Cattle breeders have long been selecting Texas Longhorn cattle to have extra long horns. In one case, the average tip to tip horn length in the population was 52 inches. The very largest ones were chosen for breeding and those parents had an average horn length of 61 inches. The heritability in that population was 0.21. How large are the horns of their offspring expected to be.

The correct answer is 53.8 inches.

Explanation:

The observable traits of an organism are considered its phenotype. It may be illustrated as the characteristics that can be seen in terms of the features that comprise physiological, physical, behavioral, anatomical, or biochemical features. These phenotypic traits arise because of the expression of the genetic code acquired by the organisms. A variation in phenotypes plays an essential part in the process of natural selection. Variation can arise due to several factors like the influence of the surroundings in which the organism prevails, genetic variation, or the association between the genetic constituents and the environment.  

Quantification is required in order to predict the amount of phenotypic variation because of allelic variance and environmental elements. In the given case, the phenotype of the cattle at the time of breeding is illustrated by the breeder's equation. This equation illustrates the association between the response of the trait selected with the intensity of heritability and selection. The equation is R = h^2S

Here R is the response to selection, h^2 is the heritability and S is the selection coefficient. In the given question, h^2 is given as 0.2, S = (61-52) inches. Therefore, R is,  

R = 0.2 * 9 = 1.8

Therefore, offspring will exhibit an enhancement in length by 1.8 inches. Hence, length will be = 52 + 1.8 = 53.8 inches.  

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