Expected efficiency of selection

Original

article

Expected

efficiency

of

selection

for

_growth

in

a

French

beef

cattle

breeding

scheme.

I.

_Multistage

selection

of bulls

used in

artificial insemination

F

_Phocas,

JJ

_Colleau,

F

Ménissier

Institut national de la recherche

_agronomique,

station de

_genetique

quantitative

et

appliquee,

78.352

Jouy-en-Josas cedex,

Prance

(Received

24

_{February 1994; accepted}

18 October

₁₉₉₄₎

Summary - Genetic

_improvement

of beef cattle for

_growth

traits

implies

selection on

both direct and maternal effects

_through

on-farm and station individual and progeny

performance

tests. To

_optimize

the use of these

_tools,

a French selection scheme of

artificial insemination

_(AI)

bulls is

_modelled,

_including

its main _components, ie 2 kinds of station

_performance

tests and 2 kinds of _progeny tests

_(farm

and

_station).

Three

_breeding

objectives

are derived in order to _represent the

_{heterogeneity}

of

_production

_systems: Hs for suckler

herds,

Hf for

_{suckler-fattening}

herds and an _average

_{objective Hg considered}

as

the most realistic for the whole breed. These

_objectives

include direct and maternal

_genetic

effects on

_{weaning weight}

and direct effects on final

weight. Economic, demographic

and

genetic

parameters are derived for the Limousin breed.

Multistage

selection

procedures

are

_{algebraically optimized by finding}

selection thresholds which maximize response for the

_{breeding objectives.}

The current scheme appears to be more efficient for Hf than

for Hs.

However,

whatever the

_objective,

maternal

genetic

response is

expected

to be

slightly negative,

due to a

_negative

correlation between direct and maternal

genetic

effects. Standard deviations of

_genetic

responses are calculated to take into account some

uncertainty

on estimates of

_genetic

_parameters. With a 95% confidence

_interval,

maternal

genetic

response could be

positive.

An alternative to this

_complex

scheme is

_considered,

using

only

one kind of station

_performance

test and the on-farm progeny test. The increase of on-farm progeny test

_capacity

reduces the value of station progeny test for

_selecting

AI

bulls,

at least when

_only

direct and maternal effects on

_growth

traits are considered. For

the

_{simplified scheme,}

maternal response is

expected

to be positive,

though

uncertain due

to a

large

standard deviation.

Résumé - Prédiction de l’efficacité d’un schéma de sélection _français sur la crois-sance en race bovine allaitante. I. Sélection par étapes des taureaux destinés à

l’insémination artificielle. En races bovines

allaitantes,

l’amélioration

_génétique

des caractères de croissance _{passe par} la sélection des

effets

directs et des

_effets

maternels par

contrôles individuel et de

descendance, en ferme

et en station. Pour

_optimiser

_l’emploi

de

ces

_outils,

un schéma de sélection

_français

des taureaux d’IA a été modélisé en considérant ses

_{principales complexités :}

2

_types

de stations de contrôle individuel et 2 types de contrôles de descendance

_(en

_ferme

et en

station).

Afen

de

_prendre

en _compte

l’hétérogénéité

des

systèmes

de

_production,

.i

_objectifs

de sélection ont été établis : Hs pour les

élevages

naisseurs, Hf

pour les

élevages naisseurs-engraisseurs

et un

_objectif

_moyen

_Hg,

considéré

comme le

plus

réaliste _pour l’ensemble des _troupeaux de la race. Ces

_objectifs

comportent

les

_effets

directs et maternels sur le

poids

au _sevrage ainsi _que les

effets

directs sur le

poids

final d’engraissement.

Les

_{paramètres économiques, démographiques}

et

_génétiques

utilisés

correspondent

à la situation de la race Limousine. La sélection à

plusieurs étapes

est op-timisée

_{algébriquement}

en calculant les seuils de troncature

_qui

maximisent la

_réponse

sur

l’objectif

de sélection. Le schéma de sélection semble

_{plus efficace}

pour un

_objectif

naisseur-engraisseur

que pour un

_objectif

naisseur.

_{Toutefois, quel}

que soit

l’objectif,

la

réponse

sur les

_effets

maternels est

_{légèrement négative}

en raison de

_{l’antagonisme génétique}

entre

_effets

directs et maternels. L’incertitude sur les estimées des

_{paramètres génétiques}

est prise en _compte en calculant les écarts _types de

_réponses

à la sélection. Si l’on

con-sidère l’intervalle de

confiance

à

_95%,

une

_réponse

_positive

_pourrait

être obtenue sur les

effets

maternels. Un schéma

_simplifié

a été

étudié,

n’utilisant

qu’un

seul _type de station

de contrôle individuel ainsi _que le seul contrôle sur descendance en

_ferme.

