Combining use of embryo sexing and cloning within mixed MOETs for selection on dairy cattle

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Combining use of embryo sexing and cloning within

mixed MOETs for selection on dairy cattle

Jj Colleau

To cite this version:

Original

article

Combining

use

of

embryo

sexing

and

_cloning

within mixed MOETs

for selection

on

dairy

cattle

JJ Colleau

Institut National de la Recherche

_Agronomique,

Station de

Genetique Quantitative

et

Appliqu6e,

78352

_{Jouy-en-Josas Cedex,}

France

(Received

17

_September

1991;

accepted

13

April

1992)

Summary - Given the same overall number of transferred

embryos,

a

_comparison

was

carried out between adult mixed

_(ie

with bull

_{progeny-testing)}

MOET

_(multiple

ovulation and

_{embryo-transfer)}

schemes with

_embryo

sexing

only

versus

_{embryo sexing plus cloning}

of female

_embryos.

In the former

_schemes,

natural and ET

_{(embryo transfer)}

animals were

allowed to breed. In the latter

schemes,

each _category of females

_(single

born or

cloned)

was allowed to

_give

birth either to new

_single

animals

(natural calvings)

or to new clones

(ET).

The

_optimal

structure

_{(subpopulation}

sizes and

_{corresponding}

selection

_pressures)

in both schemes was derived

algebraically by maximizing

the

_{predicted asymptotic}

annual

genetic

gains, assuming

an infinite

_population

but

_accounting

for the Bulmer effect.

Detailed presentation is

_given

here for the case of

_{embryo cloning}

(that

of

_{embryo sexing}

was dealt with in a _previous

_paper).

Schemes

_using

the full

reproductive capacity

of a

given

genotype allowed

_{by cloning}

were found to be superior

(+5

to

_{+10% )}

when the number of live

_replicates

per cloned heifer was moderate

(3-5).

_They

were even more

superior for

_higher

number of

_replicates

_(10-20).

This trend was confirmed

_by

Monte-Carlo

inbreeding-free

(for

the sake of consistency with the

_model)

simulations. Some Monte-Carlo simulations

_accounting

for

_inbreeding

effect were carried out until year 100 after starting

the

_breeding

schemes. With 5

_replicates

_per

_clone,

the ultimate annual rates of increase of

_inbreeding

were found to be still reasonable

_(0.20

to

_0.25%).

_Using

10

replicates

per

clone would

substantially

increase these coefficients

_(0.27

to

_0.33%),

while still

_generating

higher

observed genetic gains.

Consequently, keeping

only 5 replicates would seem to be

a reasonable

_comprise

between increases in F and in

_{genetic gains.}

dairy cattle

_/

selection

_/

genetic gains

/

embryo sexing

/

embryo cloning

Résumé - Utilisation _conjointe du sexage et du clonage des embryons dans les MOETs mixtes fermés pour la sélection des bovins laitiers. On a

_comparé

des schémas MOET

_{(superovulation}

et transfert

d’embryon)

mixtes

_{(c’est-à-dire}

conservant le _testage des taureaux sur

descendance)

adultes avec _sexage seul ou _sexage et

_clonage

des

_embryons

femelles,

en raisonnant à même nombre total

_{d’embryons transférés.}

Dans les

_premiers

reproducteurs.

Dans les

_{seconds, chaque catégorie}

de

_femelles

_(nées

_simples

ou

clonées)

peut donner naissance soit à de nouveaux animaux

_simples

(après

_vêlage

naturel)

soit à

de nouveaux clones

_(TE).

La structure

_optimale

_(tailles

de

sous-populations

et pressions de sélection

_{correspondantes)}

des 2 schémas a été calculée

algébriquement

en maximisant le gain

génétique

annuel asymptotique

espéré.

On supposait une

_population

de

grande

taille mais on tenait

_compte

de

_l’effet

Bulmer. On donne ici la

_{présentation}

détaillée de

l’algorithme

concernant le

_clonage,

étant entendu que le cas du sexage a été traité dans un article

précédent.

Les schémas utilisant la

_{pleine capacité reproductive}

des clones ont été trouvés

supérieurs

(5-10%)

quand

le nombre de

_répliques

vivantes d’une même

_génisse

était modéré

_(3-5).

