Potential benefit from using an identified major gene in BLUP evaluation with truncation and optimal selection

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Potential benefit from using an identified major gene in

BLUP evaluation with truncation and optimal selection

Beatriz Villanueva, Ricardo Pong-Wong, Brian Grundy, John A. Woolliams

To cite this version:

Original

article

Potential

benefit from

_using

an

identified

major

_gene

in

BLUP

evaluation with truncation

and

_optimal

selection

Beatriz Villanueva’

Ricardo

_Pong-Wong

Brian

_Grundy

_a

John A. Woolliams

a

Scottish

_{Agricultural College,}

West Mains

_{Road, Edinburgh,}

EH9

_{3JG, Scotland,}

UK

b

Roslin Institute

_(Edinburgh),

_{Roslin, Midlothian,}

EH25

_{9PS, Scotland,}

UK

(Received

9 June

1998;

accepted

28

_January

₁₉₉₉₎

Abstract - This

study investigates

the benefit of

including

information on an

identi-fied

_major

gene in the estimation of

_breeding

values in BLUP selection programmes.

Selection for a

_quantitative

trait is controlled

_{by polygenes}

and a

_major

locus with

known effect. The benefit of

_using

the gene information obtained in the short-term

was maintained in the

long-term by applying

a selection tool which makes use of

BLUP evaluation and

_optimisation

of

_genetic

contributions for

_{maximising genetic}

gain

while

_restricting

the rate of

inbreeding.

In the mixed inheritance model the

se-lection tool,

initially proposed

for an infinitesimal

model,

was able to restrict the rate

of

inbreeding

to the desired value and to

give higher

rates of _response than standard

truncation selection both when

_using

and

_ignoring

the information on the

_major

_gene.

The

_simple

use of BLUP

_(standard

truncation

_selection)

allowed

_long-term

benefits from

_using

the gene in situations where the favourable allele was recessive or additive

with

_large

effect.

_©

_{Inra/Elsevier,}

Paris

major gene / optimal selection _/ BLUP selection _/ restricted _inbreeding

Résumé - Bénéfice _possible de l’utilisation d’un _{gène majeur} identifié dans

une évaluation BLUP lors d’une sélection par troncature ou _optimisée. Cette

étude

_analyse

le bénéfice _pour la

_sélection,

d’inclure l’information relative à un

_gène

majeur identifié,

dans l’estimation des valeurs

_génétiques

par BLUP. La sélection porte sur un caractère

_quantitatif

contrôlé par des

polygènes

et un locus

_majeur

*

Correspondence

and _reprints: Genetics &

_{Reproduction Department,}

Animal

à effet connu. Le bénéfice à court terme de l’utilisation de l’information

_génique

est maintenu à

_long

terme

grâce

à un outil de sélection

_qui

utilise le BLUP et

_qui

optimise

les contributions

génétiques

en vue de l’accroissement du

_{progrès génétique}

à taux constant de

_{consanguinité.}

Dans le modèle d’hérédité mixte, l’outil de sélection initialement

_proposé

pour un modèle infinitésimal a été

capable

de restreindre le taux

de

_{consanguinité}

à la valeur désirée et de donner des taux de

réponse plus

élevés que la

sélection

_classique

par troncature, que l’on utilise ou _que l’on

_ignore

l’information sur

le

_{gène majeur.}

L’utilisation

_classique

du BLUP

_(sélection

standard par

troncature)

ne _permet des bénéfices à

_long

_{terme que} si l’allèle favorable est récessif ou additif

avec un effet _important.

@

Inra/Elsevier,

Paris

gène majeur

/

sélection _optimisée

_/

sélection BLUP

_/

taux de _{consanguinité} contraint

1. INTRODUCTION

Increasing

numbers of

_single

_genes with

_large

effect

_{controlling quantitative}

traits are

_being

identified in livestock

_species

_(e.g.

Booroola and

_Callipyge

_genes

in

_sheep,

’halothane’ gene in

pigs

and

_{’double-muscling’}

_{gene in}

_cattle)

and this is

_expected

to continue in the future.

_Genotyping

of animals for

_particular

_genes

is

_expensive

but _{it may} be cost effective if this information is used in selection

programmes to

_produce

additional and more

_targeted

_genetic

_response.

Studies

_evaluating

the use of a

_major

_{gene in} mixed inheritance models for

increasing genetic gain

in mass selection _programmes

_suggest

a conflict between

short- and

_{long-term gains}

_[5,

_{6, 11, 12,}

_15,

_18].

_Although

in these studies the

use of the available information on the

_major

_gene led to

_greater

total

_genetic

gain

during

the initial

_generations

of

_selection,

the accumulated _response was

lower when

_using

_genotype

information

_by

the time the favourable allele was

fixed in both schemes

_(the

scheme

_using

the _gene and the scheme

_ignoring

the

gene).

The detrimental

_long-term

effect was

_only

avoided when the favourable allele was recessive with a

large

effect

[12, 15].

The lower accumulated _response

when

_using

_genotype

information in mass selection was

mainly

due to a decrease

in the selection pressure

applied

to the

_{polygenic background}

_and,

to a lesser

extent,

to a

_higher

rate of

_inbreeding.

Many

current

_breeding

_programmes use advanced

_technologies

for

_estimating

polygenic

breeding

values of the candidates for selection. When an infinitesimal

model is

_assumed,

animals are often selected on their BLUP

(best

linear

unbiased

_prediction)

estimated

_breeding

values rather than

_simply

on their

phenotypic

values. Standard selection based _upon

_choosing

individuals with the

_highest

BLUP

_breeding

values leads to increased

_inbreeding

rates. This

can be exacerbated if information on the

_major

_gene is used in the estimation

of

_breeding

_values,

as families associated with the most favourable

_genotype

would contribute more to

_{subsequent generations}

_[15].

