The effect of hitch-hiking on genes linked to a balanced polymorphism in a subdivided population

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1 Genet. Res., Camb. (2), 76, pp With 6 figues. Pinted in the United Kingdom 2 Cambidge Univesity Pess 63 The effect of hitch-hiking on genes linked to a balanced polymophism in a subdivided population MIKKEL H. SCHIERUP *, DEBORAH CHARLESWORTH AND XAVIER VEKEMANS Institute of Cell, Animal and Population Biology, Uni esity of Edinbugh, Edinbugh EH9 3JT, UK Laboatoie de Ge ne tique et d Ecologie Ve ge tales, Uni esite Libe de Buxelles, 185 Chausse edewa e, B-116 Bussels, Belgium (Recei ed 2 June 1999 and in e ised fom 5 No embe 1999) Summay The effect of multi-allelic balancing selection on nucleotide divesity at linked neutal sites was investigated by simulations of subdivided populations. The motivation is to undestand the behaviou of self-ecognition systems such as the MHC and plant self-incompatibility. Fo neutal sites, two types of subdivision ae pesent: (1) into demes (connected by migation), and (2) into classes defined by diffeent functional alleles at the selected locus (connected by ecombination). Pevious theoetical studies of each type of subdivision sepaately have shown that each inceases divesity, and deceases the elative fequencies of low-fequency vaiants, at neutal sites o loci. We show hee that the two types of subdivision act non-additively when sampling is at the whole population level, and that subdivision poduces some non-intuitive esults. Fo instance, in highly subdivided populations, genetic divesity at neutal sites may decease with tighte linkage to a selected locus o site. Anothe conclusion is that, if thee is population subdivision, balancing selection leads to deceased expected F ST values fo neutal sites linked to the selected locus. Finally, we show that the ability to detect balancing selection by its effects on linked vaiation, using tests such as Tajima s D, is educed when genes in a subdivided population ae sampled fom the total population, athe than within demes. 1. Intoduction Models of loci unde balancing selection ecognize two genealogical pocesses with makedly diffeent time scales. These ae the genealogy of functionally diffeent alleles (the genealogy of allelic lineages) and the genealogy of functionally equivalent alleles (the gene genealogy within allelic lineages). In panmictic population models, the genealogy of allelic lineages is expected to have a neutal-like banching patten, with times escaled because of the extemely long esidence times of such alleles (Takahata, 199). The genealogy within lineages is also vey simila in stuctue to a neutal gene genealogy, but the time scale is much shote (Takahata, 199; Vekemans & Slatkin, 1994; Nodbog, 1997). Ou pevious pape exploed the consequence of elaxing the assumption of panmixia (Schieup et al., 2). We found that, as * Coesponding autho. Depatment of Ecology and Genetics, Univesity of Aahus, Ny Munkegade, Building 54, DK-8 Aahus C., Denmak. intuitively expected, the divesity between allelic lineages at such selected loci is insensitive to population stuctue, unlike that of alleles at a neutal locus, wheeas vaiation within allelic lineages is stongly affected by population stuctue, behaving like a neutal locus with a educed effective population size. Hee we add ecombination to the model and conside the expected pattens of sequence divesity at a neutal locus linked to the locus unde balancing selection (heeafte temed the selected locus). The motivation fo adding such complexity to the aleady complex situation of balancing selection in subdivided populations is two-fold. Fist, intagenic ecombination appeas to occu in both the majo histocompatibility system (MHC) (Gyllensten & Elich, 1991; Begstom et al., 1998), spoophytic selfincompatibility (SI) systems (Awadalla & Chaleswoth, 1999), and the b1 mating gene in the fungus Copinus cineeus (Badane & May, 1999), and theefoe intepetation of the pattens of sequence divesity within such loci equies an undestanding of

