multistageoptimum.searchIndexT {selectiongain}

Function for optimizing three-stage selection in plant breeding with one marker-assisted selection stage and two phenotypic selection stages

Description

This function is used to calculate the maximum of \Delta G based on correlation matrix, which depends on locations, testers and replicates, with a grid search algorithm. The changing correlation matrix of three-stage selection are the testcross progenies of DH lines in one marker-assisted selection (MAS) stage and two phenotypic selection (PS) stages.

Usage

multistageoptimum.searchIndexT (maseff=0.4, VGCAandE, VSCA, CostProd, CostTest,
  Nf, Budget, N2grid, N3grid, L2grid, L3grid, T2grid, T3grid,
  R2, R3, alg, detail, fig, alpha.nursery, cost.nursery,
  t2free,parallel.search, indexTrait, covtype,
  VGCAandE2, VSCA2, COVgca, COVsca, maseff2, q12, q22, ecoweight)

Arguments

maseff

is the efficiency of MAS.

VGCAandE

is the vector of variance components of genetic effect, genotype \times location interaction, genotype \times year interaction, genotype \times location \times year interaction and the plot error. When VSCA is specified, it refers to the general combining ability, otherwise it stands for genetic effect. The default value is 1,1,1,1,1. Variances types listed in Longin et al. (2007) can be used. E.g., VGCAandE="VC2" will set the value as 1,0.5,0.5,1,2.

VSCA

is the vector of variance components for specific combining ability.

CostProd

contains the initial costs of producing or identifying a candidate in each stage.

CostTest

contains a vector with length n reflecting the cost of evaluating a candidate in the tests performed at stage i, i=1,...,n. The cost might vary in different stages.

Nf

is the number of finally selected candidates.

Budget

contains the value of total budget.

N2grid

is the vector of lower and upper limits as well as the grid width of number of candidates in the first field test stage.

N3grid

is the vector of lower and upper limits as well as the grid width of number of candidates in the second field test stage.

L2grid

is the vector of lower and upper limits of number of location as well as the width in the first field test stage.

L3grid

is the vector of lower and upper limits of number of location as well as the width in the second field test stage.

T2grid

is the vector of lower and upper limits of number of tester as well as the width in the first field test stage.

T3grid

is the vector of lower and upper limits of number of tester as well as the width in the second field test stage.

R2

is the number of replications in the first field test stage. By default it is 1.

R3

is the number of replications in the second field test stage. By default it is 1.

alg

is used to switch between two algorithms. If alg = GenzBretz(), which is by default, the quasi-Monte Carlo algorithm from Genz et al. (2009, 2013), will be used. If alg = Miwa(), the program will use the Miwa algorithm (Mi et al., 2009), which is an analytical solution of the MVN integral. Miwa's algorithm has higher accuracy (7 digits) than quasi-Monte Carlo algorithm (5 digits). However, its computational speed is slower. We recommend to use the Miwa algorithm.

detail

is the control parameter to decide if the result of all the grids will be given (=TRUE) or only the maximum (=FALSE).

fig

is the control parameter to decide if a contour plot will be saved in the default folder of R. The default value is FALSE, which means no figure will be saved.

alpha.nursery

a value that should be 0<x<1, prelimitery test alpha fraction should be used for the stage 1. it is setted to 1 as default, when no prelimitery test "nursery stage".

cost.nursery

a vector of length two c([cost of producing a DH line],[cost of testing a DH in nursery]). The default value is 0,0.

t2free

is a logical value. If =FALSE, the cost of using T3 and T2 testers will be accounted seperately. If =TRUE, the cost of using T3 and T2 testers will be accounted according to number of testers, i.e., CostProd=c(CostProd[1],CostProd[2]*T2,CostProd[3]*(T3-T2)

parallel.search

is a logical variable to desided if the multiple cores can be used for computing, by default is FALSE. The users have to notice that assign cores also cost time. So this procedure can only be efficient if the dim >5.

indexTrait

is the control parameter for the simultaneous selection of two traits. Possible options are: "Optimum"(default), "Base" and "Restricted" for the implementation of the well known optimum, base and restricted selection indexes in plant breeding.

covtype

is the type of the covariance. Longin's type (covtype=c("LonginII")) is used by default. For the simultaneous selection of two traits possible covtypes are "2traits_PS", "2traits_GS" , "2traits_GS-PS", "2traits_PS-PS", "2traits_GS-PS-PS". If any of these five option is selected the calculation of correlation matrix will use the variance components of the two traits. If the user also require marker assited selection, the prediction accuracy of MAS for both traits should be also given to the function. Finally, if two traits are selected simultaneously, the desired index have to be defined in indexTrait

VGCAandE2

In the case of simultaneos selection of two traits (index selection) it is the vector of variance components of genetic effect, genotype \times location interaction, genotype \times year interaction, genotype \times location \times year interaction and the plot error for the second trait. When VSCA2 is specified, the VGCAandE refers to the general combining ability, otherwise it stands for genetic effect of the second trait. The default value is 0,0,0,0,0, meaning no simultaneos selection of two traits.

VSCA2

In the case of simultaneos selection of two traits (index selection) it is the vector of variance components for specific combining ability for the second trait. The default value is 0,0,0,0.

