Impact of the use of bovine somatotropin (BST) on dairy cattle selection

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Impact of the use of bovine somatotropin (BST) on

dairy cattle selection

J.J. Colleau

To cite this version:

Original

article

Impact

of

the

use

of bovine

somatotropin

(BST)

on

dairy

cattle selection

J.J.

Colleau

Institut National de la Recherche _Agronomique, Station de _{Génétique quantitative} et

appliquée, 78,i50 Jouy-en-Josas, France.

(received

27 October _{1988; accepted} 15 June

₁₉₈₉₎

Summary - A _{very simple}

_breeding

scheme for milk _yield was

_generated

_by a Monte-Carlo method in order to evaluate the _{potential impact} of bovine _somatotropin

_(BST)

on

genetic gains and on the _{discrepancies} between true and estimated _breeding values. The

parameters were treatment rate

_(10%,

_30%,

_50%),

_reporting

_(complete

or

_random),

BST

allocation system

(random,

best or worst

_cows),

data correction _system

_(none,

conventional

BLUP or bivariate

_BLUP)

and some dispersion parameters of the additional _{yield provided}

by BST.

Given that there were no herd effects and no _{embryo transfer, the range of} the decrease for _{genetic gains} was

1-10%,

not _{fully explained by} the decrease in selection accuracy, and

was _{relatively well balanced between the male and female gene transmission paths.} The

perception of this situation is difficult _especially when BST is allocated to the best cows because very large biases in the evaluation may occur

_(up

to 30% of the true selection

differentials).

These biases occur even when _reporting is _complete and when a conventional BLUP is _implemented. This _{problem disappears} when a multi-trait BLUP is _applied after

completely

discarding

the treated _parts of lactation. In this case, losses of genetic gains

are _relatively moderate as well.

Possible herd effects were _ignored in the simulation process to give the _opportunity of

correct calculations for selection accuracies. This artificial _prerequisite should be removed

in further studies.

cattle selection - milk yield - bovine somatotropin - genetic gain

Résumé - _Impact de l’utilisation de la somatotropine bovine _(BST) sur _les

pro-grammes bovins de sélection laitière. On a simulé de manière aléatoire le

fonction-nement d’un programme très _simple de sélection laitière _pour évaluer _l’impact de la BST sur le _{progrès génétique} et sur les écarts entre valeurs

_génétiques

vraies et estimées. Les

paramètres étaient le taux de traitement

_(10%,

_30%,

_50%),

le taux de déclaration

_(total

ou

aléatoire),

le _système de choix des vaches traitées

_(au

_hasard, bonnes ou mauvaises

vaches),

le _type de correction des données

_(aucune,

BLUP _classique ou BLUP

_bivariate)

et certains _paramètres de dispersion concernant le _gain de production permis par la BST.

Sachant _{qu’il n’y} avait ni _{effet troupeau} ni

_transfert

_{embryonnaire,} le taux de diminu-tion du _{progrès génétique} se situe dans la zone

1-10%,

ne _{s’explique pas} totalement _par la réduction de précision de la sélection et se _répartit assez bien entre les voies mâles et

L’utilisation d’un BLUP multàcaractère sur des lactations entières ou amputées de leur

partie obtenue sous traitement permet de

_faire

_disparaître cette nuisance. Par _ailleurs, dans cette _situation, les réductions de _{progrès génétique} sont relativement _modiques.

Les éventuels _effets troupeau ont été _ignorés dans le processus de simulation, de manière à _faciliter le calcul exact de la _précision des indices de sélection. Cette condition _artificielle devrait être levée dans les études ultérieures.

bovins - sélection - _production laitière - somatotropine bovine - progrès génétique

I. INTRODUCTION

Growth hormone obtained from

_{genetic engineering}

induces

_{large changes}

of milk

yield

in cattle

_(see

the review

_by

_{Chilliard, 1988a,}

_b).

It

_might

therefore be

integrated

into the modern

_{production techniques}

used for

_dairy

cattle. The

new

_questions

asked to breeders would be the consequences of a

relatively large

uncertainty

about the statistical and

_biological

_parameters

_concerning

the response to the hormone. Additional

_challenges

would be

_generated

in the case of

_possible

ignorance

of the real status of the _cows, treated or not treated

_(poor

_reporting

or,

at _worst,

_cheating).