2 M. H. Schieup et al. 64 how they behave unde stong, but not absolute, linkage. Since stong balancing selection leads to inceased neutal divesity ove a chomosomal egion, as discussed next, it is of inteest to study the size of this egion and the extent to which divesity is alteed at sites within the gene that ae not unde selection, and at linked loci. Secondly, such an undestanding should help to evaluate the potential to detect balancing selection though analysis of make genes, such as micosatellites, linked to putatively selected loci. Fo instance, the numbe and fequencies of alleles at linked loci have been used to infe selection on MHC loci (Pateson, 1998; Meaghe & Potts, 1997). If a neutal locus is linked to a locus unde balancing selection, vaiants at the neutal locus will be associated with diffeent allelic lineages at the selected loci. Since the allelic lineages at the selected locus ae maintained at intemediate fequencies by balancing selection, the alleles at linked neutal loci can be viewed as being subdivided into allelic classes (coesponding to the selected lineages maintained in the population), and can move between classes by ecombination. This subdivision is equivalent to the finite island model of subdivision but with the deme sizes being vaiable ove time (due to andom fluctuations in fequencies of allelic lineages at the selected locus: see Vekemans & Slatkin, 1994). Thee ae thus two types of subdivision: into demes and into allelic classes. Each of these, on its own, is elatively well undestood theoetically as egads its consequences fo neutal genetic divesity. Neutal divesity in the total population is inceased by population subdivision unde the finite island model (Takahata, 1988; Slatkin, 1991), and in panmictic populations it is inceased by linkage to a locus unde balancing selection (Stobeck, 1983; Hudson & Kaplan, 1988). Since both population subdivision and linkage to selected allelic lineages can be thought of as types of subdivision, into demes and allelic classes, espectively, with genes moving between these classes by migation and ecombination, espectively (Chaleswoth et al., 1997; Nodbog, 1997), both nucleotide divesity and Tajima s D values fo a neutal locus should incease when a set of genotypes is subdivided into demes o allelic classes. The pupose of this study is to investigate how the two types of subdivision inteact to affect pattens of sequence and allelic divesity at linked neutal loci within and between subpopulations. We focus on qualitative pattens, which do not depend stongly on the paamete values chosen fo the model, and we seek geneal pattens acoss the diffeent models of balancing selection, in ode to discuss the elevance to empiical data without elying heavily on details of the models studied. To investigate the effect of vaying selection intensity, we mainly pesent esults fo gametophytic self-incompatibility (GSI) and fo symmetical ovedominance with s 2, which epesent models with stong and modeate selection, espectively. 2. Methods Fowad two-locus simulations assuming a population of S demes, each with N individuals, giving a total population size of N t SN, wee pefomed accoding to the finite island model with pollen, but not seed, migation. We assume a migation ate equivalent to migation of diploids at ate m, as descibed in the companion pape (Schieup et al., 2). As in that pape, the model assumes a locus subject to balancing selection, at which new functional alleles aise at a ate u pe geneation, unde the infinite alleles model (Kimua & Cow, 1964). The infinite alleles model is appopiate unde the assumption, which is easonable fo self-incompatibility and the othe systems of inteest, that mutations causing changes in specificity may potentially occu at many diffeent sites in the sequence, with each amino acid eplacement that altes specificity poducing a new type. Hee, we concentate on models of symmetical ovedominance and gametophytic self-incompatibility (GSI). To study the effects of linkage to the selected locus, a selectively neutal locus was added to the simulations, with a ecombination fequency of pe geneation with the selected locus. Fo study of the numbe of diffeent alleles maintained at the neutal locus (see below), vaiation was intoduced at a mutation ate of pe geneation, also accoding to the infinite alleles model. Each un was stated with 2N t diffeent alleles in the population at both the selected and neutal locus, and allowed to evolve fo 5 geneations, at which time appoximate mutation selection dift equilibium had been eached. Gene genealogies at the neutal locus wee then tacked by the method of Vekemans & Slatkin (1994), as descibed in the companion pape (Schieup et al., 2). Simulations wee un fo a numbe of geneations equal to thee times the time needed fo all genes at the neutal locus to coalesce. At this time the gene genealogy at the neutal locus is at an appoximate equilibium (tested by sampling at intevals). The genealogy of allelic lineages at the selected locus appoaches equilibium much moe slowly than the neutal loci, because of these lineages extemely long esidence times, and is pobably not in equilibium fo most paamete values we have studied. Howeve, the numbe of allelic lineages at the selected locus is the elevant paamete fo the behaviou of the genealogy of alleles at the neutal locus, and this appoaches equilibium quickly. The following statistics wee computed fo the neutal locus:

