The spread of parasitic sex factors in populations of Armadillidium vulgare Latr (Crustacea, Oniscidea): effects on sex ratio

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The spread of parasitic sex factors in populations of

Armadillidium vulgare Latr (Crustacea, Oniscidea):

effects on sex ratio

T Rigaud, Jp Mocquard, P Juchault

To cite this version:

Original

article

The

_spread

of

_parasitic

sex

factors

in

_populations

of Armadillidium

vulgare

Latr

_{(Crustacea, Oniscidea):}

effects

on sex

ratio

T

_Rigaud,

JP

_Mocquard,

P

Juchault

Université de _Poitiers, Laboratoire de _{Biologie Animale,}

URA CNRS No _{1452, Génétique} et _Biologie des _Populations de _Crustacés,

40, Avenue du Recteur _Pineau, F-86022 Poitiers Cedex, France

(Received

24 _May 1991; accepted 4 October

₁₉₉₁₎

Summary - In the woodlouse Armadillidium _vulgare, the basis of sex determination is

under the control of heterochromosomes

_(ZZ

males and WZ

_females).

_However, in most

populations, sex is determined by 2 _{maternally-transmitted parasitic} sex factors

_(PSF).

One is a Wolbachia-like bacterium

_(F),

the other

_(f)

is _probably a _sequence of F DNA unstably integrated in the A vulgare genome. Both PSF are _{feminizing factors,} which

transform genetic males into functional neo-females

_(ZZ+F

or

_ZZ+f).

The propagation of these PSF was _{investigated by introducing} neo-females into artificial _{populations initially} formed of _genetic females. In the _majority of these populations, F bacteria were unable

to _spread, while f seemed to have a _higher invasive power. These results contrast with theoretical data: _owing to the high transmission rate of PSF, their frequency should

increase in _populations where _they have appeared. Based on the observation that PSF in _populations have a behaviour similar to that of genes with selective advantages, a new

approach was _proposed to describe the _spreading of PSF in limited-sized _populations. This model showed that even a high transmission rate and in the absence of nuclear genes

conferring resistance in A _vulgare, PSF can be lost from populations. The equilibrium probability of their _{disappearance depends} on both the number of neo-females _infesting the _population and the transmission rate of PSF. These theoretical data, combined with the _presence of genes repressing the _feminizing effects of PSF, may explain part of the

variability observed in sex _{determining systems} and sex ratios of natural _populations.

parasitic sex factor _/ sex ratio _/ simulation _{model / artificial} population / Isopoda

Résumé - _Propagation de facteurs sexuels _parasites dans les populations d’Arma-dillidium _vulgare Latr _(Crustacé, Oniscoïde): conséquences sur le taux de

mas-culinité. Chez le cloporte Armadillidium _vulgare la base du déterminisme du sexe est

hétérogamétique

(mâles

ZZ et _femelles

_WZ).

_Cependant, dans la _plupart des _populations

mater-nellement. Le premier d’entre eux est une bactérie

_(F),

le second

_(f)

est _probablement un

segment de l’ADN de F _intégré de _façon instable au _génome hôte. Ces deux FSP sont des

facteurs féminisants qui transforment les mâles

_génétiques

en néo-femelles fonctionnelles.

La _propagation de ces _{2 facteurs} a été étudiée en introduisant des _{néo-femelles} dans des populations artificielles préalablement constituées de _{femelles génétiques.} Dans la majorité

de ces _populations, la bactérie F a été incapable de se _propager, alors que le pouvoir invasif

de _f semble être _{plus fort.} Ces résultats sont en contradiction avec les données _théoriques connues _{jusqu’alors:} à cause de leurs _forts taux de _{transmission,} les FSP devraient envahir

toutes les _populations où ils _{apparaissent.}

À

_partir de la constatation que les FSP ont un

comportement dans les populations similaire à celui de gènes sélectivement _avantagés, une

nos y

velle _{approche théorique} est _{proposée pour} décrire la _propagation de ces _facteurs dans

des

_populations

à _{e,f,!’ectif} limité. Ce modèle montre que, même _lorsque le taux de transmis-sion des FSP _{est fort,} et en l’absence de _gènes nucléaires de résistance chez A _vulgare, ces facteurs peuvent ne _{pas s’implanter} dans les _populations. Leur _probabilité de _disparition à

l’équilibre dépend à _{la fois} du nombre de _{néo-femelles infestant la population} et de leur taux

de transmission. Ces données _théoriques, combinées avec l’existence de _{gènes supprimant}

les _{effets féminisants} des _FSP, peuvent expliquer une _part de la variabilité observée dans

les mécanismes du déterminisme du se!e et du taux de masculinité dans les _populations naturelles.

facteur sexuel parasite / taux de masculinité _/ modélisation _/ population arti8-cielle _{/ Isopode}

INTRODUCTION

In

_populations

of

_Isopoda

Armadillidium

_vulgare

where females

_{produce offspring}

with a 1:1 sex

_ratio,

sex is determined

_by

the classical

_{homo-heterogametic}

mode. Males are

_homogametic

ZZ and females are

heterogametic

WZ

(Juchault

and

Legrand,

1972).

