And Importance of Mating System Characteristics in Their Evolution
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Heredity 60 (1988) 91—100 The Genetica! Society of Great Britain Received 17 March 1987 Genetic structure of the European beech stands (Fagus sylvatica L.): F-statistics and importance of mating system characteristics in their evolution Joel Cuguen,* * Unitede Biologie des Populations et des Dominique Merzeaut and Peuplements, Centre Louis Emberger, CNRS, Route de Mende, BP 5051, 34033 Montpellier Cedex, Bernard Thiebaut*1 France. t Département de Physiologie des Végétaux Ligneux, Ecologie Génétique, Université de Bordeaux I, Av. des Facultés, 33045 Talence, France. Laboratoire de Systématique et d'Ecologie Méditerranéenne, Université des Sciences et Techniques du Languedoc, rue Auguste Broussonet, 34000 Montpellier, France. F-statistics are often used to study allozyme polymorphism in populations and the estimates provide a good basis to better understand selection and mating system effects. In this paper, computer simulation has been developed to determine the effects of the polymorphism level on F, estimates in finite samples. It is shown that finite samples present mostly negative F, estimates when allelic polymorphism is low. In these conditions, the high frequency of these apparent heterozygote excesses is not a consequence of frequency dependent selection acting on rare heterozygotes but only a statistical effect caused by the low probability of encountering rare homozygotes in the samples. The genetic structure of 250 European beech stands was studied using three electrophoretically detectable protein loci. F-statistics were estimated using the Weir and Cockerham method. The beech shows the highest interpopulation genetic differentiation estimates among the anemophilous pollinated forest trees. At the population level, an heterozygote deficit can be observed. Selfing estimates are not sufficiently high to explain these deficits. This suggests that limited gene flow exists in these populations and that forests of anemophilous pollinated trees are not panmictic and that these populations will be better understood using neighbourhood concepts. INTRODUCTION a function of the number of generations since their separation. Three parameters were proposed to Theknowledge of natural population genetic struc- describe the properties of hierarchically sub- ture contributes to a better understanding of the divided natural populations (Wright 1951, 1965). role selection and the mating system play in their These parameters were defined in terms of the total evolution. Since the theoretical works of Wright population (T), subdivisions (S) and individuals (1951,1965), Cockerham (1969, 1973), Kirby (I). (1975)and Nei (1977), genetic structures are often In a diploid individual, the two alleles of a analysed using F-statistics. gene may or may not be identical by descent Thedefinitions of these parameters are based (Malécot 1948). In a group of individuals, associ- on the following hypothesis: genetic drift is the ation between two identical alleles occurs with a main evolutionary force which acts on the evolu- given frequency. And this frequency varies from tion of the studied characters. Inter- and intragroup one group to another, according to the degree of genetic differentiation levels are a function of gene dependence between identical alleles in a group. flow intensity in and between groups, and are also Therefore, F,3 is the average over all subdivisions of the correlation between identical alleles that unite § Present address: Laboratoire de Genetique Ecologique et de Biologic des Populations Végétales, Université des Sciences et to produce the individuals, relative to the Techniques de LiUe, 59655 Villeneuve D'Ascq Cedex, France. gametes of their own subdivision, 92 J. CUGUEN, D. MERZEAU AND B. THIEBAUT F is the correlation between randomly empirically the various biases due to sampling and chosen identical gametes within subdivisions, the F1, estimation method. In order to do that, we relative to gametes of the total population, performed sampling simulations on theoretical "coancestry" in the sense of Cockerham (1969, populations, perfectly known, and estimated Fl, in 1973). each sample. F is the correlation between uniting iden- Furthermore, 250 beech stands have already tical gametes, relative to those of the total popu- been sampled in Europe in order to study the lation, "inbreeding" (Cockerham ibidem). alloenzymatic polymorphism of beech (Fagus syl- As pointed out by Wright, the list can be exten- vatica L.). So we dispose of an important number ded if there are further subdivisions. The above of observations in many different natural popula- three F-statistics are not independent and Wright tions. (1951) demonstrates that: Fl.variationswere examined