3 Hitch-hiking, balancing selection and subdi ision 65 (a) The numbe of diffeent alleles and expected heteozygosity, both within demes and in the total population. (b) The aveage paiwise coalescence times of alleles. The aveage of this quantity was computed within demes (T S ) and in the total population (T T ). Unde the finite island model in the absence of selection o linkage to selected loci, the expected T S and T T values ae given by: T S 2N t, and T T 2NS [(S 1) ] 2Sm, espectively (Slatkin, 1991). Assuming the infinite sites model, the expected nucleotide divesities, π, ae diectly popotional to the paiwise coalescence times: π S 2T S x G and π T 2T T x G, whee x is the mutation ate pe gene and G is the numbe of nucleotides in the gene. (c) The fixation index, F ST. This quantifies genetic diffeentiation among demes, and can be computed as F ST (T T T S ) T T (Slatkin, 1991). We compae this F ST with the value of G ST expected unde the finite island model in the absence of selection: G ST 1 2N S 1 S 11(1 m) (1 ) 11 1 (Takahata & Nei, 1984). (1) (d) Tajima s D statistic (Tajima, 1989) measues deviation in the topology of the gene genealogy fom that expected unde neutality in a panmictic population. It is computed as (2T D i L i a ), i S, T, (2) [e L i e L i (K i 1)] whee L i is the total length of the tee, i.e., the sum of all banch lengths in the gene genealogies, the subscipt i denotes S o T depending on whethe D is calculated fom samples fom the deme o total population, espectively, and a, e and e ae constants given in Tajima (1989). We substituted L i fo the numbe of segegating sites, Sn i, and T i fo the aveage numbe of nucleotide diffeences between two genes (i.e. the nucleotide divesity times the gene length) in Tajima s (1989) fomula because Sn i L i x and, as just explained, π l 2T i xg. D calculated fom coalescence times is the value expected when the genealogy of the sample is known with cetainty, i.e., when the numbe of segegating sites appoaches infinity. This is because the standad deviation of the estimation of banch length is the squae oot of its expectation when the numbe of mutations follows a Poisson distibution. In pactice, when the numbe of segegating sites exceeds 1, the appoximation is faily accuate (esults not shown). (e) The mean paiwise coalescence time of alleles sampled at the neutal locus, conditional on being associated with the same allelic lineage at the selected locus, T A. This was obtained by computing, fo each lineage at the selected locus, the aveage paiwise coalescence times fo all alleles at the neutal locus associated with the lineage, and then taking the aveage ove all allelic classes at the selected locus. We checked ou values of T A fo a panmictic population fo diffeent ecombination ates, with those expected unde the deivation of Takahata & Satta (1998) fo a selectively neutal site patially linked to a site unde symmetical ovedominance. Fo a given set of paametes the numbe of eplicates was 1, except fo the smallest migation ate (Nm 5), whee only 2 eplicates could be done within a easonable time. 3. Results (i) Nucleotide di esity at the neutal locus within and between demes Fig. 1 shows mean coalescence times between andomly sampled pais of alleles at the neutal locus, fo seveal linkage distances fom the selected locus () and migation ates among demes (Nm). Results ae shown with symmetical ovedominance with s 2, and fo selection caused by gametophytic selfincompatibility (GSI). Coalescence times ae given fo sampling at two levels, within demes (T S, Fig. 1a) and in the total population (T T, Fig. 1b). The migation axis also shows the numbes of alleles in the total population at the selected locus at equilibium, when the mutation ate to new functional allelic specificities is u 1. These numbes depend on the migation ate (Schieup, 1998). The standad deviations wee 25 4% of the mean values. Within demes, paiwise coalescence times incease monotonically with deceasing fo all Nm values (Fig. 1a), showing that linkage to the selected locus poduces the expected peak of divesity. Fo unlinked loci ( 5), T S values ae small and independent of Nm. These esults ae expected fom theoetical teatments (Mauyama, 1971). At intemediate values, T S values ae highest fo low Nm. Fo samples within demes, the peak of nucleotide divesity (linealy

