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Thèse de doctorat/ PhD Thesis Citation APA:

Vekemans, X. (1992). Evolution of plant breeding systems: armeria maritima Mill.(Willd.) as a study case (Unpublished doctoral dissertation). Université libre de Bruxelles, Faculté des sciences, Bruxelles.

Disponible à / Available at permalink : https://dipot.ulb.ac.be/dspace/bitstream/2013/212934/3/5c0d6a0b-cafb-48be-a64f-03fb08c09476.txt

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UNIVERSITE LIBRE DE BRUXELLES

FACULTE DES SCIENCES

FACULTE DES SCIENCES APPLIQUEES Section Interfacultaire d'Agronomie

Laboratoire de Génétique et d'Ecologie Végétales

EVOLUTION OF PLANT BREEDING SYSTEMS:

ARMERIA MARITIMA Mill. (Willd.) AS A STUDY CASE.

Directeur: Thèse présentée pour l'obtention du titre de C. Lefèbvre Docteur en Sciences Agronomiques

au Grade scientifique

par Xavier VEKEMANS

Année académique 1991-1992

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UNIVERSITE LIBRE DE BRUXELLES

FACULTE DES SCIENCES

FACULTE DES SCIENCES APPLIQUEES Section Interfacultaire d'Agronomie

Laboratoire de Génétique et d'Ecologie Végétales

EVOLUTION OF PLANT BREEDING SYSTEMS:

ARMERIA MARITIMA Mill. (Willd.) AS A STUDY CASE.

Directeur: Thèse présentée pour l'obtention du titre de C. Lefèbvre Docteur en Sciences Agronomiques

au Grade scientifique

par Xavier VEKEMANS

Année académique 1991-1992

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Xavier Vekemans.

Titre de la t h è s e annexe:

Quelle influence sur réiaboration d e s programmes d'amélioration et

sélection d e s végétaux pourrait avoir le s u c c è s du génie moléculaire d e s

s y s t è m e s d'autoincompatibilité multialléliques.

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CONTENTS CHAPTERl

INTRODUCTION

1.1 THE THEME OF THIS THESIS 2

1.2 ORIGIN OF THE DIVERSITY IN BREEDING SYSTEMS:AN INTRODUCTION 4

1.2.1 Inbreeding dépression 5

1.2.2 Genetic détermination of breeding Systems 7 1.2.3 Pollination ecology 8

1.2.4 Sex allocation 9 CHAPTER2

ARMERIA MARITIMA AS A STUDY CASE 11

2.1. THE PATTERN OF BREEDING SYSTEM VARIATION IN ARMERIA MARITIMA 12

2.2. ORGANIZATION OF THE THESIS 15 CHAPTER3

A MODEL FOR THE BREAKDOWN OF A NON-HETEROSTYLOUS DI- ALLELIC SELF-INCOMPATIBILITY SYSTEM 16

3.1 INTRODUCTION 17

3.2 MODELS FOR THE EVOLUTION OF SELHNG 20 3.3 MODEL AND ASSUMPTIONS 22

3.4 PARTIAL BREAKDOWN OF THE INCOMPATIBIUTY REACTION 25

3.4.1 Introduction 25

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3.4.2 Conditions for the spread of self-compatible Ib mutants. ...27 3.4.3 Study of the initial rate of increase of self-compatible Ib mutants 30

3.4.4 Study of the equilibrium frequencies of self-compatible Ib mutants 32

3.4.5 Study of the effect of asymmetrical breakdown between morphs 33

3.4.6 Discussion 33

3.5 BREAKDOWN OF A DIMORPHIC INCOMPATIBIUTY SYSTEM BY RECOMBINATION WITHIN THE SUPERGENE 35

3.5.1 Introduction 35

3.5.2 Recombination within self-incompatible individuals 37 3.5.3 Recombination within partially self-compatible

individuals 37 3.5.4 Discussion 38

3.6. EVOLUTION AND BREAKDOWN OF HETEROSTYLY 41 3.6.1. Partial self-fertility in heterostylous populations 41 3.6.2. The évolution of heterostyly 42

CHAPTER 4

PARTIAL BREAKDOWN OF SELF-INCOMPATIBILITY IN DIMORPHIC METALUCOLOUS POPULATIONS OF ARMERU MARITIMA. 45

4.1 INTRODUCTION 46

4.2 MATERIALS & METHODS 48

4.3 RESULTS 53

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4.3.1 Estimations of the outcrossing rate 53 4.3.2 Stability of self-fertility 56

4.3.3 Fruit-set under legitimate and illegitimate crosses 56 4.3.4 Inbreeding dépression 57

4.3.5 Pattems and levels of genetic variation 58 4.4 DISCUSSION 62

4.4.1 Estimations of the selfing rate 62

4.4.2 Metallicolous populations and the model of breakdown of di-allelic S.I. Systems 68

4.4.3 Population genetic structure 70

4.4.4 Is the selfing ability of metallicolous populations a relict characteristic or not? 72

CHAPTER5

EVOLUTION OF THE BREEDING SYSTEM IN ARCTIC AND AMERICAN POPULATIONS OF ARMEIUA MARITIMA 74

5.1 INTRODUCnON 75

5.2. MATERIALS AND METHODS 76 5.3RESULTS 81

53.1 Flower morphology 81

5.3.2 Biomass allocations to reproductive functions 82 5.3.3 Pollen/Ovule ratios 85

5.3.4 Pattems and levels of isozyme variation 87

5.3.5 Variation in phenolic compounds 89

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5.4 DISCUSSIONS 89

5.4.1 The évolution of monomorphism 89

5.4.2 Evolution of outcrossing within monomorphic populations 96

5.4.3 Conclusions 103 CHAPTER 7

C^£N Jï^RÀL C^)NCLUS1 ^)NjS»»»»» •••>»••••»••••••••••»•••••*••>•• ••••••••••••••••••••••••••••••••^••••••••••••••^ lOS 7.1 THE INFLUENCE OF GENETIC AND ECOLOGICAL

FACTORS ON THE DIVERSITY OF PLANT BREEDING SYSTEMS 106

7.1.1 Genetic factors 106 7.1.2 Ecological factors 107

7.1.3 What about the rôle of constraints on the diversity of breeding Systems? 108

7.2 SELECTION THINKING AND THE EVOLUTION OF

BREEDING SYSTEMS 110

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BOX 0.1. Summary of numerical parameters used in the model.

Symbol Meaning

5 1-d = Probability that a selfed ovule results in a progeny individual that survives to the next génération, relative to the probability for a non-selfed ovule

S Selfing rate of fully self-compatible phenotypes Çic and aC) Sbl Selfing rate of the partially self-compatible phenotype ACIb Sb2 Selfing rate of the partially self-compatible phenotype acib

Pl Probability of illegitimate cross-fertilization between phenotypes^ and C assuming partial breakdown of the incompatibility reaction

P2 Probability of illegitimate cross-fertilization between phenotypes a and c assuming partial breakdown of the incompatibility reaction

FL Critical size of the compatible pollen pool below which the realized female fertility déclines linearly

a 0.5/FL = size of the compatible pollen pool for self-incompatible individuals (0.5) relative

to the critical size below which the realized female fertility déclines linearly

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Box 0.2. Summary of the parameters used to describe the genetic variation within and among populations.

