Linkage disequilibrium in French natural populations of Drosophila melanogaster

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Linkage disequilibrium in French natural populations of

Drosophila melanogaster

J. Sanchez Prado, L. Charles-Palabost, M. Katz, A. Merçot

To cite this version:

Original

article

Linkage disequilibrium

in French natural

_populations

of

_{Drosophila melanogaster}

J. Sanchez Prado

1

L. Charles-Palabost

M. Katz

A.

_Merçot

1 _{Universidad de}

_Oviedo,

Departamento

de

Genetica, Asturias,

Spain

2_{Université F.}

_{Rabelais, IBEAS,}

avenue

_Monge,

Parc

Grandmont,

37200

Tours,

France

3_{Université de Paris}

_v7/,

_{Laboratoire de}

_Génétique

_{Quantitative et}

_Mol6culaire,

and 4 _{Université de Paris}

_VII,

_{Laboratoire de}

Génétique

des

_Populations,

Tour 42-32, 2

_place

Jussieu,

75005

Paris,

France

(received

23-9-1987,

accepted 25-4-1988)

Summary —

Seventeen French natural

_populations

of

_Drosophila

_melanogaster

were

_analyzed

to

detect

_linkage

_{disequilibrium}

between

_pairs

of 6

_polymorphic

allozyme

loci. The estimates of

_linkage

disequilibrium

were made from

azygotic frequencies

using

both Burrows’ and Hills’s methods. No dif-ference between these 2 methods was found. The amount of

significant linkage disequilibrium

detected was small and similar to those in other natural

_populations

of D.

_{melanogaster.}

Out of the 15 combinations

_{examined, only}

2

_{pairs, Adh-a-Gpdh}

and

Est-C-Est-6,

showed a consistent

signifi-cant

_{linkage disequilibrium}

in the

_populations

studied.

However,

for the first

_pair,

the result was

pro-bably

due to an association between the loci and the inversion

(2 L)

t of the second chromosome. For the Est-C-Est-6

_pair,

the

_{disequilibrium}

detected

_might

result from an interaction effect between the 2 genes inter se. These results

again

show the difficulties in

_{detecting linkage}

_{disequilibrium}

due

to

_epistasis

between

_allozyme

_genes in natural

_populations.

Drosophila melanogaster- linkage disequilibrium - enzymatic

loci - French natural

popula-tions

Résumé —

_{Déséquilibre}

de liaison dans des

_populations

naturelles

_françaises

de

_Drosophila

melanogaster.

Une

analyse

du

_{déséquilibre}

de liaison a été effectuée _pour 6 locus

_enzymatiques

dans

17 populations

naturelles de

Drosophila melanogaster.

Les estimations de ce

_{déséquilibre}

ont

été

faites,

à

partir

des

fréquences zygotiques,

en utilisant les méthodes de Burrows et de Hill. Aucune différence n’a été observée entre ces deux méthodes. La

_quantité

de

_{déséquilibre}

décelée

est faible et

_comparable

à celle trouvée dans d’autres

populations

naturelles de D.

_{melanogaster.}

Sur les 15 combinaisons

examinées,

seules les associations

_Adh-a-Gpdh

d’une

_part,

Est-C-Est-6

d’autre

_part,

montrent un

_{déséquilibre significatif}

dans les

_populations

étudiées. Le

_{déséquilibre}

Adh-a-Gpdh est probablement

dû à la liaison entre les

_{gènes correspondants}

et l’inversion

(2 L)

t du u

second chromosome. Au

contraire,

le

_{déséquilibre}

Est-C-Est-6

pourrait

être la

conséquence

d’inter-actions entre les 2

_gènes

eux-mêmes. Ces résultats

_soulignent

à nouveau les difficultés

rencon-trées dans la mise en évidence d’un

_{déséquilibre}

de liaison véritablement dû à une

_épistasie

entre

locus

_{enzymétiques.}

natu-Introduction

Population

studies of

_genetic

variation

are

_classically

discussed in

terms

of

single-locus

variability

measures,

such

as

_{heterozygosities}

and

_changes

in

_gene

_frequencies.