COVgca

In the case of simultaneos selection of two traits (index selection) is the vector of covariance components of: genetic effect, genotype \times location interaction, genotype \times year interaction, genotype \times location \times year interaction and the plot error. In case of hybrid breeding strategies it correspond to the covariance of general combining ability effects, while in line breeding strategies it corresponds to the covariance of genetic effects (per se performance).

COVsca

In the case of simultaneos selection of two traits (index selection) is the vector of covariance components of the specific combining ability effects as follows : sca, sca \times location interaction, sca \times year interaction, sca \times location \times year interaction. .

maseff2

is the efficiency of marker-assisted selection (MAS) for the second trait. The default value is NA, which means there is no MAS and there is not simultaneous selection of two traits. If a value between 0 and 1 is assigned to maseff2, then it is assumed that the breeder want to optimize breeding strategies for the simultaneos selection of two traits and also including marker assited selection. In this case, appropiate options have to be selected in covtype and indexTrait. The value of MAS is recommended to be higher than 0.1 to avoid illshaped correlation matrix.

q12

is the proportion of genetic variance associated with markers for trait 1 as defined by "Dekkers, JCM. 2007. Prediction of response to marker-assited..."" This parameter is only needed in the case of simultaneos selection of two traits (index selection)

q22

is the proportion of genetic variance associated with markers for trait 2 as defined by "Dekkers, JCM. 2007. Prediction of response to marker-assited..."" This parameter is only needed in the case of simultaneos selection of two traits (index selection)

ecoweight

is the vector of economic weight. In the case of simultaneos selection of two traits, this vector contains two elements, each corresponding to economical weigth of each trait

Details

for the simultaneous optimuzation of two tratis in multiple stage selection, it is assumed that all locations used during the first round of field trials are also used in the second round of field trails, i.e., the second round of field trials uses the same locations of the first round plus some new locations. The same is assumed for testers.

for the parameters "alpha.nursery" and "cost.nursery" since v2.0.47:

After producing new DH lines, breeders do NOT go directly for a selection stage in the field, neither for genomic selection. Most of the times, they prefer to make a small field experiment (called "nursery") in which all DH lines are observed and discarded for other traits as disease resistance. That means, all DH lines with poor resistance will be discarded. At the end of the nursery stage only certain amount of DH lines (alpha) advance to the first selection stage (phenotypic or genomic). Specially in maize that makes sense, because in experience around 90 percent of the new DH lines are very weak in terms of per se performance what make them not suitable as new hybrid parents. Then, budget should not be used to make genotyping on or testcrossing with them. Only the alpha fraction should be used for entering the stage 1 of the multistageoptimum.search function.

More details are available in the Crop Science and Computational Statistics papers.

Value

If \texttt{detail} = FALSE, the output of this function is a vector of the optimum allocation i.e., which achieves the maximum \Delta G. Otherwise, the result for all the grid points, which have been calculated, will be exported as a table in the Rgui.

Note

no further comment

Author(s)

Xuefei Mi, Jose Marulanda

References

A. Genz and F. Bretz. Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195, Springer-Verlag, Heidelberg, 2009.

A. Genz, F. Bretz, T. Miwa, X. Mi, F. Leisch, F. Scheipl and T. Hothorn. mvtnorm: Multivariate normal and t distributions. R package version 0.9-9995, 2013.

E.L. Heffner, A.J. Lorenz, J.L. Jannink, and M.E. Sorrells. Plant breeding with genomic selection: gain per unit time and cost. Crop Sci. 50: 1681-1690, 2010.

X. Mi, T. Miwa and T. Hothorn. Implement of Miwa's analytical algorithm of multi-normal distribution. R Journal, 1:37-39, 2009.

See Also

selectiongain()

Examples

vgv<- c(5.7, 5.19, 0.00, 0.00, 24.37) # from paper Longin 2015
vscav <- c(1.88, 2.94, 0.00, 0.00) # from paper Longin 2015
vlv<-c(0.08,0.02,0,0,0.09) #from paper Zhao 2016
vscal <- c(0.01, 0.00, 0.00, 0.00)  #from paper Zhao 2016
vcovv1<-c(-0.235,0,0,0,0) #come from Y. Zhao's email communication on June 20/2016
vcovs1<-c(-0.011,0,0,0) #testing value on Dic 07/2016


a1<-17.2 # economic weight for yield
a2<-4.5  # economic weight for protein

multistageoptimum.searchIndexT(
  maseff=0.3, maseff2=0.36, q12=0.85, q22=0.85,
  VGCAandE=vgv, VSCA=vscav, VGCAandE2=vlv, VSCA2=vscal,
  COVgca=vcovv1, COVsca=vcovs1,
  CostProd = c(0,4,4), CostTest = c(2,1,1), Budget = 1000,
  alpha.nursery=0.25,cost.nursery=c(1,0.3), Nf = 5,
  N2grid = c(5, 100, 10), N3grid = c(5, 40, 5),
  L2grid=c(7,8,1), L3grid=c(9,10,1),
  T2grid=c(1,2,1), T3grid=c(2,3,1), t2free= TRUE,
  R2=1,R3=1,  alg = Miwa(),detail=FALSE,fig=FALSE,
  covtype=c("2traits_GS-PS-PS"),indexTrait=c("Optimum"),ecoweight=c(a1,a2))