# Multivariate normal genetic models with a finite number of loci

## Abstract

A genetic model due to Russell Lande is described. The model assumes a finite number of loci at each of which there are an infinite number of alleles whose effects on the phenotype are normally distributed. Analytic and numerical results using this model depend on the allele effects remaining multivariate normally distributed. This is almost never exactly true, but may often be a good approximation. Numerical results for several kinds of natural selection are discussed. A model involving overdominance is presented which seems to exhibit the Franklin--Lewontin crystallization effect. A model is presented of the maintenance of genetic variation by a cline along which there is linear change in the optimum phenotype under optimizing selection. The equilibrium has been found analytically for the case of an infinite cline. Remarkably, there is no linkage disequilibrium maintained at equilibrium in this case.

- Authors:

- Publication Date:

- Research Org.:
- Washington Univ., Seattle (USA). Dept. of Genetics

- OSTI Identifier:
- 6315326

- Alternate Identifier(s):
- OSTI ID: 6315326

- Report Number(s):
- RLO-2225/5-39

- DOE Contract Number:
- EY-76-S-06-2225-005

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; GENETIC VARIABILITY; GENETICS; MATHEMATICAL MODELS; CHROMOSOMES; PHENOTYPE; BIOLOGICAL VARIABILITY; BIOLOGY 550400* -- Genetics

### Citation Formats

```
Felsenstein, J.
```*Multivariate normal genetic models with a finite number of loci*. United States: N. p., 1977.
Web.

```
Felsenstein, J.
```*Multivariate normal genetic models with a finite number of loci*. United States.

```
Felsenstein, J. Sat .
"Multivariate normal genetic models with a finite number of loci". United States.
doi:.
```

```
@article{osti_6315326,
```

title = {Multivariate normal genetic models with a finite number of loci},

author = {Felsenstein, J.},

abstractNote = {A genetic model due to Russell Lande is described. The model assumes a finite number of loci at each of which there are an infinite number of alleles whose effects on the phenotype are normally distributed. Analytic and numerical results using this model depend on the allele effects remaining multivariate normally distributed. This is almost never exactly true, but may often be a good approximation. Numerical results for several kinds of natural selection are discussed. A model involving overdominance is presented which seems to exhibit the Franklin--Lewontin crystallization effect. A model is presented of the maintenance of genetic variation by a cline along which there is linear change in the optimum phenotype under optimizing selection. The equilibrium has been found analytically for the case of an infinite cline. Remarkably, there is no linkage disequilibrium maintained at equilibrium in this case.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sat Jan 01 00:00:00 EST 1977},

month = {Sat Jan 01 00:00:00 EST 1977}

}