An Asymmetric Model of Heterozygote Advantage at Major Histocompatibility Complex Genes: Degenerate Pathogen Recognition and Intersection Advantage

Home , Heterozygote advantage

Rick J. Stoffels*,†,1 and Hamish G. Spencer* *Allan Wilson Centre for Molecular Ecology and Evolution, Department of Zoology, University of Otago, Dunedin 9054, New Zealand and †The Murray-Darling Freshwater Research Centre, CSIRO Land and Water, Wodonga, Victoria 3689, Australia Manuscript received September 19, 2007 Accepted for publication November 29, 2007

ABSTRACT We characterize the function of MHC molecules by the sets of pathogens that they recognize, which we call their ‘‘recognition sets.’’ Two features of the MHC–pathogen interaction may be important to the theory of polymorphism construction at MHC loci: First, there may be a large degree of overlap, or degeneracy, among the recognition sets of MHC molecules. Second, when infected with a pathogen, an MHC genotype may have a higher fitness if that pathogen belongs to the overlapping portion, or intersection, of the two recognition sets of the host, when compared with a genotype that contains that pathogen in only one of its recognition sets. We call this benefit ‘‘intersection advantage,’’ g, and incorporate it, as well as the degree of recognition degeneracy, m, into a model of heterozygote advantage that utilizes a set-theoretic definition of fitness. Counterintuitively, we show that levels of polymorphism are positively related to m and that a high level of recognition degeneracy is necessary for polymorphism at MHC loci under heterozygote advantage. Increasing g reduces levels of polymorphism considerably. Hence, if intersection advantage is significant for MHC genotypes, then heterozygote advantage may not explain the very high levels of polymorphism observed at MHC genes.

ETEROZYGOTE advantage has been a particu- validity of highly symmetric selection has been ques- H larly appealing heuristic for major histocom- tioned, because it ignores the contribution made by patibility complex (MHC) polymorphism as it follows individual MHC molecules (De Boer et al. 2004). Given immediately from the biology of the system. That is, if that MHC alleles are codominantly expressed (Abbas we allow that the function of each MHC molecule is to and Lichtman 2006) and that individual alleles affect present a set of pathogen epitopes to T-cells, then, the host’s fitness when exposed to a particular pathogen because heterozygotes present two distinct sets of epi- (Jeffery and Bangham 2000; Nikolich-Zˇugich et al. topes to T-cells, they may be immune to a more diverse 2004), significant variation—and hence asymmetry—in set of pathogens over their lifetime than homozygotes. genotype fitness may exist within host populations. This Evidence of heterozygote advantage at MHC loci is variation is important with respect to the heterozygote accumulating for populations of humans (Thursz et al. advantage hypothesis of MHC polymorphism because 1997; Carrington et al. 1999; Tang et al. 1999; Jeffery models of asymmetric heterozygote advantage do not et al. 2000; Trachtenberg et al. 2003), other primates easily lead to a high level of polymorphism (Lewontin (Sauermann et al. 2001), and various other vertebrates et al. 1978; Spencer and Marks 1988; Marks and (Penn et al. 2002; McClelland et al. 2003; Froeschke Spencer 1991; Hedrick 2002). Consequently, evolu- and Sommer 2005). tionary immunologists have called for fitness functions Some theoretical studies have shown that heterozy- that more accurately capture the biology of the gene gote advantage may lead to the levels of polymorphism products, so that the validity of the hypotheses of MHC that we see in real populations of MHC genes (Mar- polymorphism may be more rigorously assessed. uyama and Nei 1981; Takahata and Nei 1990; Taka- Using allele-based fitness functions De Boer et al. hata et al. 1992), but these models assume very high (2004) and Borghans et al. (2004) concluded that levels of symmetry in selection, which implies minimal heterozygote advantage is not a valid explanation of or even no variance in the fitness of homozygotes and no MHC polymorphism. They showed that a high level of variance in the fitness of heterozygotes. The biological polymorphism is possible only if the fitnesses of all MHC alleles are very similar, which, they claimed, contradicts what we see in reality, and so heterozygote advantage 1Corresponding author: The Murray-Darling Freshwater Research Centre, CSIRO Land and Water, P.O. Box 991, Wodonga, VIC 3689, Australia. fails to explain the high degree of polymorphism of the E-mail: [email protected] MHC. By contrast, we present a large body of evidence

