This article was published in the above mentioned Springer issue.The material, including all portions thereof, is protected by copyright;all rights are held exclusively by Springer Science + Business Media.

The material is for personal use only;commercial use is not permitted.

Unauthorized reproduction, transfer and/or usemay be a violation of criminal as well as civil law.

ISSN 0014-2336, Volume 174, Number 1

BLUP for genetic evaluation of plants in non-inbred familiesof annual crops

Jose Marcelo Soriano Viana • Isis Fernanda de Almeida •

Marcos Deon Vilela de Resende • Vinıcius Ribeiro Faria •

Fabyano Fonseca e Silva

Received: 30 September 2009 / Accepted: 23 November 2009 / Published online: 5 December 2009

� Springer Science+Business Media B.V. 2009

Abstract Best Linear Unbiased Prediction (BLUP)

has become the most widely used method for genetic

assessment of animal and perennial species, and it is

potentially relevant for annual crops. The objective of

this study was to assess this method for selection

within non-inbred families in recurrent breeding

programs. The ‘animal model’ was fitted. The data

were expansion volume (EV) and grain yield of

plants in recombination plots of two to three selection

cycles in the popcorn population Vicosa, with half-

and full-sib progenies. The ASReml program was

used to perform the analyses. For both EV and yield

the breeding values predicted from the additive and

additive-dominant models were highly correlated.

Multi-generation BLUP was, in general, more accu-

rate than single-generation analysis. These two

methods resulted in highly correlated predicted

breeding values. The dominance genetic values

predicted from the single- and multi-generation

analysis were also highly correlated. The pedigree

information reduced the percentage of coincidences

among the selected individuals relative to phenotypic

selection mainly in the population structured in half-

sib families. Based on breeding values predicted by

BLUP analysis, the most efficient selection procedure

was mass selection.

Keywords Mixed model � Animal model �Recurrent selection

Introduction

Recurrent selection aims for a continuous increase in

favorable gene frequency. Regardless of the selection

unit, its efficiency depends on accurate identification

of the individuals with the best additive genetic value.

A commonly used methodology in animal and

perennial species breeding for predicting additive

genetic values of individuals under selection is the

Best Linear Unbiased Prediction, which was pro-

posed by Henderson (1974). Ideally, predictions are

made taking into account the relationship among

individuals, using estimates of the variance compo-

nents of the model (genetic and non-genetic), with

correction for fixed effects.

Regarding the use of BLUP in annual crops, the

most relevant application until recently was prediction

of the performance of non-assessed hybrids, proposed

J. M. S. Viana (&) � I. F. de Almeida � V. R. Faria

Departamento de Biologia Geral, Universidade Federal de

Vicosa, Vicosa, MG 36570-000, Brazil

e-mail: jmsviana@ufv.br

M. D. V. de Resende

Departamento de Engenharia Florestal, Embrapa CNPF;

Universidade Federal de Vicosa, Vicosa, MG 36570-000,

Brazil

F. Fonseca e Silva

Departamento de Informatica, Universidade Federal de

Vicosa, Vicosa, MG 36570-000, Brazil

123

Euphytica (2010) 174:31–39

DOI 10.1007/s10681-009-0094-2

Author's personal copy

by Bernardo (1996), which is possible only when

sufficient relationship information among inbred lines

is available. In his study with 4,099 hybrids and 16

combinations among nine heterotic corn groups

assessed in up to 15 locations, Bernardo found

estimates of the correlation between predicted value

and phenotypic performance for grain yield ranging

from 0.49 to 0.70, with a tendency toward higher

estimates for groups with a greater number of assessed

hybrids. According to this author, these values can be

considered moderately high, and it was suggested that

BLUP might be efficient for identifying non-per-

formed crosses with superior performance.

Other relevant applications common in animal and

perennial species breeding have been incorporated

during the last 5 years in the breeding programs of

annual allogamous and autogamous crops. Piepho

et al. (2008) reviewed the use of the BLUP method-

ology in plant breeding, showing its relevance even

without pedigree information. The applications

included genetic assessment of individuals (additive

genetic value prediction) and of pure and inbred lines

(prediction of genotypic values and the effects of

general combining ability) with and without pedigree

information in single and multi-trait analyses. Flache-

necker (2006a, b) used BLUP to predict the mean

additive genetic value of parents of full-sib families of

a corn population. This permitted satisfactory predic-

tions of the performance of the progeny in the

subsequent cycle for grain moisture and/or the

selection index trait, calculated as a function of grain

yield and dry matter content. From an analysis of

wheat genotypes in several environments, Crossa

et al. (2006) concluded that the prediction of breeding

value by BLUP with pedigree information was more

precise than traditional analyses assuming fixed and

random effects. Reis et al. (2005) used BLUP in

combination with the bootstrap technique in a diallelic

analysis of inbred corn lines. They reported that the

correlation between the predicted and observed mean

yields of the hybrids decreased with a reduction in the

number of parents, and they emphasized that the

decrease was less pronounced with the use of BLUP

compared to the BLUE (fixed model) method.