in relation to (1 — = — — sample polymorphism, in theoretical and natural F)(1F)(1F') populations. Then the organisation of those vari- For example, when subdivisions are panmictic ations were compared between simulated and and isolated for a long time: F. =0in each group natural situations. So, in this paper, we will try to and F, is positive and increases with the number answer the following three questions: of generations. In this case, F =F',. (a) considering the simulation results, how are F1, However, when subdivisions are constituted of variations organised in relation to sample selfed individuals, the equilibrium values of F, polymorphism? F and F are one. (b) In European beechstands, does the organisa- The theoretical points of view of Wright and tion of F1, variations depend on the estimation Cockerham encounter difficulties in the study of method or do other mechanisms count, par- natural populations: firstly, without pedigrees it is ticularly mating system characteristics? not possible to recognise alleles identical by des- (c) In this case, what are the mating system cent. Secondly, these authors do not consider direct characteristics which are responsible for the selection effects which can strongly affects genetic observed differences between simulations and structures. natural populations: selfing and/or isolation In natural populations, identity between alleles by distance? is generally estimated according to the different allelic forms of a polymorphic gene. But the rela- tion between alleles identical by descent and alike MATERIALS AND METHODS in state ones is not simple. When two alleles are different, it is clear that they have no parental allele Simulations in common. But when they are alike, they can be We performed sampling simulations on theoretical identical by descent or only alike in state. The correctness of an estimate of identity in and populations using the Monte-Carlo method. between individuals may be increased by consider- ing many polymorphic loci. Creationof theoretical populations In a population and for a diallelic locus, the Intheoretical populations, the mating system fol- estimate of Fl, is often calculated according to the lows the mixed mating model. Populations are following formula: assumed to have reached the inbreeding equili- F,= 1 —H/2p(1 —p) brium and for a diallelic locus, the proportions of the various genotypes are a function of allelic where H is the observed heterozygote frequency frequencies and the fixation index: in the population and 2p(l —p) is the expected heterozygote frequency according to the Hardy- AA' =p'2+p'q'F, Weinberg law, calculated from allelic frequencies also estimated from the same sample. aa' =q'2+p'q'F, This estimation shows a great sampling vari- — Aa' =2p'q'(1F,) ance. Several authors have tried to estimate it (Ras- mussen, 1964; Brown eta!., 1975; Vasek and Hard- where AA' and aa' are respectively the homozygote ing, 1976). Based on different hypotheses, results frequencies for alleles A and a, Aa' the frequency differ and are therefore difficult to interpret. That of heterozygotes, p' and q' the frequencies of alleles is why we chose another method for analysing A and a, and F, the fixation index (=s/2—s, GENETIC DIFFERENTIATION IN BEECH 93 Haldane, 1924). Ten theoretical populations were where H1 is the observed heterozygote frequency created with the following allelic frequencies: in population i (i =1,2, .. , r), forlocus 1 (1 = p=O•5O, 045, 0•40, 0.35, 030, 025, 020, 0.15, 1,2 m) and for allele u (u =1,2,... , v); 0.10, 005. Two selfing rates were chosen: 0 per isthe estimated frequency of this allele and n,1 the cent for total panmixia and 13 per cent according sample size for locus 1 in population i. The average to the selfing estimates in the case of beech (Nielsen F, for a locus is a weighted average (Wright, 1965; and Schaffalitsky de Muckadell, 1954), which Kirby, 1975; Nei, 1977): means that 20 theoretical populations were created. u1 Pilji—p11jF11 — Samplingsimulation V p(i —p) Thesample size is 50, which corresponds to the u=1 average sample size for European beech stands. The genotype of each individual is randomly gen- Estimates of the three F-statistics were made for erated using the pseudo-random function of the the whole group of beech stands following the computer, from an infinite theoretical population. method of Weir and Cockerham (1984). One hundred samples of 50 individuals were con- In order to realise an estimation of the variance stituted from each theoretical population. of these estimates, a jacknife procedure was employed (Miller, 1974; Reynolds et a!., 1983; Weir and Cockerham, 1984). The estimates are beechstands European given thestandard error. Twohundred fifty beech stands were sampled in Europe out of the whole beech area in as different RESULTS as possible