Genetics 178: 1473–1489 (March 2008) 1474 R. J. Stoffels and H. G. Spencer

Figure 1.—Hypothetical interaction network among pathogens, MHC molecules, and T-cells il- lustrating potential for degeneracy in the pathogen recognition sets of MHC molecules.

implying that the fitness of MHC alleles may actually be that pathogen (Figure 1). Second, any given epitope quite similar. Before we present this evidence, however, may be bound by many different MHC molecules we must introduce some terminology that we use to (Figure 1). Indeed, there is a very large quantity of evi- describe the relationship between a pathogen strain and dence implying a large degree of degeneracy in the an MHC molecule. peptide-binding sets of MHC molecules (e.g., Siniga- Throughout this article we will define an MHC glia et al. 1988; Panina-Bordignon et al. 1989; Barber molecule by its pathogen ‘‘recognition set.’’ By saying et al. 1995; Koziel et al. 1995; Sidney et al. 1995; Bertoni that an MHC molecule ‘‘recognizes’’ a pathogen strain, et al. 1997; Doolan et al. 1997; Khanna et al. 1998; we mean that the pathogen has at least one epitope that Southwood et al. 1998; Crotzer et al. 2000; Doolan binds to the peptide-binding groove of that MHC mole- et al. 2000; Gianfrani et al. 2000; Sidney et al. 2001; Diaz cule with an appropriate affinity and/or conformation et al. 2005; Schulze zur Wiesch et al. 2005). Thus, the to activate clonal expansion of a T-cell lineage. We above two features of the pathogen–MHC interaction assume an MHC molecule has some finite ‘‘recognition combine to imply that there may be a large degree of set,’’ which is the set of pathogen strains recognized by overlap in the pathogen recognition sets of MHC that MHC molecule. Because two MHC alleles can have molecules. Consider pathogens A and B in Figure 1: disjoint peptide-binding sets but both recognize the MHC molecules 1–3 all recognize pathogen A while all same pathogen strain and hence have the same fitness four MHC molecules recognize pathogen B. It follows under single-strain infection (see Figure 1 and below), that there must exist subsets of MHC alleles with very the fitness of an MHC molecule is (partially) defined by similar fitnesses and that, while we do not know how its recognition set and not by the set of peptides that it similar the lifetime average fitnesses of MHC alleles binds. If the recognition sets of MHC molecules are actually are, we certainly do not have much evidence broad, then the specificity of the MHC–pathogen in- that implies that the fitnesses of different MHC alleles teraction is low and variation in MHC allele fitness is low. are very dissimilar. By contrast, if recognition sets are narrow, then the Thus, a paradox emerges. Population geneticists have specificity of the MHC–pathogen interaction is high shown that selection shapes polymorphism in MHC and variation in MHC allele fitness is high. genes, but at the same time immunologists have shown There is little direct empirical evidence to suggest that that they possess a great degree of functional redun- the pathogen recognition sets of MHC molecules are dancy. Here we provide a reappraisal of the heterozy- narrow and disjoint. In our view, recent advances in the gote advantage hypothesis of MHC polymorphism using understanding of MHC–pathogen interactions imply a simple, single-locus model of asymmetric selection. the opposite: First, each pathogen contains many epi- We build on the work of De Boer et al. (2004) and topes, each of which is a viable target for an MHC mol- Borghans et al. (2004) by utilizing a fitness function ecule (see Figure 1, left; Nayersina et al. 1993; Koziel that makes allowances for the dual requirements of et al. 1995; Rehermann et al. 1995; Bertoni et al. 1997; allele-specific fitness and degeneracy in pathogen rec- Doolan et al. 1997; Jameson et al. 1998; Khanna et al. ognition sets. To this end, we employ a set-theoretic 1998; Rowland-Jones et al. 1998; Crotzer et al. 2000; approach to defining the fitness of MHC alleles. This Doolan et al. 2000; Gianfrani et al. 2000; Boon et al. approach allows us to address two particular aspects of 2002; Doolan et al. 2003; Schulze zur Wiesch et al. MHC polymorphism under heterozygote advantage. 2005). It is obvious that the potential number of MHC The first is the effect of the degree of degeneracy in molecules that recognize the same pathogen will in- pathogen recognition sets among MHC alleles. If each crease with the number of epitopes contained within MHC molecule recognizes and presents a large pro- Heterozygote Advantage at MHC Genes 1475

