Chapter 8: Statistics & Their Application to Quantitative Traits

Population measures are not:

individual

Sample statistics =

• population mean estimated with sample mean

• pop.variance & standard deviation are estimated w/sample variance and sample standard deviation

More loci in genes =

more & more like normal distribution in the bell curve

Quantitative/polygenic traits =

• bell shaped curve — all of population phenotypes for 1 trait

• normal distribution

• affected by many genes

• many levels

Mean =

arithmetic average

Population mean =

every possible observation

Sample mean =

only observations from the sample

• sum of all observation in the sample divided by the sample size (n)

Variation =

how individuals vary for a particular trait in a population

Variation means:

variation in breeding values & allows for selection

Describe by:

• variance

• standard deviation

Standard deviation =

a mathematical measure of variation that can be thought of as an average deviation from the mean (square root of variance)

Once we establish that it’s a normal distribution, we assume that:

• with in 1 standard deviation from the mean, accounts for 68% of population

• 2 SDs = 95%

• 3 SDs = 99%

If an animal falls outside 2 standard deviation, it is an:

outlier/extreme

Breeding extremes causes:

the average to shift (eventually)

Adding a ^ =

estimated value

What does the sample standard deviation show?

how it disperses from the mean

Covariance =

• how two traits vary together — X & Y

• figure out if one has to do with the other

• measured by cov(X,Y)

3 aspects of covariation direction =

1. positive

2. negative

3. zero

Positive covariation =

positive deviation w/positive deviations —> when mean is subtracted, both are positive => as X inc, Y also inc (move together)

Negative covariation =

positive deviation w/ negative deviation => as ___ inc, ___ dec (opposite directions)

What does the covariance tell you?

the direction

Zero covariation =

no pattern, the deviations are doing their own thing, both traits are not really influencing each other

You can never have ___ variance, but you can have ___ covariance?

negative; negative

Correlation =

strength of relationship between 2 variables

Range of correlations =

-1 to +1

Types of correlations:

• phenotypic correlations

• genetic correlations

• environmental correlations

Some traits respond better if the:

environment is changed

• Birthing Sows: farrowing crate, have heating, clip needle teeth, etc.

Control environment to enhance survivability

Accuracy values =

association between actual and predicted

From a scatter plot you can tell:

direction & strength

• the closer the dots are to eachother, the greater the strength

0-20% Correlation =

weak

20-40% Correlation =

moderate

>40% Correlation =

strong

What type of correlation is 0.43?

strong, positive correlation

What type of correlation is -0.15?

weak, negative correlation

Regression =

the amount of change in a variable that can be expected for a given amount of change in another variable

The regression of Y on X:

Y = dependent variable

X = independent variable

In a scatter plot, the regression line slops shows:

how moving 1 X unit affects the Y units

Steep regression line =

large regression

Not steep regression line =

small regression

The prediction model for quantitative traits uses:

true values

What should we do because we don’t actually know true values?

use predictions of true values

EPD =

estimated progeny difference

MPPA =

most probable producing ability

EBV =

estimated breeding value

You always predict:

Y (since it’s the dependent variable)

Days to 230lbs for Pigs:

important to get there as quick as we can, w/o sacrificing other traits

Backfat for Pigs:

an indicator of when they are ready to be harvested

Did you complete the practice questions in the textbook?

yes/no