The value of pedigree information was investi-

gated by Nunes et al. (2008) using simulation. They

concluded that inclusion of relationship information

resulted in higher predicted gains. Bauer et al. (2006)

used molecular marker information to calculate the

relationship matrix and concluded that the BLUP

methodology could be used in inbred line selection.

The same conclusion was reported by Sebolai et al.

(2005) from a simulation study of selection of pure

lines. In another simulation study, Bauer and Leon

(2008) analyzed the efficiency of superior line

selection by multi-trait BLUP. The results showed

that this analysis was superior to single-trait analysis

for identifying superior lines and prediction accuracy.

Kruuk (2004) used the ‘‘animal model’’ to estimate

genetic parameters of natural populations and con-

cluded that the BLUP methodology permitted the

most efficient use of the available data in addition to

giving greater statistical power to the tests.

In order to show that this method can be used regu-

larly by plant breeders of annual crops, the objective of

this study was to assess its use in the selection of plants

in non-inbred families in recurrent breeding programs.

Materials and methods

Theoretical aspects

The selection efficiency in recurrent intrapopulation

breeding programs is proportional to the efficiency of

identifying the parents with superior additive genetic

values, because the other components of the genetic

value are not correlated with the number of favorable

genes present. Although the genotypic value (G) and

the additive genetic value (A) are, in general, both

positively correlated with the number of favorable

genes (N), the correlation of A with N is usually

greater or equal (in the absence of dominance) to the

correlation of G with N (Viana 2005).

Assuming an absence of epistasis we have

G ¼ Mþ Aþ D

where M is the population mean and D is the

dominance genetic value.

Thus, the phenotypic value of an individual can be

defined as

P ¼ Mþ Aþ DþX

k

ðfixed effectÞk

þX

l

ðnon-genetic random effectÞl þ error

In matrix notation, assuming no other non-genetic

random effects,

32 Euphytica (2010) 174:31–39

123

Author's personal copy

y ¼ Xbþ Zu1 þ Zu2 þ e

where y is the vector of phenotypic values, X is the

incidence matrix of fixed effects, b is the vector of

the effects of the levels of each fixed factor (including

the population mean), Z is the incidence matrix of

random effects, u1 is the vector of the additive genetic

values, u2 is the vector of the dominance genetic

values and e is the residuals vector. This model,

called by animal breeders as the ‘animal model’, is

appropriate for prediction of genetic values of the

measured individuals, which are the selection units.

In plant breeding the appropriate term is ‘individual

model’. The criterion for obtaining the best linear

unbiased predictor of a random vector is the maxi-

mization of the joint probability density function of y

and the random vectors (Henderson 1974), obtaining

(under normality) the mixed model equations.

Assuming a non-inbred population (Cov(u1, u2)

equal to a null vector) and that there is no correlation

among the errors (Var(e) = R = Ir2), the mixed

model equations are

X0X X0Z X0ZZ0X Z0Zþ r2G�1

1 Z0ZZ0X Z0Z Z0Zþ r2G�1

2

2

4

3

5bo

~u1

~u2

2

4

3

5

¼X0yZ0yZ0y

24

35

where G1 ¼ r2AAðnÞ and G2 ¼ r2

DDðnÞ are the variance

matrices of the vectors of additive and dominance

genetic values. A(n) and D(n) are the additive and

dominance relationship matrices, given by

AðnÞ ¼

2r11 2r12 � � � 2r1n

2r12 2r22 � � � 2r2n

� � � � � � . ..

� � �2r1n 2r2n � � � 2rnn

266664

377775

and

DðnÞ ¼

u11 u12 � � � u1n

u12 u22 � � � u2n

� � � � � � . ..

