A new method aimed at using the dominance variance in closed breeding populations

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A new method aimed at using the dominance variance

in closed breeding populations

M Toro

To cite this version:

Original

article

A

new

method aimed

at

using

the

dominance variance in closed

breeding populations

M Toro

CIT-INIA, Departamento de Produ.ccion Animal, Apartado 8111, 28080 Madrid, Spain

(Received

26 _{August 1991; accepted} 25 November

₁₉₉₂₎

Summary - A new method that allows use of part of the dominance effects in a closed population is proposed. In the framework of a _{progeny test} selection _scheme, the method

basically consists of _performing 2 _types of matings:

a)

minimum coancestry matings in order to obtain the _progenies that will constitute the commercial _population and that will also be utilized for _{testing purposes,} and

_b)

maximum _{coancestry matings} from which the

population will be propagated. The performance of the new method has been checked by computer simulation and results show a _superiority over the standard _progeny test in all

cases where unfavourable alleles are _{recessive, especially} when they are at low frequency.

artificial selection _/ dominance variance _{/ mating strategy /} computer simulation R.ésumé - Une nouvelle méthode visant à utiliser la variance de dominance dans des populations fermées en sélection. Une nouvelle méthode est

_proposée

_pour utiliser les

effets de dominance dans des

_populations

_fermées. Dans le cadre d’un schéma de sélection

sur _descendance, la méthode consiste à réaliser 2 _{types d’accouplements:}

_a)

_{accouplements}

avec _parenté minimale

_afin

d’obtenir les descendants _qui constituent la _population

commer-ciale et _qui en même temps servent à _l’épreuve de _descendance, et

₆₎

_{accouplements} avec parenté maximale servant à propager la population. La valeur de la nouvelle méthode a

été _{vérifiée par} simulation sur _ordinateur, et les résultats montrent _qu’elle est _supérieure à _l’épreuve de descendance _classique dans tous les cas où les allèles _{défavorables} sont

récessifs, et surtout si leurs _fréquences sont _faibles.

sélection artificielle _/ variance de dominance _/ système d’accouplement / simulation

INTRODUCTION

Traditionally,

livestock breeders select on an

_{intrapopulation basis, choosing}

those

individuals with

_highest

additive

_genetic

values. And in order to obtain benefits derived from dominance effects this selection is carried out

_separately

in each of 2 or more

_{populations hoping}

that the value of the cross is increased in addition as a result of heterosis.

The

_{justification}

of this

_approach

_is,

in

_principle,

_quite

_simple.

The additive

genetic

merit of candidates for selection is estimable and its mean value can be increased

_{by selecting}

those individuals with the most desirable values. The

dominance value is also estimable from

_pedigree

_data,

at least in non-inbred

populations

(Henderson, 1985),

but it cannot be accumulated

_by

standard selection

procedures.

Even if we had estimated the dominance

value,

it would not be

worthwhile to select those individuals with the most desirable values because its

average value will regress towards zero, as _consequence of random

_mating.

The

_{reciprocal-recurrent}

selection

_(RRS)

_{proposed by}

Comstock et al

₍₁₉₄₉₎

is the

_only

available

_{methodology designed}

to overcome this situation and when

applied

to a

single population

it involves

arbitrarily subdividing

the

population

in

2,

each _part

_being

tested

_against

the other. This last situation has been

_scarcely

studied

_(Wei

and Van der

_Steen,

_1991).

In this paper we propose a new

_methodology

of selection that can be used in a closed

_population

and that allows use of dominance

_variance,

at least

_partially.

Its

performance

in a _progeny test scheme is evaluated

_by

_computer simulation.

THEORY

As

_{emphasized by}

Hoeschele and VanRaden

₍₁₉₉₁₎

the utilization of dominance effects in a

breeding

_programme

require

working

with

pairs

of individuals. If the

offspring

of a

_particular

sire

_(S

_l

₎

and dam

_(D

_l

₎

have

_high

average dominance

effects,

the

_mating

of a

_close

relative of sire _Sl to a close relative of dam _D1 would also

produce offspring

with

_high

dominance effects. This

_implies

that we should _try to

accumulate _genes of the sire

_(S

_l

₎

for one side and _genes of the dam

(D

l

)

for the

other side

and

to combine them in successive

_generations.

Intuitively,

it seems that the process of accumulation of genes

requires

inbreeding

while to combine genes

requires

some form of

_mating

between individuals

_distantly

related in the

_pedigree.