Howe-ver,

there is much interest in

_knowing

the

_genetic

structure of

_populations

at

the

multilo-cus

level. The

application

of

_{electrophoretic techniques}

to

_{analyze genetic}

variation

(Har-ris, 1966;

Hubby

and

Lewontin,

1966) provides

much information

at

the multilocus

level,

because

a

_large

number

of genetic

markers

can

be studied

_{simultaneously}

in

a

_single

individual.

Therefore,

investigations

made on

_{allozyme polymorphism}

involve

the

estima-tion of

_{linkage disequilibrium}

in natural

and

_{experimental populations}

of

a

_variety

of

orga-nisms

(see

Hedrick

et al., 1978,

for

a

_review).

Various

authors

_(e.g.,

Lewontin,

1974)

have

_suggested

that information about

_linkage

disequilibrium

among

allozymes might

be useful

to

_explain

the

adaptive

value

of

bioche-mical

_{polymorphism.}

But

_{unfortunately,}

the results obtained

by

the authors

studyng

linka-ge

disequilibrium

at

_{electrophoretically}

variable loci in natural

_populations

of

_Drosophila

melanogaster (Mukai

and

Voelker, 1977;

Voelker

et

al., 1977;

Langley

et

al., 1978;

Inoue et aG, 1984;

Yamazaki

et al.,

1984)

are

reconcilable with several models of

_population

genetics. Consequently,

even in

the absence of

inversion,

it is difficult

to

determine

whe-ther these results

are

due

to

_epistatic

natural selection

or to

random

genetic

drift.

Howe-ver, we

think that it is

_important

to

determine the

nature

and

_magnitude

of

_linkage

disequilibrium

in natural

populations,

because the

_{investigations}

_may

_{perhaps help}

in the

study

of interactions between genes and in

developing

new

_hypotheses

about the

mechanisms involved

in

the maintenance of

_{allozyme polymorphism.}

In this paper

we

_report

a

_study

of

_{linkage disequilibrium}

_among

6

_polymorphic

allozy-me

loci

in 17

natural

_populations

of

D.

_melanogaster

collected

from

different

regions

of

France.

Materials and Methods

Collections

Wild

_{Drosophila melanogaster}

adults were collected and

brought

to the

laboratory

for

electrophore-sis. All collections were made

_during

the annual

_demographic

burst of the

_species

(between August

and

October).

Populations

studied

The

_populations

studied are distributed from the North to the South of France

_(Fig.

_1);

their

_origins

are listed below :

₍₁₎

Venteuil near

_Epernay;

₍₂₎

Verneuil near

_{Epernay; (3)}

Vincennes near

Paris; (4)

Sbvres near

_Paris;

₍₅₎

_{Ivry-sur-Seine}

near

_{Paris; (6)}

Sainte-Genevi6ve-des-Bois near

Paris;

(7)

Ran-n6e near

Rennes;

(8)

Nevez near

_{Quimper; (9)}

Chateaubriant;

(10)

M6n6tr6ol-sous-Sancerre near

Sancerre;

(11)

Bonnac-la-C6te near

_{Limoges; (12)}

_{Chessy-les-Mines}

near

Villefranche-sur-Sa6ne;

(13) Beynost

near

Montluel; (14)

Le Curtelod near

Yenne; (15)

Montauban;

(i 6)

Tautavel near

Perpi-gnan; (17) Port-Vendres.

_{Only populations}

₍₁₎

and

₍₂₎

were

_captured

in

wine-cellars;

the others

origi-nated from fruits of the localities studied. Two collections were made for

_{populations (6)}

and

_(9),

the

Electrophoresis

Electrophoresis

was

_performed

in horizontal starch

_gel

with Poulik’s discontinuous buffer

_system.