Ils étaient encore

_supérieurs

_pour un nombre encore

plus

élevé de

répliques

(10-20).

Cette tendance a été

confirmée

par des simulations aléatoires réalisées

sans

_effets

de

_{consanguinité}

_(par

souci de cohérence avec le

modèle).

Quelques

simulations

aléatoires tenant _compte de la

consanguinité

ont été

effectuées jusqu’à

l’année 100

_après

le début du _programme de sélection. Avec

_{5 répliques}

_par

_clone,

le taux annuel

final

d’élévation de la

_{consanguinité}

a été trouvé encore raisonnable

_{(0,20-0,25%).}

L’utilisation de 10

_répliques

_par clone augmenterait sensiblement ces

_coefficients

!0,!7-û,55%!

mais permettrait encore

d’augmenter

les

_gains

_génétiques

observés. En

_{conséquence,}

l’utilisation

de la

première

possibilité (5

répliques

par

clone)

semblerait être un _compromis

acceptable

entre

_{l’augmentation}

du

_{coejjîcient F}

et celle du

_{gain génétique.}

bovins laitiers

_/

sélection _{/ progrès génétique /} sexage d’embryon / clonage d’embryon

INTRODUCTION

The

_potential

of

_using

sexed clones within 1VIOET

_(multiple

ovulation and

_embryo

transfert)

schemes,

either for

_enhancing

the

_{genetic gain}

within nuclei or for

rapidly

improving

the _average

_genetic

level of the commercial

_population

has

_already

been

pointed

out and studied

_(Van

_Vleck,

_1981;

Nicholas and

Smith, 1983; Smith, 1989;

Teepker

and

_Smith,

_1989;

_Woolliams,

_1989;

De Boer and Van

_Arendonk,

_1991).

The

_objective

of the

_present

_study

is to examine the

_prospect

for mixed MOETs

(ie

MOETs

_keeping

_progeny

_testing)

to

_improve

their rates of

_{genetic gain}

_by

_using

embryo cloning

associated with

_embryo

_sexing,

_although

the

_{cloning technology}

is

not

_yet

available for animal

_breeding.

A

_previous

_study

_{(Colleau, 1991)}

has shown

that in the same context of mixed

MOETs,

adult schemes with

_{embryo sexing}

are

good

alternatives to

_{juvenile schemes, provided}

that

_comparison

is made at the same

overall number of transferred

_embryos.

_Therefore,

the

_present

_comparison

becomes

a

_comparison

between adult schemes with

_embryo

_sexing

versus adult schemes with

embryo sexing

and

_cloning

_given

the same constraint.

This

_question

is addressed

_by

_comparing

assumed

_asymptotic

linear rates of ge-netic

_gain

under a Bulmer model

(Bulmer, 1971),

either calculated

_{deterministically}

or observed

through

Monte-Carlo simulation. In this

_model,

_inbreeding

is not

ac-counted for.

_Therefore,

attention is

_given

_mainly

to situations where the number

of clones selected for

_breeding

is still

_high,

_ie,

where the number of members of the

MATERIALS AND METHODS

Adult nucleus schemes with

_embryo

_sexing

These schemes were those of a

_previous

_study

_{(Colleau, 1985),}

where the trait

selected for was assumed to be ruled

_{only by}

additive

_genetic

variation.

Each _year, 130 _young bulls

_coming

from the nucleus entered the AI center. One hundred of them were

_actually

progeny-tested,

on 50

daughters

_per bull. The best

3

_bulls,

when proven at 5.5 _years, were used for

_matings

with the nucleus females.

Usage period

for these bulls was

_only

_{1 year.}

Nucleus females were

dispersed

over farms enrolled in milk

recording.

Dams were

selected from their sole first lactation record

_ie,

the most difficult situation in order

to test the robustness of the envisioned schemes.

_Replacement

progeny, male or

female,

were allowed to come from the first 2

calvings

and 2 additional

embryo

collections at the

_beginning

of the second lactation

_(see

table

_I).