Dans une

per-spective d’accroissement de la

_capacité

d’évaluation sur descendance

en ferme, il apparaît

qu’une

sélection de taureaux d’IA sur descendance en station

_perd

de son intérêt

_technique,

du moins

_quand

seuls les

_effets

directs et maternels sur la croissance sont considérés. En schéma

simplifié,

une

_{réponse positive}

est

_espérée

sur les

_{effets maternels,}

mais n’est _pas

assurée,

en raison de

l’importance

de l’écart _type de la

_réponse.

bovin allaitant

_/

objectif de sélection

_/

croissance

_/

effets maternels

_/

variance d’échantillonnage

INTRODUCTION

Beef cattle

_breeding

in France takes 2 kinds of traits into account

_(M6nissier

and

Frisch,

1992):

beef traits

_(growth,

_morphology,

feed

_efficiency,

carcass

quality)

and

maternal

_performance

_(fertility,

ease of

calving, mothering

ability).

From a national

viewpoint,

the relative economic

_importance

of these traits

_depends

on the relative

proportion

of suckler herds and

_{suckler-fattening}

herds. In a suckler

_herd,

calves are sold at

_weaning

_(around

7-8

_months)

to be

_partly

fattened outside

_France,

in

a

_{suckler-fattening}

_herd,

calves are reared to

_slaughter

at around 14-18 months. Over the last 10 years, the decrease of industrial

crossing

and the need for

_reducing

production

costs and labor

_requirements

have led to more

_emphasis

_being

_placed

on

beef cow

productivity

(M6nissier, 1988).

This has led to the introduction of

_specific

evaluation

_procedures

for maternal

_performance

into French beef cattle

_breeding

schemes

_(M6nissier

et

al,

1982).

Modelling

and

_optimization

of these

_breeding

schemes

_{imply taking}

into account

independent

culling

levels on

_highly

correlated

_traits;

the

_{heterogeneity}

of

_genetic

levels among newborn candidates for selection due to the

_joint

use of natural service

(NS)

and artificial insemination

_(AI)

bulls;

and the

_{large uncertainty}

in estimates of certain

_genetic

_parameters,

_especially

_concerning

correlations between direct and maternal effects.

The purpose of this paper is to

_analyze

the

_{predicted efficiency}

of the current

AI bull selection scheme for

_growth,

when maternal effects are considered. This

is an extension of

previous

work

_(Colleau

and

_Elsen,

₁₉₈₈₎

which considered

_only

selection on direct effects for final

_weight.

The

_study

uses the

_parameters

and the

scheme

_organisation

of the Limousin

_breed,

taken as a

_{representative example}

of

French beef cattle

_breeding

schemes.

Three

_major

_questions

are

_investigated

in this first _paper.

1)

How can the AI

bull

_multistage

selection in the current

_breeding

scheme be

_optimized?

₂₎

Given the accuracies and

_sampling

correlations of the estimated

_genetic

_parameters,

what is _{the accuracy of}

_{predicted responses?}

₃₎

Should alternative

_breeding

schemes be

envisaged

for AI bull selection ? The

_objective

of the next paper in this issue

_(Phocas

et

_al,

₁₉₉₅₎

is to take into account both

_reproduction

methods

_(AI

and

_NS)

and

female selection

_paths.

For both papers, theoretical

problems

of

general

interest are

investigated.

How can we calculate the accuracy of

predicted

responses ?

How can we calculate

asymptotic genetic gains

in

_{heterogeneous populations ?}

MATERIALS AND METHODS

The

_meanings

of abbreviations used in the text and tables are

_given

in

Appendix

L

Deriving

a relevant

_breeding

_objective

The economic values of beef cattle

_production

traits differ

_according

to

_production

systems

and circumstantial

_parameters,

as recalled

by

Doren et al

(1985).

Hence,

the derivation of the selection

objective

should account for the existence of 2 main kinds of

_production

_{herds, depending}

on how _progeny are sold: at

_weaning

in a

suckler

herd;

and after

_fattening

in a

suckler-fattening

herd. Calves were assumed

to be sold at a constant _age: 210 d at

_weaning

_(67%)

or 500 d after

_fattening

(33%).

Only growth

was considered in the

_present

_study.

In order to

_distinguish

the

genetic

influence of dam’s

_{suckling ability}

on calf

growth

from her

_genetic

direct

transmitting

ability,

a suckler herd

_{breeding objective}

(Hs)

was

_derived,

which

includes maternal effects

_(M210)

on

_weaning

weight

(W210)

together

with direct

effects

_(A210).

For

_{suckler-fattening}

herds,

the

_{breeding objective}

_(Hf)

also took into account direct

_(A500)

on final

_weight

_(W500).

A combined

_objective

_(Hg)

was

built from Hs and Hf to

_represent

the true economic

_objective

of the breed. The economic

_weights

of

_Hg

were derived from the relative

_proportion

of calves sold at

weaning

(2:3)

compared

to calves sold at 500 d

_(1:3):

_Hg

=

2/3

Hs ₊

1/3

Hf.

In order to maximize the

_profit

for trait i _per animal

_sold,

the

_partial

derivative

of

_profit

with

respect

to a unit

_change

in that trait was

computed.

This is called

the economic

_margin

_(a

_i

₎

for trait i. Direct and maternal

_expression

of the same

trait were considered as 2 different

_{traits j}

and

k.

_Figures

used for derivation

costs differ

_according

to sex.