4 M. H. Schieup et al. 66 (a) GSI Ovedominance T S E E T S (b) GSI Ovedominance T T E T T E-4 Fig. 1. Divesity at a neutal locus (shown as the paiwise coalescence times in geneations) as a function of migation ate (Nm) and ate of ecombination () to a locus unde balancing selection. Results ae shown fo GSI and ovedominance with s 2. Thee ae 4 demes with 5 individuals. The numbe of functional alleles maintained with u 1 is also shown on the migation axis. (a) Results fo sampling at the deme level, (b) esults fo sampling at the total population level. The numbe of eplicates is 1 except fo Nm 5 (2 eplicates) s =.5 s =.1 s =.5 GSI T T E-4 Recombination ate Fig. 2. Divesity (shown as the paiwise coalescence times in geneations) as a function of ecombination ate () fo fou diffeent selection intensities: GSI, and ovedominance with s 5, s 1, and s 5. Thee ae 4 demes with 5 individuals, and a migation ate of Nm 5. popotional to T S ) aound the selected locus is thus boade in a moe subdivided population than in a panmictic one. The patten is qualitatively diffeent at the total population level (Fig. 1b). When Nm is high, paiwise coalescence times again incease monotonically close to the selected locus. With low Nm, howeve, thee is a minimum at intemediate linkage. The value at which this minimum occus depends on the value of Nm and on the stength of selection (compaing

5 Hitch-hiking, balancing selection and subdi ision F ST 6 Nm =.5 OS Recombination ate 1 Nm =.5 OS Nm =.25 OS Nm =.5 GSI Nm =.5 GSI Nm =.25 GSI Fig. 3. F ST as a function of ecombination distance () to a locus unde eithe ovedominant selection (OS) with s 2 o GSI. Results ae shown fo thee diffeent migation ates. Thee ae 4 demes with 5 individuals, and a mutation ate u 1 at the selected locus Ovedominance, v = Numbe of alleles, v = GSI, v =5 1 4 Ovedominance, v =5 1 5 GSI, v = Numbe of alleles, v = Recombination ate 1 Fig. 4. The numbe of alleles maintained at the neutal locus as a function of the ecombination ate to eithe a locus unde ovedominant selection with s 2 o GSI. Results ae shown fo two mutation ates at the neutal locus, 1 (pimay y-axis, continuous lines) and 5 1 (seconday y-axis, dotted lines). Thee ae 4 demes with 5 individuals and a mutation ate u 1 at the selected locus. Nm 5. ovedominance and GSI, with GSI epesenting stonge balancing selection than symmetical ovedominance with s 2: see Vekemans & Slatkin, 1994). With vey low migation, the effect can be so lage that expected paiwise coalescence times at loci as closely linked to the selected locus as with 1 (N t 2) can be lowe than those between alleles at unlinked loci, i.e., the peak of divesity appeas vey naow in the population as a whole. The decease in T T at intemediate levels of N is most damatic fo the GSI model (stonge selection). The effect of vaying the selection coefficient is shown in moe detail in Fig. 2, whee the dependence of T T values on is shown fo a single value of Nm ( 5), but with vaious selection

6 M. H. Schieup et al. 68 (a) (b) GSI E-4 GSI E D D Fig. 5. Tajima s D as a function of migation ate (Nm) and ecombination ate () to a locus unde balancing selection. Results ae shown fo the GSI model. Thee ae 4 demes with 5 individuals. The numbe of functional alleles maintained with u 1 is also shown on the migation axis. (a) Results fo sampling at the deme level, (b) esults fo sampling at the total population level. The numbe of eplicates is 1 except fo Nm 5 (2 eplicates). coefficients. The decease in T T is lagest fo stong selection, but eaches close to the selected locus fo weake selection. Identical simulations wee un fo the thee models of spoophytic SI involving dominance among alleles (see Schieup et al., 2), and qualitatively simila pattens of coalescence times with Nm and wee found. Fig. 3 shows the effects on F ST, calculated fom the coalescence times shown in Fig. 1. In the accompanying pape (Schieup et al., 2), we show that population diffeentiation at a locus subject to balancing selection is low even when migation is vey esticted. Linkage to a selected locus also has a substantial effect on pattens of diffeentiation. Even when the neutal locus is unlinked, F ST is expected to be lowe than the expectation fom (1), because the selected locus is in linkage disequilibium even with an unlinked locus, in genotypes migating into a deme. This is also illustated in Fig. 3 whee F ST values ae slightly lowe fo stonge selection (compaing GSI with ovedominance fo 5 and Nm 25 o 5). Howeve, the decease in F ST fo an unlinked locus compaed with expectation fo a neutal locus was neve found to exceed 1%. Fo a given level of subdivision, F ST deceases monotonically