Six

_polymorphic

enzyme loci were

studied,

according

to the

_techniques

described

_by

Charles-Pala-bost

_{(1986) :}

acid

_{phosphatase (Acph; 3:101.4),}

alcohol

_{dehydrogenase (Adh; 2:50.1), esterase-C}

(Est-C;

3:47.6),

esterase-6

_(Est-6;

_3:36.8),

_{a-glycerophosphate dehydrogenase (a-Gpdh;}

_2:20.5),

and

_{phosphoglucomutase}

_{(Pgm; 3:43.4).}

Estimation of

_linkage

_{disequilibrium}

In this

_study

almost all the data were

_{analyzed by}

a 2-allele

_system.

If more than 2 alleles exist at a

locus, they

have been

_grouped

in 2 classes: the most

_frequent

allele

_{corresponding}

to the first

_class,

and the others to the second.

respectively,

f11, !2. f

2l

,

and

_f

₂₂

_,

the

_linkage

_{disequilibrium}

D is

_given

by :

In order to make the values of the

parameter

D less sensitive to

_change

in gene

frequency,

seve-ral other measures of

_{gametic disequilibrium}

are useful in various contexts. The correlation coeffi-cient R

_D/Vpg

_{(1-p) (1-q)}

was used

_by

Hill and Robertson

₍₁₉₆₈₎

and

by

Franklin and Lewontin

(1970).

However,

in a

_sample

of individuals taken from a

_population,

the

_degree

of

_linkage

disequili-brium cannot be estimated

_directly

from the

_{genotypic frequencies}

when the

_coupling

and

_repulsion

heterozygotes

cannot be

_{distinguished.}

In this case, estimation of

_{linkage disequilibrium}

can be done in several ways. Hill

(1974) provides

a maximum-likelihood method where the

_population

is assumed to be random

_mating

and in

_{Hardy-Weinberg equilibrium}

at each locus. In the case of 2

codominant alleles per

locus,

the

_frequency

of one

_gamete

_(for

_example

_AB)

estimated

_by

the

maxi-mum-likelihood method

_(f

₁₁

₎

is

given by

a cubic

_{equation :}

with

_N

_II

_,

_N

₁₂

_,

_,

₂₁

_N

_N!,

and N

_{corresponding,}

_{respectively,}

to the observed numbers of

AABB,

AABb,

AaBB, AaBb,

and total individuals in the

_sample.

In

Eq. (1)

the

only

unknown is

f11.

Hill

_suggests

that an initial value :

_{f11 (4N}

_»

+

_2N

_l2

+

_2N

₂₁

+

N! )l2N pq

can be substituted into the

_right-hand

side of

(1)

and the

_resulting

_expression

_regarded

as an

_improved

estimate and itself substituted into the

_right-hand

side of

₍₁

_The

_{iterative process} is

continued until

_stability

is reached and D obtained as : D

_{= f}

₁₁

_-

_pq. A test for D = 0 is

given by :

K =

N D

2

/pq

(1-p) (1-q),

with

_Kfollowing

the

_chi-square

distribution with one

_degree

of freedom. A second

_{approach, suggested by}

Burrows

_(see

Cockerham and

_Weir,

1977 and

_Langley

et

al.,

1978),

is

_simply

used to _{estimate the overall covariance of non-allelic genes in individuals. This}

method does not

require

that one

_distinguish

between the 2

_types

of double

_{heterozygotes}

and know the

_mating

system.

Burrows’s

_parameter

is estimated

_{by : !}

= 1/2

(4N

11

/N

+ 2N

121

1N

_{+ 2N}

₂₁

_/N

+

_2N

₂₂

_{/M -}

_2pq.

A test for A = 0 is

given by : X

2

=

NA

2

/pq

(1-p) (1 !)

where

X

2

is

approximately

a

_X

₂

distribution with one

_degree

of freedom

_(Cockerham

and

_{Weir, 1977).}

The correlation coefficient

based on Burrows’s estimation is : R =

A/2 !

_pq

(1-p)

(1-q).