Two main

_questions,

which are distinct

_{although partially overlapping,}

arise from

an

_operational

_viewpoint:

1)

What is the reduction in the annual

_{genetic gains}

in

_comparison

with the

corresponding

value in an identical BST-free

breeding

scheme?

2)

What are the

_{discrepancies}

between the real selection differentials and the

apparent ones, as seen from the

_breeding

value estimates of elite animals?

Deterministic

_modelling

of these

_questions

is not an _easy

_task,

_especially

in the

situation where BST is not

_randomly

allocated. This is the reason

_why

the first

known numerical studies have resorted to Monte-Carlo methods

_(Burnside

and

Meyer, 1988;

Frangione

and

_Cady,

_1988;

Simianer and

_Wollny,

_1989).

Conversely,

this has

_strongly

limited the _scope to _very

_simplified

_breeding

schemes,

in attempts to mimic the main aspects of the usual

_complex

_schemes,

on

relatively

small numbers of animals to save

_computation

time.

In the present paper, this type of

_approach

is

_applied

to

_embryo

transfer-free

schemes,

as in the

_preceding

studies. The

_objective

is to

_give

clear answers to the above

_questions.

In

_addition,

the source of the

potential

losses will be examined in

reference to standard selection

_theory.

The

_potential

of more

_adequate

evaluation

procedures

such as multi-trait BLUP will be tested too.

II. MATERIEL AND METHODS A.

_Breeding

scheme

Unrelated sires

₍₁₀₀₎

were progeny tested with 50

daughters

each,

related

only

through

their sires. The _top 25 and 3 sires were considered as cow sires and bull sires

respectively.

The best 5% of the

_daughters

were considered as

_potential

bull

_dams,

B. Constants

The additional

_yield

_provided

_by

BST amounts to 1 000

_kg

on average, with a

phenotypic

standard deviation of 200

_kg.

This

_roughly

_corresponds

to the order of

magnitude

of the results obtained on cows treated for 8 months after a 2-month

BST-free

period,

in order not to alter

dramatically

the cow’s

_{energetic balance,}

as

recommended

_by

nutritionists.

The

_genetic

and

_phenotypic

_parameters

_concerning

the 2-month _part lactation and the whole lactation were drawn from the detailed results

_{given by}

Danell

(1982).

This lead to h2 values of 0.18 and 0.28

_{respectively,}

with

_genetic

and

_phenotypic

correlations of 0.85 and 0.77. Wilmink

₍₁₉₈₇₎

_{gave very} similar results. It should be

_kept

in mind that the _average effect of BST is

_equivalent

to 2

_genetic

standard

deviations for the full lactation.

C. Parameters

1)

Genetic situation

S

1

:

additional

_yield

due to BST is not heritable and

_independent

of

_preceding

yield;

S

2

:

additional

_yield

is heritable

_(h

₂

=

0.30)

and

negatively

correlated to the

preceding

yield

(r

G

= _rE =

-0.5);

S

3

:

additional

_yield

is heritable

_(h

₂

=

0.30)

and

independent

of

preceding yield;

S

4

:

additional

_yield

is heritable

_(h

₂

=

_0.30)

and

_positively

correlated to the

preceding yield

(r

G

= _rE =

0.5).

These situations were chosen because

_nothing

is known about the

_genetic

parameters of additional

_{yield. Contradictory}

information from small

_samples

is

given

on

_phenotypic

_parameters. The lack of free access to data from BST studies has

_precluded

_thorough

_analysis.

On the other

hand,

the observation that BST

_brings

an extra

_yield

for every treated cow excludes from the _{parameter space,} situations where

_genetic

and

phenotypic

correlations between the 2 total

_yields

_(with

and without

_BST)

are

too low.

_Considering

for instance that rp = _r! =

_0.8,

_as in _a

_previous

personal

study, implies

that in some cases extra

_yield

can be

_negative

(never

observed

when

_{comparing daily}

_pre- and

post-injection

yields).

All the correlations rG or

r

E

resulting

from our 4 situations are above 0.96.

2)

Treatment rates:

_{10%, 30%, 50%}

.