Adult schemes with

_{embryo sexing}

and

_cloning

As in the adult schemes with

_embryo

_sexing,

natural and ET calves were

_eligible

for future

_breeding.

Furthermore,

the system is still a

dispersed

female nucleus.

Cloning

of male

_embryos

was avoided since

_{inbreeding already originated mostly}

from the male side.

Cloning

of female

embryos

was

supposed

to be successful for each

_original

embryo

and led to 2

_categories

of dams:

_single

dams and cloned dams

_(ie,

the whole

_population

of several different clones with several members _per

_clone).

Since

each dam

_might

_give

birth to _progeny 3 times in her

_life,

6 different

_categories

of

replacement

animals of the same sex were obtained instead of 3 for

_{embryo sexing}

without

_cloning

_{(table II).}

The

_organization

was therefore more cumbersome. For

parsimony

of

_notation,

indices 1 to 3 will be attached to animals born from

_single

For each _sex,

_replacement

could be obtained from 6

_categories:

Category

1: natural first calves born when the

_single

dam is _{2 years} old and chosen

1 year later based on the dam’s first lactation.

Category

2: natural second calves born when the

_single

dam is 3 _years

_old,

based

on the dam’s first lactation.

Category

3: ET calves born when the

_single

dam is 4 _years old

_(on

_average,

_embryo

collection done after 3 months of lactation

_during

lactation

_2).

Category

4: natural first calves born from 2 years old cloned

_dams,

chosen _{1 year} later on the _average first lactation of the

_{corresponding}

clone.

Category

5: natural first calves born from 3 _years old cloned

_dams,

based on the

average clonal first lactation.

Category

6: ET calves born from _{4 years} old cloned

dams,

based on the _average

clonal first lactation.

If the

_genetic

standard deviation is taken as unit and if dams or clones are

selected on their

_{performance alone,}

the

_asymptotic

annual

_genetic

_gain

_according

to Rendel and Robertson’s formula

₍₁₉₅₀₎

is

_equal

to OG =

u/v

where

K

l

:

twice the

_genetic

selection differential

_along

the sire-son transmission

_path

(K

l

=

3.98 if no Bulmer effect is

_assumed)

since the same bulls are used in the

nucleus to

_produce

either

_replacement

males or

_females;

K

2

= twice the

_generation

interval for the _same

_path

(13.5);

p

i =

accuracy of the dam’s selection

index;

m i

f

i

:

group size of the ith

category

of

_{replacement females;}

F

_f,

+

f

2

+

f

4

+

f

5

= overall number of

_single

heifers chosen for

replacement;

F! -

!(fa 1

+

_f

₆

₎

= overall number of clones chosen for

replacement;

c

c: number of members per

clone;

t

i

:

selection threshold for dams of the ith

_category

of male

_replacements

on a

standard scale

_(mean

_equal

to 0 and variance

_equal

to

_1);

t

l

to

_t

₃

are thresholds within the subcohort of

_singles;

t

4 to

_t

₆

are thresholds within the subcohort of clones. Clones are considered as

dummy

cows obtained from

_pooling

all the progeny and all the

_performances

of the

members of the same

clone;

ti :

selection threshold for dams of the ith

_category

of female

_replacements

on the

same

scale. ti to t3 involve

the subcohort of

singles

and t4 4 to t* the

subcohort of

dummy

cows;

pi, pi :

corresponding probabilities

that within the proper

subcohort,

the

standard-ized

performance

of any

possible

candidate lies above the

thresholds;

It,,

_It!:

standardized

_phenotypic

selection differentials of the

_performances

(suppos-edly

unbiased

by

possible preferential

treatments)

of the daiiis

_giving

birth to the

corresponding

groups

of each sex.

For

_calculating

selection

_{differentials,}

an infinite number of unrelated candidates

to selection was assumed

_{(conventional procedure).}

Since

_normality

is

_assumed,

_It,

equals 4

>ti

lp

i

where

₄

_>ti

is the ordinate of the standardized normal distribution at

point ti.

Correspondingly,

₇

_f

_

4>t; /pi.

L

i

=

age of the dams

(in years)

for

category

i,

whatever the sex of calves.

