A new approach to the study of genetic variability of complex characters

V M Efimov 1, V Y Kovaleva1 and A L Markel 2

1 Institute of Systematics and Ecology of Animals, Siberian Branch of the
Russian Academy of Sciences, 630091, Novosibirsk, Russia

2 Institute of Cytology and Genetics, Siberian Branch of the Russian Academy
of Sciences, 630090, Novosibirsk, Russia

Abstract

A new approach to multivariate genetic analysis of complex organismal traits
is developed. It is based on examination of the distribution of parental
strains and the F1 and F2 hybrids in a multidimensional space, and the
determination of the directions corresponding to heterozygosity, epistatic
and additive gene effects. The effect of heterozygosity includes variability
produced by interaction between and within heterozygous loci. The additive
gene effects and the remaining epistatic interactions between the homozygous
loci can be visualized separately from the effects of heterozygosity by an
appropriate projection of the points in multidimensional space. In all, 20
morphological, physiological and behavioural characters and 21 craniometric
measures were studied in crosses between two laboratory rat strains. Linear
combinations of craniometric and of morphophysiological characters with a
high narrow-sense heritability could be identified. These combinations
characterized the organismal stress response, which had been selected for in
one of the strains. The prospects for the practical application of the new
approach and also for the evaluation of the contribution of the genetic
diversity to phenotypic variability in animals in natural populations are
discussed.

Heredity (2005) 94, 101-107. doi:10.1038/sj.hdy.6800580
Published online 10 November 2004

Keywords

heritability; selection; craniometry; behaviour; multivariate analysis

Introduction

In genetic analysis of quantitative characters, multivariate analysis
conventionally means the partitioning of the phenotypic variance into
several components due to the effects of general and specific genetic and
environmental factors and their linear or nonlinear interactions (Mather,
1949). Dimension is determined by the number of the factors, but,
conventionally, just one character at the output is ultimately considered.
Even if a number of characters are analysed in the experiment, each is
treated separately.

Views on what constitutes genetic multivariate analysis have changed notably
in the past 25 years. After introduction of the additive genetic
variance-covariance matrix G (Lande, 1979), it has become feasible to
estimate the narrow-sense heritability of any linear combination of
characters, including the principal components of the matrices G and P
(Atchley et al, 1981). Searches for composite characters with maximum
additive heritability, based on decomposition of the matrix GP-1, have
recently been proposed and performed (Ott and Rabinowitz, 1999; Klingenberg
and Leamy, 2001).

We suggest an alternative method based on analysis of the relative position
of the parents and the first two generations of hybrids in a
multidimensional space, with the axes corresponding to the measured traits.
The orientation of these three generations can be used to detect the
directions of variability due to heterozygosity, additive and epistatic gene
effects.

The proposed method appears promising for breeding. It can identify
composite characters with high narrow-sense heritability, which should
respond to selection. It may also indicate characters that might be
informative in studies of natural populations.

Model

It is well known that phenotypic variability in the F1 hybrids from two true
breeding lines is nonheritable. It follows that the variability due to
segregation of the set of genes that differ between the parents is observed
starting from F2. Let there be two parental inbred strains P1, P2, and the
F1 hybrids obtained by crossing the parental strains whose M characters are
measured. In the simplest additive-dominant model with no interactions
between loci, the mean values for each character in the F1 are xF1i=mi+hi,
where mi=(xp1i+xp2i)/2 is the mean of the parents, and hi is the deviation
due to dominance (Mather and Jinks, 1982).

As a result of segregation between the F1 and F2 generations, the means of
the F2 hybrids will be (Mather and Jinks, 1982) xF2i=mi+hi/2=(mi+xF1i)/2 and
in the nth generation they will become xFni=mi+hif(n), where f(n) is the
proportion of heterozygotes at the locus, depending on the system of mating
(for example, selfing or inbreeding, among others).

In a multidimensional space, a point formed by the means of characters for
each generation (F=P1, P2, F1, F2, ¼, Fn) will be denoted as xF=xF1, xF2, ¼,
xFM that is, xF is the centroid of F. From a simple geometric consideration,
it follows that the points xP1, m, xP2 and xF1 form a triangle in which the
points xFi lie on the straight line crossing the point xF1 and the point
m=(xP1+xP2)/2, which is the midpoint of the segment connecting the parental
means (Figure 1).

Full Text at Nature Heredity
http://www.nature.com/cgi-taf/DynaPage.taf?file=/hdy/journal/v94/n1/full/6800580a.html

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