� � �u1n u2n � � � unn

266664

377775

where rij is the coefficient of coancestry between

individuals i and j, and uij ¼ uðmfÞðm0f 0Þ ¼ rmm0 rff0 þrmf0 rfm0 is the probability of individuals i and j having

genotypes identical by descent, where m and f are the

parents of i, and m0 and f0 are the parents of j (Mrode

2005).

The fit of the model by an iterative process gives

estimates of the variance components, a prediction of

each random vector and a solution for the fixed

effects vector. The process most used to estimate the

components of variance is restricted/residual maxi-

mum likelihood (REML), which was developed by

Patterson and Thompson (1971). Alternatively, the

maximum likelihood (ML) method, the minimum

variance quadratic unbiased estimation (MIVQUE)

method and Henderson’s method III (Littell et al.

2006) can be used.

Although the model described suggests that it is

always possible to predict the additive and domi-

nance genetic values, this unfortunately is not always

true. For example, in the case of annual allogamous

species such as corn, if the population in the

recombination plot is structured in half-sib progenies,

the additive-dominant model cannot be fitted because

the dominance relationship matrix is an identity in

each cycle. Thus, as G2 ¼ r2DI and R ¼ r2I there is

no convergence in the REML process. This is not

necessarily true in the case of animal and perennial

species. If the population is structured in full-sib

progenies, even if the dominance relationship matrix

is not an identity, there is no guarantee that the

additive-dominant model can be fitted. In general, for

the additive-dominant model to be fitted there must

be at least two different covariances among relatives

that are functions of the additive variance and of

dominance variance.

The prediction accuracy of the additive genetic

values is

rA~A ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1� PEV

~r2A

� �s

where PEV is the prediction error variance and ~r2A is

the restricted maximum likelihood estimate of the

additive variance (Mrode 2005, pp. 50–51).

Two selection strategies based on EV were

considered in each cycle: selection of 9–10 plants

in each one of the 20 families selected based on the

progeny test (totaling 196 individuals) and selection

of 196 plants (mass selection). The direct and indirect

genetic gains were calculated based on the parental

control (c = 1/2 with selection within half-sib family

and c = 1 with selection within full-sib family) and

Euphytica (2010) 174:31–39 33

123

Author's personal copy

the additive genetic values of the selected individuals

(~As) by the function

DMp ¼ c1

ns

X

i

~Ais

!

where ns is the number of selected parents (196

females with selection within half-sib family, and 196

females and up to 196 distinct males with selection

within full-sib progeny). If the population is struc-

tured in full-sib families, this function is biased when

there are allelic and non-allelic gene interaction

(dominance and epistasis). Assuming Hardy–Wein-

berg equilibrium and absence of epistasis, the mean

of the population obtained after selection can be

expressed as (Viana et al. 2009)

M1 ¼Mþ ð1=2ÞEðAsÞ; if the population is

structured in half-sib progenies, or

M1 ¼Mþ Eð�AsÞ þ Eð�DosÞ; if the population is

structured in full-sib families

where M is the mean of the base population, EðAsÞ is

the expectation of the additive genetic values of the

selected individuals, Eð�AsÞ is the expectation of the

average additive genetic values of the selected full-

sib family parents, and Eð�DosÞ is the expectation of

the average dominance genetic values of the individ-

uals in selected full-sib families. The offspring

average dominance genetic value is a function of

the allelic frequencies and d, the dominance deviation

(difference between the genotypic value of the

heterozygote and m, the mean of the genotypic

values of the homozygotes), for each gene.

The prediction function is also obtained by an

equivalent derivation of that used by Eberhart (1970),

assuming that the predicted gain is proportional to a

selection differential based on predicted breeding

values (DMp ¼ bð�AS � �AÞ). Considering that the

coefficient of proportionality is the regression coef-

ficient of the genotypic value of half-sib/full-sib

family in the improved population as a function of the

additive genetic value of its common parent (selected

individual)/average additive genetic value of the

parents, we have

b ¼ CovðAs or �As; �GoÞVðAs or �AsÞ

Assuming irrelevant changes in gene frequen-

cies, b = 1/2 in the population structured in half-

sib families or b = 1 in the case of full-sib

progenies.

For comparison the genetic gains were also com-

puted from the function proposed by Cullis et al.

(2006), including the parental control. The indirect

expected genetic gain in relation to trait Y with

selection based on trait X is

EGGYðXÞ ¼ c � i � qgX;YrgY

hX

where i is the selection intensity, qgX;Yis the genetic

correlation, r2gY

is the genotypic variance and h2X is

the generalized measure of heritability (Cullis et al.