PLP : percentage of loci polymorphic, that is with the frequençy of the most common allele being less than 0.99

K : average number of alleies per locus per population

Hq : observed heterozygosity (number of hetero2ygotes/total sample size), averaged overloci

F/5 : inbreeding coefficient, réduction in heterozygosity of an individual due to nonrandom mating within its subpopulation (departure from Hardy-Weinberg genotypic proportions)

Fgj : fixation index, réduction in overall heterozygosity due to differentiation in allele frequencies among the subpopulations (Wahlund effect)

FjY : overall inbreeding coefficient, réduction in overall heterozygosity including the contributions of both previous factors

Fg : inbreeding coefficient expected at equilibrium under selfing at a rate (1-/) and computed as Fg = ( l - /)/(! + /); AF = Fjs-Fe

Hj : gene diversity in the total population (here category of breeding system) Hg : mean gene diversity within subpopulations (here single populations) DsT ' mean gene diversity among subpopulations (with = i/j+D^j).

Ggf : proportion of gene diversity between subpopulations relative to the overall diversity (G^t = D^tIHj)

RsT ' inter-populational gene diversity relative to intra-populational diversity,

computed as/?57' = DJHs, with D;„ = Npop 1)57/(Npop-1)

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CHAPTER 1

INTRODUCTION

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INTRODUCTION 2

1.1 THE THEME OF THIS THESIS

Diversity is a universal attribute of natural populations of plants and animais.

Population genetics in dealing with genetic diversity, tiy to détermine the amoimt of variation existing in natural populations and to explain it in terms of its origin, maintenance and evolutionaiy significance (Hartl, 1988). This thesis is about the origin, maintenance and evolutionary significance of diversity in plant breeding Systems^ This is a particularly exciting topic as breeding Systems have a great impact on the organization of genetic variability within and among

populations, on the one hand, and show themselves a great amount of variation, on the other hand. Thèse aspects are outlined below.

(a) Impact on the organization of genetic varlability

The breeding System is one of the most important factors in shaping the genetic composition of populations (Hamrick, 1982), and hence their potential for evolutionary changes. Breeding Systems influence the amount, nature and organization of genetic variation of populations by determining the pattem of genetic recombination among individuals. For instance to exempliiy extrême situations, in a dioecious species, the following mating pattem is observed: each zygote is formed from the fusion of two gamètes, one coming from one maie individual and the other coming from one female individual; when in a cleistogamous species, all zygotes will be produced from the fusion of two gamètes from the same individual. The offsprings issued from thèse two species will show drastic différences in terms of mean heterozygosity.

^ Throughout this thesis I shall be using the terni "breeding Systems" in a vcry broad sensé to

include all aspects of sex expression that affect the relative genetic contributions to the next

génération of individuals within a species. Other terms are also commonly used with more or less

similar meaning, namely: sexual Systems, mating Systems, sometimes even genetic Systems. In

french one would use the less ambigous term "système de reproduction".

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Table 1.1 Some common types of sex distribution within and between fiowers.

and within and between genêts of seed plants. Anthers aie designated i , and gynoeda are designated 9. Hermaphrodites are designated ^ .

Distribution of sex organs

within a within a Angiosperm

Name flower plant Breeding System species(%) dioecy <}or9 <;or? xenogamous (out-

OTJSsing) 4

gynodioecy ^ , d or 2 ^ or 9 xenogamous, geitonogamous, autogamous

7

monoecy 6 or 9 aDogamous, some

sel£ng,some Crossing

5

gynomonoecy ^ or 9 allogamousand 3

autogamous

hermaphrodity i allogamousand 72

autogamous 72

(other) 9

100

(from R i c h a r d s , 1 9 8 6 )

Table 12. Qassification of flowering plant senial systems^^Çadapted from Bawa & Beach, 1981).

A. Systems based on the spatial distribution of maie and female reproductive organs.

L Sezually monomorphic Systems diaracterized by only one gender dass of individuals L Eermaphroditism : Fiants bear only bisexual flowers.

2. Monoeeîsm : Rants bear maie and female flowers.

Z.Andromonoecîsm : Plants bear bisezual and maie flowers.

4. Cynomonoecîsm : Plants bear bisexual and female flowers.

n . Sezually dimorphic spedes characterired by only two gender classes of individuals.

1. Dîoeeîsm : Plants bear either maie or female flowers.

2. Cynodîoecîsm : Plants bear either female or bisemal flowers.

Z.Androdîoecîsm : Plants bear either maie or bisexual flowers.

B. Systems based on the temporal distribution of maie and female organs (Dichogamy).

L Protandry : Pollen removed from the anthers before stigmas attain receptivity.

2. Frotogyny. Stigmas become réceptive before anthers release pollen.

C Systems based on the spatial séparation of maie and female organs.

L Eerkogamy : Pollen présentation is spatially separated from pollen receipt, all individuals are of the same type.

2. Eeterostyly : Two or threc types of individuals bear différent fonns of flowers with respect to style and stamen length. Generally assodated with self-inccmpatîbility.

D. Systems based on the présence or absence of self-incompatibility alleles.

L Self'incompaxibilîty : Plants polymorphic with respect to the présence of self-incompatibllity alleles; pollinations involving pollen and sdgma sharing the same self-incompan'blility alleles, including self-pollinations, resuit in no fruit s e t

2. Self-compatiblU'Uy : Plants monomorphic and without the présence of self-incompatibility alleles;

all pollinations, including self-pollinations. resuit in fruit set.

* In addition to tfae Systems described below, tbere odst other Systems such as cieistogazny and various fonns of apomoda.

^ tfae Systems described below are not mutuaDy cœiusive.

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INTRODUCTION 3 (b) Variation in breeding Systems.

A wide range of variation in breeding Systems (cf. Tables 1.1. and 1.2.) is found in flowering plants and the alternatives can be summarized as follows (Richards, 1986):

- Hermaphroditism versus unisexuallty: unisexuates are obligate outcrossers while hermaphrodites can often self-fertilize.

- Self-poUination versus cross pollination: flower morphology and temporal events in hermaphrodites détermine to some extent the amount of pollen transferred from anthers to stigmas within flowers (autogamy) and between flowers (allogamy). Outcrossing (xenogamy) occurs by allogamous pollen transfer between différent plant individuals.

- Self-fertilization versus cross fertilizatlon: self-pollination may not give rise to self-fertilization in the présence of mechanisms of rejection of selfed pollen (self-incompatibility Systems).