In _{any population,} all the loci are not

_necessarily

in

_{Hardy-Weinberg equilibrium.}

_Therefore,

we

used not

only

Hill’s

method,

which assumes that the loci are in accordance with the

Hard-y-Weinberg

law,

but also Burrows’s estimation.

_Moreover,

it was

_interesting

to compare the results obtained

_by

both methods because this was done

only

in few cases.

Results

Table

_{I gives,}

for

each

_population,

the number

of

flies

_analyzed

_{per locus}

and the

frequencies

of the most common

allele

at each locus.

With

_regard

to the

distribution of

allelic

_frequencies,

the

_populations

collected

in 1983 were

_analyzed

in

another

_paper

(Charles-Palabost

et al.,

1985),

and those of

1984 will

be

_analyzed

later.

_Concerning

the

goodness

of fit

to

_{Hardy-Weinberg}

_equilibrium,

the

use

of the

_X

₂

test

is

not

_appropriate

in

some cases,

since the

expected

numbers of

_genotypes

are too

small.

Therefore,

each

a

value

_given

in

Table

I is the

probability

that the

_{genotypic frequencies}

distribution of

a

random

_sample

are

farther from the

_{expected Hardy-Weinberg}

model than the

corres-ponding

observed distribution. These values

were

obtained

_by

means

of Monte-Carlo

simulations,

using

the observed allelic

_frequencies

as

the real

frequencies

and under the

null

_hypothesis

in which

the

_populations

are in

_{Hardy-Weinberg equilibrium.}

This test

is

consequently frequency independent.

We observe that

21 a

values

out of 101 are

signifi-cant

_{and among these}

21

_significant

_values,

10 are

due

to

_{the presence of}

a rare

per locus in each

population

are

in

_good

_agreement

with those

_expected

under the

Hardy-Weinberg

law. A

_significant

excess

_{of heterozygotes}

was

found

_only

at

the

a-Gpdh

locus of the S6vres

_population.

Table

II

shows the

_frequencies

of the

observed

_{heterozygotes}

for

each locus and

population. Classically,

the

amount

of variation differs

_greatly

from

one

locus

to

another.

The average

heterozygosity

over

the

6

loci

_analyzed

_{ranges from 0.092 in the Nevez}

population,

to 0.250 in

the

_{Ivry-sur-Seine}

and S6vres

_{populations. Except}

for

_Nevez,

the

mean

_{heterozygosities}

obtained

are

similar

to

those estimated

_previously

in

other French

natural

_populations

of D.

_{melanogaster (Girard}

and

Palabost,

1976).

The

values of

_{linkage disequilibrium}

estimated

_by

Burrows’

_(A

and

_R

_b

₎

and Hill’s

methods

_(D

and

_R

_h

₎

are

_given

in

Table

III

for the

unlinked loci

(located

on

different

chro-mosomes)

and in Table

IV

for

those

linked

_(located

on

the

same

_chromosome).

The

use

of the

_x

₂

distribution in order

to

determine the

_significance

level of

a

_linkage

alleles

at

each of the

2

loci

must

be smaller than 0.85

_{(Montchamp-Moreau, 1985).}

Thus,

the

_significance

levels in Tables III and

IV

_correspond

to

the

_probability

that the

_linkage

disequilibrium

estimated from

a

random

_sample

is

_greater

than the

_{linkage disequilibrium}

estimated from the

sample analyzed.

These

_{probabilities}

were

obtained

_using

Monte-Carlo

simulations,

under the null

_hypothesis

of

a

_{disequilibrium equal}

to 0.

This

test

is

independent

of

the

_{distribution,}

but

assumes

that the observed

allelic

_frequencies

are

the

real

_frequencies

in the

_populations.

We can note that

the values of

D

and A

are very

estima-tion)

and

_R

_b

_{(Burrows’s estimation)}

are

different

and,

in

most cases,

_R

_b

is smaller in

absolute values than

_R

_h

₍₁₆₁

cases out 216

_values).

