Selection of grandparental combinations as a procedure designed to make use of dominance genetic effects

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Selection of grandparental combinations as a procedure

designed to make use of dominance genetic effects

Miguel A. Toro

To cite this version:

Original

article

Selection of

_{grandparental}

combinations

as a

procedure

designed

to

make

use

of dominance

_genetic

effects

Miguel

A. Toro

CIT-INIA,

Area de

_Mejora

Genética

_Animal,

Carretera La Coruña Km.7,

28040

_{Madrid, Spain}

(Received

2 March

_{1998; accepted}

27

_May

₁₉₉₈₎

Abstract - A

_{general procedure}

called selection of

_{grandparental}

combinations

(SGPC)

is

_presented,

which allows one to use dominance

_genetic

effects. The method assumes that there are two _types of

_matings:

either to breed the

_population

or to

obtain commercial animals. The idea is to select

_{grandparental}

combinations such that the overall

_genetic

merit of future

_{grandoffspring}

which constitute the commercial animals is maximized. Two small _computer simulated

_examples

are

_{analysed assuming}

either a infinitesimal

_genetic

model or that

QTL controlling

the trait are known.

©

Inra/Elsevier,

Paris

selection of _{grandparental} combinations

_/

dominance variance

_/

mating

strate-gies

Résumé - Sélection de combinaisons de _{grands-parents} comme une _procédure

pour utiliser les effets de dominance génétique. On

présente

une

_procédure

générale appelée

sélection de combinaisons de

_{grands-parents}

_(SGPC),

_qui

_permet

l’utilisation des effets de dominance

_génétique.

La méthode suppose

qu’il

y a deux

types

d’accouplements,

l’un pour propager la

population,

l’autre pour l’obtention

des animaux commerciaux.

_L’objectif

est de sélectionner les combinaisons de

grands-parents de telle

façon

que le mérite

génétique global

des futurs

petit-fils, qui

cons-tituent les animaux

_commerciaux,

soit maximisé. Deux

petits exemples

de simulation

sur ordinateur sont

_analysés,

l’un supposant le modèle

génétique infinitésimal,

et

l’autre introduisant des

_QTL

qui contrôlent le caractère.

_©

_{Inra/Elsevier,}

Paris

sélection de combinaisons de grands-parents

/

variance de dominance

_/

stratégies d’accouplement

1. INTRODUCTION

Breeding

programmes for

economically

important

traits are based on

select-ing

as

_parents

for the next

_generation

the individuals with

_{highest genetic}

merit

estimated

_by

mixed model

_methodology.

However,

in the near

future,

molecu-lar information will be

_integrated

into mixed models to achieve the maximum

improvement.

If the loci

_affecting

a

_quantitative

trait

(QTL),

were

known,

it

would be

_possible

to

_directly

select

_specific

_alleles,

or if

_genetic

markers linked

to

_QTL

were

_detected,

_they

could also be used in marker-assisted selection. In any case,

profit

from dominance

genetic

effects in

_breeding

_programmes

can

_only

be obtained when final commercial animals are the

_product

of

_matings

other than those involved in the maintenance of the

breeding population.

In

a

large

number of domestic

_species,

the final

product

is the result of

two-way,

three-way

or rotational

_{crossbreeding}

_{among breeds} or strains that are

maintained

_separately.

In this

context,

selection is

_{independently}

carried out in each

_parental

_{population and,}

in

_addition,

the value of the cross _may increase as a result of heterosis. An

_exception

to this

_practice

is the

_{reciprocal-recurrent}

selection scheme

_{(RRS) !1!,}

whose merits relative to

_pure-line

selection

_(PLS)

have been reviewed

_by

Wei and van der Steen

!14!.

Several authors have

_suggested

that

_although

selection should be carried out

on estimated additive

breeding values,

animals used for commercial

production

should be the

_product

of

_{planned matings}

which maximize the overall

_(additive

plus

dominance

_effects)

_genetic

merit of the

_offspring

_{[4, 8].}

More

_recently,

Toro

_[12]

claimed that dominance

_genetic

variance can also be

exploited

in a

closed

_population,

as

_long

as different

_mating

_systems

are

_applied

for

_providing

breeding

commercial animals.

