Sources of variation of the cattle secondary sex ratio

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Sources of variation of the cattle secondary sex ratio

P Astolfi, S Tentoni

To cite this version:

Original

article

Sources of variation of the

cattle

secondary

sex ratio

P

Astolfi

S

Tentoni

2

1

Università

di

Pavia, Dipartimento

di Genetica e

_{Microbiologia}

‘A Buzzati

Traverso’,

’,

via

_{Abbiategrasso, 207,}

27100

Pavia;

2

Istituto

di Analisi Numerica del

_CNR,

via

_{Abbiategrasso, 209,}

27100

_{Pavia, Italy}

(Received

9 March

_{1994; accepted}

24

_August

₁₉₉₄₎

Summary - The aim of this

_study

was to establish the

_importance

of

_genetic,

_biological

and environmental factors which _may affect sex ratio at birth in

_dairy

cattle. Four main kinds of variations may be considered:

heterogeneity

between the mothers with _respect to

the

_probability

of a male

_birth,

variation in this

_{probability according}

to

_parity

within the

progenies;

correlation between the sexes of

adjacent births,

and breeders’ decisions. We

developed

models in which all or some of these factors were

simultaneously

included,

and

tested them on a

_sample

of about 266 000 dams. The male birth

_proportion

was found

to be

_{significantly heterogeneous}

between

_{dams, increasing}

over time within

progenies,

and influenced

by

the breeder’s choice of

stopping

or

continuing

the dams’

reproductive

career. The influence of the sex of a calf on the sex of the

_following

one

_proved

to be

non-significant.

secondary sex ratio

_{/ non-random}

variation

_/

Markov _dependency

_/

_dairy cattle

Résumé - Facteurs de variation du taux de masculinité à la naissance chez les bovins.

_L’objectif

de cette étude est d’évaluer

_{l’importance}

des

_{facteurs génétiques,}

bi-ologiques

et environnementau!

_{susceptibles d’influencer}

le taux de masculinité à la nais-sance chez les bovins laitiers.

_Quatre

sources

_majeures

de variation _peuvent être

con-sidérées :

_{l’hétérogénéité}

entre

les

mères quant à la

_probabilité

de la naissance d’un

_mâle,

la variation de cette

probabilité

selon la

parité,

la corrélation entre les sexes des nais-sances successives _et,

_enfin,

les décisions des éleveurs. Nous avons établi des modèles dans

lesquels

tous ou

_quelques-uns

de ces

_facteurs

sont inclus de

_façon

simultanée et nous les

avons .éprouvés

sur un échantillon d’environ 266 000 mères. La

_proportion

des naissances

de mâles

_{diffère significativement}

entre les mères. Elle a tendance à augmenter

au fil

du

temps dans une même descendance et est

influencée

par le choix de l’éleveur d’arrêter ou

de

_prolonger

la carrière

_reproductive

de la mère. Le sexe d’une naissance ne

_présente

_pas

d’effet

statistiquement

significatif

sur celui de la naissance suivante.

taux de masculinité des naissances

_/

facteur de variation

_/

_dépendance markovienne

INTRODUCTION

The common

_finding

that sex ratio at birth

_(secondary

sex

ratio)

shifts from the

expected

equal

male/female

proportion

has

_given

rise to

_{investigations}

about the factors which

_might

influence sex at birth. Possible factors were reviewed in humans

by

James

_(1987),

and in non-human mammals

_by

Clutton-Brock and Iason

_(1986).

Although

the causal mechanisms

_through

which the various factors

_produce

their effects have not been

_{unequivocally confirmed,}

evidence of

_resulting

non-random variations in male and female births has

_frequently

been found in humans and mammalian natural or domestic

_populations.

