Black is beautiful

[MLBob Furia]

I'd point out that a couple of those, such as the "brewers duck" shown are actually F-2's rather than F-1's. Most duck hybrids are fertile and the F-2's show a range of phenotypic values.

Clint

To expand & clarify what Clint pointed out:

Phenotypic values [/url]are calculated from the genotypic values for each individual for each trait. Each individual's phenotypic value is calculated from its genotypic value with an environmental effect determined by the heritability [/url]

. The individual's genotypic value is based on the alleles it inherited at the quantitative trait loci. To calculate genetic values, we use Cockerham's general genetic model :

[/url]

(2.8)



The parameters

are the additive and dominance effects of QTL

. The

's are epistatic interactions. The superscripts on the

's are for the type of interaction: We distinguish between additive by additive (AA), additive by dominance (AD), dominance by additive (DA) and dominance by dominance (DD) interactions. The

and

are coded variables denoting the genotype of the QTL. The

take on values

for QTL genotypes

, while the

are

for heterozygotes and

for homozygotes.
This results in a vector of genotypic values, one entry per individual in the simulated data set. The genetic variance [/url]is the sample variance of this vector of genotypic values. Call it

. The environmental [/url]variance,

is defined by

(2.9)


where

is the heritability [/url]of the trait. The extra environmental effect is taken from a normal distribution with mean 0 and variance

. If the environmental variance is specified, the heritability is ignored and the environmental variance is used directly. For each individual in the data set, a random variable with mean zero and variance

is generated and added to the genotypic value. This is the phenotypic value [/url]of that individual.

"....And that, Normie, is what this thread means"

View attachment beer_cheers-cliff-norm.jpg

 

[William Stahl]

I was just going to say that MLBob!
-

 

[Gene R.]

Bob, that's clear as mud to me:0 I guess i should of payed more attenition to biology class than girls biology way back when. Mulitply that equation by Wisconson game laws and you get sucked into a worm hole! But thanks for the attempt to clear it up. My head hurts now, I may have to take a nap. Isn't retirement grand.


Gene

 

[Brad Bortner]

I'd point out that a couple of those, such as the "brewers duck" shown are actually F-2's rather than F-1's. Most duck hybrids are fertile and the F-2's show a range of phenotypic values.

Clint

To expand & clarify what Clint pointed out:

Phenotypic values [/url]are calculated from the genotypic values for each individual for each trait. Each individual's phenotypic value is calculated from its genotypic value with an environmental effect determined by the heritability [/url]

. The individual's genotypic value is based on the alleles it inherited at the quantitative trait loci. To calculate genetic values, we use Cockerham's general genetic model :

[/url]

(2.8)



The parameters

are the additive and dominance effects of QTL

. The

's are epistatic interactions. The superscripts on the

's are for the type of interaction: We distinguish between additive by additive (AA), additive by dominance (AD), dominance by additive (DA) and dominance by dominance (DD) interactions. The

and

are coded variables denoting the genotype of the QTL. The

take on values

for QTL genotypes

, while the

are

for heterozygotes and

for homozygotes.
This results in a vector of genotypic values, one entry per individual in the simulated data set. The genetic variance [/url]is the sample variance of this vector of genotypic values. Call it

. The environmental [/url]variance,

is defined by

(2.9)


where

is the heritability [/url]of the trait. The extra environmental effect is taken from a normal distribution with mean 0 and variance

. If the environmental variance is specified, the heritability is ignored and the environmental variance is used directly. For each individual in the data set, a random variable with mean zero and variance

is generated and added to the genotypic value. This is the phenotypic value [/url]of that individual.

I love it Bob. Thanks for the laugh.

Now lets start the discussion on the utility of Cockerham's General Model in this situation.

Here is a test. How many sentences of this abstract do you understand? Tod and Clint, you are already disqualified.

Modeling and detecting nonallelic (epistatic) effects at multiple quantitative trait loci (QTL) often assume that the study population is in zygotic equilibrium (i.e., genotypic frequencies at different loci are products of corresponding single-locus genotypic frequencies). However, zygotic associations can arise from physical linkages between different loci or from many evolutionary and demographic processes even for unlinked loci. We describe a new model that partitions the two-locus genotypic values in a zygotic disequilibrium population into equilibrium and residual portions. The residual portion is of course due to the presence of zygotic associations. The equilibrium portion has eight components including epistatic effects that can be defined under three commonly used equilibrium models, Cockerham's model, F2-metric, and F(infinity)-metric models. We evaluate our model along with these equilibrium models theoretically and empirically. While all the equilibrium models require zygotic equilibrium, Cockerham's model is the most general, allowing for Hardy-Weinberg disequilibrium and arbitrary gene frequencies at individual loci whereas F2-metric and F(infinity)-metric models require gene frequencies of one-half in a Hardy-Weinberg equilibrium population. In an F2 population with two unlinked loci, Cockerham's model is reduced to the F2-metric model and thus both have a desirable property of orthogonality among the genic effects; the genic effects under the F(infinity)-metric model are not orthogonal but they can be easily translated into those under the F2-metric model through a simple relation. Our model is reduced to these equilibrium models in the absence of zygotic associations. The results from our empirical analysis suggest that the residual genetic variance arising from zygotic associations can be substantial and may be an important source of bias in QTL mapping studies.


Rong-Cai Yang, Genetics. 2004 July; 167(3): 1493–1505.

 

[MLBob Furia]

I think it all means that hybrids look different and that second generation hybrids look more different than first generation hybrids.

Sure am glad I'm retired and have the time to look up all this stuff! ;-)

 

[Tim B(tbrom)]