Detection of cytoplasmic effects on production: the influence of number of years of data

HAL Id: hal-00894167

https://hal.archives-ouvertes.fr/hal-00894167

Submitted on 1 Jan 1997

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Detection of cytoplasmic effects on production: the

influence of number of years of data

A Salehi, Jw James

To cite this version:

Original

article

Detection

of

_cytoplasmic

effects

on

production:

the influence of number

of

_years

of data

A

_Salehi,

JW James

Department of

Wool and Animal

Science,

The

University of

New South

_Wales,

Sydney

2052, Australia

(Received

17

January 1995;

revised 6

_{January 1997, accepted}

3 March

₁₉₉₇₎

Summary - Data were simulated for a

single

trait determined

by

additive

genetic,

cytoplasmic

and environmental effects in a

_sheep

flock. The

proportions

of variance due

to genotype and

_cytoplasm

were

h

2

= 0.30 or 0.60 and

c

2

= 0.05 or

_0.10,

with an extra set in which

h

2

= 0.30 and

c

2

= 0. For all five _{parameter sets,} two

periods

(10

or 20

_years)

were

_considered,

with the same number of records in each case. Ten

replicates

of each were run so that 100

independent

data sets were obtained. A ten-year data set with half the number of animals was also _run,

giving

150

analyses

in all. Data sets were

_{analysed by}

derivative-free restricted maximum

_{likelihood, fitting}

four

_models,

which included additive

genotype alone or in combination with either or both an additive

_genetic

maternal effect

and a

cytoplasmic

effect. If the

cytoplasmic

effect were omitted from the

_{analysis model,}

heritability

and maternal variance were overestimated. If

_cytoplasmic

effects were

included,

parameter estimates were close to true values.

_Heritability

did not affect the power of tests for

_{cytoplasmic effects,}

which was

higher

for

c

2

= 0.10 than for

c

2

= _{0.05. Detection of}

cytoplasmic

variance was more

likely

with data

spread

over 20 rather than over _{10 years,} and power was reduced with fewer data.

cytoplasmic effect

_/

restricted maximum likelihood

_/

animal

_{model / sheep}

Résumé - Détection d’effets cytoplasmiques sur des caractères de _{production :} inci-dence du nombre des années avec données. On a simulé des données pour un

carac-tère déterminé par les

effets génétiques additifs, cytoplasmiques

et de

milieu,

dans un

troupeau de moutons. Les parts de variance

_{phénotypique}

dues aux

_{effets génétiques}

et

cytoplasmiques

sont h

2

=

_0,30

_ou

_0,60,

et c

2

=

_0,05

ou

_{0,10 respectivement,}

avec une

série

_{supplémentaire}

où

h

2

= _{0, 30} et

2

c

= 0. Pour les _cinq ensembles de

paramètres,

on

considère deux

_périodes

₍₁₀

ou 20

_ans)

avec un nombre

_égal

des données dans les deux cas. On a

_fait

dix

_{répétitions}

pour

chaque

situation, et donc 100

fichiers

indépendants

sont obtenus.

_{Un fichier}

couvrant 10 années avec un nombre d’animazix réduit de moitié

est

_analysé

aussi, soit 150

analyses

en tout. Les

fichiers

sont

analysés

par la méthode

*

du maximum de vraisemblance restreinte

_(REML)

avec un

_procédé

sans dérivées.

_Quatre

modèles ont été

_{ajustés, incluant,}

soit le

_{génotype additif seul,}

soit le

_{génotype additif}

plus

l’un des

_{effets cytoplasmiques}

ou

_génotype

additive

maternel,

ou les deux.

Quand

le modèle

d’analyse

excl!t

l’effet cytoplasmique,

l’héritabilité et la variance maternelle sont surestimées.

Quand

le modèle inclut

l’effet cytoplasmique,

les

paramètres

estimés

approchent

leurs valeurs vraies. La _puissance des tests des

_{effets cytoplasmiques}

est

_plus

élevée pour

c

2

=

_0,10

_que pour c

2

=

_{0, 05,}

_mais elle ne

_dépend

_pas de l’héritabilité. La détection

_{d’effets cytoplasmiques}

est

_{plus probable}

avec des données

_réparties

sur 20 que

sur 10 _{ans, et} la puissance du test est diminuée

_quand

le nombre de données diminue.

effet cytoplasmique

/

maximum de vraisemblance restreinte

_/

modèle animal

_/

mouton

INTRODUCTION

Although

dam and sire contribute

_equally

_(with

the

_exception

of sex-linked _{genes in} the

_{heterogametic offspring}

_sex)

to the

_genotype

of their

_{offspring, it}

is

_accepted

that

progeny

performance

is affected more

_by

the dam than

_by

the sire

_(Hohenboken,

1985).