_Thus,

economic

_margins

were

_computed

for each sex

and average values were derived

_{by weighting}

values for each sex

_by

the relative

frequency

of males

_{(or females)}

sold. The

_prices

used were those indicated

_by

Belard

et al

_(1992).

Relative economic

_margins

are

_basically

_dependent

on

_assumptions

about

_feeding

diets. Direct effects on

_{preweaning growth}

are less

profitable

than

maternal

_effects,

because an additional

_kilogram

of

_{weaning weight}

due to direct effects was obtained from

_concentrate,

which is an

expensive

feed source

_compared

to milk. Growth from maternal milk is more valuable because dams

_partly

_produce

milk from

_forage

and

_pasture,

ie a

_cheap

feed source.

_Likewise,

economic

_margin

per additional

kilogram

of final

weight

was

_higher

than before

_weaning,

because

cheaper

feed sources, such as maize

_silage,

are used.

A

P

pendix

II

_presents

a full

description

of the calculation.

FF: French francs.

The

_{following breeding objectives}

_{(in FF)}

were

_derived,

with As and Ms in

kilograms:

-

the suckler

_objective:

Hs = 10 A210 ₊ 14 M210

- the

suckler-fattening

objective:

Hf = _-5 A210 - 1 _{M210 + 12} A500

- the

global

objective: Hg

= 5 A210 ₊ 9 M210 ₊ 4 A500

In the

past,

some theoretical studies

(Hanrahan,

_1976;

Van Vleck et

_{al, 1977;}

Hanset, 1981;

Azzam and

_Nielsen,

₁₉₈₇₎

_presented

_{breeding objectives}

with the

same economic

_weight

for direct and maternal

_effects,

without _any

_{justification}

of

this choice. As far as we

_know,

_only

Ponzoni and Newman

₍₁₉₈₉₎

_separated

direct and maternal effects in the

_breeding

_objective

for Australian beef cattle.

_However,

they

assumed that 1

_kg

of W210 due to direct effects has the same cost as 1

_kg

of

W210 due to maternal effects. The

_only

difference

_they

considered was the number

effects within a

_{20-year period}

and for a

5%

discount rate.

_However,

the ratio of

numbers of direct

expressions

to maternal ones

_depends

_very much on the discount

rate

_and,

to a lesser

_extent,

on the

_{assumptions concerning}

the

population

structure. For a zero discount rate and

_overlapping

_generations,

this ratio is

_{asymptotically}

equal

to 1 for any

population

structure without a closed nucleus. Since our _purpose was to calculate

_{asymptotic genetic gains}

_(Phocas

et

_al,

_1995),

we found that it was more consistent to derive the

_breeding

objective

from the

asymptotic

ratio of

expressions,

ie for the same number of direct and maternal

_expressions.

Description

of the

_breeding

scheme

The Limousin breed is the second French beef cattle breed with about 600 000 cows;

10%

of these cows are

_registered

and

_recorded,

and

_they

constitute the selection

nu-cleus. The AI rate is about

10%

in the nucleus and about

20%

in the whole Limousin

population.

The current selection _program has been

_implemented

since 1980 and

combines both AI and NS bull selection. Selection is

performed

in a

_sequential

_way

with

_{independent culling}

levels on individual and _progeny

_performance.

Complexity

is induced

_by

the existence of 2

_paths

for AI bull selection. Each of these

paths

im-plies

an individual station

performance

test and a _progeny

performance

test

_{(fig 1).}

In the first

_path,

AI bulls are selected after a

_’long

_performance

test’ and a progeny

test in station

_(M6nissier,

_1988).

Bulls are measured over 6 months on individ-ual

_growth,

muscular and skeletal

_development

and feed

_intake;

the _{progeny test}

concerns beef traits

(on

_young bulls’

production)

and maternal

_performance

(on

primiparous

daugthers).

More

recently,

some AI bulls have

_completed

tests from a

cheaper

selection program, which reduced costs for individual

_performance

_testing

(a

4-month

_period

without feed intake

_recording)

and for progeny

testing

(on-farm,

limited to direct effects on

_preweaning

performance).

This last test is

_performed

by

using

reference AI bulls

_(the

so-called ’connection

_sires’)

that

_provide

statistical

links for

_breeding

value estimation

_(Foulley

and

Sapa,

1982).

Exchange

between

both selection

_paths

is

_currenty

_developing.

Alternative

_breeding

schemes

_might

be

_envisaged

to

_simplify

the

_breeding

scheme and to reduce costs. For that _purpose, a

simplified

scheme was

_constructed,

considering only

’short

_performance

test’ in station and _progeny

_performance

test on-farm

_{(fig 2).}

The on-farm progeny index was modified to take maternal

performance

into account: a combined index of the _average W210 of 30 sons

and the average W120 of calves of bulls’

daughters

was built. It was assumed that

_heritability

of maternal effects is lower on-farm

_(h

₂

=

0.16)

than in station

(h

2

=

0.26),

since environmental effects are better controlled in station. Derivation and

_optimization

of selection differentials

Optimization

of selection differentials for the current

_breeding

scheme The AI bull selection is

_optimized

_{by considering}

each section of the current

breed-ing

scheme as a variate within an overall multivariate selection. This leads to the use of a method

_{previously developed by Ducrocq}

and Colleau

(1989)

for

normal distribution and

_treating

candidates for selection as

_independent

observa-tions.