However,

in several

_populations

of this _crustacea, sex ratios are

often female biased and the

_majority

of females

_{regularly produce highly}

female-biased broods

_(Juchault

et

al, 1980;

Juchault and

_Legrand,

1981

_a,b,

_1989).

It has been shown

_that,

in these

_females,

sex factors override the sex chromosomes’ effects.

Two kinds of sex

_factors,

whose effects are _very

_similar,

are known to exist. The first one is a

symbiotic feminizing

Wolbachia-like bacterium

(F)

carried

by

females

located in the

_cytoplasm

of all host

_cells,

and

_especially

in _oocytes

_(Martin

et

_al,

1973;

Rigaud

et

al,

1991).

Females

_harbouring

F have a male heterochromosomal

composition

(ZZ)

and are thus neo-females

(ZZ+F) (Juchault

et

al,

1980).

The F

bacteria are

maternally

transmitted. Infected _oocytes evolve into neo-females or more

_rarely

into intersexual _types and the rare males arise from _eggs free of F. It is

_{experimentally possible}

to infect F-free A

_{vulgare by}

inoculation with tissue

extracts from neo-females

_harbouring

F.

_According

to Bull’s definition

_(1983),

F

could be called a

_cytoplasmic

sex factor that inhibits the male nuclear _genes. The

second sex factor

(named f)

is also able to transform

_genetic

males into neo-females

unknown,

but

_genetic

and

_{physiological}

data _suggest that it

_might

be a _segment of F

bacterial DNA

_integrated

in the

_isopod

_genome, with unstable behaviour

_(Legrand

and

_Juchault,

_{1984). Taking}

into account the nature of F and the

_origin

of

_f,

these 2 factors could be called

_{&dquo;parasitic}

sex factors&dquo;

(PSF).

The extension of the term

&dquo;parasitic&dquo;

for a DNA

_segment

has been used

_by

_Hickey

_(1982),

in a model on the

origin

of sex.

Numerous abnormal sex ratios are known to exist in

_animals,

but few of them are

due to PSF: in both

_Amphipoda

Orchestia

_gammarellus

and Gammarus

duebeni,

PSF are related to Protozoa

_(Bulnheim,

_1978;

_{Ginsburger-Vogel}

et

_al,

_1980).

In the

_haplodiploid

insect Nasonia

_vitripenis,

sex is

_thought

to be under the control

of cytoplasmic

microorganisms

(Werren

et

_{al, 1981; Skinner,}

_1983).

In Armadillidium

_vulgare,

natural

_populations

show _great

_variability

in their

sex ratios and in distribution of sexual factors

_(Juchault

et

_{al, 1980;}

Juchault and

Legrand,

1981

_a,b):

the 3

_categories

of females

_(WZ

females,

ZZ+F and ZZ+f

neo-females)

are mixed with _very variable rates. It has been

_suggested

that the

appearance of PSF occurs later than the

_development

of the heterochromosomal system

(Legrand

et

_al,

_1987).

_{Thus, following}

natural

_expansion

in

_Europe

from the Mediterranean basin after the last _{ice age,} A

_vulgare

have

_spread

over the

whole world

_during

the last few centuries

_subsequent

to man’s colonization of

new territories

_(mainly

in North America and a _part of South

_America).

_Today,

migration

of this

_species

is

_widely

facilitated

_by

man,

by

the

_exchange

of foodstuffs between countries

_(Vandel,

_1962),

and

_mixing

_populations

is often

_possible.

The

appearance of neo-females

carrying

PSF in an intact

_population

_(population

consisting

only

of

_{homo-heterogametic}

sex determined

individuals)

is therefore an

interesting

phenomenon

to

_study,

because this

_possibility

seems to be the main factor for the dissemination of PSF. ’

In such a context, the theoretical evolution of sex

_determining

mechanisms can be

computed

from the models of Bull

₍₁₉₈₃₎

and

_Taylor

_(1990).

