opticomp {optiSel}

Calculates the Optimum Breed Composition

Description

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

Usage

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

Arguments

f

Kinship matrix (e.g. a segment based kinship matrix).

phen

Data frame with column Indiv containing the IDs of the individuals and Breed with breed names.

obj.fun

The objective function to be maximized. For "NGD" the objective is to maximize the genetic diversity 1-c'fc in the multi-breed population, 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.

Details

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

Value

A list with the following components:

bc

Vector with optimum contributions of breeds to a hypothetical multi-breed 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.

Author(s)

Robin Wellmann

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

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=20, map=map, minL=2.0)
mb  <- opticomp(IBD, Cattle, obj.fun="NGD")

#### Optimum breed composition: ###
round(mb$bc,3)
#   Angler Fleckvieh  Holstein   Rotbunt 
#    0.469     0.444     0.041     0.046 

#### Average kinships within and between breeds: ###
round(mb$f,4)
#          Angler Fleckvieh Holstein Rotbunt
#Angler    0.0523    0.0032   0.0414  0.0417
#Fleckvieh 0.0032    0.0625   0.0036  0.0032
#Holstein  0.0414    0.0036   0.1074  0.0894
#Rotbunt   0.0417    0.0032   0.0894  0.1057

#### Genetic distances between breeds: ###
round(mb$Dist,4)
#         Angler Fleckvieh Holstein Rotbunt
#Angler    0.0000    0.2329   0.1960  0.1930
#Fleckvieh 0.2329    0.0000   0.2853  0.2844
#Holstein  0.1960    0.2853   0.0000  0.1309
#Rotbunt   0.1930    0.2844   0.1309  0.0000

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

bc <- opticomp(IBD, Cattle, obj.fun="NTD")$bc
round(bc,3)
#   Angler Fleckvieh  Holstein   Rotbunt 
#    0.264     0.447     0.148     0.141