A maternal effect _may be defined as _any influence on a _progeny

phenotype

attributable to the

_dam,

other than nuclear genes. In

mammals,

milk

production,

intrauterine environment and

_parental

care are common

_components

of maternal

effects,

which may be both

genetically

and

environmentally

determined.

Another

_possible

source of maternal effect is the

cytoplasm,

_especially

mitochon-drial DNA

_(mtDNA),

which is

_maternally

transmitted

_(Wagner,

_1972).

In recent

years several studies

following

that of Bell et al

(1985)

have

presented

evidence for the influence of

_cytoplasm

on

_production

in cattle.

_However,

_Kennedy

₍₁₉₈₆₎

pointed

out that careful

_analysis

of data was needed to demonstrate the occurrence

of a

_{cytoplasmic effect,}

and that in

_particular

it was _necessary to account for the influence of nuclear genes. An assessment of the

_importance

of

_fitting

an

appro-priate

model was made

_by

Southwood et al

_(1989).

_They

simulated data with a

conventional maternal

effect,

with a

_cytoplasmic

effect,

or with

_both,

in addition to

an additive

_genetic

effect.

_They

then

_analysed

the simulated data

_using

models that included

_only

a maternal

_{effect, only}

a

_{cytoplasmic effect,}

or

both,

as well as an

additive

_genetic

effect. When the correct model was

_fitted,

the

_parameter

estimates matched the true

values,

but estimates were biased when an incorrect model was

fitted.

_They

simulated a

dairy

cow

population

over 60 _years, and

_analysed

data

from the last 30 _years, with about 4 500 records

_being

used.

In Australian Merino

_sheep

it would be unusual to have such a data

_set,

and

most data sets would extend over 10-20 _years. Over such a

_period,

a

_separation

of

_cytoplasm

and maternal

_genotype

_might

be more difficult to achieve. We have

therefore undertaken studies of the effectiveness of

_{estimating cytoplasmic}

effects in such

_populations.

Most such

populations

would be

_undergoing

_selection,

unlike the random choice of

_parents

simulated

_by

Southwood et al

_(1989),

and so we have simulated

populations

under selection. Boettcher et al

₍₁₉₉₆₎

also used simulation

of a

_dairy

cow

_population

with

_cytoplasmic

effects but their interest was in

MATERIALS AND METHODS

Data were

_{generated by}

_computer

simulation of a

_sheep

flock with five age groups of

_breeding

ewes and _{two age groups} of rams. It was assumed that

_initially

all

breeding

animals had been

_randomly

chosen from the base

_population,

while the

juvenile

animals were also a random

sample

of the base

population. Thereafter,

a

fifth of the

_breeding

ewes and a half of the rams were culled each _year and

_replaced

by

the best available

_hoggets.

The basic simulation used 10 rams and 200 ewes,

with data

_being

simulated over 20 or 10 years. Another set of simulations used 20

rams and 400 ewes for

_mating

each _year, with data simulated over 10 _years. Each animal had an additive

_genetic

value and a

_cytoplasmic

value. These were

added, together

with a random environmental

deviation,

to

_give

the

_phenotypic

value.

Except

for the base

_population,

an animal’s

breeding

value was the average

of its

_parents’

_breeding

_values,

_plus

a

_segregation

effect in which allowance was made

for

_parental

_inbreeding.

An animal’s

_cytoplasmic

value was that of its dam. The seed for the random number

_generator

was different for _every run of the simulation so that all

_replicates

were

_independent.

The

_10-years

data sets were simulated

separately

from the

20-years

data sets.

The trait under selection was assumed to have a

_heritability

(h

2

)

of 0.3 or

_0.6,

with

_cytoplasmic

variance

_(c

₂

₎

0.05 or 0.10 as a fraction of

_phenotypic

variance.