_Optimum

selection thresholds are thresholds which maximize the selection

response.

Let us define the

following

variables:

X

l

,

the 210 d

_weight

_(W210)

X

2

,

the 400 d

_weight

_(W400)

X

3

,

the 500 d

_weight

_(W500)

X

4

,

the average W210 of 30 sons

X

5

,

the index

_(I

₉

₎

combining

the average W500 of 30 sons and the average W120

X

l

,

2

,

X

X

3

,

X

4

,

,

X

5

the

_breeding

value H and

components

of H are random

variables with a multivariate normal distribution. The function to maximize is the average

breeding

value

(H)

of the bulls

finally

selected for use in

_AI,

whatever the

origin:

where the ais and the

b

i

s

are the selection thresholds on the

X

i

variates.

To illustrate the

_reasoning,

let us consider the

_category

of on-farm _progeny tested

bulls selected from the ’short

_performance

test’. These bulls are not the best ones

at

_weaning;

their

_weight

W210 is lower than a first threshold _al but

_larger

than a second threshold

b

l

(b

l

<

X

l

<

_a

_l

_).

A second threshold occurs on

W400;

the

males selected for on-farm _progeny test are above a threshold _a2

(X

z

>

_a

₂

_).

A

final threshold a4 has to be added as the result of on-farm progeny test selection

(X

4

>

_a

₄

_).

Thresholds aland

b

l

for W210 are obtained

directly

(fig 1).

The other thresholds

are

computed

after

_optimizing

the above non-linear

function,

with constraints on

the

_proportion

of males selected for station _{progeny test}

_{(12:2 000),}

the

_proportion

selected for on-farm progeny test

(current

50:2 000 or

_envisaged

_{200:2 000)}

and the final

_proportion

of AI bulls selected

_{(20:2 000).}

A

_{Newton-Raphson algorithm}

is set up

taking

these constraints into account

through Lagrange multipliers.

Derivation of selection differentials for the

_{simplified breeding}

scheme

For the

_simplified

_scheme,

each threshold was obtained

_directly,

since the number

of candidates for each test is fixed

_(fig

_2).

_Thus,

there is no

_{optimization.}

Genetic

_parameters

Estimation

The

_genetic

_parameters

used in the

_present

_study

_(table

_II)

for direct and maternal effects on

_weight

at 120 and 210 d were estimated

by

Shi et al

₍₁₉₉₃₎

for the French Limousin breed. The other

_parameters

are literature _averages

(Renand

et

_al,

_1992).

Correlations between selection

goals

and selection indices are also

presented

in

table III. The

procedure proposed

by

Foulley

and Ollivier

₍₁₉₈₆₎

was used to test the

_consistency

of

_phenotypic

and

_genetic

covariance matrices.

Uncertainty

As underlined

_{by Meyer}

_(1992),

_sampling

covariances of estimates of variance

components

including

maternal effects are _very

high

even for

designs specifically

dedicated to the estimation of maternal effects.

_Thus,

the accuracy of

predicted

responses

(especially

indirect responses for maternal

effects)

should be assessed from

sampling

covariances of

_dispersion

_parameters.

_However,

these

_sampling

covariances

are seldom calculated because of

_{exceedingly high}

_computing

costs.

_Hence,

the

sampling

variance-covariance matrix of restricted maximum likelihood

_(REML)

estimates for

preweaning genetic

parameters

is derived from a theoretical

_layout,

roughly mimicking

the real structure of the data.

_Postweaning

parameters

are well

known

_{and, consequently,}

are not considered in this

_study.

The same _p unrelated bulls are sires

(S)

of a first _progeny

_generation

and

maternal

_grandsires

_(MGS)

of a second _progeny

_generation.

These bulls are also

unrelated to the p maternal

grandsires

of the first

generation

and the p sires of the second

_generation.

We

_additionally

assume that a constant number

_(d)

of calves is obtained from each

_pair

S-MGS and that these d

_offspring

are born from unrelated

dams. The statistical model used to

_analyse

these data is a bivariate

(W120

and

W210)

S-MGS model. For a c-trait model and the above

layout,

the

sampling

variance-covariance matrix of REML estimators is derived from matrices of maximal size 4c x 4c

_(Appendix

11!.

The number d of

_offspring

_per

_pair

S-MGS is

_equal

to 1 in our numerical

_application.

Three numbers of bulls are considered: _p =

_20,

45

or

_125;

the value 45 leads to coefficients of variation on additive variances around

0,

the vector of direct and maternal

_dispersion

parameters,

is

_easily

obtained from

₀

_*

_,

the vector of

_dispersion

_parameters

of the S-MGS model: e* = Me where

M is a constant matrix. Then

_Var(9)

=

)M-

’,

l

Var(e

*

1

M-

where

M-

l

’

is the

transposed

matrix of

M-

1

.

These

_sampling

variance-covariance matrices are then used to

compute

the

approximate

variance of selection _response H. H is

_{approximated by}

the first-order term of a

Taylor

_expansion.