- Sexuality versus asexuality: végétative reproduction and production of unfertilized viable seeds (agamospenny) are différent alternatives to sex.

(c) Sélection acting on breeding System variation.

Variation in breeding Systems often comprises an important genetic

component available for sélection. Examples of highly genetically controlled mating Systems include dioecy (Westergaard, 1958 in Bawa, 1980), self- incompatibility Systems (de Nettancourt, 1977) and gynodioecy^ (Kheyr- Pour, 1980; Van Damme, 1983). Hence, breeding Systems themselves do evolve. This raises the interesting and controversial problem as to décide at what level, between-individual or between-population, sélection is acting

(Maynard Smith, 1989). Indeed the breeding System influences not only the fitness of the individual, that is its compétitive reproductive ability, but also the evolutionaiy potential of the population (through its action on the level of genetic variability).

See Table 12. for a classification of plant breeding Systems.

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INTRODUCTION 4 The overall aim of the thesis is to seek evolutionaiy explanations for the

diversity in plant breeding Systems. This question will be kept in mind while studying spécifie evolutionaiy pathways in our biological model, the species complex Ameria maritima (Mill.) Willd. The choice of this model rely on

preliminary investigations showing a unique pattem of breeding System variation within the species complex (Baker, 1966; Lefèbvre, 1970; Lefèbvre & Vemet,

1989; see also Chapter 2).

The knowledge of the functioning of the breeding system of a species, together with a deep understanding of its conséquences on population genetic structure, are now considered as critical matter by the plant biologist or the agronomist. In plant breeding, for instance, knowing the mode of reproduction of a crop is essential to the choice of an appropriate breeding scheme and multiplication procédure. It is also important when trying to maintain any improved material in stabilized conditions. In genetic conservation management, sampling stratégies are based on the pattem of genetic diversity within and among natural

populations, which is under the control of the breeding system (Jain, 1975).

During the last two décades, the interest in studies of breeding Systems has been stimulated by two developments (Brown et aL, 1985; Hedrick, 1990). Firstly, the refinement of the procédures for foUowing mating events by the use of isozyme markers and DNA fingerprinting, secondiy major theoretical advances in several topics such as procédures for mating system estimation, effect of nonrandom mating on the organization of genetic variability, and évolution of breeding Systems. Both aspects will be illustrated in this thesis. The next section will give an overview of the main factors involved in the évolution of breeding Systems.

1.2 ORIGIN OF THE DIVERSITY IN BREEDING SYSTEMS:

AN INTRODUCTION

The difficulty in studying the évolution of breeding Systems arises as Maynard Smith (1989) quoted, "from the complexity of the phenomena that have to be explained, and the bewildering array of facts that have to be borne in mind".

Here, I would like to illustrate the effects of several important factors on the diversity of breeding Systems. Two types of factors are generally distinguished:

(1) genetic factors, like the genetic basis of sex détermination or the inbreeding

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INTRODUCTION 5 dépression; (2) ecological factors, like poUination ecology, sex allocation^, sexual sélection, seed dispersai, prédation and some others biotic or abiotic factors.

Two of each will be discussed.

IJLl Inbreeding dépression

The term inbreeding dépression is used to designate the harmfùl effects usually accompanying close inbreeding in plants or animais. Thèse effects are expressed by an obvious décline in viabili^, fertiliQr and compétitive abili^, in other words by a lower fîtness of inbred lines. Inbreeding dépression is seen as the most important sélective pressure against the évolution of selfîng gènes in self-

compatible hermaphroditic populations. Two main théories have been proposed to account for inbreeding dépression, namely the overdominance and the partial dominance hypothèses (Charlesworth & Charlesworth, 1987b). The

overdominance hypothesis is based on a superiority of hétérozygotes at fitness- determining loci over both homozygotes (hétérozygote advantage). As

inbreeding tends to lower the percent of heterozygous loci in the progeny, the resulting décline in fitness is obvious. The second hypothesis, partial dominance, is concemed with the occurrence of partially récessive deleterious alleles in the génome. Thèse alleles are produced by mutation and, despite their négative effect on fîtness, are maintained at low frequencies in natural populations

because of their récessive nature (mutation-sélection balance). The réduction in fitness observed at the population level as a conséquence of this phenomenon is called the mutational load ("fardeau génétique" in french). When individuals become homozygotes for such alleles, as promoted by inbreeding, their relative fitness will be reduced.

The way by which inbreeding dépression affects the évolution of breeding Systems dépends greatly on its genetic détermination, which can vaiy itself. This has been illustrated by modeling the effect of various selfing rates on the level of inbreeding dépression expected in natural populations assuming either

hypothesis: overdominance vs partial dominance (Charlesworth & Charlesworth, 1987b, 1990;Charlesworth et aL, 1990). Inbreeding dépression aiways increases

3 The allocation of resources between maie and female reproductive functions.

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k{S)

0.0 -i • i ' 1 ' 1 ' 1 ' I

0 . 0 0.2 0 . 4 0 . 6 0 . 8 1 . 0 S

Fig. 1.1. Relationshîp between the relative înbreeding dépression, k(S), and the selfîng rate, S, for varions values of the sélection coefficient, s, and of the degree of dominance of deleterious alleles, A, tmder the partial

dominance model (&om Charlesworth & Charlesworth, 1987b).

Fig. 1.2. Rates of change in frequency of modifier alleles changing the selfing rates i^lp) under the partial dominance model with multiplicative interactions of the fîmess loci . The modifîers were introduced into starting

populations having différent selfîng lates denoted by S

(from Charlesworth & Charlesworth, 1990b).

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INTRODUCTION 6 with the selfing rate when referring to the overdominance modeH while the reverse is true with the partial dominance model. Moreover, within the last model, a large variation in the rate of decrease of inbreeding dépression with selfing rate is found in relation with the degree of dominance of deleterious alleles and the sélection intensity (see Fig. 1.1.). However, the relative importance of thèse différent types of genetic déterminations of inbreeding dépression that actually occurs in natural populations is still unknown. The scarce expérimental data reviewed by Charlesworth & Charlesworth (1987b) seem to favour the partial dominance hypothesis, with approximately the same contribution from mildly deleterious and highly deleterious (sub-lethals) mutations.

Another point, relevant to the effect of inbreeding dépression on the diversity of breeding Systems, is worth mentioning hère. Campbell (1986) and Holsinger (1988b) have pointed out that evolutionary changes in selfmg rate should be accompanied not only by (1) a change in the level of inbreeding dépression (see above), (2) a change in the frequencies of selfing gènes, but also by (3) some degree of genetic association^ between selfing gènes and loci responsible for inbreeding dépression ("fitness loci"). The last factor can have a dramatic effect on the prédictions of the models for the évolution of selfing (Holsinger, 1991).

