9: Statistical Characterization of a Population 2

Question 1

Breeder’s equation

Answer 1

deltaG = h^2 * sd * a * (i/t)

Question 2

Measures of location

Answer 2

Mean, median, mode, percentiles, quantiles

Question 3

What is interquartile range

Answer 3

Q3 (third quartile) - Q1 (first quartile

Question 4

Normal distribution curve shows… Is used to describe…

Answer 4

a pattern of values of individuals in a population
Describe data pattern of quantitative (polygenic) traits

Question 5

What is a mean

Answer 5

Arithmetic average
Marks the center of the distribution for normally distributed variables
Required for calculation of variance and covariance

Question 6

What is variance? Equation?

Answer 6

Mathematical measure of variation, expressed in square units

= (x1 - u)^2(x2 - u)^2…/n

Question 7

Why do we divide by n-1 instead of n when calculating sample variance

Answer 7

Correct for bias caused by taking the deviations from the sample mean rather than the pop mean

Question 8

In animal breeding, variance is the measure of

Answer 8

Differences among individuals within a population

Question 9

What is standard deviation

Answer 9

Measure of variation that can be thought of as an average deviation from the mean
Square root of the variance

Question 10

Individual values vs pop values

Answer 10

Individual = genotypic, phenotypic and breeding values

Pop = covariance, correlation, regression

Question 11

The question we want to answer is if one random variable X varies…

Answer 11

does Y vary simultaneously, and if so, by how much and in what direction?

Question 12

E.g. of how two traits or values may vary together in a pop

Answer 12

Is daily weight gain related to feed conversion in swine?

Question 13

What is covariation

Answer 13

How two traits or two values vary together

Question 14

What is a strong, positive covariation

Answer 14

• positive deviations for X are quite consistently associated with positive deviations for Y (and neg w neg)
• large deviations of X are paired with large deviations of Y (and small w small)
• with some exceptions to the rule

Question 15

What is a strong, negative covariation

Answer 15

• positive deviation for X are consistently associated w negative deviations for Y (and neg w pos)
• large deviations of X are paired w large deviations of Y (and small w small)
• exceptions to the rule

Question 16

What does it mean when there is no covariation between X and Y

Answer 16

• pos is with pos, neg is with neg, and pos is with neg
• no consistency in the size of deviations

Question 17

What to the positive, negative and weak covariation scatter plots look like

Answer 17

Positive = increasing trait X increases trait Y (linear increasing points)
Negative = increasing trait X decreases trait Y (linear negative points)
Weak = broad, spread out distribution

Question 18

What are the three main aspects of covariation

Answer 18

1. Direction (sign) of the relationship between two variables
2. Indicates the strength of the relationship between two variables
3. Amount of change in one variable that can be expected for given amount of change in another

Question 19

What is the direction (sign) of the relationship between two variables?

Answer 19

Whether the relationship is pos, neg, or nonexistent
Direct of change of one variable that is expected w change in the other

Question 20

E.g. positive covariation in traits? Negative?

Answer 20

Pos = calves with heavier birth weights will have higher yearling weights, higher calving problems

Neg = heifers with heavier yearling weights will likely have lower age at puberty

Question 21

What kind of covariation is present in the Belgian Blue? Explain

Answer 21

Negative covariation
Natural mutation in the myostatin gene that has been fixed through inbreeding
Have increased efficiency to convert feed -> lean muscle, but have poor fertility, calf viability and reduced stress tolerance

Question 22

How does covariation indicate the strength of the relationship btw two variables

Answer 22

Can be weak, moderate, or strong
Strong relationship can be described as consistent or reliable

Question 23

Examples for strength of covariation

Answer 23

Animals with heavy yearling weights consistently have high breeding values for birth weight (strong relationship)

Question 24

How do we avoid calving problems using the relationship btw yearling weight and birth weight

Answer 24

Do not use a young bull with extremely high yearling weight performance. They might sire heavy calves = hard delivery

Question 25

The third aspect of covariation is…

Answer 25

concerned with how much change in Y occurs with change in X
- X increases/decreases, Y increases/decreases

Question 26

Example for amount of change between two traits

Answer 26

If you knew how much change to expect in progeny for birth weight per pound of change in yearling weight, you could predict average birth weight of the calves based on the bulls yearling weight

Question 27

Covariance vs correlation vs regression

Answer 27

Covariance = direction
Correlation = strength
Regression = amount of change

Question 28

Three aspects/measures of covariation

Answer 28

Covariance, correlation, regression

Question 29

What does covariance tell us

Answer 29

If two traits covary together and clearly indicates the direction or sign of the covariation

Question 30

As a population parameter, covariance is the average…
Equation

Answer 30

Product of deviations from the means of two variables

cov(X,Y) = (Xi -ux)(Yi - uy) / n

Question 31

Equation of covariance as a sample parameter

Answer 31

same on top but divide by n-1

Question 32

Example of notation for covariance for breeding value for traits X and Y

Answer 32

cov(BVx, BVy)

Question 33

Example of covariance notation for phenotypic value and breeding value for the same trait

Answer 33

cov(P,BV)