Longevity

and

_reproduction

_parameters

are needed for

linking

_group sizes

(m

i

, f

i

)

to the

_{corresponding}

selection thresholds

_(t

_i

_,

_tn.

It can be

_readily

shown

that for i = 1 _to

_3,

p

i =

mj /F8

j

and that for i = 4 _to

_6,

p

i =

m.1 /F’8

z

.

For

pi ,

replace

mi

by f

i

,

and

Bi by

_0*1

8

j

is the

_expected

available male progeny per initial

single

cow

_(i

_<

₃₎

or _per initial

dummy

cow

(i

>

_3),

_insisting

on the fact that

family

size is not restricted

_(eg,

1

male _per

_sibship

or _per

sire).

B2

is the

expected

available female _{progeny per} initial

_single

cow

(i

_<

3)

or _per

initial

_dummy

cow, with unrestricted

family

sizes.

Functional

_{relationships}

are obvious:

_B

₄

=

C

0

1

,

5

B

=

C

0

2

,

8

6

=

_c8

₃

_i

B4

=

C

01*, ()&scaron;

=

C

()2

’

8§

=

c83

(dummy

cows have more

_{progeny) and 0*}

₌

_c8

₃

_(female

_embryos

are

cloned and male

_embryos

are

not).

Let us take an

example

where the

_proportion

of heifers able to calve

₍

_1’1

₎

is

0.9,

the

_proportion

of first calvers able to calve

_again

is

_0.9,

the

_proportion

of the latter animals

_responding

to

_{superovulation}

is

_0.7,

10

_embryos

₍₂

x

₅₎

are

collected per

treated

cow, the

embryo

survival rate is

0.6,

the calf survival rate is

All the members of a selected clone are allowed to breed.

The

_high

value for

_B6

_originates

from the fact that

_cloning

acts twice for female ET _progeny;

_{firstly by}

_multiplying

the number of cows of a

_given

_genotype

and

secondly by

multiplying

their female _progeny.

The accuracy of evaluation of the

_single

dams is

_equal

to _pl =

p 2 =

p 3 = h

(square

root of the

_{heritability).}

Since cloned females are

dispersed

over _many

farms with no common environmental

_effect,

and the assumed

_genetic

variation is

only

additive

_polygenic,

then:

Because the constraints on the group sizes are linear

_(E

_i

_m

_i

=

_constant;

m

3 + m6 +

f

3

+

₌

₆

_f

fixed number of

_embryos

transferred x survival rate =

constant),

the annual

genetic gains possible

with a

_given

combination are

expressed

in reference to these variates and the

_optimization

of the non-linear function was

performed

according

to a

_{Newton-Raphson procedure}

_{(&dquo;inner&dquo; iteration)}

after

eliminating

2 group sizes as a result of both constraints

(The

dependent

variates are

ms = M - _{nzl - m2 - m3 - m4 -}

m

6 and

f

6

= total number of transferred

embryos

x

_embryo

survival rate x calf survival _{rate -m3 - ms -}

!3).

This is considered as

a safe

_procedure

for

_converging

towards a

_global

maximum

_{(Scales, 1985)}

when the

corresponding

derivatives can be

analytically

derived

(see appendix).

During

this

optimization,

subgroup

and clone numbers were allowed to be

_non-integer.

Deterministic evaluation of the

_asymptotic

rate of

_{genetic gain}

under a

Bulmer model

Male and female

_populations

were considered as infinite and selection differentials were

_computed

_accordingly.

_However,

reduction of

_genetic

variance

_through

induced

At the

_equilibrium,

the

_genetic

variance _among unselected males

_(V

_AM

was

_equal

to 0.5 initial

_genetic

variance

_(V

_AO

₎

+ 0.25

_genetic

variance _among bull sires +0.25

genetic

variance among bull dams.

The

_genetic

variance _among bull sires was

equal

to

_V

_AM

_{(1 -}

_ZR

₂

₎

where Z

was the

_{proportionate}

reduction of variance after selection _among the estimated

breeding

values of sires and where

_RÃ1

was the

squared

_accuracy of these EBVs.

n = number of

daughters

per bull for

progeny-testing;

V

AF

=

genetic

variance among unselected

females;

V

E

= environmental variance.