One of the conséquences of this association has been illustrated by Charlesworth et ai (1990). They show that under certain circumstances, gènes inducing a large increase in selfing rate will be advantageous while gènes inducing only minor increases in selfing rate will be selected against (Fig. 1.2.). So, for a same average level of inbreeding dépression in the population, the harmful effect of inbreeding will prevent the évolution of selfing in one case and in the other will not.

* Assuming symmetrical overdominance, that is, both homozygotes have the same fîtness while the hétérozygote has a higher fitness.

^ The existence of thèse genetic associations can be intuitively understood as follows: in a population practicing mixed selfing and outcrossing "an individual that is heterozygous at one locus is more likely to have been produced through outcrossing than is a randomly chosen individual .„ [given that] it is also more likely to be heterozygous at a second locus... This implies that an individual that is heterozygous at a locus determining the selfing rate is more likely to be heterozygous at fitness-determining loci than is a randomly chosen individual in the population.

Thus, the génotype at the selfing locus will not be independcnt of the fitness" (Holsinger, 1988b).

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INTRODUCTION 7 In short, three parameters associated with the phenomenon of inbreeding

dépression have an influence on the évolution of plant breeding Systems: the genetic détermination of inbreeding dépression, the average level of inbreeding dépression of the population, and the associations between fitness and mating System loci.

1.2.2 Genetic determinatioii of breeding Systems

The nature of the genetic détermination of a particular sexual phenotype may have an impact on its further évolution. An good example refers to the évolution of maie sterility (subsequently noted as MS) in plant populations. The

conditions for the spread of MS mutants in a population, and for their

maintenance, will dépend greatly on the mode of inheritance of MS: nuclear or cytoplasmic (Lewis, 1941; Charlesworth & Charlesworth, 1978). With nuclear inheritance, a MS mutant must be more than twice as fecund as an

hermaphrodite in order to spread, while a ratio slightly superior to one is

sufficient with cytoplasmic détermination. On the other hand, under the last, no stable polymorphism (mixed frequencies of male-steriles and hermaphrodites, that is gynodioecy) is expected.

Extensive empirical studies have found some gynodioecious Systems involving both nuclear and cytoplasmic gènes (Kheyr-Pour, 1980; Stevens & Richards,

1985; Van Damme & Van Delden, 1982; Van Damme, 1983) and it seems that nuclear-cytoplasmic inheritance of MS applies to many gynodioecious species (Ross, 1978; Charlesworth, 1981). Theoretical studies have shown that, under particular assumptions, nuclear-cytoplasmic MS may reach a stable polymorphic equilibrium (Delannay et aL, 1981; Charlesworth, 1981; Gouyon et al, 1991).

Interestingly, stable limit cycles, that is consistent fluctuations of the proportion of maie stériles in gynodioecious populations can be maintained without

invoking any ecological cause (Gouyon et al, 1991).

Beside thèse equilibrium prédictions, a dynamic model involving altemation between colonization stages with a cytoplasmic inheritance of MS and

establishment stages with a mostly nuclear détermination bas been proposed

(Gouyon & Couvet, 1985; see also Frank, 1989). This model elegantly suggests

favourable conditions for the spread of MS (conditions under cytoplasmic

détermination are easier to fulfil) together with a feedback mechanism

controUing the frequencies of male-sterile individuals.

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INTRODUCTION 8

1 . 2 3 P<riliiiation ecdogy

TWo aspects of pollination ecology are relevant to a discussion on the factors influencing breeding System diversity.

The first one is the type of pollination System. Qassical studies in pollination ecology have led to the description of pollination syndromes, sets of characters that represent adaptations to particular types of pollinators (Wyatt, 1983). Some corrélations between particular syndromes and breeding System have been observed. One example is the évolution of dichogamy in insect-pollinated plants.

Dichogamous plants poUinated by bees and Aies are generally protandrous while protogyny is encountered mostly when beetles and wasps are the main

pollinators (Bawa & Beach, 1981; Wyatt, 1983). One explanation involves the foraging pattems of pollinators, with bees and Aies generally visiting individual inflorescences form bottom to top while beetles and wasps are moving

downwards (Faegri & van der Pijl, 1979). As most plants show acropetal maturation, flowers at advanced stages are localized to the bottom of inflorescences. Thus in both cases, protandiy in upward and protogyny in downward poUinated plants, it is the présentation of mature stigmas to the newly-arrived pollinator (supposedly covered with pollen from another individual) that is maximized (Wyatt, 1983). Différent hypothèses can account for this observation. First, the avoidance of self-pollination, or of interférence between the functions of pollen receipt and pollen dispatch (Lloyd & Webb,

1986) may be favoured when pollination of flowers at the "female stage" occurs in the first place. Second, a sexual sélection argument, compétition between individuals for maie (pollen) success may have selected for a mechanism by which mature stigmas remove foreign pollen from the pollinator while the flowers at a maie stage cover the pollinator with new pollen and send them off (Chamov, 1982).

Another example of the influence of pollination type on the évolution of breeding Systems concems the distribution of selfing rates among wind- pollinated and among insect-pollinated plants. Aide (1986) has shown that anemogamous plants show a bimodal distribution of selfing rate (mostly selfed and mostly outcrossed species), while entomogamy is characterized by a

continuons distribution. Most genetic models, however, predict a bimodal distribution independently of pollination type (Schemske & Lande, 1985;

Charlesworth et aL, 1990). The discrepancy between observed and theoretical

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INTRODUCTION 9 distributions, in entomogamous plants, may be related to the greater

unpredictability of animais as pollen vectors leading to lower rate of response to sélection on the mating System (Schemske & Lande, 1986).

The second important aspect of poUination ecology is the variation in poUinator tvailability. When poUinators are scarce such as at margins of a species' range, or when plant density is too low to attract effîciently poUinators, outcrossing events become rarer and the average seed-set (percentage of ovules ripening into seeds) of the population may be dramatically reduced. Thèse conditions are favourable to the évolution of autogamy if flowers are self-compatible and floral structures are such that within-flower selfmg in the absence of poUinators is occurring (Richards, 1986). This factor has been commonly invoked to explain the évolution of the selfmg habit in plants (Arroyo, 1975; Baker, 1966; Solbrig &

RoUins, 1977; Schoen, 1982a; Piper et al, 1986; Barrett et al, 1989) and is known as the reproductive assurance hypothesis (Jain, 1976). Similarily, the rôle of poUinator limitation in the évolution of apomixis has also been suggested (Bennett & Elgar, 1987).