3)

Reporting

rates:

_{50%, 100%.}

When

_reporting

is

_{partial, cheating}

is not

_supposed

to occur, i.e. treated cows are

_reported

at random.

4)

Treatment adlocation: at

_random,

on the best or worst _cows, based on their

phenotypic

2 month

_{partial yield.}

5)

Methods

_{of analysis:}

In the first

_analysis

_(correction

_1),

the model used included

be seen, this

simple

model is not robust to a non-random allocation of BST

_and,

as

suggested by

Ducrocq

and

_Foulley

_{(personal communication),}

a multi-trait BLUP evaluation _system could be used

_by

_taking

into account the BST-free lactation

parts, which would allow a better evaluation of fixed effects. A second

_analysis

(correction 2),

i.e. a bivariate

_BLUP,

is envisioned as extreme

_{implementation}

of this idea where treatment effect is

_ignored

but where treated _parts of lactation are

deliberately

excluded. In this way, the unknown

dispersion

parameters

concerning

the effect of BST would be certain not to interfere with the evaluation

_(at

least when BST

_reporting

is

_complete).

D.

_Obtaining

BLUP evaluations

To save

_computation

time,

advantage

was taken of the block structure of the data.

By

algebraically manipulating

(aI

+

_{!3J) -}

_type matrices and their

_inverses,

it was

therefore

_possible

to solve

_directly

the linear _system and to derive the random variance-covariance errors for the

_{estimates, given}

that the model is true. The

general

linear _system can be found in Henderson

_(1975),

_Foulley

et al.

_(1982),

Schaeffer

₍₁₉₈₄₎

for instance. The detailed list of the derivations used for our case is

rather

_lengthy

_(especially

for bivariate

_BLUP)

and not essential to an

understanding

of the results. These are the reasons

_why

it will not be

_given

here.

_Obtaining

the accuracies of the estimates without any

approximation

was felt to be

important

in order to

_analyse

the

_phenomena

as

_deeply

as

possible.

An animal model was solved for the females to _get estimates for bull dams and from these

_results,

the solutions of a sire model were obtained

(to

_get estimates for cow and bull

sires),

because it can be shown that with our initial

_assumptions,

the

estimate si for a sire i is

_equal

to

where

_i

_i

_ij

is the estimate for the

_j

_th

_daughter.

In this _sequence of

_operations,

a direct inversion is needed for the incidence

matrix of fixed effects after

_absorption

of the animal effects. Herd effects were

excluded to save

_computation

_time, since 300-500 herds would have been needed. The consequences of this decision will be discussed.

E.

_Comparisons

to reference scheme

_{(see IIIA)}

Generally speaking,

all the results are

_expressed

as a _percent of the reference scheme.

Approximate

standard errors for this ratio can be obtained first

_by

linearizing

the

III. RESULTS A. Reference scheme

The results obtained from 300

replicates

are shown in Table I.

They give

for each

of the 3

_significant

gene transmission

paths,

the true selection

_{differentials,}

the

apparent selection differentials

_(from

BLUP

_evaluation),

the true accuracies

_{(r Ga)}

and the calculated accuracies. There is a very

good

agreement between observed and calculated parameters. It can also be verified that these parameters do not

correspond

to those obtained in an infinite

_population

of unrelated animals.

B. Cumulative selection differentials

The

_asymptotic

_{yearly genetic gains}

are

proportional

to the sum of the 3 selection

differentials on the

_cow-sire,

bull-sire and bull-dam

_paths

when the cow-dam

path

is

_neglected

_(Rendel

and

Robertson,

1950).

The decrease of that _sum,

_expressed

as a _percent of the

_{corresponding}

value in the reference

_scheme,

is shown in Table I1. Most values are in the range 1-10%. For accurate

_comparisons,

it should be

_kept

in mind that there is some fuzziness due to random errors

(standard

error of about

1.2%).

When no data correction is

_applied,

the total range for losses is 0-8%. When

BST allocated

_randomly.

With non-random allocation fo

BST,

its effect is

_poorly

estimated and this leads to an additional error for

_{evaluating breeding}

values. For

instance,

in the Sl

_situation,

BST used on the 30% best cows with total

_reporting,

the estimate of the hormone effect is not 1000

_kg

but 1200

_kg.