Figure 2.—Hypothetical relative ﬁtness proﬁles of genotypes to single-strain infection and coinfection generated under two levels of intersection advantage, g. MHC allele R contains X within its recognition set while r contains Y.

portion of the total set of pathogens to T-cells, then the dependent on the shape of the fitness profile under host population may not need a large number of MHC single-strain infection, and hence on the degree of in- molecules to maintain immunity to the pathogen com- tersection advantage, so the inclusion of this parameter munity. Here we test this hypothesis. is pivotal to the rigorous assessment of the heterozygote Second, we parameterize our model to control for the advantage hypothesis of MHC polymorphism mainte- form of the fitness profile of genotypes under single- nance. Finally, under single-strain infection, g ¼ 1 strain infection. Consider the following interaction means that alleles have an additive effect, which cor- 1 between two pathogen strains, X and Y, and two MHC responds to a dominance coefficient of 2. alleles, R and r. Suppose allele R contains only X in its recognition set while allele r contains only Y. Under single-strain infection with pathogen X, what are the THE MODEL relative fitnesses—as measured by, for example, pathogen density and blood cell counts—of the three host Suppose our population of MHC molecules is ex- genotypes RR, Rr, and rr? Figure 2, A and B, presents two posed to 100 pathogen strains. We assume that not all alternative fitness profiles under single-strain infection. strains have equal virulence; thus, we assume that the For the fitness profile in Figure 2A we assumed that virulence of a strain is not completely determined by its genotype RR obtains an advantage from expressing two interaction with MHC molecules. Therefore, let V ¼ {v1, alleles that both recognize X, while for the profile in v2, ..., v100}, the set of ‘‘weights’’ that defines the com- Figure 2B we assumed that RR does not obtain any munity of pathogen strains. Let vl be some arbitrary benefit from expressing two alleles that contain X in weight in V; then, for 1# l # 100, vl is drawn from a their recognition sets. Empirically derived fitness pro- uniform distribution, U½0,1. files under single-strain infection often vary between the We denote the set of n MHC alleles in the host two extremes of Figure 2, A and B (Penn et al. 2002; population as A ¼fa1; a2; ... ; ang: Suppose that allele McClelland et al. 2003; Wedekind et al. 2005, 2006) so ai codes for an MHC molecule that recognizes some we introduce a parameter, g, that enables us to control subset of V. Denote this subset as Vi. This subset has size for the relative benefit that a genotype obtains by m for all i; m is a parameter. For ease of explanation, we expressing two alleles that recognize a pathogen strain refer to Vi as an MHC allele’s recognition set. when infected with that strain. We call this benefit We assign fitnesses to individual alleles. Let vi,k be the ‘‘intersection advantage’’ since it is the proportional kth element from the set Vi and vi\j;b be the bth element benefit obtained from pathogen strains in the inter- from Vi \ Vj ; then section—i.e., the overlapping portion—of the alleles’ X X recognition sets in a diploid genotype (see the model wij ¼ ðvi;k 1 vj;kÞð1 gÞ vi\j;b: ð1Þ discussed below). Heterozygote advantage emerges un- k b der coinfection (Figure 2, E and F) when the corre- The fitness of the homozygote follows immediately by sponding alleles have opposite fitness profiles under letting j ¼ i: single-strain infection, as has been experimentally X demonstrated (McClelland et al. 2003). Also the wi¼j ¼ð1 1 gÞ vi;k: ð2Þ degree of heterozygote advantage under coinfection is k 1476 R. J. Stoffels and H. G. Spencer