These models assume

that,

in a

_panmictic

_population,

the

_frequency

_(p)

of neo-females

_harbouring

PSF

from one

_{generation n}

to another is:

where T is the

_proportion

of neo-females in broods of _pn neo-female

_mothers,

and where 1 — m is the

_proportion

of females in broods of

_genetic

females. PSF then

increase in the

_population

_only

if T > 1 — m

and,

in the case of a

ZZ/WZ

homo-heterogametic

system, it invades the

_population

_by

_inducing

the

_{disappearance}

of

the

_genetic

females.

In all natural

_populations

of A

_vulgare,

_{the average value} of T was between 0.6

and 0.8 for both ZZ+F and ZZ+f neo-females. With such

_values,

the

_{high variability}

in natural

_populations

is

_surprising,

and we wonder

_why

PSF are not the

_only

sex-factor in

_populations

where

_they

are _present, because in

_theory

_{the appearance of}

PSF induces the elimination of the W

_chromosome.

In this _paper, we discuss the

probability

of survival and

spreading

of PSF

MATERIAL AND METHODS

Test animals came from 3 strains

_sampled

in nature and reared in the Poitiers

laboratory

for many years. ZZ+F and ZZ+f neo-females came

_respectively

from

Niort

_(France)

and Rabat

_(Morocco),

while WZ females came from Nice

(F1.ance) .

Neo-females came from

offspring

where transmission of PSF was

_complete

(100%

of neo-females in these

_offspring).

To simulate the appearance of

foreign

neo-females among

genetic females,

different kinds of artificial

_populations

were created. The

parental

generation

of

each

_population

consisted of 24 males and 24 females and

_breeding

took

_place

in a

rectangular plastic

tub

₍₆₃

x 44 x 22

_cm)

_containing

moist soil and food in excess

(carrots

and chestnut

_leaves).

The ratios between neo-females and

_genetic

females

(ZZ+F

or

ZZ+f/WZ)

were:

3/21

(low

infestation rate of the

_{population by}

the

PSF)

and

_{12/12 (high}

infestation

_rate).

Males had the same

_origin

and were in the

same

_proportions

as female

_categories.

Each _category of

population

was

replicated

2 or 4 times. The tubs were

kept

at 20°C and under the natural

_photoperiod

of Poitiers. Under such

_breeding

_conditions,

1

_generation

was obtained _{per year,} but

each female could

_produce

more than 1 brood _per

_generation.

In

_November,

6 months after the first

_hatchings,

the sex ratio of 150

offspring

randomly

sampled

in each tub was determined. The tub was then cleared and

48 animals from the

_sampling

were then reared under the same conditions as their

parents. The sex ratio in these 48 individuals conforms to the one determined with

the 150

_offspring.

With this

_{procedure, overlapping}

_generations

were avoided and

each year in

November,

the size of the

population

was reduced to that at the outset.

This artificial selection was made to simulate the

_mortality

observed in nature

(Al-dabbagh

and

Block,

1981).

After 3

_generations,

the rate of PSF was estimated

by

counting

the different

_categories

among 40 females

randomly sampled

in each

population.

The 3

_categories

of females were

_{distinguished}

as follows

(Juchault

and

Legrand,

1989): i),

genetic

females

_produced

broods with a 1:1 sex ratio,

regardless

of

_rearing

_temperature and on the other

hand,

_they

could be masculinized

by

inoculation with an

androgenic gland

or

_by

_injection

of the male

_hormone;

_ii),

ZZ+f neo-females could also be

_{masculinized,}

but

_{they produced highly}

female-biased broods at 20°C and

_highly

male-biased broods at

_30°C,

after

_repression

of

the effect of f at the latter _temperature;

_iii),

ZZ+F neo-females were not sensitive

to the

_{masculinizing}

effect of the male hormone because of the bacterial presence.

The control series of artificial

_populations

was made

_{by breeding}

sisters of

the W’Z

_females,

ZZ+F and ZZ+f neo-females

_placed

in the

_{tubs, by}

_rearing their

_{offspring separately,}

and then

_{by breeding}

these

_offspring

in the same _way.

Under such

conditions,

the

_mortality

rate was _very low and we estimated that

the number of ZZ+F or ZZ+f neo-females

_produced

in such broods reflected the primary transmission rate of the PSF. For the neo-female strains, mothers were

chosen at each

generation

among broods

including

100% of

neo-females,

to obtain a

maximised estimate of the

_primary

rate of transmission. It was

possible

to calculate

a mean male

_{ratio (MMR)}

for the broods of females

belonging

to the same _category,

using

a method described

by Rigaud

et al

_(1991).