Recent

_developments

in selection

_algorithms

_using

BLUP

_breeding

values allow the

optimisation

of selection decisions for

_giving

maximum

_{genetic gain}

over several

_generations

of selection while

_restricting

the rate of

_inbreeding

to

specific

values

_{[10, 14].}

These

_procedures,

_initially

_proposed

for the infinitesimal

model,

are _very useful when

_comparing

the

_efficiency

of different schemes

(at

The

_objective

of this

_study

was to

_{investigate, using}

stochastic

simulation,

the value of

_including

_genotype

information for an identified

_major

_gene in

the estimation of

_breeding

values for

_increasing

short- and

_long-term

genetic

response in selection programmes

using

BLUP. Both standard truncation selection on BLUP

_breeding

values and

_optimal

selection for

_{maximising gain}

while

_restricting

_inbreeding

_(which

also uses

_BLUP)

were considered. The

efficiency

of

_optimal

selection for

_{maximising gain}

and for

_restricting

_inbreeding

in mixed inheritance models was also

_{investigated.}

2. METHODS

Monte Carlo simulations were used to compare schemes

using

or

_ignoring

information on the

_major

_gene when the estimated

breeding

values

(EBVs)

are

obtained from BLUP. Two selection

_procedures

were considered:

i)

standard

truncation selection with fixed number of

_parents

and

_family

_sizes;

and

_ii)

’op-timal selection’ in which the numbers of

parents

and their contributions are

optimised

each

_generation

to maximise

_genetic

_gain

while

_restricting

the rate

of

_inbreeding

_(10!.

This

_optimisation

differs from those described

_by

Dekkers and van Arendonk

[2]

and

_by

Manfredi et al.

_[13]

where the purpose of the

optimisation

was to achieve the

_right

_{emphasis given}

to the

major

gene relative to the

_polygenes

for

_{maximising gain}

without restrictions on

_inbreeding.

Comparisons

of schemes were carried out in terms of short- and

_long-term

accumulated

_genetic

progress and

inbreeding.

A minimum of 200

replicates

was run for each simulation.

2.1. Genetic model

The trait under selection was assumed to be

_genetically

controlled

by

an

infinite number of additive

_loci,

each with infinitesimal effect

_(polygenes)

_plus

a

single

biallelic locus

(alleles

A and

B)

with a

_major

effect

(major

gene).

The total

_genetic

value of the ith individual was _gi = _{iv + ui,} where _vi is

the

_genotypic

value due to the

_major

locus and ui is the

polygenic

effect. The

major

locus had an additive effect

_(a),

defined as half the difference between the

two

_homozygotes,

and a dominance effect

(d)

defined as the difference between

the

_heterozygote

and the _average of the two

_{homozygotes. Thus,}

the

_genotypic

value due to the

_major

locus was a, d and -a for individuals with

_genotype

AA,

AB and

_BB,

_respectively

_(3!.

The additive variance

_explained

_by

the

_major

gene in the base

_population

was

av =

2p(1- p)!2,

where p is the initial

frequency

of the favourable allele

_(A)

and a is the _average effect of the gene substitution

(3!.

2.2. Simulation of the

_population

The base

population

(t

=

0)

_was

composed

of N = 120

(60

males and 60

females)

unrelated individuals. Generation

_{1 (t = 1)}

was obtained from the

mating

of individuals selected at t = 0. The number of selection candidates

(N)

was

kept

constant across 20 discrete

_generations

of selection. The

poly-genic

effect for animals of the base

_population

was obtained from a normal

distribution with mean zero and variance

_{a U. 2}

The alleles at the

_major

locus

(i.e.

Hardy-Weinberg equilibrium

is

_assumed).

The

_phenotypic

value for an

in-dividual

_{i (y}

₂

₎

was obtained

by adding

to the total

_genetic

value

_(g

_i

₎

a

_normally

distributed environmental

_component

with mean zero and variance

0’ e 2

In

_{subsequent generations,}

the

polygenic

effect of the

_offspring

was

generated

as the average of the

polygenic

effects of their

_parents

_plus

a random Mendelian

deviation. The latter was

_sampled

from a normal distribution with mean zero

and variance

_{((J!/2)[1 -}

_(F.

+

_Fd)/2!,

where lfl!

and

_F

_d

are the

_inbreeding

coefficients of the sire and

_dam,

_{respectively.}

The

_genotype

for the

_major

locus

for each individual was obtained

_{by sampling,}

at

_random,

one allele from each

parent.

2.3. Estimation of

_breeding

values

In schemes

_using

information on the

_major

_gene

(genotype

_information)

it

was assumed that all individuals have known

_genotype

for the

major

_gene and

that its effect was known without error.

When the information on the

_major

locus was considered the selection

criterion was

where

_{BL UP}

_i

is the estimate of the

_{polygenic breeding}

value for individual

i and wi is the

breeding

value due to the

_major

locus effect. The estimate of the

_polygenic

value was obtained from standard BLUP

_using

the

_polygenic

variance

_(o,2)

and the total

phenotypic

values corrected for the

_major

gene effect

(y

2

=

y

2

-vi).

The

_breeding

value of the

_single

locus was

2(1-p)a, !(1-p)-p!a

and

-2pa

for individuals with

genotype

AA,

AB and

BB, respectively

!3!.

The

frequency

p and a were

_updated

each

_generation

to obtain the

_breeding

values. When the information on the

_major

locus was

_ignored

the selection criterion

was

where

_{BL UP}

_i

is the estimated

_breeding

value obtained from standard BLUP

using

the total

_genetic

additive variance

₍

₀

_&dquo;;

+

_{or 2)}

of the base

_population

and the

_phenotypic

values

_(y

₂

₎

uncorrected for the

_major

_gene effect.