Therefore, when g ¼ 0, the fitness of each homozy- selection than equilibrium-based approaches would gote is equal to the sum of the weights in its allele’s suggest (Spencer and Marks 1993). Therefore, simu- recognition set, and the fitness of each heterozygote is lations were initiated with a single allele and new alleles equal to the sum of the weights in the union of its alleles’ were introduced at one of two per-locus rates (mL ¼ 2m, recognition sets. Here, g is the degree of intersection where m is the per-gene mutation rate): 105 and 106. advantage and represents the proportional benefit that Here we consider these allele-introduction rates to a genotype obtains by having two alleles that recognize a represent the combined effects of point mutation and pathogen strain when infected with that strain (0 #g# recombination, both of which are important to the 1). If g ¼ 0, the homozygote obtains no benefit from generation of MHC diversity (Martinsohn et al. 1999; having two copies of an allele and a heterozygote obtains Ohta 1999; Richman et al. 2003; Consuegra et al. 2005; no improvements in fitness from the elements in Vi \ Vj . Reusch and Langefors 2005; Schaschl et al. 2006). By contrast, if g ¼ 1, the fitness benefit that a host We ran simulations with three different effective pop- genotype obtains in the presence of a pathogen strain, 3 4 5 ulation sizes (Ne)of10,10, and 10 , so that the rate at vi, is directly proportional to the number of alleles that it which new alleles were added to the population, mP, was carries that recognize that strain. mP ¼ mLNe; new alleles were introduced when, for We assume a monoecious, randomly mating popula- 1 generation t, t mod m ¼ 0 (the combinations of mL tion with discrete, nonoverlapping generations. We also P and Ne used here ensured that mP was an integer). We assume that the pathogen community, V, is constant for also ran simulations in which mutations were intro- each individual simulation. By making this assumption, duced at random time intervals at the same mean rate, we effectively assume that all hosts are infected by all but there was no notable difference in results. New pathogens before finding a mate, that there is no alleles were introduced with a frequency of (2N )1, and variance in pathogen abundance, and that pathogens e any p that fell below (2N )1 was eliminated from the do not evolve. Of course, this assumption is artificial, i e population. Here, we assume that all alleles in the host albeit necessary, since we wanted to isolate the effects population recognize the same number, m, of patho- of heterozygote advantage on polymorphism construction. That is, if we allowed the pathogen community to gens and simulate allele introduction and selection with ... vary, then we would no longer be studying polymor- nine levels of m: 10, 20, , 90, which correspond to phism maintenance due to heterozygote advantage fractions 0.1, 0.2, ..., 0.9. respectively. The parameter m alone, but instead studying the combined effects of represents the degree of degeneracy in pathogen heterozygote advantage and variation in selective pres- recognition by MHC molecules. Although this model sures, which are separate hypotheses of polymorphism contains a finite number of alleles, there is an extremely maintenance in the MHC (e.g., Hedrick 2002). Fur- large number of distinct combinations of the vi’s for any thermore, if we allowed the pathogen community to given value of m: 100!/½m!(100 m)!. Four values of the evolve, then we would naturally have a coevolutionary parameter g are simulated for each m-value: 0, 0.2, 0.4, model that would necessarily incorporate frequency- and 0.8. All simulations were run with and without drift. dependent fitness. Since frequency-dependent selec- Genetic drift in a population of n alleles was simulated tion may also maintain polymorphism in the MHC (e.g., by taking a sequence of n 1 conditional binomial Borghans et al. 2004), it is a hypothesis that competes samples each generation (see Gentle 2003, p. 198). with the heterozygote advantage hypothesis of MHC Drift took place after selection. Twenty replicate simu- polymorphism and we would then be confounding our lations were run for each m–g–Ne–mL combination, both treatment of heterozygote advantage. with and without drift. A new pathogen community, V, Let pi and pi9 be the frequencies of allele ai at times t was drawn for each replicate simulation. and t 1 1, respectively; the allele dynamics are then After each simulation was run for 105 generations, we described by the usual recursion equations: measured five quantities of particular interest. The first quantity is the number of alleles, n(A). For the second 1 pi9 ¼ piw wi; quantity, we measured the mean pairwise strength of P P selection across all genotypes. We defined the relative where wi ¼ j pj wij and w ¼ i wipi. fitness of a genotype as w˜ ij ¼ wij =maxðwij Þ. Selection We conducted simulations with allele introduction strength, sij, is equal to sij ¼ 1 w˜ ij and has domain ½0,1. and selection. This nonequilibrium, ‘‘constructionist’’ We then take the average of the n(n 1 1)/2 sij values as approach (following Spencer and Marks 1993) has our measure of the strength of selection. For the third proved very useful in the analysis of polymorphism quantity, as a measure of the average proportionate maintenance in the past (Spencer and Marks 1988, heterozygote advantage (hij ) relative to the fittest 1992, 1993; Marks and Spencer 1991). Researchers homozygote, we defined wij;h ¼ wij =maxðwiiÞ and then utilizing this constructionist approach have shown that hij ¼ w˜ ij;h 1, and then calculated the mean across the polymorphism is far more easily generated and main- n(n 1)/2 heterozygotes. For the fourth quantity,P we 2 tained via a simple process of allele introduction and calculated the expected heterozygosity: H ¼ 1 i pi . Heterozygote Advantage at MHC Genes 1477