When correction 2

is

_applied,

the results are better than in the no-correction

situation,

_except when

the best cows are treated with a

_high

treatment rate. The source of these losses is

obvious,

since for _many animals the old variable is

_{replaced by}

a less heritable one

and

_imperfectly

correlated with it.

Comparison

between the situations

S

l

and

_S

₃

shows that the value of h2 for

additional

_yield

has no detectable effect on the

losses,

a

_probable

_consequence of

the fact that the

_genetic

standard deviation for this

_yield

cannot be very

high

in

comparison

with the parameters for full lactations. In _contrast,

_comparison

between situations

_S

₂

_,

S

3

and

S

4

shows that the value of the correlations between additional

yield

and &dquo;BST-free&dquo;

_yield

has a

perceptible

influence. The smallest losses are

obtained when the correlation is null. Greater losses are incurred with

positive

correlations but the worst situation is obtained when the worst cows

respond

the

best to hormone and vice versa.

Therefore,

good

information on the values for the

The most detrimental situation of BST allocation is the _system when BST is

provided

to the best cows, except for

_high

treatment rates

_(50%)

where it is the

contrary.

C.

_{Discrepancies}

between real and

_apparent

sum of selection differentials

A

_general

_survey of Table III shows that overestimation or underestimation of the

cumulated selection differentials

_(i.e.

of the

_{potential genetic}

_gain)

can exist. The

total _{range goes} from -30 to +30%.

With no data

modification,

a noticeable overestimation of the selection

differen-tials occurs, except when _poor cows are

_treated,

which leads to an underestimation.

This would

_bring

some

_perturbation

into the

_breeding

scheme. For

instance,

in the situation

_S

_l

_(30%

treated at

_random),

it is found in Table II that

_{genetic gain}

is decreased

_by

5%. When

_taking

into account the

_{corresponding}

_figure

in Table

_III,

an Al

_organization

would have _every reason to believe that

_{genetic gain}

is increased

by

4%. This _type of

_comparison

is even more dramatic when BST is not allocated at random. With no

_{correction, S}

_l

(30%

on best

cows),

_genetic

_gain

is decreased

As

_{expected, partial}

_reporting

and

_correcting

does not

_help

the situation. When

reporting

is

_exhaustive,

it can be observed that correction 1 leads to _strong underestimations _except when BST is

_randomly

allocated: if

_good

cows are

_treated,

they

are overcorrected and if _poor cows are

treated,

they

are

undercorrected,

both cases

_leading

to an _apparent

_shrinkage

of the

_genetic

variation range. Correction

2 leads to an almost

_{perfect adequacy}

of the estimate

_{genetic gains.}

This is not

surprising

and can be considered a check of the soundness of the calculations. The most

_{important point}

is that this unbiased _type of estimation is

relatively

unexpensive

in terms of real

_{genetic gains,}

as seen from Table II. Therefore

multi-trait

_BLUP,

with a

_drop

of the treated _parts of

_lactation,

is

_by

far the best solution among the

possibilities

investigated

here. Better solutions can

_certainly

be obtained

if

_they

are of the

_{multi-trait-type,}

after a REML _step for

_calculating

the unknown variances and covariances on treated parts.

Table IV shows for the

S

i

example

that biases of selection differentials are

only

very

weakly

related to biases of accuracies. Once

_again,

there is a very

good

agreement between true and

_predicted

accuracies for the _type 2 correction with

D. Examination of the

_origin

of the losses for situation

_S

_l

Inspection

of all situations is not

_given:

this would lead to a

_large

amount of

figures.

Situation

_S

_l

is chosen and

exemplifies

very well the

general

pattern of results obtained. From the

comparison

between Table

II,

Table V

_(accuracies

of

selection)

and Table VI

_{(selection differentials),}

it is obvious that the reduction of

genetic

gains

cannot be

_{totally explained by}

a reduction of _accuracy. This is the

consequence of

mixing

different distributions of

_{predicted breeding}

values for total milk

_yield

_(different

_{population expectations}

and within

_population

_variances).