1.2.4 Sex allGcation

Most flowering plants are hermaphrodites (Table 1.1.). Based on this

observation Chamov et al (1976) have developed a theory, subsequently called the sex allocation theory, that tries to predict when hermaphroditism as opposed to dioecy would be an evolutionary stable strategy (E.S.S.). The theory is based on the foUowing assumptions (see Goldman & WUlson, 1986): (1) the total reproductive effort of an individual is resource limited and hence its total reproductive success also; (2) the trade-off hypothesis, that is the total

reproductive allocation is divided between maie and female functions and an increased allocation to one of thèse nécessitâtes a decrease to the other; (3) there is a genetic variation in sex allocation. Based on thèse assumptions they pointed out that the stabUity of hermaphroditism versus dioecy would dépend primarily from the shape of the trade-off between maie and female reproductive success within an hermaphrodite. More precisely several authors have shown that the ESS breeding System would dépend on the relationship between reproductive success via either the maie or the female function, and the

proportion of resources devoted to each (Chamov, 1979 and 1982; Charlesworth

& Charlesworth, 1981). If thèse relationships are less than proportional, i.e.

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INTRODUCTION 10 foUow a law of diminishing retums, then hermaphroditism is selected for. If they are more than proportional then dioecy is favoured.

The observed corrélation between dioecy and animal-dispersed seeds (Bawa, 1980; Givnish, 1980) has been interpreted in terms of the sex allocation theoiy.

The authors argued that under animal dispersai, a larger seed crop attracts a disproportionate number of dispersai agents and thus results in a more than proportional relationship between female allocation and female fitness. Thèse are precisely the conditions favouring dioecy over hermaphroditism.

My aim was not to give a complète account of the theory of sex allocation but to point out that factors like the resource limitation of maie and female

reproductive success can also influence the diversity of breeding Systems.

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o m o z c '< in

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CHAPTER 2

ARMERIA MARITIMA

AS A STUDY CASE

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Fig. 2.1. Scanning électron micrographs of the stigmatic papillae of (a) COB and (b) PAP morphs, and of the pollen of (c) œ o

and (d) PAP morphs (from L. Devos). The white line in the bottom indicates 100 and 50 \m for stigma and pollen, respcctively.

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Armeria maritima 12

2.1. THE PATTERN OF BREEDING SYSTEM VARIATION IN ARMERIA MARITIMA

Armeria maritima (Mill.) Willd. is a polymorphic and widespread perennial species, found through much of the northem hémisphère in open coastal and inland habitats. A botanical description of the plant is given in Table 2.1. Within the species important variations in the breeding System have been reported by Baker (e.g. 1966) and his work on Armeria maritima has become a classic model about the évolution of plant breeding Systems. He showed that in most of Europe the mating pattem of A. maritima is sporophytically controUed by a dimorphic self-

incompatibility System: one morph, hereafter called COB, is heterozygous at the incompatibility locus having "cob" stigma (allele C) and coarsely reticulate pollen (allele A); the other morph, called PAP, is homozygous with a papillate stigma (allele c) and finely reticulate pollen (allele a). Normally only intermorph crosses are fertile so that homo^gous PAP (acac) and heterozygous COB (ACac) morphs are expected to be found in a one to one ratio. The pollen and stigma ^ e s are illustrated in Fig. 2.1.

Table 2.1. Botanical description of Armeria maritima subsp. maritima (after Woodell & Pale, unpublished)

Perennial hcrb with a short-branchcd, woody root-stock. Leavcs 10-150 x 0.4-15 mm, linear, flat, acute or blunt, l-(3) veined at least at the base, glabrous-ciliate with veiy narrow scarious margins.

Scape 10-560 mm, crect, leafless, shortiy pubescent, rondy, glabrow, with its growing point covered by a tubular scarious sheath, 3-21 mm, which is a prolongation of the outer involucral bracts.

Outer involucral bracts 2-15 (-25) mm, more or Icss grecn on the back, acuminate or mucronate;

inncr involucral bracts wholly scarious, blunL Head a capitulum, 10-25 (-30) mm in diamcter;

fiorets usually bracteate in groups of 2-4 sequentially developing in bracteate cymose spikelets.

Spikelet bracts 4.5-10 x 33-9 mm, blunt with a wide scarious margin surrounding a green central portion; florct bracts much smaller, clliptic-oval, scarious. Calyx 4.5-9 mm, stalked, funnel-shaped, pubescent, (sometimes only on the 10 ribs). Calyx-teeth 5, acute, less than half the calyx length, joined by a scarious pleat Corolla of five petals, joined only at the base, 7-11 x 2.5-4.5 mm, normally reddish-purple, but vaiying through pale pink to white, occasionally deep red-purple.

Stamens, 5, joined to the base of the petals, their filaments, 5-8 mm, broadened below. Styles 5,

filiform, free to near the base, pubescent below. Fruit single-seeded, endosed in the calyx by a

persistent corolla, dehiscing transversely above or irregularly below.

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F i g n n î ^ SchcmcloiQustimtethcapcrmtionofwithm-motphincompatibility

in thc thrift. Arment mtritima. Upid i* bomc cxtcmal to thc pollen ; n i n in the findy rcticuUtcd papillate grain (below), and is ablc to adhère to thc unooth cob ftigma. but I c u well to the papillate itigma. In thc coaraciy rcticulatcd cob g n i n , the Upid is suniwn in the tcctum apertures, whert it can only makc contact with

the papillate »ti5ina.(from R i c h a r d s , 1 9 8 6 )

Oimorphic population T y p e A : 5 0 A C j c Type B:50ac.ae

lOOAc^c' Monomorphic population

FicX.S.Sdinnc ibewinf tht functloniai ef Uw brccdini lyittn in Armtria. Letnid: ^^^mm natuni fertile combinatiom; — — expérimental fertile comfainationi; — . - — itcrile rambination.

(from Lefèbvre, 1970)

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Armeria maridma 13 The physiology of the incompatibility reaction has been studied by Dulberger (1975) and Mattsson (1983). Thèse authors have shown that the pollen-sculpturing

dimorphism is likely to be involved in the functioning of the incompatibility (Fig.

2.2.), a situation which is rarely encountered in heteromorphic spedes (Richards, 1986). In A. maritima the incompatibility reaction is inhibiting the processes of hydration and germination of the pollen grains. Mattsson (1983) showed that a close contact between pollen exine oils and the stigma cuticle are necessary for thèse processes to occur normally. He also found that, in the coarsely reticulate pollen from the COB morph, the exine oils are sunken in the bottom of the apertures so that they are only accessible to the prominent narrow papillate stigma papillae of the PAP morph. On the other hand, exine oils in the finely reticulate pollen are borne relatively extemally so that a close contact with the smooth stigma surface of the COB morph is assured. This mechanism does not explain however why the finely reticulate pollen fails to germinate on a papillate stigma.