with deceasing, and the decease is lage with stonge selection. Fo intemediate migation ates (Nm 5 and 25), the effect of the selected locus on the neutal one is noticeable even fo elatively loose linkage ( 1), povided that selection is sufficiently stong, as can be seen in the case of GSI. (ii) The numbe of alleles and di esity The same set of simulations also yielded allele numbes and divesity (expected heteozygosity) values at the neutal locus unde the infinite alleles model. Two mutation ates ( 5 1 and 1 ) wee chosen fo study, to epesent easonable values fo micosatellites o isozymes, espectively (Amos et al., 1996; Nei, 1987). Fig. 4 shows the numbe of alleles fo the total population, fo Nm 5. This suffices to illustate the main similaities and diffeences compaed with those fo coalescence times. Compaison of Figs. 1 and 4 shows that the numbes of alleles and T T co-vay closely, both showing minima at intemediate linkage. The minimum numbe of alleles is found at a highe ecombination ate in the model with stonge selection (GSI) because the effect of associative ovedominance is lage. When measued as the numbe of alleles maintained, the peak of divesity aound the selected locus is less damatic but it spans a somewhat boade egion than was obseved with coalescence times. (iii) Tajima s D within demes and in the total population Seveal statistics have been poposed to test fo deviations of nucleotide sequences fom expectations in a panmictic population unde the neutal model. We focus on Tajima s D because it is widely applied, and it has been shown to be among the most poweful statistics while elying on elatively few assumptions (Fu & Li, 1993; Simonsen et al., 1995). Tajima s D is the diffeence between the estimates of 4Nu calculated fom the paiwise nucleotide diffeences, and the numbe of segegating sites, Sn, standadized by the standad deviation of the diffeence, and should theefoe have an expectation of zeo with standad deviation one in an ideal population; simulations show that the expectation is slightly below zeo (Tajima, 1989). Instead of Sn and the numbe of paiwise nucleotide diffeences we used the total times in the genealogy and the paiwise coalescence times as

7 Hitch-hiking, balancing selection and subdi ision 69 Ovedominance T A Fig. 6. The divesity fo alleles at the neutal locus associated with the same functional allele at a locus unde ovedominant selection (s 2) as a function of migation ate (Nm) and ecombination ate (). Results ae fo sampling at the total population level. Thee ae 4 demes with 5 individuals. The numbe of functional alleles maintained with u 1 is also shown on the migation axis. The numbe of eplicates is 1 except fo Nm 5 (2 eplicates). explained in Section 2. Selection is detectable by this test, because it changes the fequency distibution of polymophic vaiants. Balancing selection inceases vaiant fequencies so that the numbe of paiwise nucleotide diffeences tends to exceed the value expected fom the neutal theoy, given the numbe of segegating sites, poducing positive Tajima s D values (Tajima, 1989). Positive values ae also expected fo a subdivided population sampled at the total population level (Simonsen et al., 1995). In both cases, Tajima s D is positive because the subdivision (into demes o allelic classes) sepaates the alleles into a numbe of classes within which coalescences occu apidly, but between which coalescences occu moe slowly (Nodbog, 1997). Fig. 5 shows how Tajima s D values fo the neutal locus ae affected by Nm and, fo the GSI model. When alleles ae sampled within demes (Fig. 5 a), Tajima s D inceases with deceasing values of fo all migation ates (with ovedominance the esults ae simila and ae not shown). Linkage to the selected locus inceases Tajima s D in a boade egion when migation is low than when it is fequent, in line with the patten fo paiwise coalescence times (Fig. 1 a). Standad deviations (not shown) wee up to 1 5 units, so the standad eos fo Nm 5, whee only 2 eplicates wee made, ae quite lage. When alleles ae sampled fom the population as a whole, howeve, this is no longe tue. As expected, Tajima s D fo loci unlinked to the selected locus inceases monotonically with deceasing migation (population subdivision). Similaly, if the population is panmictic, D inceases with inceasing linkage to the selected locus (subdivision into allelic lineages at the selected locus). Howeve, in a subdivided population, geatly deceased Tajima s D values can aise fo genes closely linked to the selected locus. In othe wods, Tajima s D is much less likely to detect selection in a subdivided population, unless the neutal