As underlined

by

Harris

(1964),

this is a common

method for

_deriving

variance of

_complex

functions.

where

_e

_o

is the vector of unbiased

_point

estimates

_(E(e)

=

e

o

)

Obtaining

the first derivatives is tedious.

Thus,

they

are

_{computed by}

finite

differences of H:

where

_G

_i

₍₀

₀

₎

is the ith term of

_G(e

_o

₎

and ei is a vector of zeros

_except

the ith term which is

_equal

to e. For e between

10-2

and

10-

5

_kg

₂

_,

the results are _very stable: the first 4 decimals of the

_sampling

standard deviation of the standardized selection differential are

_always

the same.

RESULTS AND DISCUSSION

Efficiency

of the current selection scheme

Optimum

choice of AI bulls

according

to their

_origin

The

_optimum

number of AI bulls to select after on-farm _{progeny test} is almost

independent

of the

_objective

and of the farm progeny test

capacity

(either

50 or

200

_bulls).

It varies from 13 to 14 males out of the 20 AI bulls selected

_{(table IV).}

The

_majority

of AI bulls are selected after the on-farm _{progeny test} due to a

_larger

progeny test

capacity compared

to the station progeny test

_capacity

₍₁₂

_bulls).

However,

the

_probability

of selection is

_higher

for a _{station progeny} tested bull: more than

50%

(6

or 7 bulls out of

₁₂₎

versus less than

30%

(13

or 14 bulls out of . 50 or

200)

for on-farm _{progeny tested bulls. If the}

objective

includes final

weight,

the station progeny tested bulls are favored

because

the corresponding

direct effects are better assessed in the

_{’long performance}

test’. If the

_objective

concerns

_weaning

weight, they

are favored because

they

are the best at

_weaning

_{(fig 1)}

and also because the maternal

_performance

of their

_daughters

is assessed.

By

assumption,

all the AI bulls selected after station progeny test were first

evaluated in a

’long

performance

test’.

Conversely,

the location of

performance

test

of the 13 or 14 bulls selected after on-farm _progeny test

_depends

_very much on

breeding objective

and on _progeny test

capacity

(table IV).

At low _progeny test

capacity,

the numbers of these AI bulls first selected in the

_{’long performance}

test’

are

_9,

3 and

6,

respectively

for

_Hs,

Hf and

_Hg;

at

_higher

_progeny test

_capacity,

the

corresponding

numbers are

_3,

2 and 3.

Therefore,

different selection

policies

should

be

_employed

for bulls used in suckler herds or

_{suckler-fattening}

herds.

Selection responses

The maximal selection responses for each of the 3

objectives

studied are

_presented

in table V. In each case, the selection response in

Hg

is

_given

in order to evaluate the loss of

_efficiency

_occurring

when the

_objective

considered

_{(Hs, Hf)}

does not

correspond

to the true economic

_objective

for the breed

_(Hg).

At _{low progeny} test

_{capacity on-farm,}

selection responses range from 1.38 aHs

when

_selecting

on Hs to 1.72 _aHg when

_selecting

on

_Hg.

The scheme _appears

to be more efficient for

suckler-fattening

herds than for suckler herds.

However,

the

_{highest efficiency}

occurs when

_selecting

for

_Hg.

Whatever the

_objective,

an

improvement

of direct effects is

expected,

but the

genetic

trend of maternal effects

on W210 is

_negative

(table VI).

This stems

_basically

from the

_{genetic antagonism}

between direct and maternal effects

_(rg

=

-0.24).

Selection responses are

3-6%

larger

at

_high

versus low farm test

_capacity.

This increase is more

_significant

for

_Hg

than for Hs or

_Hf,

due to the

_higher

_accuracy of

on-farm progeny selection index

If,

(table

III)

for

predicting Hg

than for

predicting

Hf or Hs.

_Moreover,

the

_impact

of a

_higher

farm _{progeny test}

_capacity

is less

significant

for Hs than for

_Hg

or

_Hf,

since farm _progeny tested bulls are not

Whatever the

_objective,

selection response for

Hg

has been derived. From this

calculation

_(table

_V),

it can be concluded that selection _response is robust to errors

Limousin

_population

_(evaluated

on

_Hg)

would be

_negligible

whatever the

_breeding

objective:

-3 and

-1%

when

_{breeding objectives}

are Hs and

_Hf,

_{respectively,}

at low progeny test

_capacity;

-1%

whatever the

_objective,

at

_higher

_{progeny test}

capacity.

Change

in

_efficiency

in a

_simplified

selection scheme

The evolution of

_efficiency

_depends

_very much on the

_objective

and on-farm _progeny

test

_capacity

_{(table V).}

At low

_capacity

of on-farm _progeny

_test,

the differences between the 2 schemes in selection _{responses range} from -12 to

+2%.

The lowest value is for the fattener

_objective

_(Hf),

the

_highest

for the calf

producer

objective

(Hs).