Since the

_beginning

of this

_century

many authors have

analyzed

sets of

_data,

mostly

relative to

_humans,

in order to

_identify

which kinds of

_variations,

in addition

to

_{chance, might}

affect the

_secondary

sex ratio. These

_analyses,

carried out

_using

models which did not

_provide

simultaneous controls for many

effects,

nevertheless

indicated the

_importance

of different kinds of variation

_(Gini,

_1951;

_Edwards,

_1958;

Edwards and

_Fraccaro,

_1960;

Renkonen et

al, 1962;

Beilharz,

1963;

Edwards,

1966;

Greenberg

and

_White,

_1967;

_James,

_1975).

_{Genetic, biological}

and environmental factors may

produce

different kinds of variation which are

_generally

ascribed to the

following

4 classes:

_(a)

variation in the

_proportion

of male and female live births between

_families;

_(b)

variation in the

_proportion

of male and female live births

according

to birth orders within

_families;

_(c)

influence of the sex of one birth on

the sex of the

_following;

and

_(d)

variation due to rules in

_limiting

reproduction

according

to

_preferences

for a _{certain progeny size} or sex

_composition.

According

to

_(a)

and

_(b),

the distribution of

_progenies

is

_expected

to follow 2 extensions of the binomial

_{distribution,}

the former formalized

_by

Lexis and the latter

_by

Poisson. Edwards

₍₁₉₆₀₎

_suggested

a third

_{generalization by assuming}

that the sex of one birth

_{might depend}

on the sex of the

_previous

one

_(Markov

dependency

(c)).

However,

he

_emphasized

the difficulties in

_identifying

these

_effects,

which _may confound each

_other,

work in

_opposite

_ways and in some cases cancel

each other out.

The fourth

_type

of variation

_(d)

is related to choices in

_limiting

_procreation

aimed at

_obtaining

a more

_{economically profitable}

_male/female

_ratio.

_Depending

on the

_population

_considered,

_progeny sex ratio can be influenced

_by

birth

_control,

as in _man, or

by

breeders’ criteria of

_selection,

as in domestic

_species.

The _purpose of this work was to

_investigate

which kinds of non-random

_variation,

if any, affected the sex ratio of live born calves in a

_sample

of

_dairy

cattle.

In a

_previous

_analysis

(Astolfi, 1989),

evidence of the Lexian sex ratio variation

between

_sibships

of the same size was found.

_However,

the

_underlying

model

_only

allowed for this kind of

_variation;

the other effects were not included.

In this

_analysis

we followed a method similar to the one outlined

_by

Pickles et al

_(1982);

in addition to the variations of

_points

_{(a), (b)}

and

_(d),

included in their

models,

we assumed that the

_probability

of a male birth is conditioned

_by

the sex

of the

_preceding

calf

_(c),

_according

to

_{non-stationary}

Markovian

_dependency.

The

The relative effect of each source of variation was evaluated

_by

comparing

the

complete

model with

_simpler

models obtained

_{by alternatively excluding}

some

factors.

MATERIALS AND METHODS

From a

_large

data set

_{provided by}

AIA

_(the

Italian breeders’

_association)

on the

fertility

of Italian

_dairy

breeds in the

_period

1971-1987,

a

sample

of 266 518 Friesian

dams was selected

_according

to the

_following

criteria. The dams were bred in 4

_provinces

of Northern

_Italy

and bore at most 10 calves in the

_period

_1975-1984,

without any abortions or still births. The total number of

calves

was 696

377,

of which 353 167 were males. In this

_sample,

_complete

information about the calves

born was available: the birth

_date,

the number of inseminations

_preceding

the

pregnancy and the sex. The

sibships

were assumed to be

_{completed by}

1984,

and all mothers were considered to have

_{stopped reproduction by}

this _year since the available information

_regarding

which dams continued

_reproductive

activity

after 1984 was

_incomplete.

In this

_work,

we considered the sex _sequences of

_length

_1,

2 and 3 in

_progenies

consisting

respectively

of the first

_1,

2 and 3

_calves,

as well as the sequences of

length

4 in

_progenies

of size

_greater

or

equal

to 4

_(see

table I for the

_complete

_list).