2006).

Experimental data

Were analyzed the phenotypic values of expansion

volume (EV; ml/g) and grain yield (g/0.18 m2) of

plants in the recombination plots (areas of crosses

between selected families) of cycles 1, 2 and 3 of the

selection program with half-sib families, and of the

cycles 1 and 2 of the selection program with full-sib

families, both with the popcorn population Vicosa.

The two breeding programs aim the development of

superior open pollinated populations. Each cycle

consisted of evaluation of 196 families in a repli-

cated trial, selection of the best 20 progenies,

recombination of these families in isolated area

(recombination plot), using remnant seeds, and

selection of 196 superior plants for the next cycle.

The tests were designed as a 14 9 14 simple lattice

and carried out in the experimental station of the

Federal University of Vicosa (UFV) in Coimbra,

Minas Gerais (MG), Brazil, in the 1999/2000, 2001/

2002, 2002/2003, 2003/2004 and 2004/2005 growing

seasons. They are simultaneously conducted to offer

experimental data appropriate to studies on Quanti-

tative Genetics and Statistical Genomics (compara-

tive analysis of genetic parameters and selection

efficiency, influence of the effective population size

on genetic variability, genetic evaluation based on

BLUP, marker assisted selection based on linkage

disequilibrium (LD) between molecular markers and

QTL, among others).

The recombination plots with half-sib progenies

were conducted at the experimental station of the

UFV in Ponte Nova-MG, Brazil, in the 2000/2001,

2002/2003 and 2004/2005 growing seasons. The

34 Euphytica (2010) 174:31–39

123

Author's personal copy

twenty selected families were randomly planted inter-

calating one row of male plants to every four rows of

female plants. Two rows were also planted with the

single hybrid IAC 112 (control), developed by the

Agronomic Institute of Campinas (IAC). Each row

was 20 m long with up to 100 plants. The rows of

females and the control were detasseled at flowering.

The recombination plots with full-sib progenies were

conducted in an experimental field at UFV in Vicosa-

MG in the 2003/2004 and 2005/2006 growing seasons.

The 20 selected families were randomly planted in

rows with 10 m long with up to 50 plants. Crosses were

controlled at flowering so that at least 19 full-sib

families were obtained for each progeny (one male

from each of the other 19 families). The plants used as

males were not measured. In the analyses they were

inserted in the pedigree to permit prediction of their

breeding values. The prediction is possible only for

those with pedigree information.

In the half-sib family recombination plots, 20

plants were measured for each progeny and 5–10

plants in each row of the control. In the full-sib

family recombination plots, 8–31 plants were mea-

sured for each family, totaling 324 and 390 plants.

The EV was assessed in a hot air popcorn machine

(1,200 w) using 10 g samples.

Statistical analysis

The software ASReml v2.00 (Gilmour et al. 2006)

was used for the analyses. In the analyses with data

from the half-sib family recombination plots the IAC

112 was inserted in the pedigree as an individual with

unknown parents. In the multi-generation BLUP

model (see the ASReml code in the Appendix), since

the single hybrid IAC 112 is not a genotype from the

base population, we inserted a fixed effect of

population. Once we grouped populations structured

in half- and full-sib families, from two different

selection cycles, conducted in two locals and in

4 years, to be parsimonious we define a second fixed

factor named environment (the environment effect

includes confounded effects of population structure,

cycle, local and year). It is important to note that the

estimation of additive and residual variance in the

single generation analysis of the population struc-

tured in full-sib families was possible since G1 ¼r2

AA 6¼ R ¼ r2I in each cycle.

Results

The most probable application of the BLUP method-

ology, by breeders of annual allogamous plants,

would be estimation of genetic parameters and

prediction of the breeding values of the individuals

under selection for each cycle. The tests showed that

there is genetic variability for EV and grain yield in

the populations regardless of their family structure

(Tables 1, 2). The test relative to EV in cycle 1 of the

full-sib family population is associated with a prob-

ability value of 17%. For both traits, the estimates of

Table 1 Parameters estimated by BLUP/REML, population and IAC 112 means, direct gain in EV (ml/g) and indirect gain in yield

(g/0.18 m2) in the half-sib family population

Parameters Cycle 1 Cycle 2 Cycle 3

EV Yield EV Yield EV Yield

Additive var.