Both processes are

contradictory

and for this reason

the more obvious solution is to

_apply

a different

_mating

_system for the _process

of

_propagation

of the

_population

and for the process of

testing

and

_obtaining

commercial animals. We therefore _suggest a

methodology

that

_basically

consists

of

_{performing alternatively}

2 _types of

_matings:

₍₁₎

minimum _coancestry

_matings

between the candidates for selection for _progeny

_testing

and

_replacement

_matings

in the commercial

_population

and

₍₂₎

maximum

_coancestry

_matings

between the selected sires and dams from which progeny the

population

will be

propagated.

In the next section simulation results are

presented

focused on

testing

if the

proposed

method can

exploit

dominance variance in a better _way than classical

SIMULATION

Breeding population

The

simplest

way to

implement

the

proposed

method is in the _{progeny test} scheme.

Here,

M candidates for selection of each sex are mated with a criterion of minimum coancestry. From the progeny of each of the M

matings, n

individuals are measured and on the basis of the _progeny means the best N individuals from the M _parents of each sex are selected. These individuals are mated

_following

a criterion of maximum

coancestry in order to obtain the 2M candidates for selection in the next

_{generation. ?}

The values for

Nl,

n and N were

_64,

5 and 16

_{respectively.}

The

_breeding

scheme is

shown in

_figure

1.

This new method is

_compared

with a classical progeny test that follows the same scheme of

_figure

1 but where both _types of

_matings

were at random. The

_comparison

criterium is the

_performance

of the commercial

_population,

that is the mean value

of the

_{progenies coming}

from the M minimum coancestry

matings

(or

from the

equivalent

random

_mating

of the classical progeny

test).

Mating

method

Maximum and minimum _coancestry

_matings

were obtained

_{applying linear}

pro-gramming

techniques

as in Toro and P6rez-Enciso

(1990).

If the matrix of

coances-tries C =

{c2!

among

selected sires and dams are

known,

the

_problem

of maximum

coancestry

matings

reduces to

_finding

a X =

{x2! !

matrix _{where xij represents} a decision variable

_indicating

whether the i-sire and the

_j-dam

are

(x2!

=

1)

_{or are}

not

_(xZ!

=

0)

_to be mated. Such _a matrix is chosen _to maximize

L

xijcij

subject

Obviously

the minimum _coancestry

_matings

are solved in a similar _way.

Genetic models

The trait of interest was simulated as controlled

by

64

equal independent

loci.

Genotypic

values of each locus were

1, d, -1

for the allelic combinations

BB,

Bb

and

bb,

respectively.

Values of d = _{0, 0.25,}

_0.5,

_{0.75, 1} and 1.125 _were

_considered,

representing

different

_degrees

of

_recessivity

of the unfavourable allele. The initial

frequency

of the b allele was _0.8, 0.5 or 0.2.

A 2 locus additive x additive

_epistatic

model was also tested. The

_genotypic

values for this model are

_given

in table 1.

_{Thirty-two pairs}

of such loci were simulated with an initial

_frequency

of alleles b and c of 0.8.

In all cases the

phenotypic

values were obtained

adding

a random normal deviate to the

_genotypic

value such that

_heritability

in the narrow sense was 0.20. The number of runs was 100.

RESULTS

The mean values of the trait of the individuals in the commercial

_population

(deviated

from the base

_population)

after 5 and 10

_{generations using}

the classical

progeny test

_(Rp)

and the new method

(R

N

)

are

presented

in table

II,

for different

degrees

of

_recessivity

and different initial _gene

_{frequencies of}

unfavourable alleles

together

with the mean

inbreeding

coefficients of these individuals. The last column shows the effectiveness of the new method with _respect to the standard one.

Results after 5

_generations

of selection indicate a clear

_superiority

of the new method when unfavourable alles are _recessive,

_especially

if

_they

are at low

_frequency.

With

_complete

_recessivity

and the lowest

frequency considered,

the

_advantage

is

up to 68%. After 10

_generations

of selection the new method behaves worse for

very

important

(up

to

_36%).

_Obviously

the overdominance situation would allow a

dramatic

_superiority

for the new method.

For a better

understanding

of how the new method is

working,

table III _presents

the evolution of

_genotypic

_frequencies

_showing

_that,

with _respect to the standard

selection

_procedure,

a

_{higher frequency}

of

_{heterozygotes}

and a lower

_frequency

of unfavourable

_homozygotes

is maintained.

The

_epistatic

situation has not been

_analyzed

in detail but in the additive x additive

_example

studied the new method leads to an

_advantage

of 14 and 4% after

5 and 10

_generations

of selection which indicates that in could also be useful in at least some

_epistatic

situations.

