 1 substitution: R = ! z 1 , where the 1 stands for trait 1. ! z 1 = V A (1) V P (1) S 1 substitution: h 1 = V A (1) V P (1) ! z 1 = V A (1) V P (1) COV( w , z 1 ) substitution: S 1 = COV( w , z 1 ) ! z 1 = V A (1) COV( w , z 1 ) V P (1) re-arrangement. ! z 1 = V A (1) B ( w , z 1 ) substitution: COV( w , z 1 ) V P (1) = B ( w , z 1 ) the selection gradient. ! z 1 = G 11 B 1 V A(1) = G 11 and B (w,z 1 ) = B 1 ! z = GB the standard form for correlated traits, where G is the additive genetic variance/covariance matrix, and B is the vector of selection gradients ! z 1 ! z 2 . . . ! z p " # \$ \$ \$ \$ \$ \$ \$ \$ \$ % = G 11 G 12 . . . G 1 p G 21 G 22 . . . G 2 p . . . . . . . . . G p 1 G p 2 . . . G pp " # \$ \$ \$ \$ \$ \$ \$ \$ \$ % B 1 B 2 .

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Correllated traits - L567 Evolution C Lively 2008 Problem...

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