Cytoplasmic

and additive

_genetic

effects were uncorrelated. For a

_heritability

of

0.3,

another series of runs with

_cytoplasmic

variance set to zero was carried

_out,

making

a total of five models. Ten

replicates

were simulated for each model. With

three data structures described above

_(population

_size,

number of

_years)

this _gave

150 data sets for

_analysis.

The data were

analysed

_using

an animal model restricted maximum likelihood

procedure

and a derivative-free

_algorithm

(Graser

et

_al,

_1987).

The DFREML

computer

package

(Meyer,

1989,

1991)

was

employed

to fit four different models to

the data. These were models

_{1, 2,}

3 and 7 in DFREML

_terminology.

The models

are described in table I.

The

_complete

model fitted to the data

_{(model 7)}

was:

where _y is a N x 1 vector of

_{observations,}

b is a vector of fixed effects and

_X,

Z

a

,

Z

m

and

_Z,

are incidence matrices

_relating

fixed effects

_(b),

random additive

genetic

effects

_(a),

maternal

_genetic

effects

_(m),

and

_cytoplasmic

_origin

effects

_(c)

to y,

respectively,

and e is a vector of random residual effects. The variance-covariance

structure among the random effects for the full fitted model was:

with all covariances zero. Here A is the additive

_genetic

_relationship

matrix between

animals,

afl is

additive

_{genetic variance,}

₀

_{,2 m}

is maternal

_{genetic variance,}

_a

₂

_is

cytoplasmic

variance,

!e is

environmental

_{variance, I}

c

is an

identity

matrix of order

equal

to the number of

_{cytoplasm origins,}

and

I

e

is an

_identity

matrix of order

_equal

to the number of records. For model 3 it was assumed that c =

0,

for model 2 that m = 0 and for model 1 that both c and m were 0. Fixed effects included in the

model were _year of record and sex. A

_single

record at

_hogget

_age was

_analysed.

For the

_fitting

of the

_cytoplasmic

effect the female in the base

population

from whom the

_cytoplasm

descended was identified. The _convergence criterion chosen for

stopping

the estimation

_procedure

was a variance of

10-

7

in the likelihood values for the

simplex.

Standard errors of

_parameter

estimates were obtained from variation

between

_replicates.

The

_probability

of

_{finding significant cytoplasmic}

effects was

assessed

_by

use of likelihood ratio tests of model 7 versus model

_{3, assuming}

that -2 2

times the difference in

_log

likelihoods had

_{approximately}

a

_chi-squared

distribution

with one

_degree

of freedom. This test is an

_appropriate

_way to test

_significance

of the

_changes

in the likelihood function when additional terms are included as

explained by

Rao

_(1973).

RESULTS

Parameter estimates with their standard errors

_(calculated

from _{variation among}

replicates)

are

_presented

in tables

_II,

III and IV for different data structures. The results of the

_log

likelihood tests are

_presented

in tables V and VI.

When there was no

_cytoplasmic

effect in the simulated data the estimated

heri-tability

was

_always

close to the true value. In the _presence of a

_{cytoplasmic effect,}

heritability

was

always

overestimated when

c

2

was omitted from the fitted model.

Estimates of

h!

and

C

2

with the model

_fitting

additive

_genetic

and

_cytoplasmic

effects

_{(model 2)}

were all close to the true values for all data sets across all sets

of

_parameters,

_although

a few values differed from the true value

_by

more than

two standard errors. With a model that included the maternal

_genetic

effect as

the

_only

additional random effect

_{(model 3),}

estimates of

h

2

were

_higher

than for model 2.

_According

to the

_log

likelihood ratio test

_presented

in table V a

_complex

model

_(model

₇₎

_fitting

the additive

_{genetic effect,}

maternal

_genetic

effect and

the

_ability

to detect a

_cytoplasmic

effect. The _average

X

2

values

were

higher

for

the

_larger

data

sets,

but among the

larger

data

sets,

they

were

_higher

for 20 _years

rather than 10 _years.

_Furthermore,

table

_VI,

in which the numbers of

_significant

x

z

values for

_replicates

for each data set are

_presented,

also indicates that the

20-year period

was

_slightly

more

_likely

to show

_significance

than a

_{10-year period,}

even with the same amount of data. In table V it can be seen that the _average

X2

2

value for 20 years is about twice that for 10 years with an

_equal

amount of

_data,

and thus with smaller

_cytoplasmic

contributions the difference in power would be

more noticeable.