In one _category of

neo-females,

In addition to these

_experiments,

we wanted to test the evolution of the

proportion

of F in a

_population

after horizontal transmission of this factor to

genetic

females. In order to obtain this horizontal

_{transmission,}

ovaries from 10

ZZ+F neo-females were

ground

and mixed with 1 ml of

physiological

solution,

and WZ females were inoculated with 1

_pl

of this extract. Since

_recipient

females transmitted F

_vertically,

their

_offspring

consisted of the

_following:

It is known that the fraction of

_offspring

infected

_by

F in broods of these females is

the same as that in broods of _ZZ+F neo-females

(Juchault

and

Mocquard,

1989).

We reared the WZ+F females in artificial

_populations

as described

_above,

and these

females were

distinguished

in the same _way as the ZZ+F neo-females.

Finally,

to describe the behaviour of the 2 PSF when

_they

are in contact with

each

_other,

20 ZZ+f neo-females were inoculated with F. These

_recipient

neo-females were then

_paired

and their

_offspring

reared

_separately.

After

_separation

of the sexes

in this

F

1

,

2 males and 2 females in each

_offspring

_(thus

80

_animals)

were

placed

in a

plastic

tub. This

_population

was reared under the same conditions as the

_preceding

ones, but no artificial selection was

performed.

After the fourth

generation

(3

_years

after the installation in the

_tub),

the sex ratio was determined in a

sample

of 150

individuals.

_Moreover,

40 neo-females were inoculated with male hormone to attest

the _presence or absence of F.

RESULTS

Course of the

_frequency

of

_parasitic

sex factors

_(PSF)

in artificial

populations

Figures

1 to 3 show both the course of the sex ratio and

_frequencies

of PSF in

artificial

_populations.

In

_{populations containing}

ZZ+F neo-females

_{(fig la,b),}

the

_general

rule was that

the fraction of males decreased

_during

the first 2

_generations,

and then increased

by

about 50%. After 3 or 4

_generations,

sex ratios of all these

populations

were not

significantly

different from 1:1

₍

_X

_Z

test

_{non-significant}

in all

_cases).

The neo-female

frequencies during

the third

_generation

were _very

_low,

_except in one

_population

(fig 1b).

In

_populations

with ZZ+f neo-females

_{(fig 2a,b),}

the course was _very different

from the

_preceding

case. When the

_{parental populations}

consisted of 50%

neo-females,

the male

_{frequencies strongly}

decreased in the

_{following generations.}

In

_F

₄

_,

in the

_only

evaluable

_population

_(high

_{mortality appeared}

in the other

one),

this

_frequency

increased

_slightly

and stabilized at around 40%

_{(fig 2a).}

The

proportion

of 70% of neo-females

_(21/30

neo-females tested

_{by breeding}

at 20°C

and

_30°C)

showed that invasion

_by

f was in progress. In both

populations

where

f infestation rate was low at the

_beginning

of the

_experiment

_{(fig 2b),}

2 _types of

course were observed. On one

_hand,

the fraction of males remained at about 50%

during

successive

_generations

_(x

₂

_{non-significant}

at each

_generation),

and at the

_F

₃

surviving

females after the

_tests).

Stabilization of the sex ratio at 50%

during

the 2

generations

following

the

_F

₃

_suggests that the PSF have

_disappeared.

On the other

hand,

the _percent of males

_strongly

decreased

_during

the first 3

_generations,

’and then stabilized at about 18%. In

_F

₃

_,

no

_genetic

female was observed _among the 31

The course of

_composition

of

populations

_containing

WZ females and

F-inoculated WZ females reminds us of those of mixed

populations

containing

WZ

females and ZZ+F neo-females

_{(fig 3a,b).}

In

_F

₃

_,

the F factor tended to regress and

the sex ratio became stabilized arround l:l.

’

The F bacteria’s

_{disappearance}

could also be observed in F-inoculated ZZ+f neo-females. In the first

_generation,

18 of the 20 inoculated neo-females

_produced

broods,

in which the mean male ratio

_(MMR)

was

_equal

to 9.6% ± 3.6. In

_theory,

these

_{breedings produced}

the

_following

_categories

of

_individuals,

with

_proportions

dependent

on f and F transmission rates:

However, analysis

of the artificial

_population

made on individuals in this

F

i

(2

males and 2 females in each

_brood)

showed

_that,

in the fourth

_generation,

the percent of males was 31.2% and all females were masculinized

_by

the male hormone

(31!31

females

_tested).

_Thus,

after 4

_generations,

the

_population

consisted

_solely

of ZZ males and ZZ+f neo-females.

