9: Statistical Characterization of a Population 2 Flashcards
Breeder’s equation
deltaG = h^2 * sd * a * (i/t)
Measures of location
Mean, median, mode, percentiles, quantiles
What is interquartile range
Q3 (third quartile) - Q1 (first quartile
Normal distribution curve shows… Is used to describe…
a pattern of values of individuals in a population
Describe data pattern of quantitative (polygenic) traits
What is a mean
Arithmetic average
Marks the center of the distribution for normally distributed variables
Required for calculation of variance and covariance
What is variance? Equation?
Mathematical measure of variation, expressed in square units
= (x1 - u)^2(x2 - u)^2…/n
Why do we divide by n-1 instead of n when calculating sample variance
Correct for bias caused by taking the deviations from the sample mean rather than the pop mean
In animal breeding, variance is the measure of
Differences among individuals within a population
What is standard deviation
Measure of variation that can be thought of as an average deviation from the mean
Square root of the variance
Individual values vs pop values
Individual = genotypic, phenotypic and breeding values
Pop = covariance, correlation, regression
The question we want to answer is if one random variable X varies…
does Y vary simultaneously, and if so, by how much and in what direction?
E.g. of how two traits or values may vary together in a pop
Is daily weight gain related to feed conversion in swine?
What is covariation
How two traits or two values vary together
What is a strong, positive covariation
- 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
What is a strong, negative covariation
- 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
What does it mean when there is no covariation between X and Y
- pos is with pos, neg is with neg, and pos is with neg
- no consistency in the size of deviations
What to the positive, negative and weak covariation scatter plots look like
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
What are the three main aspects of covariation
- Direction (sign) of the relationship between two variables
- Indicates the strength of the relationship between two variables
- Amount of change in one variable that can be expected for given amount of change in another
What is the direction (sign) of the relationship between two variables?
Whether the relationship is pos, neg, or nonexistent
Direct of change of one variable that is expected w change in the other
E.g. positive covariation in traits? Negative?
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
What kind of covariation is present in the Belgian Blue? Explain
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
How does covariation indicate the strength of the relationship btw two variables
Can be weak, moderate, or strong
Strong relationship can be described as consistent or reliable
Examples for strength of covariation
Animals with heavy yearling weights consistently have high breeding values for birth weight (strong relationship)
How do we avoid calving problems using the relationship btw yearling weight and birth weight
Do not use a young bull with extremely high yearling weight performance. They might sire heavy calves = hard delivery
The third aspect of covariation is…
concerned with how much change in Y occurs with change in X
- X increases/decreases, Y increases/decreases
Example for amount of change between two traits
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
Covariance vs correlation vs regression
Covariance = direction
Correlation = strength
Regression = amount of change
Three aspects/measures of covariation
Covariance, correlation, regression
What does covariance tell us
If two traits covary together and clearly indicates the direction or sign of the covariation
As a population parameter, covariance is the average…
Equation
Product of deviations from the means of two variables
cov(X,Y) = (Xi -ux)(Yi - uy) / n
Equation of covariance as a sample parameter
same on top but divide by n-1
Example of notation for covariance for breeding value for traits X and Y
cov(BVx, BVy)
Example of covariance notation for phenotypic value and breeding value for the same trait
cov(P,BV)