(conf. interval)

19.12570.0000

(11.76–26.49)

646.190.0060

(253.87–1038.52)

12.29400.0423

(0–26.27)

519.600.0001

(247.41–791.78)

13.08070.0000

(8.21–17.95)

388.600.0495

(0–850.43)

Residual var. 8.1768 327.57 14.8737 281.51 9.9519 668.15

Heritabilitya 0.7239 0.6932 0.2881 0.3717 0.2015 0.1525

Genetic corr. -0.1485 -0.0779 0.7972

Pop. mean 29.52 89.66 34.78 84.30 34.42 91.07

Gain w/mass sel. 1.40 0.48 0.98 0.86 1.20 0.29

Gain w/within sel. 1.15 0.29 0.77 1.31 0.78 -0.15

Gain w/sel.a 2.73 -2.4 1.50 -0.76 1.43 6.19

Mean of IAC 112 38.00 113.68 37.90 89.60 41.90 66.17

a From Cullis et al. (2006)

Euphytica (2010) 174:31–39 35

123

Author's personal copy

the additive genetic variance were greater in the half-

sib progeny population. The estimates of genetic

correlation between EV and yield were consistent in

sign in the two populations for cycles 1 and 2,

although the magnitudes were greater in the full-sib

family population (Tables 1, 2). However, selection

based on quality should not imply a significant

change in grain yield. The first cycle of among and

within selection based on EV reduced the magnitude

of the genetic correlation in the two populations. In

the third cycle in the population structured in half-sib

families the estimate was closer to 1.

An alternative approach is the multi-generation

BLUP. The main advantage is the increment in the

prediction accuracy. For both populations in general

an increase in accuracy compared to the single

generation analysis for EV and yield was observed

with the BLUP multi-generation method (Table 3).

The increase in accuracy ranges from 8.9 to 42.6%.

For both traits, in cycles 2 and 3 of the half-sib

progeny population, the correlations among the

additive genetic values predicted by single and

multi-generation BLUP were high, with estimates

close to 1 (0.985 and 0.935, and 0.996 and 0.963,

respectively). In the full-sib family population the

correlations were also high (0.975 and 0.984).

A general apparent limitation of these approaches,

relative to annual crops, is the impossibility of fitting

the additive-dominant model in a population struc-

tured in half-sib families. In relation to a population

structured in full-sib families it is possible to fit this

model, depending on the cycle (in the first cycle this

is not possible) or depending on the number of cycles

considered in the multi-generation analysis. Fortu-

nately this is not a limitation. As there is one base

population and given the equivalence (in number of

selection cycles) among the cycles 1 and 2 of the

half- and full-sib populations, it was possible to fit the

complete model, combining the populations

(Table 4). For yield, the additive-dominant model

was fitted only by multi-generation analysis. In the

analyses by cycle the REML process produced

negative estimates of the dominance variance. The

estimates of genetic parameters are in general com-

parable with the values obtained from the additive

model. The most important results, however, are the

correlations between breeding values predicted from

the additive model and the values predicted based on

Table 2 Parameters

estimated by BLUP/REML,

population mean, direct

gain in EV (ml/g) and

indirect gain in yield

(g/0.18 m2) in the full-sib

family population

a From Cullis et al. (2006)

Parameters Cycle 1 Cycle 2

EV Yield EV Yield

Additive var.

(conf. interval)

2.81360.1703

(0–8.60)

92.59540.0152

(8.78–176.41)

2.40720.0650

(0–5.52)

67.49010.0175

(4.71–130.27)

Residual var. 50.0469 266.5100 22.5853 197.9900

Heritabilitya 0.2008 0.4604 0.2259 0.3317

Genetic corr. -0.2098 -0.1457

Pop. mean 30.31 41.22 31.94 35.94

Gain w/mass sel. 0.31 0.16 0.34 0.20

Gain w/within sel. 0.19 0.24 0.17 0.60

Gain w/sel.a 1.05 -1.27 1.06 -0.80

Table 3 Accuracy of the BLUP/REML analyses

Analysis Half-sib families Full-sib families

EV Yield EV Yield

Cycle 1 Cycle 2 Cycle 3 Cycle 1 Cycle 2 Cycle 3 Cycle 1 Cycle 2 Cycle 1 Cycle 2

Single-generation BLUP 0.82 0.54 0.76 0.77 0.78 0.42 0.42 0.45 0.63 0.63

Multi-generation BLUP (c1 ? c2) 0.77 0.56 0.49 0.69

Multi-generation BLUP

(c1 ? c2 ? c3)

0.71 0.52

36 Euphytica (2010) 174:31–39

123

Author's personal copy

the complete model (Table 5). For both EV and yield

the predicted breeding values were highly correlated.