In the latter case, attention was focused on the sex of the first 4

_calves,

_pooling

Models

_allowing

for more than one factor

The effects of more than one factor on the

_probability

of a male birth were

examined

_{simultaneously,}

under the

_hypothesis

that different factors _may influence the

_probability

of a

_given

sex _sequence.

Let us denote

by

’sex

sequence’

S of

length

n, an ordered

n-tuple

of sexes

(m

and f

_standing

for male and female

_{respectively),}

and

_by

_Prob(S)

the

_probability

of

_observing

S in the first n births within the same _progeny.

In a model where all dams have the same

_probability

_p of

_bearing

a male calf and sexes at birth are considered as

_independent

events,

the

_probability

of

_observing

the sex

sequence S

is: ..

where

and n is the

length

of the

_sequence:

On the basis of this

_model,

more

complicated

models were examined

allowing

for the 4

previously

cited sources of variation.

To account for Lexis

_variation,

the

_probability

of the first male birth was

considered to vary between dam’s

progenies.

Let us denote

_by

P,

the

underlying

random variable and

_by

_{f (p}

_l

₎

its

_probability

_density

function. For each dam the

probability

of the ith male birth _pi, with i > 1

_according

to

_parity,

was considered

to be a

function

of _PI and of sex of the

preceding birth,

thus

accounting

for Poisson

variation and

non-stationary

Markov

_dependency.

More

_precisely,

the conditional

_{probabilities}

of the ith

male

birth

_(i

>

₁₎

were

expressed

as:

’

.

and

with

_k

_im

_,

k

if

positive

constants,

which amounts to

_assuming

that

non-stationarity

occurs in a similar form across the dams.

Hence,

recursively,

the

_probability

of the ith birth

_being

male in a _progeny where

PI

=

P I is:

As an

_example,

the

_{probabilities}

of

observing

the sex _{sequences m,}

fm,

mfm and

In a more

_{complete model,}

the

_possibility

of

_limiting

_procreation

was taken into

account and the

_{corresponding ’stopping}

probabilities’

included in the model. The

probability

q(S)

of

_stopping

a progeny after the occurrence of a

_particular

_sequence

S was considered

independent

of

P

I

but

dependent

both on _{progeny size and} sex

composition.

When the

_possibility

of

_{stopping procreation}

_according

to size and sex

composi-tion of _{the progeny} is taken into

account,

the

probabilities

in

_[2]

become:

Prob[fmIP, = p

i]

=

(1 - pi)(l - q(f))k

2f

P

l

Prob[mfmIP,

=

pi]

=

p

l

(1 - 9

(m))(l - k

2mPl

)(I -

q(mf))k

3

f

p

l

Prob[mffmlP

l

= p

i]

= PI(1-q(m))(1-k

2mPI

)(1-q(mf))(1-k

3fPd

(1-q(mff))k

4fPI

Let us remark

that,

when

evaluating

the

probability

of a sex _sequence of

length

n in a _progeny of size

_equal

_{to n,} an

_ending

factor

q(!)

must be considered:

Prob[fmlprog

size

_{2, P}

_I

_{= pi] = (1 -}

_PI

_{)(l -}

_{q( f))k}

_2fP

_iq(fm)

Prob[mfmiprog

size

_3,

_P

_I

=

pi]

=

pi(l - q(m))(1 - k

)(1 -

2m

1

p

q(mf))k

3f

p

l

q(mfm)

Prob[mffmlprog

size

_4,

_P

_I

=

pi]

=

(1 - q(m))(1 - k

l

p

2m

p

1

)(1 -

q(mf))(1 - k

3fP

i

l’

(1 -

q(mff))k

4f

p

l

q(mffm)

Let us denote

_by

{Sj}!i,3o

all the

_possible

_sequences

_{of length equal}

to or lower

than

_4;

the

_expected

_proportion

of

_progenies

with a

_particular

sex _sequence

_S

_j

_may

be found

_{by integration}

of the sequence

probability

over pi:

From the definition of rth noncentral moment of the

P

i

distribution,

f.1,!