We compare levels of heterozygosity and polymor- levels of polymorphism (see ‘‘Neutral’’ expectations in phism with those expected under neutrality. Levels of appendices a–d). heterozygosity under neutrality can be obtained from In the absence of genetic drift, the level of poly- Kimura and Crow (1964). In addition, we constructed a morphism increases nonlinearly to a maximum at m ¼ simple neutral computational model, which was similar 90 (Figure 3, a–c; appendix a). Including genetic drift to the model outlined above, in that alleles were causes the maximum level of polymorphism to occur at introduced at a per-locus rate of mL to an originally lower levels of recognition degeneracy (Figure 3, d–f; monomorphic locus, which was then subject to genetic appendix a). As discussed above, weak selection across drift without selection. Because levels of H and nA are so genotypes is required for the coexistence of large num- variable in small populations under neutrality, we ran bers of alleles. However, weak selection also leaves a more replicates for the smaller population sizes: 104,103, polymorphism more susceptible to erosion by the forces 3 4 5 and 200 replicates for Ne ¼ 10 ,10 , and 10 , respectively. of genetic drift and limits the ability of new alleles to Our computational estimates of heterozygosity agree invade (Crow and Kimura 1970, p. 422). Therefore, very well with analytic estimates from Kimura and Crow levels of MHC polymorphism may be maximized by (1964), so we can have some confidence that our genetic increasing recognition degeneracy, but only to a thresh- drift algorithm is correct (appendix a). old level of m, at which the erosive effect of genetic drift begins to take over (Figure 3, a–f). Levels of polymorphism were severely affected by genetic drift, even for very large population sizes (N ¼ RESULTS e 105; Figures 3 and 4; appendix a). The highest mean Recognition degeneracy: We first consider the effect level of MHC polymorphism recorded was 233 alleles; of recognition degeneracy, m, on the level of polymor- this occurred in the absence of genetic drift with mL ¼ 5 5 phism at g ¼ 0. Recall that the intersection advantage, g, 10 , Ne ¼ 10 , g ¼ 0, and m ¼ 90, while the highest mean determines the proportionate benefit that a host obtains level recorded in the presence of drift was 43 alleles, by having two alleles that recognize a pathogen when which occurred at the same parameter values (compare infected with that pathogen. Thus, at g ¼ 0, a host ob- appendices c and d). As a consequence of the negative tains no further benefit from having a second allele that relationship between selection and recognition degen- also recognizes that pathogen. We therefore draw the eracy, m, the loss of polymorphism due to genetic drift is reader’s attention to points connected by the solid line in greatest at high levels of recognition degeneracy. This Figure 3, which shows how mean levels of polymorphism relationship is clearly demonstrated in Figure 4. In- n(A) and heterozygote advantage (hij ) vary as a function terestingly, the greatest net loss of polymorphism due of both recognition degeneracy (m) and degree of to genetic drift occurred at the largest population size 5 intersection advantage (g). (Ne ¼ 10 ; Figure 4). This result may, at first, seem We expected the level of polymorphism to be nega- counterintuitive. However, at high levels of recognition tively related to recognition degeneracy. By contrast, the degeneracy selection becomes very weak, which means level of polymorphism was generally positively related to that new alleles either do not easily invade (Crow and m (Figure 3, a–f; appendices a–d). This relationship was Kimura 1970, p. 422) or invade but are easily lost from particularly strong in the absence of genetic drift the population. Because large, finite populations are (Figure 3, a–c) and was consistent across rates of allele subject to more frequent introductions of alleles, un- introduction (mL; appendices a–d). The mechanisms der such weak selection the proportion of successful underlying this relationship are as follows: At low levels invasions may be negatively correlated with population of m there is greater variance in the composition of the size in the presence of drift. Alternatively, allele invasion alleles’ recognition sets than that expected at high levels rates may not vary with population size, but the pull of of m. Thus there is the potential for much more vari- the attractor about the polymorphic equilibrium may be ance in allele fitnesses and a more asymmetric form of negatively correlated with the number of alleles in the selection at low levels of m. Selection strength across population and hence negatively correlated with pop- genotypes is then strongest at low levels of m (Figure 4; ulation size also (e.g., Kimura and Crow 1964). Thus, appendix a), and small sets of alleles dominate the the average lifetime of alleles may be negatively corre- population of MHC molecules. As recognition degen- lated with population size, which may result in a rela- eracy increases, the compositions of recognition sets tively greater loss of polymorphism to genetic drift in become increasingly similar, which in turn lowers selec- larger populations. tion strength (Figure 4; appendix a), makes selection Intersection advantage: Intersection advantage, g, more symmetric, and enables the coexistence of more had surprisingly complex effects on both the statistical alleles. However, while weak selection, or near neutral- properties of fitness sets and polymorphism. The most ity, is apparently a requirement for high levels of MHC obvious effects of increasing g are to reduce polymor- polymorphism under heterozygote advantage, com- phism and mean levels of heterozygote advantage plete selective neutrality generally results in very low (Figure 3; appendix a). It is obvious that m and g have 1478 R. J. Stoffels and H. G. Spencer