locus is extemely tightly linked to the selected locus (N t 1). When Ns was deceased, Tajima s D values wee, not supisingly, less likely to detect the selected locus (esults not shown), paalleling the educed effect of the selected locus on nucleotide divesity with weake selection. (iv) Nucleotide di esity within allelic classes In a panmictic population with complete linkage, mean paiwise coalescence times within allelic lineages, T A, ae expected to be much smalle than between allelic lineages, because the coalescence pocess within a lineage should behave appoximately like a neutal coalescence pocess with an effective population size detemined by the hamonic mean ove time of the numbe of copies of the allelic lineage (Vekemans & Slatkin, 1994; Takahata & Satta, 1998). Population subdivision, howeve, inceases divesity within allelic lineages, even though coalescence times between lineages ae lagely unaffected (see Schieup et al., 2). Paiwise coalescence times of genes at the neutal locus within allelic lineages at the selected locus ae shown in Fig. 6 fo the ovedominance model, fo vaious ecombination fequencies. Fo the high migation ate (Nm 12 5), T A deceases as deceases, deviating less than 1% fom theoetical expectations fo a panmictic population accoding to

8 M. H. Schieup et al. 7 Takahata & Satta (1998) (esults not shown). With esticted migation, T A also deceases with deceasing. Oveall, subdivision inceases divesity within allelic classes fo any level of linkage, with the elative incease being of simila magnitude. 4. Discussion The pimay pupose of this study was to investigate the qualitative effects of a locus unde balancing selection on vaiation at linked neutal loci, allowing fo population subdivision. Seveal genetic systems, in paticula self-ecognition systems, with these chaacteistics ae known, which motivate the explicit modelling. The model extends the esults of Chaleswoth et al. (1997) who investigated a two-deme model with a locus with two alleles maintained by balancing selection at equal fequency in each deme. Hee, population subdivision into many demes amplifies the effects of the polymophism at the selected locus, but the same qualitative effects ae expected as in a two-deme model. The model of subdivision studied is clealy a vey simple one and we investigated only a limited set of paametes in ou simulations. We theefoe focus on qualitative pattens and thei implications fo detecting selection at a locus using data fom linked makes. These qualitative esults should be obust to deviations fom the model analysed, such as the numbe of subpopulations, and migation of diploids, athe than pollen. Within demes, both π and Tajima s D incease with inceasing linkage to the selected locus. The peak of nucleotide divesity extends ove a geate map distance the geate the subdivision. Two factos can account fo this esult. Fist, fewe allelic lineages ae maintained in each deme at the selected locus when Nm is small, leading to stonge selection fo each lineage. Secondly, the deme effective size deceases with deceasing Nm fo neutal genes linked to a selected locus. This is because selection leads to nonconsevative migation (Nagylaki, 1982), which invalidates Mauyama s (1971) invaiance pinciple fo the case of stict neutality in the island model. This lowes the effective ecombination ate, N t. The elative contibutions of these two factos ae not easy to disentangle, in quantitative tems. Ou esults show, howeve, that the two types of subdivision, into demes and allelic classes, do not act additively on π and Tajima s D values when alleles ae sampled fom the total population. When both types of subdivision ae simultaneously pesent, the incease in π is smalle than with each sepaately, and the ability to detect eithe subdivision o balancing selection though effects on the site fequency specta (e.g., using Tajima s D test) is geatly educed. Unlike panmictic populations, when a population is physically subdivided, π estimated fom a total population sample eaches a minimum value fo an intemediate level of linkage. The eason fo this is that two opposing foces affect π. Linkage to a selected allele inceases π (associative ovedominance: see Fydenbeg, 1963; Stobeck, 1983; Chaleswoth et al., 1997). Subdivision also inceases π though an inceased effective population size of the whole population (Nei & Takahata, 1993). Linkage to an allelic lineage at the selected locus, howeve, inceases the effective migation ate though hitchhiking, as evidenced by the decease in F ST with linkage (Fig. 3). This deceases π elative to the unlinked case. At intemediate linkage, the decease