Although

the main

_objective

of the

_study

was to

_investigate

the

im-pact

of

_using

_genotype

information in BLUP-based selection

methods,

some

schemes

_using

mass selection were also simulated for

_comparison.

When the

genotype

information was used in mass

selection,

the selection criterion was

EBVi

=

!(y2 -

v

J

h

2

]

₊

Wi

,

where h£

is the

polygenic heritability

in the base

population

(hu =

(J!/((J;

+

_ae))

_!15!.

When the information on the

_major

lo-cus was

_ignored,

selection was carried out on uncorrected

_phenotypic

values

(EBVi

=

y

i).

2.4. Selection

procedures

The benefit of

_including

the information on the

major

gene in the estimation

of

_breeding

values was evaluated

_using

either standard truncation selection or

optimal

selection

_[10].

The first case is static with fixed numbers of

_parents,

2.4.1. Truncation selection

With standard truncation

_selection,

a fixed number of individuals

(N

S

= 10

males and

_N

_d

= 20

females)

with the

highest

estimated

breeding

values were

selected to be

_parents

of the next

_{generation. Matings}

were hierarchical with each sire

_being

mated at random to two dams and each dam

_producing

three

offspring

of each sex.

2.4.2.

_Optimal

selection

Optimal

selection is a

_dynamic

selection

_procedure

in which the numbers

of individuals selected and their contributions are not fixed but

_they

are

opti-mised for

_{maximising genetic}

_progress while

_restricting

the rate of

_inbreeding

to a

_specific

value each

_generation.

The

procedure,

initially

proposed

for an

infinitesimal

_model,

uses BLUP

_breeding

values and the

_augmented

numerator

relationship

matrix

_[10]

to

_give

the

_optimal

selection decisions. A short

descrip-tion of the

_algorithm

used for

_finding

the

optimal

numbers of

parents

selected each

_generation

and their

_optimal

contributions is

_given

in the

_Appendix.

For a more detailed

explanation

of the method see

_Grundy

et al.

_!10!.

The EBVs used

in the

_optimisation

_algorithm

were those described in section 2.3

(i.e.

not

_only

the

_polygenic

effects but also the

_major

_gene were considered in the

optimisa-tion).

When

_optimal

mass selection was

simulated,

the

augmented

numerator

relationship

matrix was still used to restrict the rate of

_inbreeding.

The solutions obtained with this

algorithm

are

expressed

as

_mating

propor-tions

_(genetic

contributions to the next

_generation)

which sum to a half for

each sex. The

_optimal

number of

_offspring

for individual i is

_2Nc

_i

_(a

real

num-ber),

where ci is the

optimal

solution

(mating

proportion)

for individual i. The actual

_(integer)

number of

_offspring

for each

_parent

was obtained as described

in

_Grundy

et al.

_!10!.

Each

_parent

was

randomly

allocated to different mates

(among

the selected

_individuals)

to

_produce

its

_offspring.

2.5. Parameters studied

The

_polygenic

and the environmental variances were

<7! =

0.2 and

_af

₌

_0.8,

respectively, giving

a

_polygenic

heritability

of 0.2. When the effect of the

_major

gene was

_completely

additive

(d

=

0)

different values for a were considered and

results are

_presented

for a =

_0.5,

_a = 1.0 and _a = 2.0. The initial

frequency

of

the favourable allele was 0.15.

_Thus,

at t =

0,

the additive variance

explained

by

the

_major

locus and the total

_heritability

were

av =

_0.06,

0.26 and 1.02

and ht =

0.25,

0.36 and 0.60 for a =

_0.5,

1.0 and

_2.0,

respectively.

These

combinations of

_parameters

avoided the loss of the favourable allele in all

replicates,

both in methods

_using

and

_ignoring

genotype

information. Cases where the favourable allele was

_completely

recessive

(d

= _-a = -0.5 and

d = -a =

-2.0)

were also studied. With recessive alleles some

_replicates

lost

3. RESULTS

3.1. Truncation selection

Table I shows a

_comparison

of

_genetic

_progress obtained when

_ignoring

(IT)

and

_using

_(G

_T

₎

the information on the

_major

_{gene in} the selection criterion with truncation BLUP selection. The effect of the

_major

gene was

_completely

additive

_(i.e.

d =

0).

The scheme

_using

the individuals’

genotypes

yielded

a

greater

total

_{genetic gain}

than the scheme

_ignoring

the

genotype

in the initial

generations

of

_selection,

while the

_major

locus was still

_{segregating. However,}

at the time when the favourable allele is fixed in both

_IT

and

_G

_T

_,

the accumulated

genetic

response was lower with

G

T

when the

_major

locus has a moderate

effect

_(a

=

0.5).

Fixation of the favourable allele occurred after six

_generations

of selection in scheme

_G

_T

but after 18

_generations

with scheme

IT

(although

by

generation

8 the

_frequency

of the favourable allele was

_{already higher}

than

0.95).

At t = 18 the

_gain

obtained when

_using

the

genotype

information was

around 2

%

lower than the

_gain

obtained when

_ignoring

that information.

On the other

_hand,

when the

_major

_gene had a

_larger

effect

_(a

=

2.0),

the

advantage

of

_using

the individuals’

genotype

observed in the

_early

_generations

was maintained for several

_generations

after the favourable allele was fixed

in both schemes. Fixation of the favourable allele occurred after

_only

three

generations

of selection and at t = 4 the

_advantage

of

G

T

_over

_IT

_was

around 1

%.

The lower

_gain

in the medium- and

_long-term

obtained with

G

T

and a = 0.5

was due to the faster increase in the

_frequency

of the favourable allele which led

to a lower

_{polygenic gain}

in the

_{early generations,}

when the

_major

gene was still

was obtained when the favourable allele was fixed. With a =

0.5,

the initial loss

in

_{polygenic gain}

with

_G

_T

was not

_compensated

for in later

_{generations by}

the

higher

accuracy in

estimating

the EBVs with this

method,

and the result was

that the use of the _gene led to a decreased

_gain.