=

fi

11

p

i f (

p

l

)d

p

l

,

it follows that

_1f

_(Sj)

_may be

_expressed

as a function of the

noncentral moments of the

P

l

distribution. For

_example:

’

More

_generally,

the

_{expected frequencies}

₇

_r(S

_j

₎

are the

product

of 2

_terms,

each

Maximum likelihood estimates of the

_parameters

were then obtained

_by

maxi-mization of the function In L over all the

_possible

_sequences:

The maximization of the

_{log-likelihood}

function may be achieved

separately

for the 2 sets of variables. Each

_probability

_q(S)

was estimated as the

frequency

of

the

_particular

sequence S followed

by

no more

births,

N(S),

over all the

possible

sequences

starting

with S and

_possibly

continuing

with further

births,

N

*

(S):

Since these are maximum likelihood estimates

(Pickles

et

al,

1982),

they

were

included in the model after the maximization of the first term

.M,

in order to

simplify

the

_equations

and reduce the

computing

time. The non-linear

_optimization

of the function

_{M (f.1,! ,}

... ,

f.1,4,

k

2m

,’

.. ,

j

C4f

)

was

performed by

means of the routine

E04UCF of the NAG

_library,

Mark 15. In the estimation

_procedure,

all the variables must be constrained to

_positive

values.

Moreover,

the moments must

_satisfy

the

following Liapounoff inequalities:

’

In order to evaluate the

importance

of each source of

_variation,

3 different models

with fewer

parameters

were considered beside the

complete

model:

Model 1. Poisson and Lexis variations and

stopping

rules

_by

sex _sequence were

considered; by

assuming ki

m

=

ki

f

= k

i

(i

=

2, 3,

4),

Markov

dependency

was

excluded.

Model 2.

_Stationary

Markov

_dependency,

Lexis distribution and

_stopping

rules

_by

sex _sequence were

considered;

by assuming

that

k

im

=

,

m

k

ki

f

=

k

f

(i

=

_{2, 3,}

4),

Poisson variation was excluded.

Model 3. Poisson variation and

stopping

rules

_by

sex _sequences were

considered;

by

assuming

kz

m

=

k

if

=

k

i

’

and a

= 0

(i

=

2, 3,

4),

Markov

dependency

and Lexis

variation,

respectively,

were excluded.

The

_frequency

distributions

_expected

under the 4 models were fitted to the observed distribution. Then the

_goodness

of fit of the

complete

model was assessed

by

the

G-test,

while the effects of the 3

_biological

factors were evaluated

_by

the likelihood ratio

_(LR)

test of the

_simpler

Models

_{1, 2,}

3

_against

the

_complete

one.

To evaluate the breeder’s influence in

_limiting

the dams’

_{reproductive activity}

according

to sex _sequence,

stopping

rules

by

_progeny size

independently

of sex

q(ff)

=

q(2), q(mmm)

_

...

= q(fff)

=

q(3).

In this case,

J

r(Sj )

takes a form similar

to

_!3!:

1f(Sj)=Mj(f.1,!,...,f.1,4,

!m,...,!4f)-!(9(l),

q

(

2

), q

(3))

and the

_{log-likelihood}

function becomes:

ln!=.M(!,...,/4 !m,...,!4f)+!(9(l),

q

(2), q

(3))

An LR test was then

performed

between the

quantity

!(q(m), ... , q(fff))

in

[4]

and the

_analogous

quantity

!’(q(1), q(2), q(3)).

RESULTS

Table I shows the observed

_frequencies

of all the

_possible

sex _{sequences in}

progenies

ranging

from 1 to 3 calves and with 4 or more calves. The

probabilities

of

limiting

procreation, allowing

for both progeny sex

composition

and size or for size

only,

were estimated

according

to

_[5]

and are shown in table II.

Physical

difficulties in either

_carrying

on _pregnancy or

_{during delivery,}

and udder

pathologies, foreseeably

increasing

as the progeny size

increases,

and

lowering

milk

yields,

are the main causes of the breeder’s choice of

stopping

dams’

procreation.