If selection concerns final

_weight,

_{simplification}

of the scheme leads to a loss

of

_efficiency

since final

weight

is better assessed in the

_{’long performance}

test’. If selection concerns direct and maternal effects at

_weaning,

it leads to a

_gain

of

efficiency

since all bulls _progeny tested are evaluated on W210 of their sons and on

the maternal

performance

of their

_daughters.

At

_high

on-farm _progeny test

_capacity,

a

_large

_gain

of

_efficiency

occurs when

_selecting

on Hs

(32%)

or

Hg

(5% )

with the

simplified scheme;

the loss of

_efficiency

when

_selecting

on Hf is still

11%.

In the

_{simplified scheme,}

_positive

maternal _response is

_expected

for Hs and

_Hg

at _{low progeny} test

_capacity,

whatever the

_{breeding objective}

at

_higher

progeny test

_capacity.

Accuracy

of

_predicted

selection _response

Some idea of the variance of

_predicted

response is

required

to

_plan

and

_justify

a

breeding

progam.

Assuming

that

genetic

parameters

are

_{really known, variability}

of selection _response is due to

_genetic

_sampling

and drift. Woolliams and Meuwissen

(1993)

show how

_sampling

variance and

_expectation

of selection _response can be

weighted

to choose between alternative

_breeding

schemes

using

utility theory.

In our

study,

another

_aspect

is

_considered,

the variance of the

_predicted

_response due to inaccurate estimates of

_genetic

_parameters.

The _purpose is to

_clarify

the situation for maternal

_genetic

_response.

Sampling

variances and correlations

Three different levels of

_uncertainty

in

_genetic

_parameters

of W120 and W210

are

_studied,

_depending

on the number of bulls evaluated as sires and maternal

grandsires:

20,

45 or 125 bulls. The

_sampling

variances and the

_sampling

correlations

between estimates of

_genetic

_components

are

_presented

in tables VII and VIII

respectively.

It should be noticed that the

_magnitude

of

_sampling

variances and correlations is

_{nearly independent}

of the trait considered

_(W120

or

W210).

For the case of 20

_{bulls, uncertainty}

(expressed

as the ratio of the

_sampling

standard deviation to the absolute value of the estimate of

_genetic

_component,

called coefficient of

_variation)

in direct

_{(co)variances}

is around

40%

whereas

_uncertainty

in maternal

_{(co)variances}

is around

80%.

Uncertainties in direct and maternal

(co)variances

decrease to 20 and

30%

respectively

in the case of 45 bulls and to 10 and

14%

in the case of 125 bulls. However the

_largest

uncertainties concern the

case of 20

_bulls,

100%

for the case of 45 bulls and

50%

for the case of 125 bulls.

Sampling

correlations do not differ very much

according

to the number of bulls. Whatever the number of

bulls,

the

_{highest sampling}

correlations

_(in

absolute

_values)

are obtained between

_genetic

_components

of the same kind

(2

additive

(co)variances,

or 2 maternal

_{(co)variances,}

or 2 direct-maternal

_{covariances).}

Within

_trait,

our results lead to the same conclusions as those obtained from

different structures of data and different

_genetic

_parameters

_by

_Meyer

_(1992).

Sampling

correlations between additive or maternal

_genetic

variance and the direct-maternal covariances are medium

(0.3-0.6).

_Sampling

correlation between additive

variance and maternal variance is smaller than

previous

correlations. In our

_study,

this correlation is around

_0.07;

in

_Meyer’s

work the value

_ranged

from 0.04 to

_0.48,

depending

on the structure of data.

Standard deviation of

predicted

selection responses

Standard deviations of

_predicted

selection responses are

presented

in table IX

for the 3

_sampling

variance-covariance matrices defined above. These standard deviations are similar whatever the structure of the selection scheme

_(current

or

simplified),

but

_depend

_very much on the

_{breeding objective. They}

are

_high

for Hs

and almost nonexistent for Hf. This is

_easily

_{explained by}

the fact that

_uncertainty

was

only

considered for

_preweaning

_parameters.

Sampling

standard deviations of

differentials for Hs are in the _range of

_uncertainty

in maternal variance of W210.

Standard deviations for selection differentials in

_Hg

are in the range of uncertainties

in direct

_genetic

variances. For the current

_scheme,

these standard deviations

are

_nearly

_independent

of the _progeny test

_capacity.

For the

_{simplified scheme,}

standard deviations increase when progeny test

capacity

increases. More males

are evaluated on maternal

_performance

and thus the

_uncertainty

in

_preweaning

parameters

has a

larger

_impact.

The same comments can be made for the standard

deviations of the

_objective

_components

_{(table VI).}

Standard deviations of direct and maternal _{responses in} W210 are in the _range of the

_respective

uncertainties in direct and maternal variances for W210. If

95%

confidence intervals are

_considered,

the

_following

remark must be made. For the current

_scheme,

the

_predicted

maternal response could be

positive

but for the

simplified

scheme it could be

negative.

In animal

_{breeding, only}

Tallis

_(1960),

Harris

₍₁₉₆₄₎

and Sales and Hill

_{(1976a, b)}

seem to have considered the influence of uncertain statistical

_dispersion

_parameters

on the variance of

_{predicted genetic gains.}

_They

found

_high

variances of

_predicted

efficiency

of a selection index. Our

_study

for a more

_complex

selection

_suggests

that

this

_aspect

should not be overlooked when

_setting

_up

_{breeding plans}

and

_evaluating

genetic

responses.