With a = 2.0 there was also a

reduction in the rate of

_polygenic

_gain

in the

_early

_generations

before fixation but the increased accuracy when

using

the

genotype

information

_compensated

for the initial loss in

_polygenic

_gain.

The extra accumulated response when

using

genotype

information on a

major

gene of

large

effect

(a

=

2.0)

disappeared

several

generations

after the

favourable allele was fixed in both selection schemes

(G

T

and

IT).

This

long-term detrimental

effect, however,

was not a _consequence of

_using

the

_genotype,

but rather was due to differences in the rate of

_inbreeding

between the schemes

(table IQ.

After

_fixation,

the

_heritability

used in

_IT

becomes biased

upward

and this affects the rate of

inbreeding and,

thereby,

the

_long-term

_response

[9,

17!.

With a _gene of

_large

effect the bias in the

heritability

used was

_large

(0.6

versus

0.2)

and this led to a substantial reduction in the rate of

_inbreeding

(6.

F

;:::j

3

%

with

_IT

versus 6.F ;:::j 5

%

with

G

T

).

_Hence,

the

long-term

effect of

using

the information on the

_major

_gene should be evaluated at the

generation

where the favourable allele is fixed in both selection schemes

_(G

_T

and

_IT).

In a

complete

infinitesimal model the correct

heritability

to be used in the

BLUP evaluation is the one from the base

_population.

_However,

when a

_major

gene is also

segregating

the use of the initial total

heritability

in

IT

is debatable as the

_changes

in the _gene

frequency

are not accounted for with BLUP. In order to assess the effect of the

_heritability

in the selection scheme

ignoring

the _gene, a further

study

was carried out

_using

different choices of

heritability

in

_IT.

using

the new _gene

frequency

(i.e.

ht*

_

(a!

+

afl) /(a£ +0!+0!),

where

_Q

_v

is

updated

each

_{generation using}

the new _p but

a!

remains

_constant).

The use of

the

_polygenic

_{heritability yielded}

the lowest

_{genetic gain.}

When

_using

the total

heritability,

both hf

and

_h!.

led _{to very} similar

_patterns

in the

_polygenic

_gain

and in the

_frequency

of the favourable allele.

3.2.

_Optimal

selection

Results from the

_previous

section show that with BLUP selection the

advantage

of

_using

information on a

_major

_gene with additive effect can be

maintained after the favourable allele is fixed. This

_advantage

disappeared,

however,

in the

_long-term

due to a

higher

accumulation of

_inbreeding.

Schemes

using

or

_ignoring

the

_genotype

information can be

_objectively

_compared

at

the same

inbreeding

level with

_optimal

selection

(which

also uses BLUP

estimates of

_breeding

_values)

since maximum

_{possible gains}

can be obtained under constrained OF. Table IV shows results from

_optimal

selection with OF restricted to 0.03. This value was

_{approximately}

that obtained when

_ignoring

the

_major

gene in truncation selection

(IT)

and was lower than that obtained

with

_G

_T

_(see

table

_1!.

As

_intended,

with

_{optimal selection,}

the increase in

inbreeding

was maintained at the desired constant rate

_{(6.F ;:::j}

3

_%)

over

generations

and

_consequently

the accumulated

_inbreeding

was _very similar for

both the scheme

_using

the

genotype

information

_(Go)

and the scheme

_ignoring

the

_major

_gene

_(I

_o

_).

The

_optimum

number of individuals selected

_(which

was

practically

constant across

_generations)

was the same for both sexes

_(i.e.

the

optimum mating

ratio was

one)

and

_higher

for

Ct!

(N

5

.:;

_N

_d

_*

14)

than for

As in the case of truncation

selection,

the scheme

using

the

_genotype

information _gave more _response before the favourable allele was fixed in both

schemes.

_However,

in contrast with truncation

_selection,

the

_advantage

of the scheme

_using

the

_genotype

information was not detectable at the time of fixation when the _gene had a

_large

effect

(a

=

2.0).

In

comparison

with

truncation selection the

_{optimisation procedure}

led to a faster increase in

the

_frequency

of the favourable allele and therefore to a

higher

difference in

polygenic gain

between the schemes

_using

and

_ignoring

_genotype

information when the _gene was still

_segregating

(see

also table

II).

After

fixation,

the rate

of

_polygenic

_gain

was

_higher

in

Go

than in

_I

_o

due to a

higher

_accuracy of

evaluation. The difference in the

polygenic

rates in both schemes increased

over time and at t = 20 the total accumulated

_{genetic gain}

was around 3

%

higher

in

_Go

than in

_I

_o

_.

With an additive _gene of moderate effect

(a

=

0.5),

optimal

selection was not able to

_maintain,

at the time of

_fixation,

the

short-term benefit from

_using

the _gene

_(results

not

_shown).

_Thus,

not

_only

with truncation selection but also with

_{optimal selection,}

the effect of the additive

gene needs to be

large

in order to obtain more

_gain

with G than with I at fixation.

Optimal

selection

_always

_yielded

more

_gain

than truncation selection at a

fixed rate of

_inbreeding.

A

_comparison

of

_I

_o

with

_IT

_(see

also

_{table !}

shows

that,

for

_instance,

at t = 20 the

_gain

was 4

%

_higher

with

optimal

selection than with truncation selection. The benefit from

_optimal

selection was

expected

as

the numbers of individuals selected and their contributions are

_optimised

for

giving

maximum

_gains.

When

_using

_genotype

information the

_advantage

of

gain

was even

_greater

(around

9

%

by

generation

20)

and the

_inbreeding

was

substantially

lower. The

_higher

_gain

with

_optimal

selection was due to the

optimisation

of the individuals’ contributions

_given

the restriction

_applied

on

the rate of

_inbreeding.