This situation is encountered even for the 100%

_recording

correction 2 situation. It should remembered that the conventional _way of

_predicting

selection differential

_(selection

intensity

x selection accuracy x

_genetic

standard

_deviation)

is

_only

correct if there is 1

_population

and if

_linearity

of

_regression

and

_{homoskedasticity}

of error variances

hold. None of these 3 conditions is met in a BST situation. The

_impact

of BST is

not a mere reduction of

_{heritability.}

As

_might

be

_anticipated,

the bull-dam

_path

is the most affected in terms of accuracy and in terms of selection differential. The sire

_paths

are much less affected

the reduction of

_genetic

_gain

comes from the male

_paths,

as shown

_by

a detailed

examination of the

_figures.

The

_impact

of BST on

breeding

schemes cannot either be

_{oversimplified}

as a process that weakens the

efficiency

of the bull-dam

_path.

E. Treatment rates within the elite

_populations

Results are shown

_only

for situation

_S

_l

but

_{they give}

a

_good

idea of the other

situations

_{(Table VII).}

From the random BST _{treatment, it appears} that the

probability

for a treated cow to be considered as a bull dam is

_considerably

increased

(by

2 or

3).

For correction 2 and total

_reporting,

the

probability

is

decreased,

as

might

be

_anticipated

since the standard deviation of the

_breeding

values estimates is smaller for the treated cows. As to the allocation to best cows, all bull dams

are treated and then a doubt comes into mind: are these cows considered as

_good

because

_they

were treated or is it the _contrary: were

they

treated because

they

are

really

good?

From the

_multiple

trait

results,

we known that in this situation a

_large

fraction of the treated animals

_{(41/87, 71/98, 87/100)}

would have _great chances to

be chosen as bull dams

anyhow.

_However,

we are in the artificial situation where we

Hence the

_{psychological}

interest of

_excluding

treated _parts of lactation for data

processing.

IV. DISCUSSION A. Biases of this

_study

Here, experimental

conditions are rather mild ones to evaluate the

_impact

of BST.

- Due

to

_{operational considerations,}

the between-herd

_variability

was

dropped,

although

it is well known that a between-herd

variability

exists. This

variability

would be very

likely

increased

by

use of

BST,

since the

specialists generally

agree in

_saying

that additional

_yield

is all the more substantial as the

_feeding

level is

_good

(probably

BST x herd

_{interaction).}

_Furthermore,

there is no clear reason

_why

_every

farmer would

_{apply strictly}

the same _system for

_choosing

the cows to be treated.

Finally,

if

_{non-reporting}

and

_cheating

cannot be

_eliminated,

this

_implies,

for human

-

Embryo

transfer situations were not

_{studied, despite}

their

_growing

influence in

practical

dairy breeding

schemes. Given that female _gene transmission

paths

have

more

_importance,

then it can be

_anticipated

that the losses would be _greater. B.

_Comparison

with

_previous

studies

Simianer and

_Wollny

₍₁₉₈₉₎

studied in their alternative IV a situation similar to

our situation

S

1

:

the additional

_yield

_(ic

= 1 000

kg,

sp = 250

kg)

_{was not} heritable

and did not

_depend

on

_{anything. They}

nevertheless

_supposed

an additive herd effect.

_They

found also that a _type 1 correction decreases _{the accuracy} of selection

except when BST is allocated at random or almost. In the most favourable case

(total

reporting,

BST allocated at

_random),

_they

found a decrease of 10% for the

genetic

gain

when 20% of the animals are treated. This is much more than the value

obtained here for this case

(around

_2%).

Burnside and

_Meyer

₍₁₉₈₈₎

concentrated

_only

on sire evaluation

_problems,

as-suming

a

_{multiplicative}

effect of BST and a between-herd

_variability,

and stretched

the range of

genetic

situations to as far as 0.6 for the

_phenotypic

or

_genetic

cor-relation between

_yields

with and without BST. In these

_{circumstances,}

_accuracy is

_badly

decreased. For a more

_likely

situation

_(r

_G

=

_1,

rp =

0.8),

the accuracy is not

_{greatly changed}

but noticeable biases are induced: in

_comparison

with the

reference

_situation,

the mean absolute difference between the true

_breeding

value and its estimate increases

_by

25% when the best

_2/3

cows in

_2/3

of the herds are

treated. This

_implies

that the mean value of elite sire estimates would be biased as

well.