The

_inbreeding

of commercial animals is lower with the new method because

they

are

_{produced by}

minimum _coancestry

_matings.

On the _contrary, the

_inbreeding

of the candidates for selection is

_quite

_high,

because

_they

are the result of maximum

coancestry

matings.

The

_inbreeding

coefficient of these individuals is shown in table

IV and attains values as

high

as 0.39 and 0.59 after 5 and 10

_{generations respectively.}

In order to visualize the

_{inbreeding depression}

that would occur in the candidates

to selection table IV also _presents the

_performance

of the

_offspring

coming

from the maximum _coancestry

_matings

_(R!)

_compared

with the

_offspring

of the

_equivalent

random

_mating

of the standard progeny test

(Rp).

The level of

_inbreeding

can be reduced

if,

in

_setting

up the linear

programming

problem,

we introduce the additional restriction that not all

_possible

brother-sister

matings

are

allowed,

but rather a

_proportion

of them

(p

=

_{0.75, 0.50,}

0.25 and

0.00).

Here,

the decision if whether a

particular

brother-sister

_mating

is

_possible

is taken at random. Table V presents the results obtained with d = _1,

indicating

that a lower

inbreeding

and, therefore,

a better

_performance

of the candidates for

selection,

can be obtained

_maintaining

at the same time an

_important

selection response for the commercial

population.

DISCUSSION

Several authors have

_suggested

that if there is evidence that dominance effects are

important

for a trait of _interest, the animals that constitute the final commercial

product

should be obtained from a _type of

mating

different from that involved in the maintenance of the

_{breeding population}

_(Jansen

and

_Wilton,

_1985;

_Kinghorn,

1987).

The idea is that selection should be done

_according

to the estimated additive

breeding

value but the animals

_going

to the market should be the

_product

of

_planned

matingsthat

maximize the overall

_(additive

_plus

dominance

_effects)

_genetic

merit of the

_offspring.

More

_recently

a

_mating

_strategy for utilization of dominance effects

within a

breed,

based on

predicted

sire-maternal

grandsire combining

abilities was

investigated

via simulation

_by

DeStefano and Hoeschele

₍₁₉₉₁₎

and

_applied

to cattle data of conformation traits

_by

Lawlor et al

_(1991).

Although

the above

_{proposal is}

_{static, in}

the sense that the dominance effects are not

_{accumulated, it}

_opens the

_possibility

of the

_development

of new

_{methodologies,}

once the value of

distinguishing

between

_propagation

and test

_matings

is

_accepted.

similar individuals in order to obtain the next

_generation

_although

the commercial animals should be

_{produced by}

other

_{planned matings}

that will benefit from the

interaction.

In this article we have shown that the combination of maximum and minimum

coancestry

matings

can be an effective _way to

_profit

from dominance effects. In the

simulation,

these effects come from the existence of recessive alleles unfavourable to the direction of selection

_practised.

The

_logic

of this

_assumption

is based on 2

_pieces

of evidence.

First,

no

_quantitative

trait of economic

_importance

shows

_negative

heterosis as would be the case if dominance variance were due to loci at which the recessive alleles are favoured.

Second,

lowly

heritable and heterotic traits are

usually

those connected with fitness such as

_{fertility, prolificacy}

or

_longevity

and there exists

_evidence,

at least in

_{Drosophila melanogaster,}

that

_genetic

variation

for fitness is

_essentially

caused

_{by segregation}

of rare deletereous recessive alleles

(Mackay, 1985).

As shown in table

II,

the new method is

especially

useful in this

situation with a relative

_efficiency

over the classical _progeny test scheme of up to

68%,

after 5

_generations

of selection for

_{f (b)}

= 0.20 and d = 1.

In the short term

_{(5 generations)}

the

_superiority

of the new method is clear for all

situations considered _except for

_{complete additivity,}

where the

_performances

of the

2 methods

_equal.

In the medium term

₍₁₀

_{generations),}

_however,

the

_advantage

is

maintained

_only

for

_complete

or

quasi-complete recessivity

of unfavourable alleles. The reason seems to be that the _system of maximum _coancestry

_mating

induced an increased

_genetic

drift

and, therefore,

a more

rapid

reduction of additive

genetic

variance

_(Caballero

and

_Hill,

_1991).

_Furthermore,

simulation results not

_presented

here indicate that with

_{complete additivity}

a reversal of the _types of

_matings

(maximum

coancestry

matings

for

_testing

and minimum _coancestry

_matings

for

breeding)

will be a better solution.

Recently,

several authors have indicated the value of a

reappraisal

of the use of

inbreeding

in selection _programmes.