In this

note,

we

_present

a more

general

procedure,

i.e. selection of

grand-parental

combinations

_(SGPC),

as

_{proposed by}

Toro

!13!,

which is not restricted

to the progeny test scheme.

Moreover,

SPGC benefits from the use of mixed

model

_methodology,

which is considered as the method of choice for

_genetic

evaluation in animal

_breeding.

2. THEORY

The

_methodology

_suggested

_by

Toro

_[12]

_basically

consists in

_making

two

different

_types

of

_matings

in the framework of a _progeny test scheme:

_a)

minimum

_coancestry

_matings

to obtain commercial animals that will also be used for

_{estimating breeding}

values of nucleus

animals;

and

_b)

maximum

coancestry

matings

from which the

_population

will be

_propagated.

Simulation results showed that the

_superiority

of this new method over the standard progeny test

depends

on the

genetic

architecture of the trait and that it is

_especially

effective if there is overdominance or if there are unfavourable

recessive alleles at low

_frequencies.

This method has two main limitations.

First,

it is not

_optimized

with

respect

to the

_proportion

of

_matings

_among relatives both to obtain commercial animals and to

_propagate

the

_population.

_Second,

it is limited to a _progeny test

breeding

scheme. The method

proposed

in the

_present

paper, called selection of

and it is aimed at

_optimizing

the

_proportion

of

_matings

among relatives in both the commercial and the

_{breeding population.}

Consider,

for the sake of

simplicity,

a

population

of three males

(1,

_2,

3)

and

three females

_(4,

_5,

_6).

The

_objective

is to select two

_{mating pairs}

to

_propagate

the

_population

from the nine

_potential

ones shown in table L At some future

time,

the commercial animals will be the

_{grandoffspring}

of the individuals

considered

_{and, therefore,}

_{the progeny} of one of the 18

_{potential grandparental}

combinations, assuming

that each male can

_only

be mated with one female

(table 7).

Thus,

we should select the combination which maximizes the

_expected

value of the overall

_genetic

merit of the future commercial animals.

_If,

for

example,

the

_{expected genetic}

merit of the

_{grandoffspring}

of

₍₁

x

₄₎

x

₍₂

x

₆₎

is the

_highest,

we should select

_mating

_pairs

1x4 4 and 2 x 6 for the

_propagation

of the

_population.

The

_genetic

values of these

_{expected grandoffspring}

could be

predicted using

mixed model

_{methodology including}

dominance and

_inbreeding

genetic

effects. An intuitive

_{interpretation}

would be as follows.

_If,

for

_example,

a trait is controlled

_by

a biallelic locus

_showing

overdominance,

the best

grandparental

combination for

_obtaining

future commercial animals would be

(AA

x

AA)

x

_(aa

x

_aa),

because it

_produces

_heterozygous

Aa

_{grandoffspring.}

Obviously,

mating pairs

AA x AA and aa x aa should be chosen to

_propagate

the

_population.

3. SIMULATION

Because of the rather intuitive

_{justification}

of the method

_{given above,}

the

_performance

of the

_{newly proposed}

method was checked

_by

computer

simulation

_assuming

either an infinitesimal model or a model based on known

genetic

loci.

3.1.

_Breeding

scheme

Selection was carried out over six

_generations

_{following closely}

the scheme

presented

in table I but

_considering

a

population

of 32 candidates

(16

males

and 16

_females)

instead of six candidates

_(three

males and three

_females).

Each

generation,

four combinations of

_{potential grandparents}

_(eight

_mating

_pairs)

were selected

_according

to the

_{predicted genetic}

merit of their

_{grandoffspring.}

Although

the most

_appropriate

_technique

for

_selecting

the best

_{grandparental}

combinations would be linear

_programming,

a

simpler

and

computationally

faster

_strategy

that

_sequentially

chooses the best available combinations was

used

_!9!.

As indicated

by

this

author,

this

strategy

is

_generally

close to

_optimal.