The restriction on AF avoided some of the loss in

polygenic

gain

observed with standard truncation.

3.3.

_Efficiency

of

_optimal

selection in a mixed inheritance model Results from table IV show that the

optimal

selection

procedure

was able

to constrain the rate of

_inbreeding

to the desired value at _any

_generation

of selection.

However,

the

parameters

considered in table IV

_(major

_gene effect and restriction on

AF)

led to fixation of the favourable allele after _very few

generations

of selection. The

_frequency

of the favourable allele was 0.94 in

_I

_o

and 1.00 in

Go

at

_{generation 2,}

the first

_generation

with non-zero

_inbreeding

coefficient. After fixation the

_system

works as an infinitesimal model and

previous

studies have also shown the

_efficiency

of the method for

_restricting

AF

_[10].

In order to

_investigate

whether the

_procedure

is able to restrict the rate of

_inbreeding

to the desired value while the

_major

_gene is still

_segregating,

a

_major

_gene with smaller effect

_(a

=

0.5)

and _{a more severe} restriction _on

OF (OF

= 0.5

%)

_was considered. In

_theory,

_{more severe restrictions on} OF

would lead to an increase in the numbers of individuals to be selected and this

together

with the smaller effect of the

_major

gene would retard the fixation of

the favourable allele. Results for a = 0.5 and OF = 0.5

%

are shown in table V. The

_optimal

selection

_procedure

was able to maintain the rate of

_inbreeding

to the desired value before fixation both in the scheme

_using

the

_genotype

information and in the scheme

ignoring

the

genotype

information.

Figure

1 shows a

_comparison

of

_genetic

responses obtained with truncation

and

_optimal

selection with a = 1.0. With _truncation selection the _rate of

inbreeding

when

_using

or

_ignoring

the

genotype

information was 5 and 4

%,

respectively.

With

_optimal

selection the rate of

_inbreeding

was restricted to the lowest value

₍₄

_%).

In the short-term there were benefits from

_using

the

major

gene information

(at

t = 2 the

_gain

_was around 30

%

higher

when

_using

the _gene than when

_ignoring

the

_gene)

and from

_optimal

selection

_(at

t = 2

the

_gain

was around 25

%

higher

with

optimal

selection than with truncation

selection).

The combination of the use of the _gene and the

_optimisation

led to

an increase in

_gain

of 64

%.

In the

_long-term

there was not much difference

between

_using

or

_ignoring

the

_genotype

information.

_However,

there was still a benefit from

_{using optimal}

selection

(at

t = 20 the

gain

was around 10

%

higher

with

_optimal

selection than with truncation

_selection).

3.4.

_Comparison

of BLUP with mass selection

The

_advantage

of the method

_using

the

_genotype

information in mass selection

programmes has been

previously

described for the case when the favourable

allele is recessive with

_large

effect

_(e.g.

_[15]).

Figure

2 shows a

_comparison

of

BLUP and mass truncation selection in this situation. Schemes

_ignoring

the

genotype

information led to the loss of the favourable allele in some

_replicates

analysis.

With a = -d =

0.5,

the number of

replicates

excluded were 58

(out

of

₅₀₀₎

and 40

_(out

of

₂₀₀₎

in mass and BLUP

selection,

respectively.

There were

proportionately

more losses with BLUP than with mass selection

_(11.6

%

cf. 20.0

_%;

P <

_0.01).

The

_{corresponding figures}

for a = -d = 2.0 _were 13

(out

Contrary

to the case of

additivity

of the

_{major locus,}

the

_advantage

of the

method

_using

the

_genotype

information was maintained with BLUP after the

favourable allele was fixed when the gene had a moderate effect

_(a

=

0.5).

With mass selection and a = 0.5 the benefit from

_using

the

_genotype

_was

lost at fixation. With a _gene of

_larger

effect

(a

=

2.0)

_greater

extra

gain

was

obtained in both mass and BLUP selection and the benefit of

_using

the gene

information was retained at fixation with both selection methods. In both mass

and BLUP selection there was a clear

_advantage

of

_using

the

_major

_gene after

fixation of the favourable allele

_although

the

_advantage

was

higher

with BLUP.

The maximum extra total

_gains

from

_using

the gene were at t = 4 and t = 2

for a = 0.5 and a =

2.0,

respectively.

At the time of this

maximum,

although

BLUP

_always

produces

higher

gains

than mass

selection,

the extra benefit from

_using

the

_genotype

information was

_higher

with mass selection due to a

higher

difference in p between the methods

using

and

_ignoring

the

_genotype

information.

Figure 3

shows

_equivalent

results for the case of

_optimal

selection when

restricting

the rate of

_inbreeding

to 1

%

in both mass and BLUP selection.

The trends were similar to the case of truncation selection

(figure

2)

_although

the absolute benefit from

_using

the

major

gene information was

_higher

before

fixation and lower after fixation when

_optimal

selection was

applied.

4. DISCUSSION

This

_study

has shown that the

apparent

conflict between short- and

long-term

_{gains reported}

when the

_major

_gene information is

_present

in the

_genetic

evaluation can be made

_negligible

when

_using

a selection tool

involving

BLUP

evaluation and

_optimisation

of selection decisions to maximise response while

controlling

the rate of

_inbreeding.

Whereas with truncation mass selection

it had been

_reported

_[5,

_6,

_12,

_15]

that selection

_strategies

which

_explicitly

use

(rather

than

ignore)

the

_major

_gene information to enhance the short-term

_{gain appeared}

to suffer

_long-term

loss of response, the use of the _gene

information with the selection tool allowed short-term benefits to be obtained and retained in the

_long-term.