The MMR in isolated broods of control WZ

_females,

ZZ+F and ZZ+f

neo-females in 3

_generations

allowed us to estimate the mean

_primary

transmission

rate of the PSF

_(T

= 1 -

MMR) (fig 4).

In

fact,

PSF were transmitted

_by

neo-females in a _very variable _manner,

despite

the fact that in each

_generation

mothers came

solely

from male-free _broods. The F transmission was more

_regular

than the

f one: for

F,

T varied between 0.76 and

_0.82,

while for

f,

T varied between 0.53

and 0.8.

_However,

more

_precise

_analysis

of these broods showed that mothers in

each

_generation

could be

_separated

into 2 main

_categories:

_i),

neo-females that

highly

or

_completely

transmitted their PSF and which then conserved the maternal

trait;

and

_ii),

neo-females that had not conserved the maternal _trait, and which

transmitted PSF more

_weakly

_(see

as an

_{example fig}

_5).

Genetic females

_always

produced offspring

with sex ratios near 1:1

(fig 4).

Simulation of the course of the

_frequency

of PSF introduced in intact

populations

We

_sought

to

_investigate

the

_probability

of

_spreading

of

_PSF,

after the appearance

by

migration

of neo-females in some intact and finite-sized

_populations.

To establish the basis for this

_simulation,

we started with the observation that

PSF in Armadillidium

_vulgare

have a behaviour in

populations

similar to that of

genes with selective

advantage. Indeed,

if we consider

_that,

with females

producing

offspring

of the same size

(2n),

a

_genetic

female

produces n

females on _average

and a neo-female

_produces

n(1

+

_c)

neo-females. The _parameter c is a function

of the transmission rate of

_{PSF, and,}

if c is

_positive,

it _represents the selective

advantage

of neo-females versus

_genetic

females. This

_analogy

allowed us to evaluate

the

_{probabilities}

of

_complete

invasion or

disappearance

of neo-females

harbouring

PSF,

after their appearance in a

_panmictic

unharmed

population.

The

_problem

is

_quite

different in a

population

with a finite size. To obtain such a

population,

we assumed that the number of mothers from one

_generation

to the

ignored

in the model. On the other

_hand,

as one male could fertilize several

females,

we avoided

_giving

values for rates of transmission

_equal

to 100%.

If in a

_population

whose size is limited to N

_mothers,

there are x neo-females in

Since in each

_generation

the size of the

_population

is reduced to

N mothers,

the

mean number of neo-females will be

_Np!,

and the

_probability

for

_obtaining

_y

neo-females

_(y

=

0, 1, ... ,

N)

from _one value of _x

depends

_{on a} binomial law with

parameters N and _px. The

_{probabilities}

for all values of x

_(from

0 to

_N)

are

_given

by

the

_following

matrix:

The

_{probabilities}

of

_obtaining

from 0 to N neo-females in the

_population

from one

generation

to another are then

_given

by

the

following

_equation:

where

_Pg

for the g

generation

is a vector

_composed

of

_{probabilities}

_p9,y of one

population

containing

y neo-females

(y

= 0 to

N),

and where the

generation

0

represents the

_starting

conditions with the appearance of x neo-females in the

population

(in

fact,

po,y = ₁ for _x

= y and po,y = 0 for any other values of

Y

) -

Therefore,

the simulation is that of the evolution of

_{probabilities}

of

_obtaining

Therefore,

the simulation is that of the evolution of

_{probabilities}

of

_obtaining

from 0 to N neo-females in the

_population,

from one

_generation

to

_another,

for

a

_given

baseline number of x neo-females

_(what

we called &dquo;number of

infesting

neo-females&dquo; )

and for a

_given

selective

_advantage

c.

In order to _compare this simulation with our

preceding

_experiments,

the size

of the

_population

was set at a low level

(N

= 24

females).

Among

all

possible

examples,

here we

_reported

the case where the number of

_infesting

neo-females

in the

_population

was x =

_3,

with 2

very different values for c: c = 0.05

(which

corresponds

to a transmission rate of PSF

_equal

to

_52.5%,

_ie, the lower mean rate

observed in isolated

_broods),

and c = 0.7

(transmission

rate of

85%,

the

higher

mean rate observed in isolated

_broods).

Despite

the very different appearance in the 2

profiles

(fig 6),

the first

finding

that _may be

_reported

was a common trend which could

_logically

be deduced from

the model used: PSF

_progressed

either toward fixation in the

_population

₍₂₄

neo-females out of 24 females

_comprising

the

_population),

or toward

_{disappearance}

(0

neo-females).

