The Number of effective factors:
This is a simplified (and biased) version of the Castle-Wright estimator (Castle, WE 1921. An improved method of estimating the number of genetic factors concerned in cases of blending inheritance. Proc. Nat. Acad Sci. 81:6904-6907.) The assumptions underlying estimators of this sort are:
1) the number of segregating genes affecting the trait in question is large (>2)
2) the positive alleles each have an equal (and small) impact on the phenotype.
3) the positive alleles all derive from one parent, the negative alleles from the other
ne=(µp1-µp2)/ 8δ 2s
ne is the 'number of effective factors', the number of genes if the assumptions were valid
µp1-µp2 - the difference between the parental means
δ2s - the total genetic variance
(N.B.- for ease of calculation I've omitted the compensating factor, C, the squared C.V. of additive effects, and I'm likewise ignoring the use of variances of parental means. Herein I'm assuming that we measure things really well and our error variances are small).
Heritability, the ratio of genetic variance to total variance, is an important and useful estimator of the gain we can expect to achieve through selection. In our simple experiment, broad sense heritability may be calculated as:
h2 = (entry MS - error MS)/r/(errorMS + (entryMS - errorMS)/r) where r = number of replications.
From these two equations, it's apparent that (entryMS - errorMS)/r =δ 2s (=δ2g ) , so we can easily estimate ne and h2 from your ANOVA table and your parental means values.
QTL Analysis
QTL, quantitative trait locus (singular) or loci (plural) analysis provides us with an excellent way to test Sewell Wright's model. When you estimate the number of effective factors segregating in your population using Wright's estimator, what is your result? When you estimate the number of effective factors using Mapmaker (let's set the minimum LoD score at around 2.4), how many do you find?
Heritability is an important estimator of the amount of gain you can make in a population through selection. In this population, what portion of the variance for the trait you've measured is heritable? The Mapmaker-QTL output provides an estimator of the amount of phenotypic (total) variance accounted for by segregation at that locus. If you sum the significant effective factors' contributions to phenotype and divide that sum by heritability, what proportion of the heritable variance is accounted for by the QTL you've identified?
Mapmaker provides a relatively opaque perspective on the relationship of QTL to heritability. A more direct estimator is the regression between your best markers for a trait (1 marker per QTL) and phenotype. Cut and paste your selected QTL markers into a spreadsheet, along with your phenotype means. Perform the regressions using SAS. Do these results differ in a meaningful way from those you observed using Mapmaker-QTL?
Write your report and get it to me by Oct. 15.