optiSel (version 0.9.1)

opticomp: Calculates the Optimum Breed Composition

Description

Calculates optimum contributions of breeds to a hypothetical synthetic population with maximum diversity. Additionally the average kinship within and between breeds and the genetic distances between breeds are computed.

Usage

opticomp(f, Breed, obj.fun="NGD", lb=NULL, ub=NULL, ...)

Arguments

f

Kinship matrix (e.g. a segment based kinship matrix, or a IBS based kinship matrix).

Breed

Vector containing the breed name of each individual.

obj.fun

The objective function to be maximized. For "NGD" the diversity 1-c'fc is maximized, or equivalently, the mean kinship c'fc is minimized, where f is the matrix containing the mean kinships within and between breeds. For "NTD" the term c'(1-F)+c'(F1' - 2f + 1F')c is maximized, where F=diag(f). This puts more weight on between population diversity.

lb

Named vector providing lower bounds for the contributions of the breeds can be provided. The names of the components are the breed names. The default lb=NULL means that the lower bound is 0 for all breeds.

ub

Named vector providing upper bounds for the contributions of the breeds can be provided. The names of the components are the breed names. The default ub=NULL means that the upper bound is 1 for all breeds.

...

Further parameters passed to the solver solve.QP of R package quadprog.

Value

A list with the following components:

bc

Vector with optimum contributions of breeds to a synthetic population with maximum diversity

value

The value of the objective function, i.e. the maximum diversity that can be achieved.

f

Matrix containing the mean kinships within and between breeds.

Dist

Genetic distances between breeds.

Details

Calculates optimum contributions of breeds to a hypothetical synthetic population with maximum diversity. Additionally the average kinship within and between breeds and the genetic distances between breeds are computed.

References

Wellmann, R., Bennewitz, J., Meuwissen, T.H.E. (2014) A unified approach to characterize and conserve adaptive and neutral genetic diversity in subdivided populations. Genetics Selection Evolution. 69, e16

Examples

# NOT RUN {
library(optiSel)
data(map) 
data(Cattle)
dir   <- system.file("extdata", package = "optiSel")
files <- paste(dir, "/Chr", 1:2, ".phased", sep="")

#####################################################################
#   Find the optimum breed composition using segment based kinship  #
#####################################################################
IBD <- segIBD(files, minSNP=15, map=map, minL=1.0)
mb  <- opticomp(IBD, Breed=Cattle$Breed, obj.fun="NGD")

#### Optimum breed composition: ###
round(mb$bc,3)
#   Angler Fleckvieh  Holstein   Rotbunt 
#    0.484     0.395     0.072     0.049 

#### Average kinships within and between breeds: ###
round(mb$f,4)
#          Angler Fleckvieh Holstein Rotbunt
#Angler    0.0699    0.0171   0.0584  0.0590
#Fleckvieh 0.0171    0.0956   0.0135  0.0138
#Holstein  0.0584    0.0135   0.1233  0.1065
#Rotbunt   0.0590    0.0138   0.1065  0.1227

#### Genetic distances between breeds: ###
round(mb$Dist,4)
#          Angler Fleckvieh Holstein Rotbunt
#Angler    0.0000    0.2561   0.1953  0.1930
#Fleckvieh 0.2561    0.0000   0.3098  0.3087
#Holstein  0.1953    0.3098   0.0000  0.1284
#Rotbunt   0.1930    0.3087   0.1284  0.0000

#####################################################################
#   The optimum breed composition depends on the kinship matrix     #
#   and the objective function:                                     #
#####################################################################

bc <- opticomp(IBD, Breed=Cattle$Breed, obj.fun="NTD")$bc
round(bc,3)
#   Angler Fleckvieh  Holstein   Rotbunt 
#    0.253     0.433     0.168     0.146 

# }