An intermediate state of

_{populations consisting}

of mixed

_genetic

females and neo-females was

_merely

a transient state which

_disappeared

when the

equilibrium

was reached. In addition to differences between these

_profiles

in values

of

probabilities

at the

_equilibrium,

the basic difference was the time _necessary to

reach this

_equilibrium.

When c was low

_(fig

_6a),

after 35

_generations

the

_probability

of fixation of PSF was

_equal

to 0.15 and the

_probability

of

_{disappearance}

0.67.

Between these 2 _extremes, the

_probability

of

_finding

between 1 and 23 neo-females

was about 0.01.

Moreover,

the

probability

of the

_{disappearance}

of PSF _very

rapidly

reached 0.5

_(in

10

_{generations),}

while the fixation was

_{possible only}

after

_generation

then reached after 100

_generations.

In the

_opposite

case, when c was

_high

(fig

6b),

the

_equilibrium

was reached _very

_rapidly:

7

_generations

were

_enough

to reach 3% for

_probability

of

_{disappearance}

of the

_PSF,

while after 25

_generations,

the level for the

_probability

of fixation was 97% and the

_equilibrium

was then reached.

Another simulation was

_performed,

_using

a variable c value. If c varied

during

the

first 9

_generations

from 0.7 to

_0.1,

and then

_stabilized,

the

_{probability progressed}

in a _way that was _very close to that where c = 0.7

(fig

7):

the

probability

of

_{disappearance}

of the PSF after 35

_generations

was then much lower than

the

_probability

of fixation.

_However,

it could be noted that the decrease in c

the

_probability

of fixation of the factor was

equal

to 77% and the

_probability

of

. disappearance

was about 9%.

_Thus,

there was still a 14%

_probability

of

_finding

some mixed

_{populations containing}

both

_genetic

females and neo-females. In this

case, the

equilibrium

was reached after 85

_generations.

The

_{equilibrium probability}

of elimination of a PSF was

_computed

for several

values of _c, as a function of the number of

_infesting

neo-females in an intact

population

(fig 8).

Calculations were

_performed

for a

_population

of 24 females and for an unlimited

_population.

The

_{probabilities}

of

_{disappearance}

of the PSF were

As a

_{general rule,}

the closer c was to _0, the

_higher

was the

probability

of

disappearance

for the same number of

_infesting

_neo-females,

and the more the

limit where the

_{probabilities}

of

disappearance equal

to 0

_progressed

toward

_high

rates of

_infesting

neo-females. It was

_interesting

to note that for a transmission

rate of PSF

_equal

to 100%

_(ie

for c =

1),

but with low infestation rate

by

neo-females,

the

_{disappearance}

of the PSF at the

_equilibrium

could be considered. On the other

_hand,

differences between limited and unlimited

_populations

were

only

perceptible

with low values of c

(<

_0.1).

In these _cases, differences were _greater for

high

infestation rates

_by

PSF: the

_{probabilities}

of

_{disappearance}

were then

higher

in a

large population

than in a small one. In the

_opposite

case, when

only

one

neo-female infested the

_population,

a

_population

of 24 females could be considered as

unlimited,

because the

_{probabilities}

of

_{disappearance}

of the PSF were _very similar in the 2 cases.

DISCUSSION

Investigation

of the mean

_primary

transmission rates of the PSF in Armadillidium

vulgare

showed that ZZ+F neo-females have a

_high

rate of

transmission

of bacteria

to their

_offspring,

while mean transmission of f was more

_irregular.

_However,

the mean _transmission rate of PSF is

_always

at least

_50%,

which means that neo-females

always produce

on _average more

_daughters

than

_genetic

females. The _appearance of

PSF in a

_population

that contained

_only

_genetic

females

_{(intact population)}

should

then

_{theoretically}

lead to an

increasing

rate of neo-females in the

_population,

and

to the

_{disappearance}

of

_genetic

females. The rate of neo-females in the

_population

should then

_equal

the transmission rate of the PSF

_{(Taylor, 1990).}

However,

analysis

of artificial

_populations

showed that in

_populations

where the

invading

factor was

F,

neo-females were often eliminated

and,

consequently,

the

male ratio reached

50%

after a few

_generations.

In _contrast, the invasive power of f

seems to be

_higher,

and the sex ratio in the

populations generally progressed

toward

female-biased.

_However,

failure of

_propagation

of f was

possible

in a

population

where infestation rate was low. These results _may be

compared

to the

_spreading

of

_{symbiotic maternally-transmitted}

_{microorganisms}

in artificial

_populations

of

insects,

although

these

_{microorganisms}

do not interfere with the sex

determining

mechanisms. In

_Sitophilus

_oryzae

_{(Coleoptera),}

the

_{endocytobiote}

_(a

_{Gram-negative}

bacteria)

spreads rapidly

in

_populations

_(Nardon

and

_Grenier,

_1989).

