From: <arthur.gilmour_at_DPI.NSW.GOV.AU>

Date: Wed, 20 Jun 2007 09:22:03 +1000

Date: Wed, 20 Jun 2007 09:22:03 +1000

Dear Matt

You wrote (complete text at bottom)

I wish to test whether the additive genetic variance of a trait is

changing over time. I have a study population where for the last 30 years,

all of the individuals born each year are measured for the trait at birth.

I have a pedigree for all individuals within the population.

I've set up a model as follows:

BYR is a 30 level factor for birth year included as a fixed effect to

control for temporal trends in environmental conditions.

sBYR is a standardized linear covariate of birth year centred on the mean

value and ranging from -1 to 1.

ANIMAL is the identity of the individual linked through the pedigree as a

pedigree factor (!P)

leg(sBYR,1).ANIMAL fits ANIMAL as a first order polynomial function of the

standardized birth year.

Trait ~ mu BYR !r leg(sBYR,1).ANIMAL

From this model I think I get estimates for the intercept, slope, and

covariance between the two from the random term:

int

cov slope

====

I'm sure someone else could offer a comment but here's may take.

The model term leg(),ANIMAL is typically used when there are repeated

observations on the animal,

but an animal is only born once so the data to estimate the terms is very

sparse.

You need two points at least to fit a slope but no ANIMALs have two

observations.

Furthermore, the A matrix accomodates a primary source of change in

genetic variation, that due to selection.

What other mechanism do you propose would change genetic variance over

time. Surelely it would

also change residual variance, so you would need to allow for that as

well.

You probably need a good number of years, which means a lot of animals

which means a big analysis,

Any change in variance that is systematic over time would need to be slow,

unless you have in mind

a particular change (say a change in technology measurung the trait at

some point in time)

If the heritability is low, it will be hard to detect any trend. If the

heritability is high, the trend may be evident

in the phenotypic variances calculated within years.

So, I would not be surprised if it proved very difficult, if not

impossible to fit such a model. But its probably worth a try.

May Jesus Christ be gracious to you,

Arthur Gilmour, His servant .

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Dear all,

I was wondering if anyone had any thoughts on the following problem:

I wish to test whether the additive genetic variance of a trait is

changing over time. I have a study population where for the last 30 years,

all of the individuals born each year are measured for the trait at birth.

I have a pedigree for all individuals within the population.

I've set up a model as follows:

BYR is a 30 level factor for birth year included as a fixed effect to

control for temporal trends in environmental conditions.

sBYR is a standardized linear covariate of birth year centred on the mean

value and ranging from -1 to 1.

ANIMAL is the identity of the individual linked through the pedigree as a

pedigree factor (!P)

leg(sBYR,1).ANIMAL fits ANIMAL as a first order polynomial function of the

standardized birth year.

Trait ~ mu BYR !r leg(sBYR,1).ANIMAL

From this model I think I get estimates for the intercept, slope, and

covariance between the two from the random term:

int

cov slope

I can then run the model again changing the random term to

leg(sBYR,0).ANIMAL and compare the log-likelihoods to see whether the

additive genetic variance is changing over the study period.

I can also back transform the value I get onto the values of the

polynomial to get estimates of additive genetic variance for each birth

year and estimate the approximate standard errors using the matrix from

the vvp file, which I can then use to plot a graph of changing additive

genetic variance over time.

I see this as a potential way to test for the effects of selection acting

upon the trait to reduce additive genetic variance over time.

Would this work?

Thank-you all very much for your time.

Best wishes

Matt

*****************************************************

Matt Robinson

Institute of Evolutionary Biology

The University of Edinbrugh

Room 102, Ashworth Laboratories,

King's Building's Campus,

West Mains Road,

Edinburgh.

EH9 3JT

Tel: +44 (0)131 650 5462

e-mail: matthew.r.robinson_at_ed.ac.uk

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Received on Sun Jun 20 2007 - 09:22:03 EST

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