The

_genetic

variance _among bull dams was

_equal

to:

where:

_W

_i

was the reduction of variance after selection _among the estimated

breeding

values of dams of

_group

i males:

In the last

_{expression, u corresponded}

to the

_genetic

difference: subcohort of

clones - subcohort of

_singles

_(for

the same _year of

_birth).

In the

_nucleus,

_V

_AF

_represented

the

_{pooled genetic}

variance between

_single

heifers

and distinct clones

_altogether

_(ie,

_V

_AF

is

_larger

than the

_genetic

variance between unselected

_heifers,

since some of them are

_replicates).

_V

_AF

can be calculated from

the same formula as for males

_by

_replacing

_by

_i

_W

_W

_Z

_*

_(reduction

of variance after selection _among the estimated

_breeding

values of dams of

_group

_{i females),}

mi

by

Reasoning

after

_{asymptotic equilibrium}

was

_obtained,

it can be shown that:

As for the

_previous

_study

on

_optimizing

_embryo

_sexing

_only,

_optimization

was

carried out at two

_levels,

within and between sets of

_genetic

_parameters,

until

predicted

genetic gains

and

_genetic

_parameters

_eventually

stabilized.

1

Simulation of the

_asymptotic

rate of

_genetic

_{gain undei-}

a Bulmer model

Single

performances

were

_generated

_by

_adding

a random environmental effect

(constant

variance

_equal

to

_3),

to a

_{genetic effect}

(initial

_genetic

variance

_equal

to

₁₎

which

_corresponded

to the _average

_{parental breeding}

value

_plus

a random within

family

segregation

effect

_(constant

variance

_equal

to

_0.5).

This last

_assumption

was introduced for the sake of

_consistency

when

_comparing

results with Bulmer’s

predictions.

Clonal

_performances

were

_generated

in the same _way

_except

that the

environ-mental variance for the _average of the ₇₁ c animals involved in the same clone was

equal

to

_3h

_lC

_.

The selection _pressures and _groups sizes used for the Nlonte-Carlo simulations

were those

_given

_by

the

_optimization

_procedure

under a deterministic Bulmer

model,

for the same set of technical parameters.

The _response to

_{superovulation}

was simulated

exactly

in the same manner as

in the

_prediction,

_ie,

a

probability

of non-response

equal

to 0.3 and for

_responding

cows, a constant number of transferable

_embryos.

The number of

_embryos

used for

describing

the situations

_corresponded

to the average number of

embryos

for all cows, as in the

prediction.

The

_asymptotic

rates of

_gain

were evaluated between annual cohorts 90 and 100

(starting

from an unselected

_population

at cohort

_zero).

The

_regression

coefficient

of the average

points

on _year was then measured. Each _average

_point

represented

the _average of 200

_replicates

for _every scheme.

Accounting

for

_inbreeding

Though

the main

_{predicting algorithm}

and the

_previous

Monte-Carlo simulations assumed a constant within

_family

_genetic

_variance,

this

_assumption

was removed

during

some additional Monte-Carlo simulations where this variance was

multiplied

by

1 -

2

1

(F

S

+

_F

_D

₎

where

_Fs

and

_F

_D

were the

_inbreeding

coefficients for sire and

dam

_{respectively.}

The

_objective

of these additional

_computations

was to examine whether

_ranking

between alternative schemes could be

_{significantly}

affected when

moving

towards more realistic examination of the results and to throw some

light

on

_possible

future studies about how to use

_cloning.

In our

layout, overlapping

_generations

_during

100 _years led to

_heavy

manipu-lations on

_kinship

matrices. To save

_computations

time and

_storage,

these addi-tional Monte-Carlo simulations were restricted to situations where the number of

genetically

different dams were rather limited

(fewer

than _{100 per} annual cohort of

Situations

_investigated

Given that each

_physically

different donor

_provided

8 or 10

embryos

(after

2

collec-tions)

the survival rate of which was 0.4 or

_0.6,

situations were

investigated

where

1 000

_embryos,

2 000

_embryos

and 4 000

_embryos

were transferred to

_recipients.

Within each such

_situation,

variations for the number of live members _per female clone were introduced. The overall _range of this number

_(c

in the

_equations)

was

_3,

5,

10, 20,

30.