Moreover,

the

_greater

difficulties in pregnancy and

_delivery

of male

_offspring,

on _average heavier than the female ones, increase the

probability

of

limiting

reproduction

in

_progenies

with

_prevalence

of male calves.

The

_{complete model,}

which takes into account the 3

_biological

factors

_(Markovian

dependency,

Poisson and Lexis

_variations)

and the breeders’ choices in

_limiting

In order to evaluate the effect of each

_{biological factor,}

we

_performed

the LR test between the

_complete

model and Models

_{1, 2}

and

_{3, which}

excluded one factor

at a time

_{(table IV).}

The results obtained

_by

the LR test of model 1 show that the influence of

_{non-stationary}

Markov

_dependency

_(as

formalized in

_[1a]-[lb])

is not

_significant.

_{However, suggestions}

of a weak effect

_might

follow from the

_k

_jm

values,

which are

always

_greater

than the

_{corresponding}

_k!

_values,

thus

_revealing

that after a male calf the

_probability

of a male birth was

_{slightly higher}

than the

probability

of a female birth. On the

_contrary,

the LR tests of Models 2 and 3 show that Poisson variation between birth orders and Lexis distribution of

_P

_I

between

progenies

significantly

contributed to the sex ratio variation.

The effect of the breeders’ selection

_according

to _{progeny size} and sex

composi-tion,

rather than size

_{only, proved}

to be relevant

_by

the

_{highly significant}

LR test of

!’(q(1), q(2), q(3))

against

!(q(m), ... , q(fff)) (LR

=

217.24,

11 df,

P «

0.001).

DISCUSSION

In this paper we

simultaneously

considered the factors which

_generally

are assumed to influence the

_secondary

sex ratio. This

_{investigation,}

_though

limited to the sex

sequence of the first 4

births,

demonstrated that 3 sources of non-random variation seemed to influence the sex ratio at a

_significant

level: the male

_proportion,

which

increases with

_parity;

the

_probability

of the first

male

calf,

which varies between the

mothers;

and the effect of the breeders’ rules in

_stopping

the dams’

_reproductive

life.

The

_hypothesis

that the sex of a born calf _may be influenced

_by

the sex of the

preceding

one was not confirmed at a

_significant

level.

_Analyses

of this factor in different data sets of humans and domestic

_species

showed controversial results. For

example,

in human

_populations,

Renkonen et al

₍₁₉₆₂₎

and Edwards

₍₁₉₆₆₎

_and,

in

_cattle,

Astolfi

_(1990a,b)

found a

_positive

_significant

correlation between sexes in consecutive

_births,

while Edwards and Fraccaro

₍₁₉₆₀₎

and

_Greenberg

and White

and

_Gray

and Katanbaf

_(1985),

in

_swine,

did not obtain

_{statistically}

_significant

results, though

correlations between sexes were

generally

_{positive. However,}

in these

investigations

the other sources of variation had not been

_explicitly

_considered,

in

particular

the maternal

_tendency

to

generate

offspring

of one _sex, which may be confounded with the

_positive

interaction between sexes in consecutive births. In our

_analysis,

in which Lexian variation between the mothers was

_considered,

the influence of the sex of a birth on the

following

_one, formalized as a

_{non-stationary}

Markov process, showed a

_{non-significant}

effect

_and,

when

_excluded,

the reduced

Model 1 still fitted the data well. This confirms the results of Pickles et al

_(1982),

which found a

_{good fitting}

of human data

_using

models not

_allowing

for Markovian association.

The

_significant

effect of

_parity

was confirmed

by

the LR test of Model 2

_against

the

_complete

model

_{(table IV).}

The

_probability

of

_bearing

a male calf seems to increase with

_parity

up to the fourth birth at a rate of about

1%.

Evidence of a

positive

trend in cattle was found

_{by Skjervold}

and James

(1978),

while in humans

To

_explain

these

_opposite

trends we must take into account the differences in

reproductive

activity.