_Lopez-Fanjul

and Villaverbe

₍₁₉₈₉₎

have shown

that one

_generation

of full-sib

_mating

increased 4 times the realized

_heritability

of

egg-to-pupa

viability

in

_{Drosophila !nelanogaster.}

The authors

_suggested

that in this

trait selection schemes

_involving

subdivision and selection between and within lines could be more efficient than mass selection. Dickerson

₍₁₉₇₃₎

and Sirkkomaa

₍₁₉₈₆₎

have

_{argued theoretically}

and shown

_by

simulation that the _{response to} selection

is 10-20% faster with full-sib

_mating

and random

_mating

in alternate

_generations

than with random

_mating

exclusively.

Usefulness of

_inbreeding

in the above

_{proposals rely}

on the fact that

inbreeding

increases

_homozygosity

and hence the effectiveness of selection

_against

recessive

detrimental alleles.

However,

the behaviour of the new method

_suggested

here is different. The increased selection _response is due to a

_quicker

reduction in the

frequency

of unfavourable

_homozygotes

while at the same time a

higher frequency

of

_{heterozygotes}

is maintained. The overall balance is not a

_higher

reduction of the

frequency

of unfavourable genes

(table III).

Although

the idea of

_{using mating}

_among relatives is

_against

normal

_practice

in animal

_breeding,

it must be

_emphasized

that in the new method the

inbreeding

coefficient is

_high

in the candidates for selection but not in the

_progenies

of the

minimum _coancestry

_matings

that we have assumed constitute the commercial

depression

of candidates for selection even if the tactic of

_imposing

additional

restrictions is utilized

_{(table V).}

This cost will

_depend

on several _parameters such as the relative

_proportion

of both types of

matings

and the

_magnitude

of

_inbreeding

depression,

either for the

_quantitative

trait of economic

_importance

or for other fitness-related traits. The first

_factor,

in its _turn,

_depends

on the

reproductive

rate of the

_species,

the

_generation

interval and the structure of dissemination of

_genetic

progress. Therefore the

application

of this method in

practical breeding

programmes would

_require

an economics evaluation

_including

this cost.

In the new scheme commercial animals are

_{produced by}

minimum _coancestry

matings

and _part of their better

_performance

is due to

_{avoiding inbreeding}

and therefore

_{avoiding inbreeding}

_depression.

It is not clear how to discount for this

effect because it is inherent in the new method to induce a _process of

sublining

in the

_{propagated population}

that will cause a _very low level of

inbreeding

in the commercial

_population.

Even if we had avoided

inbreeding

in the standard selection method

_using

minimum _coancestry in both _types of

_matings,

the values of

_Rp

and

Fp,

after 10

_generations

of selection and for d = 1 and

f (b)

=

_0.20,

would be 3.31

and 0.11 and the new method will still show its

_advantage.

_Furthermore,

the results of the additive x additive

_{epistatic model,}

where

_{inbreeding depression}

is

absent,

are indirect evidence that

avoiding inbreeding

is not the

_{only explanation}

for the better

_performance

of the new method.

The present

study

has some limitations that warrant further research.

_First,

there has not been a

_systematic

consideration of different

_{heritabilities,}

_gene

_frequencies,

selection intensities or

population

sizes.

Second,

no

_comparison

with other methods

except a

special

_type of _progeny test with one dam _per sire has been made and

only

short-term _responses have been considered.

_Third,

the method has not been

Finally,

for the method to be

_applied

in

_{practical breeding schemes,}

it is

_necessary

to take

_advantage

of mixed model

_methodology.

For

_example,

the limitation of a progeny test scheme could be overcome if estimated values of the

_expected

_progenies

rather than actual values are used. Recent _papers have shown how to estimate

dominance effects either in non-inbred or in inbred

_populations

_(Smith

and

Maki-Tanila, 1990;

Hoeschele and

_VanRaden,

_1991; De Boer and Van

_Arendok,

_1992).

In

_conclusion,

the use of dominance variance in within

_population

selection

programmes is an _open

_question

that can be tackled

_by

an

_{adequate planning}

of

_evaluation,

selection and

_mating

_policy.

The next _step of the research will be to

_study

these ideas in the framework of the standard

_methodology

of

_genetic

evaluation.

ACKNOWLEDGMENTS

-I am _grateful to the staff of Area de Informitica Cientifica of the INIA for their kind

cooperation. I would also like to thank L Sili6, M _{P6rez-Enciso,} C Garcia and one

anonymous reviewer for their critical comments. This work has been _{supported by} a

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