Figure 3.—Mean levels of polymorphism (6SD) as a function of recognition degeneracy, m, and intersection advantage, g, without genetic drift (a–c) and with genetic drift (d–f). (g–i) Mean levels of average heterozygote advantage (6SE) as a function of recognition degeneracy and intersection advantage (with genetic drift). Solid line: g ¼ 0; dashed line: g ¼ 0.2; dotted line: g ¼ 6 0.4; dash–dot line: g ¼ 0.8. Data presented for all three population sizes and allele-introduction rate mL ¼ 10 .

an interactive effect on both nA and hij ; the relative levels of polymorphism evolve under the lowest levels increase in polymorphism due to increasing m is great- of heterozygote advantage (at high m-levels) to see that est for low levels of g (Figure 3, a–f; appendix a), and the high levels of heterozygote advantage alone are not relative reduction in hij with decreasing g is greatest at sufficient for high levels of polymorphism (Figure 3). low levels of m (Figure 3, g–i; appendix a). Since in- Therefore, in addition to the effect that g has on creasing g lowers mean heterozygote advantage and mean levels of heterozygote advantage, g must affect levels of polymorphism, one might expect that the lower some other statistical property of the fitness structure levels of polymorphism are a consequence of dimin- of the population, which in turn affects levels of ished heterozygote advantage and that high levels of polymorphism. heterozygote advantage are necessary for high levels of Before exploring the additional effects that g has on polymorphism in the MHC. However, the full explana- polymorphism construction, recall that in our model tion is more complicated. By our definition of hij , when the set of all genotypes—and hence fitnesses—available hij , 0, wi6¼j , wii;max, on average, so that when hij , 0, a to the host population is finite and defined a priori by homozygote is most fit, directional selection will result, the set of weights from which alleles are drawn, V, and and polymorphism will vanish. Lewontin et al. (1978) the parameters (m, g) that determine how the recogni- obtained a similar necessary condition for a stable tion sets of individual alleles are transformed into the polymorphic equilibrium under overdominant selec- fitnesses of diploid genotypes. It is therefore possible, tion: mean heterozygote fitness must be greater than for any combination of V, m, and g, to determine the mean homozygote fitness for a polymorphic equilib- distribution of the set of all genotype fitnesses available rium to occur (wij . wii). Thus the condition hij . 0 to the host population before any mutation, selection, may be necessary for high levels of polymorphism to and genetic drift takes place. We call these distribu- evolve, but one needs only to observe that the highest tions of available genotype fitnesses ‘‘preselection fitness Heterozygote Advantage at MHC Genes 1479