In the circumpolar arctic tundras, a radical change in the breeding System occurs (Baker, 1966) : populations are monomorphic, ail the individuals having the fully self-compatible combination papillate stigma-coarsely reticulate pollen (Ac^c). By controUed crossings, however, Baker has shown that the stigmas of thèse plants have lost additionally their incompatibility to finely reticulate pollen, so that their genetic formula should be Ac'Ac' (Fig. 2.3.). Such monomorphic self-compatible populations are also found in arctic and subarctic North America and in the southem part of South America. Along the west coast of North America, from south Oregon to mid Califomia, monomorphic A. maritima populations are gynodioecious^

More subtle variations have been observed in European metallicolous populations (Lefèbvre, 1970; Richards et al., 1989). In thèse populations, the dimorphic

hermaphrodite state is conserved but some individuals are potentially self-fertile, showing up to 40% seed-set in bagged heads. In such populations the PAP morph was found to be a better selfer than the COB (Richards et al., 1989). Baker (1966)

^ Populations are monomorphic with respect to the incompatibility locus (al! individuals aitAc'/Ac")

but are composed of two différent sexual phenotypes, hermaphrodites and females (male-steriles).

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Aimeria maritima 14 found a rather similar situation in a population from the Shetland Islands where he sampled out a self-compatible papillate individual.

An evolutionaiy scheme for the variational trends shown by A. maritima has been hypothesized by Baker (1966) as follows. The dimorphic System is the primitive state from which monomorphic populations are derived in response to poUinator-poor arctic environment and/or establishment after long-distance dispersai. A crossing- over in the ACac type has produced the AcAc self-compatible morph, followed by a loss of stylar inhibition toward the finely reticulate pollen grains by mutation (c ^ c'). The occurrence of gynodioecy in monomorphic populations of Califomia was interpreted as a conséquence of sélective pressures promoting outcrossing in an insect-rich environment.

The evolutionary significance of the partial self-fertility in metallicolous populations

has been recently discussed by Lefèbvre & Vemet (1989). They argued that it would

be related to low density during the early stages of mines colonization by the few

pre-adapted métal tolérant individuals. At présent, this partial self-fertility could be

viewed as a relict characteristic, possibly maintained by continuous perturbation

occurring at the mine sites by industrial activity. Lefèbvre & Vemet (1989)

addressed also the question as to why, of the two possible recombinants, the

papillate stigma-coarsely reticulate pollen combination is the only one found in

monomorphic populations. They hypothesized that this situation could be related to

gender specialization in dimorphic populations between the PAP and the COB

morphs, the former allocating relatively more to female function than the latter. In

this respect, it is worth noting that 15 out of the 16 monomorphic species of the

related genus Limonium are represented by the papillate stigma-coarsely reticulate

pollen combination (Baker, 1966).

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Aimeria maritima 15

2.2. ORGANIZATION OF THE THESIS

Until now, no attempt has been made in Amena maritima to characterize precisely the différent mating Systems and to compare them in terms of variation in floral traits, allocation pattems and population genetlc structure. Empirical results conceming thèse features will be presented in chapters 4, 5 and 6 devoted

respectively to the metallicolous, monomorphic and gynodioecious populations. The foUowing chapter présents the results from a theoretical investigation on the

évolution of a dimorphic self-incompatibility System, without heterostyly, such as

that found in European populations oiA. maritima. A gênerai conclusion is given in

chapter 7.

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CHAPTER 3

A MODEL FOR THE BREAKDOWN OF A NON- HETEROSTYLOUS DI-ALLELIC

SELF-INCOMPATIBILITY SYSTEM

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r«.3.1.Reciprocal anther and stigma posiuons in the pin and thrum forms of a distylous plant. The arrows indicate the directions of compatible pollinations.

(from GANDERS,1979)

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MODEL FOR BREAKDOWN OF S.I. 17

3.1 INTRODUCTION

Heterostyly' is the most common form of sporophytic^ di-allelic self-incompatibility (S.I.) Systems in flowering plants (Richards, 1986). It has been recorded in 24

families and more than one hundred gênera of Angiosperms, with a scattered distribution among distant phyla (Ganders, 1979). Therefore it is certain that heterostyly has occurred independently many times.

Empirical studies on the différent forms of heterostyly are numerous (Ganders, 1979). The genetical (Emst, 1933; de Nettancourt, 1977) and physiological (e.g.

Shivanna et al, 1981) basis of the self-incompatibility system, the level of pollen flow occurring between morphs (e.g. Omduff, 1979, 1980; Piper & Charlesworth, 1986), the différences in fertility (Piper et aL, 1984) and spatial distribution (Levin, 1974) of both morphs havé been investigated.

^ Heterostyly will be used here to name heteromorphic self-incompatibility Systems were two or three types of individuals ('morphs') bear différent forms of flowers with req)ect to style and stamen length (often accompanied by différences in pollen size and shape) (see Table 1.2. and Fig3.1.). Two types of heterostyly can be distinguished : (1) dystyly in which one morph has a long style and short stamens ('pin') and the other a short style and longs stamens ('thrum'), that is with redprocal herkogamy; (2) tristyly with three morphs, each having its own style length and two out of three stamen lengths. In both cases individuals are self-incompatible and fertilization does only occur in crosses between morphs.

Non-heterostylous will refer to heteromorphic self-incompatibility Systems where no reciprocal herkogsuny is found (no différences with r e ^ c t to style and stamen length).

Homostyly will be used in its narrow sensé, that is in référence to non-heterostylous individuals or

^ c i e s that are secondarily derived from heterostylous ancestors (Richards, 1986).

^ In a sporophytic self-incompatibility system, the behaviour of the pollen is controlled by the diploid génotype of the sporophyte while in gametophytic Systems it is controlled by its own haploid

génotype.

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Fig. 32. Schcmatic représentation of the Charlesworths' model for the évolution of distyly.

Stage 1. Self-compatibility and long homostyle floral structure. Stage Z Di-allelic self-incompatiblility.

long homostyle floral structure. Stage 3. Di-allelic self-incompatiblility, one morph with long

homostyle floral structure and one with thrum floral structure. Stage 4. Di-allelic self-compatibility,

one morph with pin floral structure, and onc with thrum floral structrue. Legitimate pollination

occurs between anthers and stigmas of the same shade. (from Piper & Charlesworth, 1986).

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MODEL FOR BREAKDOWN OF SJ. 18 On the other hand theoretical studies on heterostyly are scarce. Some topics such as the prédiction of type frequencies in tristylous species (Heuch, 1979) and the rôle of sex allocation (Chamov, 1982; Casper & Chamov, 1982) have been investigated, but there has been only one attempt to model the évolution of dislyly (Charlesworth «fe Charlesworth, 1979). In this study the authors critically discuss the factors that could promote the évolution of heterostyly and the nature and séquence of intermediate steps. After performing numerous computer simulations they favoured the séquence of events depicted in Fig. 3.2. They argue for the évolution of a di-allelic S.I. as the first step, assuming self-compatibility in the ancestor, and the subséquent advent of reciprocal herkogamy linked to the incompatibility locus as the next step. The first step arose probably in response to sélection for cross-fertilization while the second occurred as a conséquence of one or a combination of the three following causes (Piper & Charlesworth, 1986): (1) to reduce self-fertilization if incompatibility is not complète; (2) to reduce the possible inhibition of compatible pollinations by large amount of incompatible pollen on stigmas (stigma dogging); or (3) to reduce the waste associated with the présence of incompatible pollen on stigmas, thereby promoting a pollen saving efTect that results in increased maie fertility. It must be noted that the conditions necessary for performing the first step are very difficult to meet (concurrently high selfing rates and inbreeding dépression in the ancestor).