DISCUSSION

some of these effects are then attributed to the additive

_genetic

effect. When

C

2

is accounted for

_{by fitting}

model

_{2, C}

2

estimates are not different from the

true values.

_Higher

estimates of

_heritability

with model 3

_compared

to model

_2,

showed that with model 3 some of the

cytoplasmic

effects are then attributed to

the additive

genetic

effect and most attributed to a maternal effect. Southwood

et al

₍₁₉₈₉₎

stated that if an

_appropriate

animal model is

applied

to the

data,

variance

_components

can

correctly

be

partitioned

among additive

direct,

additive maternal and

_cytoplasmic

effects. Model

7,

including

the additive

genetic effect,

maternal

_genetic

effect and

_cytoplasmic

effect was used to demonstrate

_cytoplasmic

variation,

distinct from maternal

_{genetic effects,}

since in real data as distinct from our simulated data we can not know that there is no maternal effect other than that

of the

_cytoplasm.

The

_ability

to detect a

_cytoplasmic

variance

_component

does not

of 10 years, power was lower when the amount of data was halved.

However,

for a

given

amount of

_data,

the power is

higher

if the data is

spread

over 20 rather than

10 _years. Thus data

extending

over a number of _{years is}

preferable,

but if

enough

records are

_available,

it is worth

analysing

data from a short

_period.

The

_major

difference between 10 years and 20 years of data for the detection

of

_cytoplasmic

effects is the difference in number of

_generations

in which the

cytoplasm

may become

independent

from nuclear genes of the founder females. The

distributions,

averaged

over all

simulations,

of

cytoplasmic

generation

numbers are

shown in table VII. Distributions were checked for different simulation models and were

_virtually

identical in all cases

_except

for the difference between the number

of years. With

10-year data,

less than

20%

of

cytoplasms

are

_separated

from the

In this

_study

there were no

_{non-cytoplasmic}

maternal effects to

_complicate

the simulation. Further work _{is in progress} to

_investigate

cases where a

_genetic

maternal

ACKNOWLEDGMENT

The senior author is

_grateful

for a

_scholarship

from the

Ministry

of Culture and

_Higher

Education of Iran for the PhD

study during

which this

_study

was conducted. Grateful

acknowledgment

is also made to Dr K

_Meyer

for

_providing

the DFREML program for

analysing

the data.

REFERENCES

Bell

BR,

McDaniel

BT,

Robison OW

₍₁₉₈₅₎

Effects of

cytoplasmic

inheritance on

production

traits in

_dairy

cattle. J

Dairy

Sci

_68,

2038-2051

Boettcher

_PJ,

Kuhn

_MT,

Freeman AE

₍₁₉₉₆₎

_Impact

of

cytoplasmic

inheritance on

_genetic

evaluations. J

_Dairy

Sci

_79,

663-675

Graser

HU,

Smith

SP,

Tier B

₍₁₉₈₇₎

A derivative-free

_approach

for

_estimating

variance

components in animal models

_by

restricted maximum likelihood. J Anim Sci

_64,

1362-1370

Hohenboken WD

₍₁₉₈₅₎

Maternal effect. In: World Animal Science. General and

quanti-tative

_genetics

_(AB

_Chapman,

_ed),

_{Elsevier, Amsterdam,}

135-149

Kennedy

BW

₍₁₉₈₆₎

A further look at evidence for

_cytoplasmic

inheritance for

production

traits in

_dairy

cattle. J

_Dairy

Sci 69, 3100-3105

Meyer

K

₍₁₉₈₉₎

Restricted maximum likelihood to estimate variance _components for animal models with several random effects

_using

a derivative-free

algorithm.

Genet Sel

_{Evol 21,}

317-340

Meyer

K

₍₁₉₉₁₎

DFREML program to estimate variance components

by

restricted max-imum likelihood

using

a derivative

_{free-algorithm.}

User

_Notes,

Version

_{2.0, University}

of New

England

Rao CR

₍₁₉₇₃₎

Linear Statistical

_Inference

and its

_{Applications.}

J

_Wiley

and

_Sons,

New

York, 417-420

Southwood

_{01, Kennedy BW, Meyer K,}

Gibson JP

₍₁₉₈₉₎

Estimation of additive maternal and

_{cytoplasmic genetic}

variances in animal models. J

_Dairy

Sci

72,

3006-3012