The two

_components

of this tool

_(BLUP

and

optimising

contributions)

both act to counteract the

_{conflict, although perhaps}

the

_{major impact}

arises from the

_optimisation

of the

_genetic

contributions of the ancestors. It is notable that the selection tool

_ignoring

the

_genotype

does

as well as

_using

the

_genotype

without the selection tool in the short-term and

better in the

_long-term

_(figure

_1).

When

_comparing

methods which use

_genotype

information

_(G)

with meth-ods that

_ignore

that information

_(I)

it is useful to divide the selection process into three

_stages:

₁₎

where the _{gene is}

_segregating

in both G and

_I;

₂₎

where the _gene has been fixed in G but not in

_I;

and

₃₎

where the gene is fixed in

both. In the first

_stage

G

_{gives higher}

total

_{gain owing}

to a

_greater

_accuracy

and a

_greater

increase in the

_frequency

of the favourable allele.

_However,

at

this

_stage

G

_gives

a lower rate of

_polygenic

_gain

due to the differential pressure

is still

_{giving gain}

due to the

_major

gene. In the third

stage

the

_comparative

gain

will

_depend

on the kind of evaluation

(e.g.

what

_heritability

is

used)

and

this will also affect the rate of

_inbreeding

observed in the two schemes. The result of

_using

BLUP was that a net benefit at the time of fixation in the I scheme was obtained from

_using

information on the

_major

_gene

when beneficial alleles were recessive or additive with

large effect,

but not when additive alleles had small effect. This

_represents

an

_advantage

over mass

selection where

_only

recessive

_major

_genes of

_large

effect retained the benefit of

_using

the _{gene in} the

_long-term

_(e.g.

_!15!).

The main reason

_why

with BLUP evaluation the

long-term

loss observed when

_using

_genotype

information is avoided

_(or

_{substantially}

_reduced)

com-pared

to

_ignoring

the

_genotype

is an extra bias in the EBVs

occurring

when the

_major

_genotype

is

_ignored.

The additional bias comes from the fact that

with

_BLUP,

the EBV of an individual is

_regressed

toward its

_parents

perfor-mance. This

_regression

is

_appropriate

for a

complete

infinitesimal

model,

but

it is not

_appropriate

when a

_major

_{gene is}

_segregating.

Although

the

_genetic

effect due to the

_major

_{gene is} the same for individuals of the same

_genotype

group, BLUP would

adjust

their EBVs

according

to their

_parental

mean and

this leads to biased estimates. Table VI

_gives

an

_example

of the bias induced

when

_ignoring

information on the

_major

_gene with mass and BLUP selection

(when

using

the gene there is no

bias).

The bias

(EBV g)

was calculated in the

offspring

of a

_randomly

selected base

_population

_(so

here there is no

_problem

arising

either from the use of an incorrect

heritability

or from the

linkage

dis-equilibrium

between the

_major

locus and the

_polygenes).

With mass selection

the bias is the same for

_offspring

with the same

_genotype

independent

of the

genotypes

of the

_parents.

Thus,

within

_genotypes,

the

_ranking

of the candidates

is not

_changed

relative to the

_ranking

obtained when

_using

the information on

the

_major

_gene.

_However,

with BLUP the bias also differs among candidates

with the same

_genotype

(i.e.

it

_depends

on the

_genotype

of the

parents).

This causes additional

_ranking

errors within

_genotypes

which affects the

_polygenic

gain

achieved.

There are other factors which can also contribute to

_explain

the

_long-term

advantage

of

using

the

genotype

information with BLUP evaluation.

First,

the

greater

accuracy of the

polygenic

EBVs when

using

BLUP leads to a reduction

in the

_{weight given}

to the

_major

_gene relative to the

_{polygenes, resulting}

in a

greater

intensity

of selection

applied

to the

_polygenes

and thus

_reducing

the

potential long-term

loss.

_Second,

the

_{linkage disequilibrium}

between the

_major

locus and the

_polygenic

effects induced

_by

selection is

_expected

to be better accounted for when the

genotype

information is used in the selection criteria.

The BLUP evaluation used to estimate the

_polygenic

EBV was carried out

on the

_phenotypic

records corrected for the

_major

gene effect.

Therefore,

it

would be

expected

that any bias in the EBVs as a _consequence of the

_linkage

disequilibrium

would be

_{substantially}

reduced.

_Third,

the use of the

_genotype

information to correct the

_phenotypic

records eliminates the

_problem

of bias in

the

_heritability

used in the BLUP evaluation. In a

_complete

infinitesimal model the correct

_heritability

to be used is the

_heritability

in the base

population.

However,

when a

_major

_{gene is}

_segregating,

the standard BLUP evaluation

does not account for the

_change

_{in gene}

_frequency

due to selection. There is

the

_phenotype

includes

major

gene effects. The

problem

is,

however,

avoided

when the

_genotypic

information is used to correct the

_phenotype

before the BLUP evaluation.

BLUP selection had a

_greater

chance of

losing

the favourable recessive allele

than mass selection. This

negative

effect of

using

BLUP in the survival of rare favourable alleles has been

reported by

Caballero and

Santiago

[1]

who

suggested

that it is due to the

_greater

reduction in effective

_population

size

with BLUP. In

_{addition, procedures}

which

_ignore

the

_major

_gene information

have a

_greater

chance of

_losing

the favourable allele and this will be

potentiated

with small gene effect and low initial

frequency

of the favourable allele. In

these circumstances the benefit of

_using

information on the

_major

_{gene in} the

selection criterion could be

_greatly

enhanced.

The most

_important

reason for

_higher

rates of

_inbreeding

observed when

using

genotype

information with BLUP in truncation schemes is the use of a

lower

_heritability

_(polygenic)

relative to that used when

ignoring

the

_genotype

information

_(total).