The dominance genetic values predicted from the

single- and multi-generation analysis were also

highly correlated. For EV the correlations between

values predicted from the analysis based on the two

cycles and those predicted from the analysis from

cycles 1 and 2 were 0.9980 and 0.9982, respectively.

When selecting for EV in each generation based

on the additive genetic values from the BLUP single

generation analysis, greater predicted gains were

observed in both population with mass selection,

relative to within progeny selection (Tables 1, 2). In

the population structured in half-sib progenies the

increase in predicted gain for EV with mass selection

relative to within family selection ranged from 22 to

61%. In that structured in full-sib families, the

increments were 63 and 100%. In both populations

the predicted gains for EV with mass selection were

small, ranging from 1.0 to 4.7%. The indirect

predicted gains for yield ranged from 0.3 to 1%.

Equivalent results were obtained by Matta and Viana

(2003) in cycle 1 of the popcorn population Beija-

Flor, using BLUE/Henderson’s method III. The

predicted gains for EV were 0.53 and 0.35 ml/g with

mass selection and within family selection, respec-

tively. The limitation of mass selection is a reduction

in the effective population size. In general, in three to

six families none to five plants were selected and in

four to five progenies more than 14 plants were

selected. In the case of within family selection 9–10

plants would be selected in each progeny. The

expected genetic gains in EV computed as proposed

by Cullis et al. (2006) were greater than those based

Table 4 Parameters estimated by BLUP/REML in the population structured in half- and full-sib families, relative to EV (ml/g) and

yield (g/0.18 m2)

Parameters Cycle 1 Cycle 2 Cycles 1 and 2

EV Yield EV Yield EV Yield

Additive var.

(conf. interval)

5.30480.0089

(0.92–9.69)

589.45209.5E-13

(425.39–753.51)

4.59450.0086

(0.81–8.38)

489.04800.0000

(370.18–607.91)

4.91400.0006

(1.93–7.90)

281.81704.7E-7

(169.13–394.51)

Dominance var.

(conf. interval)

25.11931.2E-12

(18.09–32.14)

– 13.30180.0008

(5.01–21.59)

– 19.10831.4E-13

(13.98–24.23)

93.56460.1232

(0–251.75)

Residual var. 7.8947 190.6960 8.1000 124.1920 7.9607 261.0730

Accuracy 0.51 0.87 0.56 0.89 0.56 0.73

Heritabilitya 0.2742 0.7551 0.2114 0.4681 0.2799 0.5434

Additive corr. -0.0924

Dominance corr. -0.0980

Gain w/sel.a 1.06 0.86 1.03 -0.72b

a From Cullis et al. (2006)b Indirect gain

Table 5 Correlations

between breeding values

predicted by the additive

and additive-dominant

models, relative to EV

(ml/g) and yield (g/0.18 m2)

a Additive model for yield

Pop. structure Half- and full-sib

fam., cycle 1, add.

-dom. modela

Half- and full-sib

fam., cycle 2, add.

-dom. modela

Half- and full-sib fam.,

two cycles, add.-dom.

model

Half-sib fam., cycle 1,

additive model

EV 0.8676 0.8585

Yield 0.9986 0.9397

Half-sib fam., cycle 2,

additive model

EV 0.9556 0.9268

Yield 0.9951 0.9813

Full-sib fam., cycle 1,

additive model

EV 0.9905 0.9630

Yield 0.8600 0.9636

Full-sib fam., cycle 2,

additive model

EV 0.9888 0.9747

Yield 0.8281 0.9595

Euphytica (2010) 174:31–39 37

123

Author's personal copy

on the predicted breeding values. The predicted

indirect gains in yield were not concordant in

magnitude and/or sign.

