Question

1. A farmer was interested in determining if genetic variation plays a role in the weight of cattle. The farmer measured the average weight of 12 different parents and their offspring at five years of age. The data is presented below. What is the mean and variance for the weight of the parents and of their offspring? What is the correlation between the parents’ weight and the weight of their offspring? For each 1 kg increase in a parents’ weight, how much does the weight of their offspring change? What is the narrow sense heritability for weight? Please show your work for all questions and make sure that you answer all questions. Please minimize rounding. (12 points)

Average

Parents’           Offspring’s

Weight (kg)     Weight (kg)

570                  568

572                  560

575                  585

584                  605

590                  583

599                  623

599                  624

602                  580

603                  624

616                  603

625                  580

631                  586

Answer 1

Let parents weight be X

Mean of Parents weight (Xi)

ΣX/n

n is the number of observations.

Variance of Parents weight =

(Σ(X-Xi)2)/n-1

The mean of the parents' weight is 597.17 kgs, and the variance is 402.33 kgs.

Let ofspring weight be Y

Mean of Offsprings weight (Xi)

ΣXY/n

n is the number of observations.

Variance of Offspring weight =

(Σ(Y-Yi)2)/n-1

The mean of the offspring weight is 593.42 kgs and variance is 484.434 kgs

It is not feasible to calculate the variation of the offspring for 1 kg increase in the parents' weight, since the data is randomly distributed. But the both parents' and offsprings weight are positive but weakly correlated, having a correlation of 0.29.

The narrow sense heritability can be calculated as:

h2 = Var(offspring) / (Var (Offspring) + Var( Parents')) = 484.434/(484.434 + 402.33) = 0.546