The new method was

_compared

with a standard selection method in which

potential

grandparents

were selected

_according

to their _average

_predicted

additive

_genetic

value. The number of

_replicates

was 200 for the infinitesimal

genetic

model and 100 for the finite loci model. 3.2. Infinitesimal

_genetic

model

where a is the additive

value,

b and F are the

_inbreeding

_depression

and the coefficient of

inbreeding

of the

individual,

d the dominance effect and e an

environmental random deviate. The dominance

_{effect, ignoring}

_inbreeding,

was

simulated as its sire x dam combination effect

_plus

mendelian

_sampling

_[7]

where

_f

_S

_,

_D

_represents

the average dominance effect of many

hypothetical

full-sibs

produced by

the individual’s sire S and dam

_D,

and 6 is the individual’s deviation from the sire x dam subclass effect. Variances are

V(fs,

D

)

= 0.25

V

D

and

_{V (6)}

= 0.75

V

D

,

where

V

D

is the dominance variance.

Genetic evaluation was carried out

_using

_only

_phenotypic

information from

where yi is the

phenotypic

value of animal

i,

b is the

_{inbreeding depression}

(assumed

to be

_known),

and ai and

d

i

are additive and dominance effects of

animal

_{i, respectively.}

Other

_possible

fixed effects such as

_generation

effect were

ignored

for

_simplicity.

Now,

if m is the vector of

_genetic

merit m = _{a +}

d,

the BLUP of _m is the

solution of

_equations

where M =

(A

V

A

₊ D

V

D

)/V

E

,

V

E

being

the environmental variance.

The

expected

additive

plus

dominance

_genetic

merit of the

_{grandoffspring}

of a

_grandparent

combination

_(i

x

_j)

x

_(k

x

_l)

was calculated

_using

[6]

where

_Gij

_kl

is the covariance between the

_genetic

merit of the

_{grandoffspring}

of the

_{grandparental}

combination

_{(i x j)}

x

_(k

x

_l)

and the vector of

_genetic

merits m,

computed

from the additive and dominance

relationship

matrices.

Finally,

the

predicted

total

_genetic

merit was corrected for the

_{inbreeding depression.}

The standard

_procedure

is based on a

_genetic

evaluation

_using

the same model

(including dominance)

as for the

_proposed

method.

Different situations with the same

_genetic

_{parameters V}

A

=

_{3.25, V}

D

= 6.55 and

V

E

= 6.55 but

_increasing

levels of

_{inbreeding depression}

_were considered.

3.2. Finite loci model

The trait of interest was simulated as controlled

by

100

independent

loci

with

equal

effects.

_Genotypic

values at each one were

_1,

d, -1

for the allelic

combinations

_BB,

Bb and

_{bb, respectively.}

Values of d =

0, 0.25,

1,

-1 and 1.5

were considered

_representing

different

degrees

of

_recessivity

of the unfavourable

allele. The initial

_frequency

of the b allele was 0.20.

A two-loci model with

_epistatic

interaction was also tested. The

_genotypic

values are

_given

in table Il

_assuming

additive x additive and

_diminishing

epis-tasis

_!2!.

_Fifty

_pairs

of such loci were simulated with initial

_frequencies

of alleles

bandcof0.8.

In the SGPC

method,

the

_expected

overall

_genetic

merit of the

grand-offspring

of a

_{grandparental}

combination

(i

x

_j)

x

_(k

x

_l)

was

_predicted

calculating

the

_{genetic composition}

of the

_{grandoffspring}

from

_simple

mendelian rules. In the standard

method, the

breeding

values of the

_{potential grandparents}

4. RESULTS

4.1. Infinitesimal

_genetic

model

The values of the

_genetic

mean of the trait

during

the first six

generations

of

selection, using

the standard

_procedure

and the new method are

_presented

in

table

_{III, together}

with the mean

_inbreeding

coefficient for both the commercial

and the

_breeding

populations.

Strictly speaking,

the

_performance

of the

breed-ing population

is an observed

_value,

while the

_performance

of the commercial

population

is an

_expected

value that will be realized with a

_{one-generation}

delay.

The cases

A,

B,

C and D in table III refer to different situations with the same

_genetic

variance

_components

but

_increasing

levels of

_inbreeding

depression.

This is

_possible

in a

_genetical

infinitesimal model

_where,

unlike the

typical

biallelic

_{genetic model,}

_inbreeding

_depression

and dominance variance

are

_independent.

