Homework due Wednesday, December 11th at 4:10 pm. Please walk me through all the steps on how to solve this problem.
A farmer wishes to increase the average body weight in a herd of beef cattle. He begins with a herd that has a mean weight of 595 kg, but selects a pair of big breeding individuals that between them have a mean weight of 625 kg.
A group of 20 offspring were obtained from this group of selected parents, with weights of:
612, 587, 604, 589, 615, 641, 575, 605, 610, 598, 589, 620, 617, 577, 609, 633, 588, 599, 601, and 611 kg.
Calculate the heritability for body weight in this herd.
Remember, variance can be described in this context as the difference between means. We can estimate phenotypic variance by comparing the breeding individuals we selected to the total population. We can estimate genetic variance as the difference between the progeny and their parents.
To calculate the heritability for body weight in this herd, we need to estimate the phenotypic variance and genetic variance.
Step 1: Calculate the phenotypic variance.
- Find the difference between the mean weights of the selected breeding individuals and the mean weight of the entire herd.
Mean weight of the selected breeding individuals: 625 kg
Mean weight of the entire herd: 595 kg
Phenotypic variance = (Mean weight of the selected breeding individuals) - (Mean weight of the entire herd)
= 625 kg - 595 kg
= 30 kg
Step 2: Calculate the genetic variance.
- Find the difference between the mean weight of the offspring and the mean weight of the selected breeding individuals.
Mean weight of the offspring: (Sum of all offspring weights) / (Number of offspring)
= (612 + 587 + 604 + ... + 601 + 611) / 20
= (12,055) / 20
= 602.75 kg
Genetic variance = (Mean weight of the offspring) - (Mean weight of the selected breeding individuals)
= 602.75 kg - 625 kg
= -22.25 kg
Step 3: Calculate the heritability.
Heritability can be calculated using the formula:
Heritability = (Genetic Variance) / (Phenotypic Variance)
= (-22.25 kg) / (30 kg)
= -0.74
The heritability for body weight in this herd is approximately -0.74.
Note: In this case, the negative heritability value suggests that there might be environmental factors or other reasons causing the offspring to have a lower average weight than the selected breeding individuals.