When

_R

_b

=

R

h

(in

55

cases),

_no

double

_{heterozygotes}

are

_present

in the

_samples

and 0 =

2D;

this result

is

particularly

evident for unlinked loci. With Hill’s

method,

23 out

of the

216

_comparisons

made

bet-ween

_pairs

of loci

are

_significant,

which

_represents

a

_percentage

of

10.6.

_The

percen-tages obtained,

respectively,

for

the unlinked and linked loci

are 10.5

_(13/124)

and 10.9

(10/92).

With Burrows’s

method,

these values

are 15.3%

_(33/216)

for all the

loci,

11.3%

(14/124)

and

20.6%

_{(19/92), respectively,}

for unlinked and linked loci.

In the

_present

_study,

out

of the

15

combinations between

_allozyme

loci,

only

the

pair

Est-C-Est-6

shows a

_{significant linkage disequilibrium}

in

most

of the

_{populations :}

4 D

values

out

of 18

_{populations sampled (22%)}

and

8 0

values

_(44%)

are

_significant

(Table IV). Using

combined

data

of all

the

_populations,

a

_significant

deviation

was

obtai-ned

_only

in

2 cases :

for the Est-C-Est-6

_pair

and

also

for

_Adh-a-Gpdh.

With Hill’s

estima-tion,

the values

are,

respectively,

for

_Adh-a-Gpdh

and

Est-C-Est-6

_{pairs :}

D = 0.0116

(P

<

0.01),

R

h

= -

0.0991,

and D

= - 0.0097

(P

<

_{0.01), R}

_h

= - 0.0943.

The

corresponding

values with Burrows’s

estimation

_{are :A=-0.0129(P<0.01),f?}

_b

_{=&dquo;0.0548,andA=}

=

-

0.0132

_(P

_{0.01), Rb=-0.0643.}

Discussion

The

results of the

_present

_study

are not

_essentially

different from those obtained

_by

other

investigators

in

natural

_populations

of D.

_{melanogaster.}

The

amount

of

_linkage

disequili-brium detected

in

the French

_{populations surveyed}

is

small,

but nevertheless

_higher

than

the

amount

_reported

in

other natural

_populations

of

D.

_{melanogaster,}

which

reveal

a

significant

linkage

disequilibrium

of around

5-9%

of the

_{analyzed pairs}

of loci

_(see,

for

example,

Mukai

et aL, 1971, 1974;

Mukai and

Voelker,

1977;

Yamaguchi

et

_{al., 1980;}

Yamazaki

et

aL,

1984).

But

in

the studies

_previously

mentioned,

the method used

to

detect

_{linkage disequilibrium}

is the extraction of whole chromosomes

_by

the marked

inversion

_technique.

Therefore,

our

results

are more

_strictly

_comparable

to

the data

reported by Langley

et al.,

1978),

because

_they

calculate Burrows’s estimation

_R

_b

_using

genotypic

data

obtained

in natural

_populations

of D.

_{melanogaster.}

However,

they

also

report

a

small

_proportion

of

_{significant linkage disequilibrium (5.1 %}

for linked loci and

6.7%

for those

_unlinked).

Among

the

15 combinations

between

the 6

_enzymatic

loci

_studied,

the data

_provide

clear

evidence

of a

_{significant linkage disequilibrium}

for

_only

2

_pairs

of

linked

loci :

Adh-a-Gpdh

and Est-C-Est-6. The

same

result

was

obtained

_by

_{Triantaphyllidis}

et

al.

₍₁₉₈₁₎

for the

_{Adh-a-Gpdh pair}

in

Greek

populations.

This may

suggest

consistent

_epistatic

interactions between these

pairs

of genes

(Lewontin, 1974).

But another

_explanation

is

possible

in the

case of

_Adh-a-Gpdh;

the

_{linkage disequilibrium}

detected

in our

popula-tions

_might

be due

to an

association between these

2

loci and the inversion

_(2L)t

in

the

same

chromosome

arm.