According to this scheme, an intermediate stage between the first and second steps consisting in a non-heterostylous di-alIelic S.I. must have occurred. This particular breeding System has been found exclusively in the Plumbaginaceae (Baker, 1966).

The examination of evolutionaiy possibilities for the évolution from this

intermediate stage suggests at least four possible events (Fig 33.): (1) stability of the non-heterostylous di-allelic S.I.; (2) évolution of reciprocal herkogamy giving typical distyly (step 2); (3) partial or total breakdown of the incompatibility reaction

leading to self-compatibility of one or both morphs; and (4) recombination within the locus of incompatibility leading to completely self-compatible stigma/pollen combinations. This last event is very similar to the évolution of homostyly from heterostyly by recombination.

It is remarkable that in the plant family, Plumbaginaceae, the four trends have been

observed (Baker, 1966; Lefèbvre, 1970; Vekemans et ai, 1990): stable dimorphic

non-heterostylous self-incompatible species (Armeria sp., Limoniastrum sp., six

sections of the genus Limonium); typical heterostyly (one section of the genus

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(0)

Partial breakdown (1)

Recombination (2)

Fig. 3.3. Evolution from a non-heterostylous dimorphic S.!. System.

Stage 0. Di-allelic self-incompatibility and non-heterostylous floral structure.

Stage 1. Partial breakdown of the incompatibility reactiion and non heterostylous floral structure.

Stage 2. Recombination, i.e. self-compatibility, and non heterostylous floral structure.

Stage 3. Reciprocal herkogamy, i.e. heterostyly, one morph with pin floral structure, and one with thrum floral structure.

Legitinnate pollination occurs between anthers and stigmas of the same shade. Illegitimate

self-pollination occurs in stage 1.

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MODEL FOR BREAKDOWN OF SJ. 19 Limonium); partial breakdown of the incompatibility reaction without

morphological change in some dimorphic non-heterostylous populations of Armeria maritima; and recombination between stigma/pollen ^ e s in monomorphic self- compatible taxa (Armeria maritima ssp., Limonium sp.).

As the évolution and breakdown of heterostyly has been studied in détail

(Charlesworth & Charlesworth, 1979a, 1979b), I shall concentrate on the évolution of self-compatibility from a non-heterostylous di-allelic S.I. ancestor (events (3) and (4)).

It is common knowledge that a di-allelic S.I. System is not veiy efficient as an outcrossing mechanism because only half of the individuals within a population are cross compatible. As we have seen, non-heterostylous di-allelic S.I., an intermediate stage in the évolution of heterostyly, is encountered only in one family of

Angiosperms while heterostyly is widely distributed. It is worth noting also that one- locus di-allelic S.I. is strictly associated with heteromorphic^ S.I. (Richards, 1986;

Charlesworth, 1988). Ail homomorphic S.I. Systems have indeed multi-allelic and/or multilocus déterminations (de Nettancourt, 1977). It is tempting to conclude that di- allelic S.I. Systems are unstable uniess they are associated with morphological features promoting for instance disassortative pollination (as reciprocal herkogamy in heterostyly). Nevertheless, the conditions for the breakdown of a di-allelic S.I.

System have never been extensively investigated.

In this chapter I shall first give a short introduction to models of the évolution of selfmg, followed by a présentation of the model applicable to the évolution of di- allelic S.I. Systems. The results on the breakdown of S.I. both with and without stigma/pollen recombination (events (3) and (4) ) will then be presented. Finely I shall discuss the biological interest of thèse models with référence to the current literature on heterostyly.

* In heteromorphic S.I., as opposed to homomorphic S.I., the two incompatibility phcnotypes have

différent floral morphologies implying the existence of a supergene of incompatibility.

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MODEL FDR BREAKDOWN OF S.I. 20

3.2 MODELS FOR THE EVOLUTION OF SELFING

Stebbins (1950, 1957) bas developed the idea that évolution of selfing from

outcrossing relatives is a major pathway in the évolution of plant breeding Systems.

The understanding of the mechanisms of this shift in mating System has become a dassical topic in populations genetics. An important factor for the évolution of selfing has been pointed out by Fisher (1941) and subsequently termed the cost of outcrossing or automatic sélection for selGng gènes. Fisher showed that, providing that selfing does not alter the contribution of an individual to the pollen pool, self- fertilization is genetically favoured because it will resuit in ail the gènes of the progeny being contributed by one parent, compared with only one-half with cross- fertilization. Another advantage of selfing occurs when the conditions for

outpollination are unfavourable (reproductive assurance hypothèses, Jain, 1976; see

§1.23.). Some other factors are discussed in §5.4.1.

As selfing species are less common than outcrossing species, there must be strong sélective forces against the advantages of selfing. Qassically, advantages at the level of populations such as the effects of différent amounts of recombination on genetic variability and evolutionaiy success were proposed (Darlington, 1939; Stebbins,

1950). Referring to factors acting at the individual level, inbreeding dépression has been proposed as a major force opposing sélection for increased selfing

(Charlesworth & Charlesworth, 1987b; see §1.2.1.) but other factors like pollen discounting rate^ (LLoyd, 1979a; Holsinger, 1988b) or differential dispersai rates (Holsinger, 1986) have also been invoked.

Within the last fifteen years, numerous models for the évolution of selfing have been published (e. g. Maynard Smith, 1977; Lloyd, 1979a; Charlesworth, 1980;

Holsinger et aL, 1984). Most of thèse models have considered a fixed level of inbreeding dépression and found that selfing would evolve if the coefficient of inbreeding dépression^ is less than a critical value of 0.5. Relaxing the hypothesis of

' Altération of an individual's contribution to the pollen pool associated with selfing.

^ The coefBcient of inbreeding dépression is defined as one minus the relative fitness of selfed versus

outcrossed ovules, that is one minus the probability that a selfed ovule results in a progeny individual

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MODEL FOR BREAKDOWN OF SJ. 21 a constant level of inbreeding dépression with respect to average selfing rate bas not changed the prédictive value of the initial level of inbreeding dépression (Lande &

Schemske, 1985). Recently however, Campbell (1986) and Holsinger (1988b) have stressed the importance of genetic associations between a locus modifying the selfmg rate and the loci responsible for inbreeding dépression (viability loci). Thèse associations arise because a proportion of the viable progeny from selfers carries on average fewer deleterious mutations than their parents, so that higher fitness can become associated with the probability of being derived from selfmg, hence with the selfing gènes. The conséquences of thèse associations have in some cases an

important influence on the prédictive value of the initial level of inbreeding dépression (Charlesworth & Charlesworth, 1990a, 1990b; Holsinger, 1991; see

§1.2.1.).