RESULTS

Bulmer

_predictions

for moderate

_cloning

Table III shows the results obtained

_by

_{optimizing sexing}

and

_cloning

with 3 or 5

members _per clone. These results are those of the

_{asymptotic genetic gain}

_including

Bulmer effect but

_{excluding inbreeding}

effect.

_Taking

the S scheme

_(embryo

_sexing

only)

as a

_reference,

it can be observed that this

_{asymptotic genetic gain}

can still be

enhanced after

_optimizing

the relative

_proportions

of

_single

and clonal

_populations,

and the

_{corresponding}

selection _pressures. The order of

_magnitude

is

+6%

for c = 3

and

-I-11%

for c = 5.

Table IV show that even for c =

_3,

the

of males is born from clones.

However,

the overall number of distinct clones born in a

_given

_{year is} not

_negligible

_(at

least 98 in these

_examples).

The basic facts

_explaining

such a result are that clones are similar to

_dummy

cows with much

_higher

accuracy of estimated

breeding

values and with much

higher

reproductive potential: good

genotypes can be found this way and disseminated into the nucleus

_breeding

_population

later on. Under these

conditions, breeding

status

of female clones resembles its

_counterpart

on the male side.

Table V shows that

_only

a small

proportion

of

_single

cows are

_selected,

a

consequence of a lower selection _accuracy.

However,

clonal selection intensities are

still _very

_high.

Combined with a

_high

selection _accuracy, this is the reason for the success of clonal selection vs

single

selection.

Verification

_through

Monte-Carlo simulations

The simulations were carried out

_during

a _very

_long

_{time span}

_ie,

100 _years,

_starting

from the no selection situation. The detailed results showed that the

_asymptotic

regime

was not obtained before year 50 because of the erratic variations

occuring

during

the first years of any

breeding

scheme,

the

relatively long

generation

interval

Examination in table VI of the

_{inbreeding-free}

simulations for the situations

where 5

_embryos

were obtained _per donor and per

collection,

and with a survival

rate

_equal

to

_0.6,

shows that the realized annual

_{genetic gains}

between years 90

and 100 were

_{substantially}

lower than the

_predicted

ones

(5

to

_14%).

c was then

The

_discrepancy

is similar to that found for the

_embryo

_{sexing schemes,}

under the

same

_{genetic assumptions}

(Colleau, 1991),

_except

for situations where the

predicting

algorithm

utilizes

_misleading

selection pressures obtained with fractional clones

(ie,

less than 1 clone

_provides

all the

_{replacement animals, given}

the total

_reproductive

capacity

of this

_clone).

This is the case for the situations with 1000

embryos

transferred and

c >

10.

_Giving

_up the basic

_assumption

that selection pressures

are continuous

_functions,

in order to

_adopt

a more realistic

_stepwise

function is useful for extreme situations but

hampers

numerical

_optimization

for more

_general

cases.

Accounting

for

_inbreeding

effects

When

_{cloning females,}

the useful number of dams decreases and

_therefore,

inbreed-ing

is

_expected

to increase.

Table VII shows that

_{limiting reproductive}

_capacity

of clones below that

theor-etically

achievable in order to reduce increases in

_inbreeding,

would lead to a

significant drop

of

_{genetic gains.}

If the overall

_capacity

of such clones

_corresponds

approximately

to the

_capacity

of a

_single

_cow, no

_advantage

could be found when

comparing

with

_embryo

_sexing.

This observation

_emphasizes

the role of

_reproductive

capacity

in such schemes.

Realistic

_{genetic gains}

were observed between _years 90 and 100 for situations

where c = 5 _or 10

(table VIII)

after

implementing

Monte-Carlo simulations

including inbreeding

effects. It was clear that a _very

_{significant drop}

_(about

- 20%)

occurred when

_compared

to the

_{corresponding inbreeding-free}

Monte-Carlo

simulations. This result is not

_surprising

due to the

_long

_{time span,} and the final

inbreeding

coefficients

_(0.20-0.25)

that affect

_genetic

variances _very much.