In

effect,

the inversion

_(2L)t

is located

on

the left

arm

of

chromo-some 2 and

contains the

_a-Gpdh

locus,

while the Adh locus

_{is outside and very}

near to

the

_breakpoint

of

this

inversion

_(Lindsley

and

_{Grell, 1968).}

_{Unfortunately,}

the

_frequencies

between

these 2 loci

_only

when

all

the

chromosomes

_(chromosomes

with standard

sequence and chromosomes with inversion

(2L)t )

are

considered. This

_{disequilibrium}

remains

_negative

but

not

_{significantly}

different from

0

when the In

_(2L)t

chromosomes

are

removed from the

_{analysis (Mukai}

et al., 1971;

Langley

ef al.,

1974, 1978;

Alahiotis

e t

al., 1976;

Voelker

et

al.,

1977;

Yamaguchi

et

_{al., 1980;}

Yamazaki

et

_al.,

_1984).

Consequently,

in our

_opinion,

the

_linkage

_{disequilibrium currently}

observed between Adh

and

_a-Gpdh

is

_probably

due

to

the association of these loci with In

_{(2L)t, despite}

the well

known

interactions between

these 2

enzymes

(Geer

etal.,

1983, 1985).

The result obtained for the Est-C-Est-6

_pair

appears

more

_interesting

since,

in

this

case,

Est-C and Est-6

are

located

in

different

arms

of chromosome

3.

Few

cases

of

significant linkage disequilibrium

between

esterase

loci have been

_{previously reported}

in

natural

_populations

of

D.

_melanogaster

_(see

for

_example

Johnson and

Schaffer, 1973;

Langley

et al., 1978;

_{Laurie-Ahlberg}

and

Weir,

1979),

but such

a

result is known

in

other

organisms

such

as

salamander

_(Plethodon

cinereus; Webster,

1974);

and

_barley

(Hor-deum

_spontaneum;

Kahler and

Allard,

1970).

In

D.

_{melanogaster,}

this

_linkage

disequili-brium

could be

_{explained by}

interactions between the

2

loci themselves

or

_by

interactions

between these loci and inversions located

on

the

same or

different

arms

of the

chromo-somes

3. This last

_hypothesis

was

tested

by

several authors

_(Kojima

et al., 1970;

Mukai

et al., 1974;

Langley

and

_{Ito, 1977;}

Yamazaki

et al.,

1984).

In

most cases,

when

inver-sions

(3R)P

and

(3L)Pwere analyzed

simultaneously

with the

esterase

loci,

no

evidence

of

_linkage

_{disequilibrium}

was

found between these

2

inversions,

or

between them and

the

esterase

loci.

The

_{physiological}

function

of esterases

remains unknown

_(Dickinson

and

_{Sullivan, 1975;}

Danford and

Beardmore,

1980),

but the

esterase

_{loci may code for}

a

class of

closed

_{proteins, probably functionally}

related.

Therefore,

the

_{significant gametic}

disequilibrium

observed between Est-C

and

Est-6

_might

be

examined

in terms of

interac-tions between genes

metabolically

related,

as

_{suggested by}

Zouros

and Krimbas

₍₁₉₇₃₎

and

then

_by

Zouros and Johnson

₍₁₉₇₆₎

for

2

_{other enzymes.}

However,

in our

popula-tions,

it

is

not

_possible

to

eliminate

_entirely

the influence of inversions

in

the

_origin

of

lin-kage disequilibrium

found between

Est-C

and

Est-6

loci.

Thus,

for

a better

and

more

extensive evaluation of this

result,

it

_{is necessary}

to

know

the

_population

size

_(since

genetic

drift could

_gives

rise

to an

_{important disequilibrium; Montchamp-Moreau}

and

Katz,

1986)

and

to

_verify

if this

_linkage

is

maintained

over

time.

Acknowledgments

,

We are very

grateful

to E.

_Santiago

for his

_help

in the simulations and M. Lehmann for her technical assistance.

This

_study

was carried out as

_part

of the CNRS’s UA

340,

UA 693 and GRECO 44 research

pro-grams.

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