This invasion is due to the fact that bacteria

_provide

the insect with

_greater

_fertility

and more

rapid development.

In the flour beetle Tribolium

_confusum,

the rate of

_spread

of a

Rickettsiale

_responsible

for

_{reproductive incompatibility}

is a function of infestation

rate in the

_population

_(Stevens

and

Wade,

1990).

However,

in this latter _case, if the infestation rate is below

_0.37,

the

_cytoplasmic

factor is lost from the

_population.

In these 2

_{examples, experimental}

observations follow the theoretical models.

The models

_previously

used to describe the course of

_parasitic

sex determination

in Armadillidium

_vulgare

do not consider the

_{disappearance}

of F or f observed in

artificial

_populations

in the absence of any

genetic

control

_by

the

_host,

since the

transmission rate of these PSF is

_higher

than 50% on _average

_(Bull,

_1983;

_Legrand

appear in an intact

population.

This

_point

was made with limited

_populations,

but

. in fact we saw that the size of the

population

was

only

an

_important

factor when

the selective

_advantage

of the PSF was low. In the latter _case, the

probability

of the

disappearance

of the PSF is lower when the

_population

is small. As the PSF tended

to be either fixed or eliminated in the

_population,

the _presence of

_genetic

females mixed with neo-females is then

_always

a transient _stage which _may be of variable

duration. When PSF transmission rate is

low,

or when it decreases

_{progressively}

from one

_generation

to the next, the time necessary to reach

_equilibrium

is

_longer

than when the transmission rate is

_high.

From this

model,

some courses observed in artificial

populations

may be

ex-plained, particularly

in

_{populations harbouring}

f. It is still more difficult to

_explain

the

_{quasi-systematic}

elimination of

F,

especially

in cases where 50% of the females

at the

_beginning

of the

_experiment

were ZZ+F neo-females. In

fact,

events occur as if the transmission rate in the artificial

_populations

was lower than the one

ob-served in the isolated

_offspring,

_ie,

as if the number of ZZ+F

daughters

reaching

adulthood was lower than the number of

_{daughters produced}

_just

after the

_primary

transmission rate of the PSF. Since ZZ+F neo-females used in artificial

_populations

and those used as control were

_sisters,

the

_only

notable difference between them is

their

_competition

or not with

_genetic

females.

To

_explain

the very

frequent

and

rapid

loss of F in the

populations,

we

must assume that ZZ+F neo-females showed a

_competitive

disadvantage

_among

genetic

females,

leading

them to

_produce

fewer

_daughters

in their

_offspring.

This

phenomenon

(under

conditions of

_competition)

may occur in 2 _ways: either

i),

the

mortality

of ZZ+F

daughters

is

_higher

than that of the WZ

_daughters;

or

ii),

the

ZZ+F mothers overall

_produced

fewer

_descendants,

and thus fewer

_daughters.

To

date,

no observation has confirmed the first

hypothesis.

On the _contrary, it has

been shown that the F

_{endocytobiote,}

when inoculated into WZ

_{females, depresses}

the

_growth

of its new host.

_Moreover,

in the Niort natural

_population,

ZZ+F

neo-females are

smaller

on _average than ZZ+f neo-females

_(Juchault

and

_Mocquard,

1989).

It is also known that

_fecundity

in terrestrial

_isopoda

is a linear function of

the size of the female

_(Sutton

et

_{al, 1984;}

Juchault and

_Mocquard,

_1989).

Then,

it could be

_suggested

that,

under conditions of

_competition,

a decrease in

_fertility

in neo-females

_harbouring

the F bacteria

_might

be the result of a difference in the

rate of

_growth

between the 2

_categories

of mothers.

However,

in view of our

_model,

the number of ZZ+F

daughters

do not have to be smaller than the number of WZ

_daughters

to induce a

disappearance

of F: reduction of the difference between

these 2 values is sufficient to increase the

_probability

of

_{disappearance}

of the PSF. To

_explain

such a

_phenomenon,

it is difficult to

_postulate

a difference between genotypes of the

mothers,

because F

_{disappeared rapidly}

in

_populations

_consisting

of ZZ+f neo-females or WZ females inoculated with bacteria and their intact sisters.

The _present

_study

can

provide’ some

answers to the

_{problem presented}

in

the introduction:

_why

haven’t PSF invaded the natural

_populations

in which

they

are _present, since their transmission rates are _very

high?