Another reason is that the number of favourable alleles the

_parent

carries is a substantial selective

_advantage

for

obtaining

selected

offspring

and so between

_family

selection is

_increased,

and

consequently

so is

inbreeding.

The biased

_heritability

used when

_ignoring

the

_genotype

information and the

consequent

decrease in the rate of

inbreeding

[9, 17]

complicates interpretation

in the _very

_long-term.

An alternative selection

procedure

would be to

_change

the

_heritability

used when

ignoring

the

_major

_gene to its

_polygenic

value after fixation. The benefit of the method

_using

the gene would then be retained in

the

_long-term.

Selection in two

_stages

_(with

an initial within

_family

selection on

the

_major

_gene and

subsequent

selection on the

_polygene

and the

_major

_gene)

could also increase the benefits from

_using

_genotype

information and BLUP

Comparisons

of rate of

_gains

in truncation selection schemes were made

in the context of static schemes and hence with different rates of

_inbreeding.

It is natural to _compare the schemes at the same rates of

_inbreeding,

and when selection was carried out

_using

the

_dynamic

selection tool of

_Grundy

et al.

_[10]

the short-term benefit of

_using

the

_major

_genotype

was still retained.

Moreover,

the

_optimal

selection

_{procedure eliminated,}

or at least

_{substantially}

reduced,

the

_long-term

loss often observed in truncation selection schemes when

_using

the

_genotype

information.

_Dynamic

selection schemes result in

more

_gain

than truncation schemes either with or without the use of

_genotype

information.

_{Therefore, dynamic}

schemes

_using

BLUP have even less conflict

between the

_long-

and the short-term

_gains

than BLUP truncation schemes when

_compared

at the same rate of

_inbreeding.

The use of the selection tool

allows both the selection and the

_{mating proportions}

to be made in relation

to the desired

_expected

_long-term

_genetic

contribution conditional on all the current

_information,

_including

the

_major

_genotype

_[10].

It

_might

be

_expected

that similar results would be obtained

_using

the

_procedure

of Meuwissen

_[14]

although

this has

_yet

to be confirmed.

The

_optimality

of the tool of

_Grundy

et al.

_[10]

for

_maximising

_progress

with a constraint on

_inbreeding

has been shown for the infinitesimal model but it should also prove near

_optimal

in the mixed inheritance model. The selection decisions and

_{mating proportions}

conditional upon the estimated

breeding

values are

independent

of the inheritance model. Since in this

_study

the effects of the

_major

_genotype

are assumed to be

known,

subtraction from the

_phenotype

and

_prediction

of

_breeding

values

_using

the base

_polygenic

heritability

derives true BLUP values.

_However,

the _very small

_advantage

from

_ignoring

the _gene at fixation

_(see

table

_IV)

_suggests

that there remains

an additional

_{multiple-generational}

_{problem arising}

from the

_partition

of the

population

caused

_by

the

_major

_gene. This

_problem

has been addressed

_by

Dekkers and Van Arendonk

_[2]

and

_by

Manfredi et al.

_[13]

who describe

procedures

for

_optimising

the

_weight

_given

to the

_major

_gene to maximise

_gain

after a

_given

number of

_generations.

Future

_development

to combine elements

described in these methods with the

_operational

tool of

_Grundy

et al.

_[10]

_may result in maximum

_gains

in both the short- and the

_long-term.

The

_methodology

has

_only

been

_applied

for the case with identified _genes of

known effect but it

_might

be

_anticipated

that it would have some benefits to

marker-assisted selection

_(MAS).

_However,

in MAS neither the

_frequency

of the

gene of

large

effect,

its

_magnitude

or its recombination events with the marker would be known with

_certainty

_{at any}

_stage

and so the

_procedure

is

_unlikely

to be

_{optimal. Nevertheless,}

these

_problems

are inherent in the methods of Fernando and Grossman

_[4]

_(used

for instance

_by

Ruane and Colleau

_(16])

and it would be

_anticipated

that the selection tool of

_Grundy

et al.

_[10]

would be

_equally

_applicable

to

_breeding

values estimated

_using

markers and these

techniques.

Since the work of Gibson

_[6]

there has been concerns over the conflict

between

_long-

and short-term benefits of

_using

known _{genes in} selection schemes. This

_study

has shown that when all the information is used with BLUP

_evaluations,

in static and

_dynamic

schemes with constraints on rates of

encouraging

framework _upon which to

_develop

further enhancements such as

those considered

by

Dekkers and Van Arendonk

_!2!.

ACKNOWLEDGEMENTS

This work was funded

_by

the

Biotechnology

and

Biological

Sciences Research

Council

_(BBSRC)

and

by

the

European

Union. SAC also receives financial support

from the Scottish Office

Agriculture

and Fisheries Department. Work in Roslin

Institute receives _support from the

Ministry

of

_Agriculture,

Fisheries and Food

_(UK).

We thank Dr G. Simm and Dr L.

_Gomez-Raya

for useful comments.

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[1]

Caballero

_{A., Santiago E.,}

Survival rates of

_major

_genes in selection

pro-grammes, in:

Proceedings

of the 6th World

Congress

on Genetics

Applied

to Livestock

Production,

11-16

_{January, Armidale,}

vol. 26,

University

of New

_{England, Armidale,}

Australia, 1998,

pp. 5-12.

[2]

Dekkers J.C.M., van Arendonk

J.A.M., Optimizing

selection for quantitative

traits with information on an identified locus in outbred

populations,

Genet. Res., Camb. 71

₍₁₉₉₈₎

257-275.

[3]

Falconer

_{D.S., Mackay T.F.C.,}

Introduction to

_{Quantitative Genetics,}

4th ed.,

Longman,

1996.

[4]

Fernando R.L, Grossman

_M.,

Marker assisted selection

_using

best linear

un-biased

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Genet. Sel. Evol. 21

₍₁₉₈₉₎

467-477.

