If beak shape were determined by an environmental factor, there would be less of a relationship between parental and offspring beak depth, since the reason for depth would be environmental conditions when born, which could be very different for parents and offspring.
Work Step by Step
Think about the difference between genetic and environmental determination of a trait. Genetic determination means that the trait will tend to follow what the parents have since the parents provide the genes to build that trait. Thus, parental and offspring versions of the trait should be correlated, giving a line in Fig. 21.2b. Environmental determination tends to decouple parents and offspring since the environment may shift, without an obvious correlation, between the time when parents are young and the time when offspring are young. This would lead to a rounder graph in Fig. 21.2b without a clear correlation.