First,

we showed

experimentally

and

_{theoretically}

_that,

even with a

_high

transmission rate and in the

absence of

_genetic

control

_by

the

_host,

the invasion of PSF after their appearance in intact

_populations

is not a

_systematic

event. It appears that fixation of the

accordance with data obtained in natural

_populations,

in which F is less often observed than f

_(Juchault

and

_Legrand,

1981

_a,b).

In

_light

of these first results

a _part of the

_{interpopulation variability}

observed in nature

_(both

at the level of

sex ratio and sex

determining

mechanisms)

may be

explained by

the

probability

of fixation and

_{disappearance}

of the PSF in

_populations.

However,

if

_only

this

_point

of view is

_considered,

a state of

_equilibrium

must

be

_{theoretically}

reached,

that is to _say that

_populations

must be

_composed

sooner or later either

solely

of

_genetic

females or of ZZ+F or ZZ+f neo-females. Such

a condition in nature is _{very rare,} since a

_majority

of

_populations

consist of a mixture of different

_categories

of

females,

with very variables rates

_(Juchault

and

Legrand,

1981

a,b,

1989).

An

_explanation

of these observations _goes

_beyond

the _scope of this

_study.

This model and these

experiments

are

_only

valid for

isolated intact

_populations,

infested

_by

PSF,

and which evolved in a closed world.

Such a situation must be _very rare in _nature, since

_migrations

between distant

populations

of A

_vulgare

are favoured

by

human _contacts,

and,

on a more local

scale, populations

must be

_closely

interconnected.

_Migration

among

populations

should

_{explain variability,}

since the former cannot evolve

_individually

toward the

equilibrium.

Another factor that

_might

_explain

the

_{interpopulation variability}

is the

variation in the transmission rate of the PSF. In natural

_populations,

some nuclear

genes of A

vulgare

that override the

expression

of PSF are known to exist. The first

one is a

masculiriizing

gene

(M)

that thwarts the

feminizing

effect of f

_(Legrand

et

al,

1974;

Juchault and

_Legrand,

_1989).

This gene

(closely

related to the restorer genes observed in the case of

_{male-sterility}

in

_{higher plants}

_(Couvet

et

_al,

₁₉₉₁₎

is

present at a

_high

rate in

_populations

where sex is controlled

by

PSF. The other

nuclear elements are _genes

_conferring

resistance to the

_cytoplasmic

sex factor F

(Rigaud

and

_Juchault,

_1992).

These _{resistance genes}

_(R)

_appear to be a

_polygenic

system which _prevents bacterial transmission to _oocytes. These 2

_categories

of _gene reduce the

_primary

transmission _rate, and then allow the

_production

of a male rate

high enough

to enable fecundation of all the females.

_{Theoretically,}

selection of

such genes in

populations

is

frequency-dependent

(Bull,

1983;

Taylor,

1990),

but

by migration,

M and R _genes could be introduced in all

_categories

of

_populations.

In

our

_model,

we saw that if the transmission rate of PSF decreased

_during

successive

generations

(after

selection of the M

_gene

in a

population

in the _process of

_invasion,

for

_example)

the time to reach the

_equilibrium

was

_longer

than if the transmission

rate was

_high.

Such M and R genes could then enable

preservation

over a

_{long period}

of mixed

_populations

_(genetic

females +

_{neo-females),}

but it is

difficult

to

_anticipate

whether their incidence could reach a value

high enough

to _prevent

disappearance

of

_genetic

females.

_However,

the _presence of these _genes

_{might explain}

_part of the

variability

observed in the sex ratio of natural

populations

when the fixation of PSF

is reached.

_Taylor

₍₁₉₉₀₎

showed that the more a resistant allele is effective

_against

effects of

PSF,

the more the

_equilibrium

sex ratio is close to 1:1 for the same PSF

transmission

_efficiency.

In

_fact,

it is

_possible

to _say that the

_composition

of natural

_populations

observed

at a

_given

moment is

_simply

a

_snapshot

of a _system in constant

_evolution,

_composed

of transient

_populations

_{that progress toward several types} of

_equilibrium

with different rates of

_speed.

Some events such as the selection of _{restorer genes} of the

categories

of females may be the source of the wide

variability

in the

population

structure. Another mechanism able to increase this

_variability

and which

_develops

in

parallel

is the internal evolution of the sex

_determining

mechanisms.

_Considering

the

model

_{proposed by Legrand}

et al

_(1987),

the continuous _appearance in

_populations

of the f factor from the F bacteria could still increase the

_probability

of

_finding

situations where different

_categories

of females could be mixed.

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