CONCLUSION

The _present

_study

cannot be considered as exhaustive on the

_topic.

_However,

it is clear that the

_possible

_problems

in

_{dairy breeding}

schemes

_brought

about

_by

BST administration should not be underestimated.

_{Unfortunately,}

_simple

ideas that could

_justify

comfortable

_solutions,

are not at all

supported

by

the _present

results,

as confirmed

_by

the

_preceding

studies when a

meaningful

_comparison

was

possible.

Losses of

_{genetic gains}

are not

_proportional

to losses of accuracy, which

implies,

for

_instance,

that

_{only increasing}

the number of

_daughters

_per bull would not be sufficient to eliminate these losses. The losses are almost

_equally

balanced between female and male

_paths,

which

_implies

that attention should be

_given

to

each

_{path: contracting herds,}

for

_instance,

for bull

_sampling

would therefore be a

partial

solution.

_Finally,

even

_considering

_{only genetic gains}

is not sufficient since in some situation

_{genetic gains}

can be

_kept

almost intact whereas the sire and dam evaluations are

_{significantly}

_biased,

a fact

_likely

to introduce mistrust from the farmers towards the breeders.

The solution

_{proposed here,}

i.e. to exclude the treated parts of lactation for

breeding

purposes and to use a multi-trait

_BLUP,

is

_{only satisfactory}

if

_reporting

is correct.

_Furthermore,

it would

_complicate

the calculations. I

modified towards contracted and artificial _systems. This

_might

result in an increased

cost of Al.

ACKNOWLEDGMENTS

Both referees chosen

_by

this

_journal

are thanked for their comments and

_suggestions.

Helpful

discussions with Dr H. Simianer

_(Hohenheim

_University,

_FRG)

and informal review of the

_manuscript

by

Dr R.L.

_Quaas

_(Cornell

University,

USA)

were

_greatly

appreciated.

REFERENCES

Burnside E.B. &

_Meyer

K.

₍₁₉₈₈₎

Potential

_impact

of bovine

_somatotropin

on

_dairy

sire evaluation. J.

Dairy

Sci. _71, 2210-2219

Chilliard Y.

_(1988a)

R61es et m6canismes d’action de la

_{somatotropine}

_(hormone

de

_croissance)

chez le ruminant en lactation.

_Reprod.

Nutr.

_Dévetop.

28,

39-59 Chilliard Y.

_(1988b)

Review:

_long-term

effects of recombinant bovine

_somatotropin

(r BST)

on

_dairy

cow

_{performances.}

Ann. Zoot.

_37,

159-180

Danell B.

₍₁₉₈₂₎

Studies on lactation

yield

and individual

_test-day

yields

of Swedish

dairy

cows. 4. Extension of _part lactation records for use in sire evaluation. Acta

Agric.

Scand.

_32,

103-114

Foulley

J.L.,

Calomititi S. & Gianola D.

₍₁₉₈₂₎

Ecriture des

_equations

du BLUP multicaract6res. Ann. G6n6t. S61. Anim.

14,

309-326

Frangione

T. &

_Cady

R.A.

₍₁₉₈₈₎

Effects of bovine

somatotropin

on sire summaries

for milk

_production

and milk

_yields

heritabilies. J.

_Dairy

Sci. 71

_{(Suppl. 1),}

239 Henderson C.R.

₍₁₉₇₅₎

_Comparison

of alternative sire evaluation methods. J. Anim. Sci.

_41,

760-770

Rendel J.M. & Robertson A.

₍₁₉₅₀₎

Estimation of

_{genetic given}

in milk

_{yield by}

selection in a close herd of

_dairy

cattle. J. Genet. _50, 1-8

Schaeffer L.R.

₍₁₉₈₄₎

Sire and cow evaluation under

multiple

trait models. J.

Dairy

Sci.

_67,

1567-1580

Simianer H. &

_Wollny

C.

₍₁₉₈₉₎

_Impact

of the

_potential

use of Bovine

_Somatotropin

(BST)

on the

_efficiency

of a conventional

dairy

cattle

breeding

scheme. Livest. Prod.

Sci.

_22,

31-47

Wilmink J.B.M.

₍₁₉₈₇₎

_Efficiency

of selection for different cumulative

_milk,

fat and