AnS 652A Animal Breeding Strategies
Homework Assignment # 1
Part I - Due Wed Jan. 12 at 5 PM
Part II - Due Fri Jan. 21 at 5 PM
PART I – due Wed Jan 12 at 5 PM
1. a. Use Excel to stochastically simulate phenotypes for a total of 200 progeny and their parents for an
additive trait with the following parameters:
Population mean = 50
Phenotypic standard deviation = 10
Heritability = 0.3
and according to the following family structure: 10 sires are mated to 5 dams each; each dam has 4
progeny. The sires and dams are from an unselected and unrelated base population.
To generate this data, first generate the breeding values and phenotypes of the 5 sires and 20 dams by
generating numbers from the appropriate Normal distribution, then use these to generate the breeding
values and phenotypes of the progeny. Use the following function to generate a random number for a
standard Normal distribution (N(0,1)):
+(SQRT(-2*LN(RAND()))*COS(RAND()*6.2831853))
To use this, copy and paste this equation into the formula bar of the Excel spreadsheet.
b. Now rank the progeny based on phenotype, select the 20 progeny with the highest phenotype, and
compute their average phenotype and their average breeding value, and compare this to what you
would have expected based on the theory of response to selection.
The easiest way to do this selection in Excel is demonstrated in the HMWK1_EX spreadsheet that is
included in the Ans652X/Homework_1 folder (rank the individuals, give all individuals that rank <21
a 1 and those that rank >20 a 0, multiply that value (0/1) by the phenotype (or breeding value) and
average the resulting values. To get the mean of the selected individuals, you need to multiply by
200/20 to remove the impact of the 180 zero’s that are included in the mean.
You may need to replicate your data set several times (e.g. 10) and use the average of the values
obtained from each replicate to get a reasonable answer. You can replicate your data by pushing F9,
which will draw a new set of random numbers for your spreadsheet. In fact, any time you change
something in your spreadsheet, it will generate a new set of numbers. If you want to create a
‘permanent’ data set (this may not be needed), copy the data and then ‘paste special’ as ‘values only’.
E-mail your spreadsheet and answers to jdekkers@iastate.edu by 5 PM on Wednesday Jan 12. Please
label the information in the spreadsheet appropriately, such that I can make some sense of it.
PART II – due Fri Jan 21 at 5 PM
To get full credit, show your work and derivations
2. a. Use the spreadsheet and data you generated under part I to estimate the heritability of the trait based on
the observed (i.e. calculated from the data that you have generated) variances of the progeny breeding
values and phenotypes and compare this to the heritability that you used to generate the data. Explain
any discrepancies. You may need to replicate your data set several times (e.g. 10) and use the average
of the estimate obtained from each replicate to get a reasonable answer.
3.
Estimate the following coefficients of regression from the data you have generated (you can use the
function slope(y-cells, x-cells)) and, for each, your estimate (or the average of estimates over multiple
(10?) replicates) to what you would expect this coefficient to be equal to:
a.
Regression of progeny breeding value on progeny phenotype.
b.
Regression of progeny phenotype on progeny breeding value.
c.
Regression of progeny phenotype on the dam’ s phenotype.
d.
Regression of progeny phenotype on the average phenotype of the sire and dam.
4. a.
Derive the equation that can be used to estimate the breeding value of an individual from own
phenotype. Use the parameters that you used to simulate the data (i.e. the true parameters).
Use this equation to estimate the breeding values of each progeny in your spreadsheet. Use these EBV
and the true breeding values of the simulated progeny to compute the following parameters and
compare them to their expectations (you will again need to replicate):
b.
The mean and variance of the EBV for the 200 progeny.
c.
The (realized) accuracy of the EBV (= correlation between true and estimated BV)
d.
The coefficient of regression of true BV on the EBV.
e.
The coefficient of regression of EBV on the true BV.
f.
Now rank the progeny based on their EBV, select the 20 progeny with the highest EBV and compute
their average EBV, phenotype and true breeding value and compare these to what you expect (you may
again need to replicate to get an accurate values).
g.
Also, compare the average phenotype and breeding value of the selected individuals to the averages
you obtained under question 1b (part I of this assignment), and explain any differences/similarities.