The mode! that I shall présent in the following section take into account the effects of automatic sélection for selfmg gènes, inbreeding dépression, efficiency of pollination, and other factors spécifie to the di-allelic S.I. System. It does not, however, integrate the complex associations between fitness and selfing rate just described, but the probable conséquences of thèse associations will be discussed.

that survives to the next génération, relative to the probability for a non-sclfed ovule (Charlesworth

& Charlesworth, 1979c).

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MODEL FOR BREAKDOWN OF S.I. 22

3.3 MODEL AND ASSUMPTIONS

The model is adapted from Charlesworth & Charlesworth (1979a, 1979b) dealing with the évolution and breakdown of distyly.

rm assuming an infinitely large population (deterministic model), with discrète nonoverlapping générations. Mating pattem is govemed by a sporophytic self- incompatibility System under the control of a supergene with two component loci : Alleles A and a of the first locus are assumed to control pollen morphology and incompatibility reaction, Alleles C and c control stigma morphology and

incompatibility reaction. Dominance is complète at both loci and no crossing-over nor mutations within the supergene are allowed during the course of the simulation.

Thus in a population with 50% phenotype AC (génotype ACac) and 50%

phenotype ac (acac), the probabilities of fertilization of each pollen phenotype^ on each stigma phenotype are as^ :

POLLEN DONOR PHENOTYPE

STIGMA A a

PHENOTYPE

C 0 1

c 1 0

^ Pollen phenotype here means parental phenotype as we have a sporophytic self-incompatibility System.

^ Combinations with a probability of 1 are called compatible or legitimate while those with a

probability of 0 are called illegitimate.

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Fig. 3.4. The calculation of realized female fertilities

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MODEL FOR BREAKDOWN OF S.L 23 Hence individuals with phenotypes/lC or ac have an incompatible combination and cannot self-fertilize. Ail their ovules are available only for cross-fertilization.

However if individuals with self-compatible phenotypes Ac or aC appears in a population, they will have a proportion S of their ovules self-fertilized before any cross-fertilization can occur (prior self-fertilizatlon as defmed by Lloyd, 1979). Ail génotypes have the same ovule production but realized female fertilitles (i.e. seed output) differ according to the amounts of compatible pollen received. For example, if individuals producing 'a* pollen are scarce in the population then it is reasonable to predict that the seed-set of individuals with 'C stigma will be lowered by a lack of compatible 'a' pollen in the pollen pool. So the proportion of ovules available for outcrossing will be multiplied by a coefficient of female fertllity (<1) to give the actual amount of successful cross-fertilization (Charlesworth & Charlesworth, 1979a). This coefficient is taken for each génotype firom fig. 3.4., as a function of the size of its compatible pollen pool (sum of the frequencies of génotypes having their pollen compatible to the stigma of this particular génotype) and of the parameter FL (critical size of compatible pollen pool below which the realized female fertility déclines linearly). All génotypes are assumed to contribute equally to the pollen pool (no discounting rate).

Initial zygote frequencies are chosen appropriately for each particular investigation.

A typical di-allelic self-incompatible population consists of only two génotypes, AC.ac and acac, with a one to one ratio. The method used to compute the zygote

frequencies in the next génération is described in détail in Appendix 1. and is taken from Charlesworth & Charlesworth (1979a). In short:

The genotypic frequencies of the différent zygotes produced by selfing are calculated. Then, thèse frequencies are reduced by multiplying by a factor 1-S ^ which is "the probability that a selfed ovule results in a progeny individual that survives to the next génération, relative to the probability for a non-selfed ovule (which may or may not be fertilized)" (Charlesworth & Charlesworth, 1979c).

This factor combines the opposite effects of inbreeding dépression, affecting

^ S will be referred to as the inbreeding dépression parameter although it combines both the effect of

inbreeding dépression and the effectiveness of pollination

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MODEL FOR BREAKDOWN OF SX 24 selfed-ovules, and of the effectiveness of poUination, affecting the probabiliQr of cross-fertilization regardless of the génotype of the mother.

The genotypic frequencies of the ry^gotes produced by outcrossing are obtained by combining the gamète frequencies in the compatible pollen pool with the gamètes produced by the female génotype under considération. Realized

female fertilities for each female parent are calculated (as explained above) and are used to adjust the total output of outcrossed progenies. Finally the zygotes produced by selfing and outcrossing are combined and normalized so that the sum of their frequencies becomes equal to 1.

In order to study the effect of a recombination within the supergene (§ 3.5), low frequencies of recombinant Acac and aCac génotypes are initially introduced in a population made of ACac and acac génotypes in 50:50 ratio The value

of the parameter S represents the selfmg rate of the recombinants.

For the study of the partial breakdown of the incompatibility reaction (§ 3.4), I have introduced a third locus (linked or unlinked to the supergene) which controls the effectiveness of the incompatibility reaction. The wild-type allele, Iw, assures full self-incompatibility while a dominant or récessive mutant allele, Ib, induces a partial breakdown of the incompatibility reaction affecting either the pollen or the stigma. Hence individuals with phenotype [Ib] are self-compatible The

proportions of self-fertilized ovules are Sbi and Sb2 for [ACIb] and [acib]

phenotypes, respectively. Moreover with phenotype [Ib] an individual can now be cross-fertilized with every other individual in the population. Probabilities of cross- fertilization are assumed to be the foUowing, given that either the pollen or stigma has a phenotype [IbJ :

POLLEN DONOR PHENOTYPE

SnGMA A a

PHENOTYPE

C Pl 1

c 1 P2

with 0 ^ pip2 ^ 1.

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enfant ou un adolescent sur ses loisirs, il ne pensera pas à l'école, qui lui semble le plus souvent comme une contrainte, mais bien au temps dont il dispose librement après

lignes; mais on doit tenir compte du gonflement extraordinaire de la paroi anté- rieure du vajçin et du col de la vessie, qui avait disparu en grande partie après la délivrance et

résista pas longtemps à ces secousses nouvelles et sou- vent répétées, et il fut bientôt affect é du délire des ivre-.. Sa femme le fit contenir par plusieurs hommes;

Les il;l3tances I~2~4-&#34;5-6 sont beaucoup plus importantes dans le crâno ratle que dans le crâne femelle ; le gorille mâle possède donc une face plus développée que la femelle ;

L’œuvre ne peut être stockée dans une autre base de données dans le but d’y donner accès ; l’identifiant unique (permalink) indiqué ci-dessus doit toujours être utilisé

° Parallèlement, l'érosion des forces classiques des partemires de l'Alliance s'est poursuivie sans discontinuer pour des raisons diverses, de nature économique, de