In the half-sib progeny population, coincidence

involving the 196 individuals selected by mass selec-

tion using BLUP single generation analysis and

phenotypic selection decreased over the cycles. In

the BLUP analyses, 85.7, 77.5 and 53.1% of the

individuals selected in the first, second and third cycles

were also indicated as superior by phenotypic selec-

tion. Therefore, as the pedigree information was added

to the BLUP individual analyses, the coincidence

decreased between the methods. When selection was

based on predictions from the multi-generation anal-

ysis, there were slightly higher coincidence values

with phenotypic selection, of 83.7 and 58.2% for the

second and third cycles, respectively. In the population

structured in full-sib families, the coincidence among

the individuals selected by mass selection using

individual BLUP analyses and phenotypic selection

also decreased from the first to the second cycle, from

85.7 to 82.6%. In contrast, an increase in coincidence

between phenotypic selection and selection based on

multi-generation BLUP analysis was observed, from

70.0 to 98.0% in the two selection cycles.

Discussion

The most important aspect that should be discussed

when using the BLUP method through the animal

model is the fit of the additive model, even when it is

known that the expression of the trait depends on

interactions between alleles (dominance). This, how-

ever, is never taken into consideration in many

applied and simulated studies, probably because there

is a consensus among breeders that the methodology

adequately predicts the true additive genetic values

that are generally more accurate than those obtained

by other methods (Kumar et al. 2008). This was

demonstrated in our study. Simulation studies by

Leclerc et al. (2008) and Stock et al. (2007) involving

continuous and categorical traits and molecular data

in QTL analyses have shown the great efficiency and

usefulness of the BLUP methodology, even with

multi-trait and random regression analyses.

There is also a consensus that the technique offers

adequate prediction of additive genetic values when

there is generation overlay and/or partial or total lack

of pedigree information and selection effect, whether

by man or natural. Kruuk (2004) indicated that the

BLUP/REML methodology is a powerful way to

estimate the components of variance and to predict

additive genetic values in natural populations. But

Cantet et al. (2000), in a simulation study, reported

underestimation of heritability in the population

under selection, because the relationship information

was only partially available and the existence of

selection makes heritability biased.

There is no doubt, however, that the fit of the

additive-dominance model is important in combining

ability studies, especially when there is interest in

predicting non-performed crosses (Bernardo 1996).

In the study by Flacheneckar et al. (2006a, b), where

the additive model was fitted, the prediction of the

performance of the full-sib families by the mean

additive genetic value of the parents was not satis-

factory for yield, but it was satisfactory for a less

important characteristic (grain moisture) and for a

second characteristic called the selection index

(which is a function of the yield and dry matter

content), probably because it not does not depend

greatly on dominance effects.

Although the results obtained in many theoretical

and applied studies have systematically shown the

superiority of the BLUP method compared to BLUE,

because of the greater accuracy of the predicted

values compared to the phenotypic values, the

difference between the different selection methods

is not always emphasized (Kumar et al. 2008),

especially when the data are balanced and from only

one generation (Knott et al. 1995).

Acknowledgements We thank the Foundation for Research

Support of Minas Gerais State (Fapemig), the Brazilian Federal

Agency for Support and Evaluation of Graduate Education

(Capes) and the National Council for Scientific and

Technological Development (CNPq) for financial support.

Appendix

ASReml code for the additive-dominant model

!Workspace 200

BLUP analysis, population structured in half- and

full-sib families, two cycles

38 Euphytica (2010) 174:31–39

123

Author's personal copy

a 1535 !p # additive value

d 1535 # dominance value

pop 2 # population

env 4 # environment

ev # expansion volume

y # grain yield

z ! = ev ! ? y # to permit estimation of gen./

non gen. corr./covariance

ped.txt # pedigree file

Amatrix.grm # additive relationship matrix

Dmatrix.grm # dominance relationship matrix

data.asd # data file

!ddf # correction of df by the Kenward-Roger

method

!continue # to continue REML process

!maxit 30 # maximum number of interactions

ev or y or z * mu pop env pop.env !r a d

predict a !vpv # necessary to compute generalized

measure of heritability

The additive and dominance relationship matrices

files were generated by a program developed in

REALbasic 5.5. To read the prediction error variance

matrix in the file .pvs another REALbasic 5.5 program

was developed.