Analysis of sensitivity

to direct-maternal correlations

Alternative

_analyses

were carried out

_according

to different values of direct-maternal correlation

_(r

_AM

_):

rAM = 0 and _rAM = -0.6.

Indeed,

very variable values

are observed in the literature. Table X

_presents

_{corresponding}

_{selection responses for} the 3

_objectives

and for the 2

_breeding

schemes considered in this

_study.

Of course, all the selection responses are lower when rAM is more

_negative.

Hovewer

only

maternal response and response in Hs are _very sensitive to rAM value. Whatever

the direct-maternal correlation

_(between

0 and

_-0.6),

the choice of the most efficient

breeding

scheme is

_unchanged.

The

_simplified

scheme is

_really

_interesting

_(compared

to the current

_scheme)

for

_high

_progeny test

_capacity

and

_objective

_Hs;

the

_gain

in

_efficiency

in Hs is

_higher

as direct and maternal effects are

opposed

(42%

for

r

AM = -0.6 instead of

26%

for _rAM =

0),

because,

in the

simplified

scheme,

a

_larger

number of bulls are evaluated on maternal

performance.

For the same _reason, the

loss in

_efficiency

in Hf due to

_{simplification}

of the

_breeding

scheme is

_higher

as

r

AM becomes

negative.

The same comment can be made for

_Hg

at low _progeny test

capacity.

At

_higher

_progeny test

_capacity,

a small loss in

efficiency

in

Hg

(-3%)

is

observed for very

negative

direct-maternal correlation

_(r

_AM

=

-0.6),

but otherwise

CONCLUSION

In this _paper,

_only

a section of the whole

_breeding

scheme of a beef breed was

considered,

ie the

_multistage

selection of AI bulls. The next _paper will

present

calculations of

_{expected genetic gains}

for the selection nucleus. Current French beef bull selection programs, such as the Limousin _progam, can

_{provide important}

genetic gain

for

_objectives

_concerning

direct and maternal effects on

_growth.

The

scheme _appears to be more efficient for a suckler-fattener’s

_objective

_(Hf)

than

for a suckler’s one

(Hs).

A combined

_{objective Hg,}

which combines Hs and

Hf,

is taken as a reference for economic

_profit

of the whole breed. Whatever the

breeding

objective

considered to derive

optimal

selection

_thresholds,

response in

Hg

is robust and is

_larger

than _{responses in} Hs and Hf. This _{is very}

_satisfying

from a national

viewpoint.

A

_slight

_{negative genetic}

_{response in} maternal effects

is

_predicted,

but is

_subject

to

_uncertainty

in

_{preweaning genetic}

_parameters.

This is

_relatively

_{disappointing}

since

_improving

maternal effects will

_probably

become

more and more

_important.

The trend towards extensification leads to an increased

relative

_{margin expected}

from

_improvement

in maternal effects in

_comparison

with

improvement

in direct effects.

A

_simplified

_{scheme, keeping only}

a ’short

performance

test’ and an on-farm

progeny test with bull evaluation on maternal

_performance,

would allow us to

overcome this

problem,

at least if the true direct-maternal

_genetic

correlation is not too far from its estimate

_{(around -0.2).}

_Moreover,

it could induce an

important gain

in

_efficiency

in Hs and

_Hg

when on-farm _{progeny test}

_capacity

increases. Thus

_increasing

on-farm progeny test

_capacity

_through

the use of an

animal model evaluation

_system

_applied

to all beef recorded herds

_(Lalo6

and

M6nissier,

1990)

while

_simplifying

the

_breeding

_{scheme, might}

be considered as an efficient alternative to the current scheme.

However,

a full evaluation of the

efficiency

of such selection schemes would

require

more

_complex

models

_integrating

feed

_efficiency,

carcass

_composition,

morphology

and

reproductive

traits

_(such

as

_fertility

or ease of

_calving...).

Indeed these traits are

_mainly

evaluated in the

_’long

performance

test’ and in the station

progeny test.

However,

as underlined

_by

Newman et al

_(1992),

our

_knowledge

of

genetic

parameters

is deficient in these areas. The lack of estimates is

_especially

important

for maternal

_performance

and the

_relationship

between direct and maternal effects

_(M6nissier

and

_Frisch,

_1992).

_Moreover,

the

_necessity

of

_obtaining

accurate estimates of

components

of variance is underlined

_by

the

_importance

of variance in selection _response due to

_uncertainty

of

_genetic

_parameters

when maternal effects have to be considered. This is essential for

_{correctly ranking}

selection

_policies

and

_predicting

_{genetic gains.}

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APPENDIX I.

_Meaning

of abbreviations used in tables and

_figures

Selection criteria

W120:

_weight

at 120 d

W210:

_weight

at 210 d or

weaning weight

W400:

_weight

at 400 d

W500:

weight

at 500 d or final

weight

Is:

optimum

index

combining

average W500 of 30 bull’s sons and _average W120 of 20 calves of bull’s

_daughters

with maternal

_heritability

of station W120

_equal

to 0.26.