The annual

_inbreeding

rates obtained for c = 5 _are

primarily

the result of

_using

If selection were at random and if a _very

_large

number of females were

used,

the

annual

_inbreeding

rates would be around

0.17%

(1/24L

2

),

where L is the interval

between

_{genera.tions).}

Table VIII shows that

_going

from c = 5 to c = 10 led to a substantial increase of the

_asymptotic

annual

_inbreeding

rates.

_However,

even after 100 _years,

instanta-neous

_{genetic gains}

were still

_higher

with c =

_10,

despite

_a

larger discrepancy

with

the

predicted

results under a Bulmer model. The cumulated

_superiority

of the

sit-uation c = 10 us c = 5

corresponded

_to about 1 initial

genetic

standard

deviation.

The relative

_advantage

of

_cloning

more

_intensively

was all the more clear as the

overall number of females is

_higher

_(high

overall number of transferred

_embryos).

DISCUSSION

The

_previous

results showed that

_embryo

_sexing

and

_{cloning might}

be used for

breeding

purposes within

nuclei,

as

_{already suggested}

for beef cattle

_by

Smith

(1989).

Even with the severe constraint of a constant overall number of transferred

embryos,

some

_{cloning might}

enhance rates of

genetic gain

due to better selection

accuracy and

prolificacy

of female

genotypes.

This is not

_{contradictory}

to

_previous

results on conventional

_ET,

_showing

that

_{genetic gains}

increase with

_prolificacy

coming

from

_{high superovulation}

rates

_(Nicholas

and

_Smith,

_1983;

_Colleau,

_1985;

Meuwissen,

1990).

The

_complexity

of current

_algorithms

for

_predicting

F values under selection

adjustment

of

_predicted

_{genetic gains}

for these values and

_{subsequent algebraic}

op-timization.

_Therefore,

no

_analytical

solution was

_proposed

for

_finding

the

_optimum

size of a

_given

clone for

_breeding

_purposes. Predictions under the Bulmer effect

led to the

_finding

that

_genetic

_gains

were

_larger

as clone size increased. It can be

questioned

that the

_optimum

number of clones is 1 since

_high

values for F would

be deleterious for

_{genetic gains.}

The observations

_coming

from Monte-Carlo simulations

_accounting

for

inbreed-ing

were _very

_interesting

since

_they

showed that additional

_{genetic gains}

could still be obtained after

_changing

from 5 members

_{(live females)}

per clone to 10 members

per clone.

Therefore,

keeping only

5 members

(moderate cloning)

would

probably

not be a bad solution because this situation is still in the

_ascending

_part

of the

curve of

_genetic

_gains.

In

_comparison

with _pure

_{embryo sexing}

without

_cloning,

the

_superiority

of such a scheme could

_correspond

to about

10%

of

_genetic

_gain.

It

_should

be mentioned that in this

situation,

the

_optimum

_organization

becomes

very

simple,

since all the male and female

replacements

come from cloned females

superovulated during

lactation 2.

It is not certain that this

_finding

could be

_generally

obtained in every kind of

1 B /

IOET on

_dairy

cattle. Some characteristics of the schemes

_analysed

here allow

them to take

_profit

from

_cloning

without

_suffering

too much of its main

_drawback,

ie a virtual lift for

inbreeding

rates.

Indeed,

annual

_inbreeding

rates are not too

excessive

_{(around 0.25%)}

because of

_{relatively long}

interval between

_generations

(around

5

_years),

and of

_{relatively high}

numbers of dams _per

_generation.

When

considering

the situations &dquo;5 members _per clone&dquo; for tables IV and

_V,

the number of female clones per

generation

used for

_providing

dams is about 50 for 1 000

_embryos,

100 for 2 000

_embryos

and 200 for 4 000

_embryos.

This

_rough

estimate

_corresponds

to the number of years per

generation

(5)

multiplied by

the annual number of new

clones candidates for selection and

_by

the selection pressure used for

providing

the

larger

group of females

(group 6).

Fyirthermore,

selection on

_performance

for females

rather than on EBVs has been

_already

referred to as a _way to moderate

_inbreeding

increases,

ie

_protecting

_{long-term genetic}

_gains

while

_{obtaining good}

short-term

gains

(Dempfle,

1990;

Senou,

1990;

Toro and

_{Perez-Enciso,}

_1990;

Verrier et

_al,

1991).