References

Bauer AM, Leon J (2008) Multiple-trait breeding values for

parental selection in self-pollinating crops. Theor Appl

Genet 116:235–242

Bauer AM, Reetz TC, Leon J (2006) Estimation of breeding

values of inbred lines using best linear unbiased predic-

tion (BLUP) and genetic similarities. Crop Sci 46:2685–

2691

Bernardo R (1996) Best linear unbiased prediction maize sin-

gle-cross performance. Crop Sci 36:50–56

Cantet RJC, Birchmeier AN, Santos-Cristal MG, de Avila VS

(2000) Comparison of restricted maximum likelihood and

Method R for estimating heritability and predicting

breeding value under selection. J Anim Sci 78:2554–2560

Crossa J, Burgueno J, Cornelius PL, McLaren G, Trethowan R,

Krishnamachari A (2006) Modeling genotype x environ-

ment interaction using additive genetic covariances of

relatives for predicting breeding values of wheat geno-

types. Crop Sci 46:1722–1733

Cullis BR, Smith AB, Coombes NE (2006) On the design of

early generation variety trials with correlated data. J Agric

Biol Environ Stat 11:381–393

Eberhart SA (1970) Factors effecting efficiencies of breeding

methods. Afr Soils 15:669–680

Flachenecker C, Frisch M, Falke KC, Melchinger AE (2006a)

Modified full-sib selection and best linear unbiased

prediction of progeny performance in a European F2

maize population. Plant Breed 125:248–253

Flachenecker C, Frisch M, Falke KC, Melchinger AE (2006b)

Trends in population parameters and best linear unbiased

prediction of progeny performance in a European F2

maize population under modified recurrent full-sib selec-

tion. Theor Appl Genet 112:483–491

Gilmour AR, Gogel BJ, Cullis BR, Thompson R (2006)

ASReml user guide release 2.0. VSN International Ltd,

Hemel Hempstead

Henderson CR (1974) General flexibility of linear model

techniques for sire evaluation. J Dairy Sci 57:963–972

Knott SA, Sibly RM, Smith RH, Moller H (1995) Maximum

likelihood estimation of genetic parameters in life-history

studies using the ‘‘animal model’’. Funct Ecol 9:122–126

Kruuk LEB (2004) Estimating genetic parameters in natural

populations using the ‘‘animal model’’. Philos Trans R

Soc Lond B Biol Sci 359:873–890

Kumar A, Gandh RS, Singh A, Haile A (2008) Comparison of

animal model with other conventional methods of sire

evaluation for milk production in Karan Fries cattle.

Indian J Anim Sci 78:1393–1396

Leclerc H, Wensch-Dorendorf M, Wensch J, Ducrocq V,

Swalve HH (2008) A general method to validate breeding

value prediction software. J Dairy Sci 91:3179–3183

Littell RC, Milliken GA, Stroup WW, Wolfinger RD, Scha-

benberger O (2006) SAS for mixed models, 2nd edn. SAS

Institute Inc., Cary

Matta FP, Viana JMS (2003) Eficiencias relativas dos processos de

selecao entre e dentro de famılias de meiosirmaos em popu-

lacao de milho-pipoca. Ciencia e Agrotecnologia 27:548–556

Mrode RA (2005) Linear models for the prediction of animal

breeding values, 2nd edn. CABI Publishing, Oxfordshire

Nunes JAR, Ramalho MAP, Ferreira DF (2008) Inclusion of

genetic relationship information in the pedigree selection

method using mixed models. Genet Mol Biol 31:73–78

Patterson HD, Thompson R (1971) Recovery of inter-block

information when block sizes are unequal. Biometrika

58:545–554

Piepho HP, Mohring J, Melchinger AE, Buchse A (2008)

BLUP for phenotypic selection in plant breeding and

variety testing. Euphytica 161:209–228

Reis AJD, Chaves LJ, Duarte JB, Brasil EM (2005) Prediction

of hybrid means from a partial circulant diallel table using

the ordinary least square and the mixed model methods.

Genet Mol Biol 28:314–320

Sebolai B, Pedersen JF, Marx DB, Boykin DL (2005) Effect of

control plot density, control plot arrangement, and

assumption of random or fixed effects on nonreplicated

experiments for germplasm screening using spatial mod-

els. Crop Sci 45:1978–1984

Stock KF, Hoeschele I, Distl O (2007) Estimation of genetic

parameters and prediction of breeding values for multi-

variate threshold and continuous data in a simulated horse

population using Gibbs sampling and residual maximum

likelihood. J Anim Breed Genet 124:308–319

Viana JMS (2005) Dominance, epistasis, heritabilities and

expected genetic gains. Genet Mol Biol 28:67–74

Viana JMS, Faria VR, Silva AC (2009) Bias in the prediction

of genetic gain due to mass and half-sib selection in

random mating populations. Genet Mol Biol 32:497–506

Euphytica (2010) 174:31–39 39

123

Author's personal copy