In _man, births occur

_during

a

_long

interval in the fertile

period,

while in

_dairy

cattle the breeders’ selective

_{choices, aiming}

at economic

profit,

make the dam’s

_reproductive

_{activity precocious}

and

short,

generally lasting

only

4 or _{5 years} for

_healthy

and

_{highly productive}

dams.

_Therefore,

it is believable that the

_reproductive

effort

_starting

at a

_juvenile

_age, the

_high

milk

_yield

and

the inseminations

_performed

soon after

_parturition

are

_{heavily stressing}

factors.

In some mammal

_populations

many authors found evidence that young males

are less viable than females and in

_particular

fetal losses are more

frequent

for

male

_{fetuses, especially early}

in pregnancy

(for

extensive

_references,

see Trivers

and Willard

_1973;

Clutton-Brock et

_{al 1985).}

The Trivers-Willard model

₍₁₉₇₃₎

assuming

that &dquo;sex ratio at birth is a measure of

_tendency

to invest in one sex more than the

other&dquo;, predicts

that &dquo;females in better conditions tend to invest in

males&dquo;;

therefore we could _{argue that} as the maternal conditions

_improve,

the sex

ratio increases. With

_respect

to this

_{investigation,}

we

_might

_suggest

_that,

due to

her

_precocious

_{exploitation,}

the dam

_gradually

reaches

_{complete development}

and

optimal

conditions to bear a calf

_during

her fertile

_period.

The _consequence

_might

be a

decreasing probability

of male abortions and an

increasing

_proportion

of male

births over time. This

_hypothesis

would have to be

_{supported by}

further

_analyses

of the

_complete

_reproductive

career of the cow.

A further

_significant

effect concerns

_{heterogeneity}

between

_sibships

in the

probability

of the first male birth

_(table

_IV,

_{Model 3).}

Since the sire’s contribution

generally

varies within

_sibships

and hence calves of the same dam are

_halfsibs,

this effect _may be considered due to a maternal

_{genetic heterogeneity. Assuming}

that

P

I

follows a

_{,(3-distribution,}

the 2

_shape

_parameters

(a

=

89.334,

b =

88.473)

_were

evaluated

_by

a least _squares

_fitting

of the first 4 noncentral moments estimated under the

_complete

model. The

_{resulting probability density}

_{(fig 1)}

is

_nearly

symmetric,

with most values concentrated around the mean.

From the noncentral moments

_(f.1,!

and

_f.1,!)

estimated under the

_{complete model,}

the variance of the distribution has been evaluated as

_0.00190,

close to 0.00265 found

by

Pickles et at

_(1982),

and in the range 0.0012-0.0032 evaluated in a

_previous

_paper

(Astolfi, 1989).

The third very

important

factor results from the selective criteria. Breeders

_prefer

to

_stop

the

_reproductive

_activity

of cows that bore more male than female

calves,

hence

_causing

the sex ratio to lower as the _{progeny size increases.} In

fact,

for _progeny

size

_ranging

from 1 to

_10,

the male

_proportion

was found to decrease

_regularly

from 0.515 to 0.498

_{(Astolfi, 1989).}

In

_conclusion,

among the factors

that,

in addition to

_chance,

are

_generally

considered to influence the

_secondary

sex

_ratio,

3 seem to have

_significant

effects. We

_hypothesized

that 2 of these are associated with

_breeding

conditions aimed at economic

_profit:

the artificial selection that favors dams

_bearing

female calves and

directly

lowers the sex

_ratio;

and the criteria of herd

_management

that

_physically

stress the

youngest

mothers and

_indirectly

increase the

_probability

of male fetal losses in the first

_pregnancies.

The third seems to be a

_{genetic factor,}

which

_might

account for different maternal

_{probabilities}

in

_generating

male or female

_offspring,

ACKNOWLEDGMENTS

We are most

_grateful

to C Matessi for his valuable

help

in the discussion of the models and to L Zonta for the valid comments on the

_manuscript.

This work was

_supported

by

the National Research Council

_(CNR)

_’Gruppo

nazionale difesa e valorizzazione del

germoplasma

animale’.

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