As shown in table III the new method achieved the

_objective

of

_obtaining

superior

performance

of the commercial

_population

in all cases. This

_superiority

was attained

_by

inducing

some

_matings

_among relatives in the

breeding

population,

in order to

_profit

from dominance.

_{Consequently,}

the

_performance

of the

_{breeding population}

was worse with SGPC when

inbreeding depression

was

_larger,

as in cases C and D.

Nevertheless,

with

_SGPC,

the

_inbreeding

coefficient of commercial animals is

automatically adjusted depending

on the

_magnitude

of

_{inbreeding depression.}

In case

_A,

_inbreeding

_depression

is not

_important

and

_therefore,

a considerable

rate of

_inbreeding

is

_allowed,

whereas in case

_C,

the

_magnitude

of

_inbreeding

depression imposes

a

_stronger

restriction.

_Obviously,

in case

_D,

the lower

inbreeding

in the commercial

population

is the factor that determines its

performance.

In cases

_A-D,

it has been assumed that

only

the

performance

of the

commer-cial

_population

is

_economically

_valuable,

but SGPC could

_easily

accommodate selection for both commercial and

_{breeding population performances.}

Case E of table III is the same as case D

_except

that the

objective

of selection is a

combination of the

_{expected genetic}

merit of the commercial

_{grandoffspring}

and the

_{expected genetic}

merit of candidates for selection in the next

gener-ation,

giving

the same

_weight

to both

_expected

values.

_Although

this

_equal

weighting

is

_arbitrary,

it

_highlights

the fact that both commercial and

_breeding

population

performances

could be included. The results indicate that the lower

performance

of the commercial

_population

is

_compensated

_by

the

_superior

per-formance of the

_breeding

population.

4.2.

_QTL

identified

Table IV shows that the results with the defined

_genetic

model are similar to

those of the infinitesimal one. With

_SGPC,

the

_performance

of the commercial

animals is

_always

_superior,

_especially

in the case of overdominance or

diminish-ing epistasis. However,

as a _consequence of

_matings

_among relatives induced in

of commercial

_population

is lower than with the standard

method,

and in the

cases of

complete

dominance and

_{overdominance,}

the avoidance of

_inbreeding

is maximum.

However,

in the case of d = -1 the SGPC induces

inbreeding

in both the commercial and the

_breeding

_population,

because in this case

_inbreeding

in-creases the

_genetic

mean and therefore both

_populations

have better

perfor-mance than with the standard method. And if

_inbreeding

_depression

is

_absent,

as in the case of additive x additive

_epistasis

_[2]

or when

_positive

and

nega-tive effects of

_inbreeding

are cancelled because at half of the loci d = 1 and

at the other half d = -1

(case

G,

table

IT!,

the

optimal

level of

inbreeding

is

automatically adjusted.

5. DISCUSSION

Although

the idea of

_using

deliberate

_inbreeding

in selection _programmes is

generally

disfavoured in animal

_breeding,

several authors have indicated that

a

_reappraisal

of the

_subject

is needed

_{[5, 12].}

Inbreeding

has two

_opposite

effects. It increases selection response because it allows the accumulation of dominance effects but it also decreases

_genetic

mean due to

_inbreeding

depres-sion. The SGPC method

proposed

here is intended to take

simultaneously

into

account both

aspects

of the

problem.

The idea is that we should select

grand-parental

combinations such that the overall

_genetic

merit of future commercial

grandoffspring

will be maximum. In this _way, the

_proportion

of

_matings

_among relatives is

_optimized

both to obtain commercial animals and to

_propagate

the

population.

The main aim of the

_present

paper has been to _propose this new

_procedure,

which _{appears to} be a

_general

method of

_utilizing

additive and dominance

effects. The method has been checked

_by

computer

simulation of a

breeding

scheme which was

_{unrealistically}

small in order to achieve

_{computational}

feasibility

and assumed an

unrealistically

high

value of the dominance variance

15

%

in cases B and C

_(table

III).

This casts some doubt on the

_practical

advantages

of the new method and more work remains to be carried out

simulating

more

_practical

situations of current nuclei of selection

_including

the cost associated with

_{inbreeding depression}

of the

_{breeding population}

and

specifying

the structure of dissemination of

_genetic

progress. But two facts should be

kept

in mind.