Analytical

optimization

becomes easier in such a case. To end

_with,

it should

be recalled that any

cloning

of sires in such schemes would be

detrimental,

since

the limited number of sires

_{already explains}

the

_major

_part

of

_inbreeding,

before

any

cloning.

Inbreeding

depression

might

affect

_performances

as

_well,

if non-additive

_(eg,

dominance)

genetic

variation occurs

_ie,

a situation not envisioned here.

_Taking

inbreeding depression

into account would lead to

_change

the

_genetic

model and to

adapt

the

_prediction

_{theory accordingly.}

Given the numerous

_precautions

alluded to

_{previously, embryo cloning might}

be considered as a 2 sided

_activity:

the first side

_{corresponding}

to detection and utilization of

_good

female clones for

_breeding

purposes within selection

nuclei,

the second side

_(not

considered

_here)

_{corresponding}

to a

_larger

diffusion of the _very best

clones into the

commercial

populations

(supposing

that

_recloning

of stored

_embryos

is

_technically

_feasible).

_Moving

from one to the other would

_require

no additional

by cloning

to diffuse the _very best of

_accurately

known females

_(thus

_contributing

to

_dairy

_economy)

should be

stressed,

even in the case where the annual

_genetic

gains

are unaffected. The fact that these

_{genetic gains}

seem to be

_slightly

_improved

in addition allows one to

_keep

this conclusion.

A

_major

_part

of the

_present

_findings

and of the

_{corresponding}

recommendations

for a

possible

future

implementation

within and outside selection nuclei does not

coincide with those of

_previous

works on

_{embryo cloning}

in

_dairy

cattle and

_showing

small losses on

_{genetic gains}

_(Teepker

and

Smith,

1989;

Woolliams, 1980;

De

Boer and Van

_Arendonk,

_1991).

Because no

cloning

was recommended within the

nucleus,

the

_question

about how to

_improve

the accuracy of evaluation on clones

disseminated into commercial herds remained open,

contrarily

to the

_present

_study.

It can be assumed that the set of constraints used has a

_{major impact}

on the results

obtained. The afore-mentioned researchers set _up their constraints on fixed numbers

of recorded females

_{(testing capacity)}

and most of

all,

fixed numbers of sires and dams.

_Subsequent

introduction of

_cloning

in this context led to substantial decreases

of selection intensities.

_Here,

recorded females were

_supposed

to be

_dispersed

among conventional

farms,

as

_part

of a

regular

milk

recording

scheme,

so that

the overall number of transferred

_embryos

could be chosen as the main constraint.

Furthermore,

the number of dams was not fixed but

owing

to the moderate

_cloning

rate

_envisioned,

no

_major

_consequences

on

_inbreeding

rates ensued.

APPENDIX

Derivatives needed for

_optimizing

the

_{genetic gains}

_(nucleus

with

_embryo

sexing

and

_cloning

Pl, tni, .f!! e!, e2 , t2, ti ,?!!, !i ! It!, It! , !t; ! !t; , Nj, F, F’,

c are defined in the main text.

Let us define

AG,

the

_asymptotic

annual

_genetic

_gain

is

_equal

to the ratio

_u/v

where the full

expression

of u and v is

_given

in the Materials and Methods.

The first derivatives of u and v with

respect

to ml, m2, m3, , 4mm!,

f

l

,

,

2

f

f

3

,

f

4

,

f

5

are _very

_simple:

The second derivatives were obtained from the

general

expression

of the

deriva-tives of u or v

according

to _any

_couple

of variates

_(a;,!

_/

_).

This

_procedure

led to

rather cumbersome

_expression

_(available

on

_request

to the

_author)

but _easy to

implement

since the first derivatives

_{6F/6x, 8F’/6x, 6m}

_i/

_6x,

_bf

_i/

_6x

are

straight-forward

_{(1, -1, 0,}

or

-1/c

depending

on the

case).

ACKNOWLEDGMENTS

Two anonymous reviewers are

_acknowledged

for useful

_suggestions.

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