in π caused by hitchhiking outweighs the incease caused by associative ovedominance. The paallel patten in Tajima s D has the same basic cause. Tajima s D can be intepeted as measuing the elative numbe of old vesus new mutations in the genealogy (Fu, 1997). In a subdivided population, many of the most ecent coalescences happen within demes on a fast time-scale (Nodbog, 1997). Similaly, coalescence is fast among neutal vaiants within a given selected allele class. Thus, with only one of these types of subdivision, long banches with many old mutations connect demes (unde physical subdivision) and diffeent selected alleles (unde balancing selection). With both types of subdivision, howeve, neutal alleles associated with any given selected allele ae likely to be pesent in diffeent demes, and neutal alleles in paticula demes ae likely to be associated with the diffeent selected alleles, so the genealogy will display fewe old mutations, and will thus have a close to neutal fequency spectum of vaiants, and low Tajima s D if data ae analysed fom the set of demes as a whole. These esults demonstate that, if one wishes to infe the opeation of balancing selection, the sampling stategy is vey impotant if the species in question is, o has ecently been, subdivided. Futhemoe, no species confoms exactly to the symmetical island model with equal migation. In paticula, migation ates and deme sizes ae expected to vay ove time. This might cause some of the non-linea chaacteistics discussed above fo sampling at the total population level to aise even in a sample fom a single deme, and the potentiality fo detecting balancing selection by Tajima s D may thus be educed even fo the best possible sampling stategy. The magnitude of such effects emains to be investigated. (i) Implications fo neutal sites within a locus with balanced polymophism Recombination and o gene convesion pobably occu within genes in both the MHC (Begstom et al., 1998) and Bassica spoophytic SI system (Awadalla & Chaleswoth, 1999), and intepetations of pattens of nucleotide divesity must theefoe

9 Hitch-hiking, balancing selection and subdi ision 71 incopoate this, togethe with the possibility of population subdivision. In MHC (HLA) loci in humans, high levels of polymophism ae thought to be maintained by balancing selection acting on the peptide binding egion of these poteins (Hughes & Nei, 1988; Ayala, 1995; Salamon et al., 1999). Recently, silent nucleotide divesity has been estimated fo seveal MHC egions at vaious ecombination distances to the peptide binding egions, both within and between allelic classes defined eithe by seotypes o infeed fom nucleotide sequence similaity (Takahata & Satta, 1998; Satta et al., 1998). Takahata & Satta (1998) calculated the expected divesity within lineages as a function of ecombination fo a simple population genetic model of symmetical ovedominance and andom mating. When this model is fitted to the data, it is difficult to account fo the high divesity within lineages unde any easonable value of the ecombination ate (Takahata & Satta, 1998). Ou esults show that the inclusion of subdivision may account fo some of this discepancy, because within-lineage divesity can be consideably inceased without affecting the between-lineage divesity. Howeve, the extent of subdivision of the human population duing the time span elevant fo the polymophism at the HLA loci is at pesent unclea (Hapending et al., 1998; Hais & Hey, 1999). In the spoophytic SI system of Bassicaceae, a numbe of functionally diffeent alleles have been sequenced fom the two loci involved in self-incompatibility: SLG and SRK (Kusaba et al., 1997). The egions of the sequence that ae involved in the ecognition have not been identified with any degee of cetainty, so it is not yet possible to ask about divesity at sites at diffeent linkage distances fom these pats of the sequence. Howeve, it is known that levels of polymophism thoughout the two genes ae high, even seveal hunded base pais fom the S- domain hypevaiable egions, which ae found in all SI loci that have been studied (Sims, 1993; Kusaba et al., 1997) and may include the specificity-detemining sites (Awadalla & Chaleswoth, 1999). In the SRK locus, divesity is high in the kinase egion, which is sepaated fom the S-domain by a lage inton and is pobably not involved in ecognition functions. In this gene, divesity is found in both exons and intons. The allele sequences cuently available ae taken fom cultivated stains of the species studied, so that subdivision of the population fom which they oiginated is quite likely and this may influence the divesity