_First,

recent

_developments

have allowed

_computations

with models

_including

dominance

_[10]:

this has created the

_possibility

of

obtaining

a benefit from such evaluation even if it is small.

Second,

the method

could also be

_generalized

to include multibreed situations. In

crossbreeding

the

method will

_optimize

the

_matings

to be made in _pure breeds in order to achieve maximum

_profit

from commercial crossbred

_{grandoffspring.}

The new method has some

analogies

with

reciprocal-recurrent

selection.

Both methods

_rely

on the crucial distinction between commercial and

_breeding

populations.

But RRS

_begins

with two

_populations,

and an essential

pre-requisite

is that there should be some difference in gene

_frequency

between

the two lines at the

_beginning

_!1!.

The start of SGPC is a closed

_population

and any

subsequent

subdivision that can occur in the

breeding population

will

be a _consequence of the selection process and will

depend

on the

genetic

basis of the selected trait.

Some theoretical and estimation

_problems

remain if additional

_phenotypic

information is used. In the

present

paper evaluation is based

only

on infor-mation

_coming

from the nucleus but it could be

_improved

if information from commercial animals of

_{previous generations}

_might

be included. We have also used a

straightforward

infinitesimal model that includes dominance variance

and that accounts for the _average effect of

_inbreeding

on the mean

_{by including}

the

_inbreeding

coefficient as a covariate. The value of this

approach

has been

discussed

_by

de Boer and van Arendonk

!3!,

but it is clear that for a detailed

un-derstanding

of how the SGPC method is

_working

a more

_{sophisticated}

model

for

_simulating

and

_analysing

the data is needed. The best candidate is the model

_{proposed by}

Smith and Maki-Tanila

_!11!,

which considers the reduction of base dominance

_variance,

the increase in dominance variance of

_completely

inbred individuals and the covariance among additive and dominance effects with

_inbreeding.

The

_present

_study

has additional limitations

_requiring

further research. The

properties

of SGPC in the medium and

_long

term have not been

_investigated

but it can be

_conjectured

that the additive variance in the

_long

term will be

reduced,

since the method

_imposes

some

_inbreeding

in the

_breeding

_population.

Furthermore, computation

could also be a

limiting

factor: with N

grandparents

of each sex, there will be

N

4

grandparental

combinations. The

present

study

has shown that dominance

_genetic

effects can be accumulated

_by

_adequate

planning

of selection and

_mating

_policy.

REFERENCES

[1]

Comstock

_R.E.,

Robinson H.R.,

Harvey P.B.,

A

_{breeding procedure designed}

to make maximum use of both

_general

and

_{specific combining ability, Agronomy}

J.

41

₍₁₉₄₉₎

360-367.

[2]

Crow

_{J.F., Kimura M.,}

An introduction to

_{population genetics theory, Harper}

[3]

De Boer

_I.J.M.,

Van Arendok

_J.A.M.,

Prediction of additive and dominance effects in selected and unselected

_populations

with

_inbreeding,

Theor.

_Appl.

Genet.

84

₍₁₉₉₂₎

451-459.

[4]

DeStefano

_A.L.,

Hoeschele

_I.,

Value of

_including

dominance

_genetic

merit in

mating

progress, J.

Dairy

Sci. 75

₍₁₉₉₂₎

1680-1690.

[5]

Dickerson

G.E.,

Lindhé

_{N.B.H., Inbreeding}

and heterosis in

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in: Pol-lack

_{E., Kempthorne 0., Bailey}

Jr.

_(Eds.),

_Proceedings

of the International

Confer-ence on

_{Quantitative Genetics,}

Iowa State

_{University Press, 1977,}

_pp. 323-342.

[6]

Henderson

C.R.,

Best linear unbiased

prediction

of nonadditive

_genetic

merit

in

_mating

_programs, J.

Dairy

Sci. 84

₍₁₉₈₅₎

451-459.

[7],

Hoeschele

_I.,

Van Raden

_P.M.,

_Rapid

inversion of dominance

_relationship

matrices for noninbred

_{populations by including}

sire x dam subclass

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