[5]

Fournet

_{F., Elsen J.M., Barbieri M.E., Manfredi}

E., Effect of

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gene information in mass selection: a stochastic simulation in a small

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₍₁₉₉₇₎

35-56.

[6]

Gibson

_J.P.,

Short term

_gain

at the _expense of

_long

term response with

selection on identified

loci,

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Proceedings

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University of Guelph,

Guelph, Ontario, Canada, 1994,

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Gomez-Raya

L., Klemetsdal

G., Two-stage

selection _strategies

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marker-QTL

information and individual

_performance,

J. Anim. Sci.

_{(1999) (in press).}

[8]

Gomez-Raya

L., Klemetsdal

_G.,

Hoeschele I.,

Two-stage

selection

_strategies

utilizing

marker-QTL

information and individual

_performance,

in: 46th Annual

Meeting

of the

_{EAAP, Prague,}

4-7

_{September, 1995,}

_p. 44.

[9]

Grundy B.,

Caballero

_{A., Santiago E.,}

Hill

_W.G.,

A note on

_using

biased

parameter values and _{non-random mating} to reduce rates of

_inbreeding

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(1994)

465-468.

[10]

Grundy B., Villanueva B., Woolliams J.A., Dynamic

selection

_procedures

for constrained

inbreeding

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pedigree development,

Genet. Res.,

Camb. 72

₍₁₉₉₈₎

159-168.

!11!

Hospital F., Moreau L., Lacoudre F., Charcosset A.,

Gallais

A.,

More on the

efficiency

of marker-assisted

selection,

Theor.

_Appl.

Genet. 95

₍₁₉₉₇₎

1181-1189.

[12]

Larzul

C., Manfredi E., Elsen

J.M., Potential

gain

from

_{including major}

_gene information in

_breeding

value estimation, Genet. Sel. Evol. 29

₍₁₉₉₇₎

161-184.

[13]

Manfredi E., Barbieri

M.,

Fournet F., Elsen

J.M.,

A

_dynamic

deterministic model to evaluate

_{breeding strategies}

under mixed

_inheritance,

Genet. Sel. Evol. 30

[14]

Meuwissen

_{T.H.E., Maximizing}

the _response of selection with a

predefined

rate of

inbreeding,

J. Anim. Sci. 75

₍₁₉₉₇₎

934-940.

[15]

Pong-Wong R.,

Woolliams

_{J.A., Response}

to mass selection when an

identi-fied

_major

gene is

segregating,

Genet. Sel. Evol. 30

₍₁₉₉₈₎

313-337.

[16]

Ruane _J., Colleau J.J., Marker assisted selection for

_{genetic improvement}

of

animal

_populations

when a

single QTL

is

marked,

Genet.

Res.,

Camb. 66

(1995)

71-83.

[17]

Villanueva

_B.,

Woolliams

_J.A.,

Simm

_{G., Strategies}

for

_controlling

rates of

inbreeding

in MOET nucleus schemes for beef

cattle,

Genet. Sel. Evol. 26

₍₁₉₉₄₎

517-535.

[18]

Woolliams

_{J.A., Pong-Wong R.,}

Short- versus

long-term

_responses in

breed-ing schemes,

in: 46th Annual

_Meeting

of the

EAAP, Prague,

4-7

_September,

_1995, pp. 35.

[19]

Wray N.R., Thompson R.,

Prediction of rates of

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in selected

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₍₁₉₉₀₎

41-54.

APPENDIX:

_Optimal

solutions for

maximising genetic gain

while

restricting

the rate of

_inbreeding

to a

_specific

value

The

_optimal

solutions are found

_by

_maximising

the function

where ct is the vector of

mating proportions

of the N selection candidates at

generation

t

_(i.e.

_genetic

contributions of the selection candidates to the next

generation),

EBV is the vector of estimated

breeding

values obtained from

BLUP,

A* is the modified numerator

_relationship

matrix

_{(augmented A)}

of candidates

_!10!,

Q

is a known incidence matrix N x 2 with ones for males and

zeros for females in the first column and ones for females and zeros for males

in the second

column,

C is the constraint on the rate of

_inbreeding,

h is a

vector of halves of order 2 and

_A

_o

and 71

_(a

vector of order

₂₎

are

_Lagrangian

multipliers.

The

_augmented

A matrix

_[10]

at

_generation

t is obtained as

where D is a

_diagonal

matrix with elements

equal

to

_1/2

and

_Z

_t

_{_}

₁

is a N x N matrix

_relating

individuals of

_generation

t -

1 to

_generation

t - 2 and whose elements are either 0 or

1/2.

Element

(p, q)

of

Z

t

is

1/2

if the

individual

q of

generation

t is a

_parent

of individual _p in

_generation

t + 1

_!19!.

For t =

_0,

A*

= I. The constraint used to obtain a constant rate of

_inbreeding

over

generations

was

C

t

=

[

6

.F(1 - 3 6.F + 12

6

.F

2

)]t,

where OF is the desired rate

of

_inbreeding

_[10].

Maximisation of

_H

_t

is

_equivalent

to

_{maximising genetic gain}

at

_generation

t + 1

_{(ct EVB}

_t

₎

under a constraint on the rate of

_inbreeding

_{(ct At c,}

=

C

t

)

and on

_{mating proportions}

(ct Q

=

_h;

i.e. the _sum of contributions for each

sex adds up to

1/2).

Expressions

for

solving explicitly equation

(1)

for ct are

given by

Meuwissen

_!14!.

With this

procedure

solutions for some animals can

be

_negative

_(c

_i

<

_0,

for some

i).

As in Meuwissen

!14!,

animals with

_negative

contributions are eliminated from the

_optimisation

which is

_repeated

until all ci are

_{non-negative.}

A contribution ci = 0 indicates that individual i is not