pattens. Theefoe, it will be valuable to obtain compaable esults fom natual populations, and to compae andomly sampled alleles fom within individual populations, as well as between them. Futhemoe, since thee is evidence fo ecombination both within the SLG gene, and also between the SLG and SRK loci (Awadalla & Chaleswoth, 1999), it would be wothwhile to test whethe inton divesity declines with distance fom the SRK locus S-domain. At pesent, howeve, not enough intons have been sequenced fo this to be possible. Inton data fom self-incompatibility genes in species with gametophytic self-incompatibility systems would also be valuable. (ii) Implications fo linked neutal loci It is often assumed that geate divesity should be found at makes linked to the MHC than at loci elsewhee in the genome. In an ealy study of Mus musculus, Nadeau et al.(1982) found that isozymes on chomosome 7, whee the MHC is located, had significantly highe divesity and moe alleles than loci on othe chomosomes. Since the mice analysed wee sampled wold-wide and M. musculus populations ae highly subdivided (Dallas et al., 1998), this is unexpected unless the effective size of the metapopulation is extemely small, o the loci studied ae extemely closely linked to MHC. A moe detailed study using micosatellites found moe alleles at loci within 1 cm of the MHC than at loci 2 5 cm fom the MHC (Meaghe & Potts, 1997). Applying ou finding that a detectable peak of divesity is unlikely unde any level of subdivision to extend futhe than a linkage distance coesponding to N t 1, and assuming that the peak of divesity in M. musculus extends a minimum of 2 5 cm, we would then have to infe a maximum N e value of about 2 5 fo the M. musculus population studied, and possibly much lowe if it is subdivided. Since the oigin of the inbed stains used was not stated it is difficult to know whethe this numbe epesents the wold-wide population size o a egional one. In Soay sheep sampled fom a single population, Pateson (1998) epoted inceased heteozygosities fo two micosatellites located within, and at a distance of 2 6 cm fom the polymophic class II DRB locus of the MHC, compaed with thee micosatellites at distances of 5 5, 15 8 and 17 2 cm. Futhemoe, Watteson s test (Watteson, 1978) detected deviations fom neutality at the two closely linked loci but not at the moe distant loci. The inceased polymophism fo the micosatellite as fa as 2 6 cm away fom DRB, togethe with significant linkage disequilibium between this micosatellite and DRB, suggests that the effective size of this population is also vey low (less than 1). In the HLA-H pseudogene in humans, Gimsley et al. (1998) epoted a moe than 1-fold geate nucleotide divesity than is geneally found in the genome. Howeve, Tajima s D was not significant. The HLA-H locus is located appoximately 1 kb fom the highly polymophic HLA-A locus. Gimsley et al.(1998) concluded that the high HLA-H divesity

10 M. H. Schieup et al. 72 is most pobably caused by balancing selection at the HLA-A, athe than being caused by selection at HLA-H befoe it became a pseudogene. Assuming a ecombination ate of 1 cm Mb (Satta et al., 1998), HLA-H would be at a distance 1 1 fom HLA-A, a 1-fold incease in divesity compaed to an unlinked locus would equie a human effective population size of 5 5, depending on the selection intensity at HLA-A (see Fig. 1). This calculation is based on the assumption of panmixia. Past and cuent subdivision of human populations would decease the population size estimate. Most othe estimates ae highe than this (the minimum epoted by Satta et al. (1998) is 1 ). This discepancy implies that at least pat of the inceased divesity at the HLA-H locus may have to be attibuted to diect selection in the past. In conclusion, it appeas that the ability to detect the pesence of a multi-allelic locus unde balancing selection in a species with population stuctue equies sampling at the deme, athe than the total population level. If sampling is both within and between populations, and if data ae available fom efeence loci unlinked to the gene of inteest (to help povide evidence about population stuctue), F ST analysis may offe a bette way to detect balancing selection than tests based on the fequency spectum of alleles such as Watteson s and Tajima s D tests. It is clea, howeve, that the oveall effect of multi-allelic balancing selection on vaiation in flanking egions is limited in a subdivided population, unless effective population sizes ae low. Thee is, howeve, evidence that this may be the case in seveal empiical studies eviewed hee. 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