I

f1

:average

W210 of 30 bull’s sons.

I

f2

:

optimal

index for Hi

_combining

_average W210 of 30 bull’s sons and _average W120 of

20 calves of bull’s

_daughters

with maternal

_heritability

of on-farm W120

_equal

to 0.16.

Breeding

values

A120: direct effects on W120

M120: maternal effects on W120 A210: direct effects on W210

M210: maternal effects on W210

A400: direct effects on W400 A500: direct effects on W500

Selection

_objectives

Hg: global objective

Hs: suckler

_objective

APPENDIX II. Derivation of

_{breeding objectives}

Derivation of

_margins

for suckler herds

o The economic

_margin

_afl for direct effects on final

_weight

_(A500)

in a suckler herd is

equal

to 0

_FF,

since calves are sold at

_weaning.

o _{The economic}

_margin

a d1

for direct effects on

_weaning

_weight

(A210)

in a suckler herd

is

_equal

to 10.3 FF _per

_kg.

This

_corresponds

to the difference between the

_price

_per

_kilogram

sold at

_weaning

(16.8

FF)

and the feed cost

_(6.5

_FF)

of one additional

kilogram

at

_weaning,

due to direct

genetic

effects. This cost is assumed to amount to 5

_kg

of concentrate at the

_price

of 1.3

_FF/kg.

Recommendation for breeders

_{(ITEB, 1991)}

is from 5 to 15

_kg

of concentrate

per additional

kilogram

at

_weaning.

The lowest value is considered in our

_{calculations,}

because it seems to be the most

_likely

choice for the breeder.

o The economic

_margin

_aInl for maternal effects on

_{weaning weight}

(M210)

in a suckler

herd is

_equal

to 13.8 FF per

kg.

Maternal effects on W210 are

_supposed

to be

_only

due to dam’s milk

_yield.

Their

marginal

cost

_corresponds

to the

_marginal

cost of dam’s feed intake. To _get 1

_kg

heavier calves at

_weaning,

dams should

_produce

8

_kg

more milk. This value

_corresponds

to the ratio of the milk

_production

to the

gain

of

weight

from birth to

_weaning

in the Limousin breed. This may be an underestimate of the

_marginal

number of

_kilograms

of milk needed

per additional

kilogram

over _{the average}

_W210,

which could be around 15

_kg

more milk. Estimates from 6 to 24

_kg

are observed in the literature

_(Drewry

et

_al,

1959;

Neville, 1962;

Jeffery

et

_{al, 1971;}

Le Neindre et

_al,

_1976).

As

_uncertainty

in the correct value is

important,

the same _strategy as for calculation of _ad1 is considered. The minimum

_possible

value is

used,

ie 8

_kg.

The INRA feed recommendation

_(INRA,

₁₉₈₈₎

_per additional

_kg

of milk for

a Limousin cow is 0.45 UFL

_(French

energy units for cattle with low

daily requirement,

as

lactating

cow)

and 0.3 UEB

_(French

fill

_unit).

_Therefore,

3.6 UFL per additional

kilogram

of calf weaned are

_required,

which

_corresponds

to 2.4 UEB. The

_period

from

_calving

to

weaning

can be

_separated

into 2

_{periods. During}

the first 3

_months,

animals are in cowsheds and cows are fed with a mixed ration of concentrate and

_{forage. During}

the last 4

_months,

animals are on _pasture. In order to

_simplify

the

calculation,

it is assumed that

_during

the 7

months,

the diet is a mixed ration of concentrate and of a _very

_{digestible forage}

(value

of buffer: 0.95 UEB _per

_kg

of

_dry

matter of

_forage).

As

_forage

is _very

_digestible,

a substitution rate of -0.5

_kg

of

_forage

_per

_kilogram

of concentrate must be taken into

account. Under these assumptions, the 3.6 additional UFL can be

_{provided by}

1.5

_{kg dry}

matter of

_forage

and 2.1

_kg

concentrate if their

_respective

_energy contents are 0.83 UFL

and _{1.12 UFL per}

_kg.

With a cost of

_{forage equal}

to 0.2 FF _per

_kg

of

_dry

metter and a

cost of concentrate

_equal

to 1.3 FF _per

_kg,

the

_marginal

cost of 1

_{kg change}

in maternal effects on

_{weaning weight}

is 3.0 FF.

Derivation of economic

_margins

for

_{suckler-fattening}

herds

Let _yl be the average

W210,

Y2 be the average W500 and x be the

daily postweaning

gain,

derived as x =

(y

2

-

y

l

)/290.

We denote

_by

_W(t)

the

_weight

of the calf at a

_day

t between 210 and 500 d.

_Assuming

a linear

_{growth during}

this

_period,

_{W (t)}

=

y l + x

(t - 210).

Production costs

_(c)

of a calf sold at 500 d can be

_split

in 2 _parts: costs before

_weaning

(c

l

)

and costs after

_weaning

_(c

₂

_),

such that c =

cr + C2 - Costs before

_weaning

are assumed