Figure 4.—The relationship between loss of polymorphism due to drift, recognition degeneracy, m, and mean selection 6 strength, s. Here, mL ¼ 10 , g ¼ 0, s ¼ðsij 1 sij;drift Þ=2, where sij is the mean level of selection obtained in the absence of genetic drift (deterministic) and sij;drift is the mean level of selection in the presence of genetic drift (stochastic). Loss of polymorphism is simply the difference between the mean level of polymorphism in the absence of drift and the mean level of polymorphism in the presence of genetic drift. distributions’’ (PFDs) and each combination of V, m, pathogen community, V, used to construct the PFDs and g results in a unique PFD. As explained below, we above and, in turn, by subjecting that locus to selection argue that g has its greatest impact on polymorphism (no genetic drift). The parameters used for this poly- 4 6 construction through the direct effect that it has on the morphism construction were Ne ¼ 10 ; mL ¼ 10 ; m ¼ PFDs. 20, 80, 90; and g ¼ 0, 0.2, 0.8. After 105 generations, we To determine the additional effects that intersection recorded mean heterozygote and homozygote fitness advantage has on polymorphism construction, we con- and the proportion of the PFD greater than or equal to ducted an analysis of invasion dynamics, which showed these means after selection (f) for each of the nine that increasing g enabled certain alleles to dominate the pairings of m and g. We also determined invasion rate of population and precluded all other new alleles from new alleles (i) for each of the above simulations: An invading. Such a dynamic might result if there were a introduced allele was deemed a successful invasion if its positive correlation between g and the variance of the frequency increased from 1/(2Ne) after one generation PFD. That is, higher variance in the PFD may make it of selection. easier for selection to favor small subsets of particularly The results of these analyses are given in Figure 5 fit alleles, which may dominate the population and (homozygotes) and Figure 6 (heterozygotes). All PFDs preclude most alleles from invading, thus lowering of homozygotes and most fitness distributions for levels of polymorphism. We therefore needed to know heterozygotes were normal (Figures 5 and 6). Hetero- (1) if the standard deviation of the homozygote and zygote PFDs at high values of m and low values of g were heterozygote PFDs increases as g increases; (2) if in- skewed to the right and more multimodal (Figure 6, d, creasing g results in selection pushing mean homozygote e, g, and h). Within such distributions, fitness values in and heterozygote fitnesses closer to their maximum the long left tail have many elements in the intersection or farther into the right tail of the PFDs; and (3) if of the allele recognition sets, while the reverse is true for increasing g lowers the invasion rate. To this end, we those values at the right of the distribution. The fitness constructed PFDs for homozygotes and heterozygotes class with the highest frequency in Figure 6g represents using the fitness determination algorithm described the upper limit of heterozygote fitness at the values of g above: We constructed a single set of 100 pathogen and m (the fitness for this class is simply the sum of the weights, V, from which we constructed alleles and, sub- elements in V, since the size of the set intersection is at its sequently, a very large number of both heterozygotes minimum, nðAi \ Aj Þ¼80, and the intersection advan- and homozygotes for m ¼ 20, 80, 90 and g ¼ 0, 0.2, 0.8. tage is zero). We then determined the standard deviation of both the We first wanted to show that the standard deviation homozygote and heterozygote PFDs. of each PFD was positively related to g. Increasing g After determining the PFDs, we then wanted to consistently increases the standard deviation of homo- determine how selection transforms mean heterozygote zygote PFDs (Figure 5), but increases the standard and homozygote fitness and contrast these transformed deviation of heterozygote PFDs only at high values of fitnesses with the PFDs. Following the same algorithm recognition degeneracy (m; Figure 6, d–i). However, the outlined in the model, we then constructed a poly- increase in standard deviation of homozygote PFDs with morphism by bombarding an originally monomorphic g may be great enough to increase variation in the locus with new alleles drawn from exactly the same marginal fitnesses of alleles, which is what ultimately 1480 R. J. Stoffels and H. G. Spencer

Figure 5.—Homozygote PFDs for m ¼ 20, 80, and 90 and g ¼ 0, 0.2, and 0.8. Means of PFDs are indicated by dotted lines. Mean homozygote fitness after selection (see text) is indicated by dashed lines. f, proportion of PFD greater than or equal to mean homozygote fitness after selection; s, standard deviation of PFD; i, invasion rate of new alleles. determines variance in the rate of change of allele 5, g and i). The increase in mean heterozygote fitness frequencies. Therefore, these patterns generally imply due to increasing g is more severe: At m ¼ 90, .46% and that the standard deviations of PFDs are positively ,1% of the PFDs are greater than or equal to mean related to g. Also, it is worth noting that decreasing m heterozygote fitness after selection for g ¼ 0 and g ¼ 0.8, increases the standard deviation of the PFDs, particu- respectively (Figure 6, g and i). Finally, it is clear from larly for heterozygotes, across all levels of intersection data presented in Figure 5 that invasion rate (i) declines advantage (Figures 5 and 6), which is concordant with with increases in intersection advantage across all levels our implied mechanisms underlying effects of m on of recognition degeneracy. polymorphism (see above). Now it remains to be shown that g is negatively related to the proportion of the DISCUSSION homozygote/heterozygote PFD greater than or equal to the mean homozygote/heterozygote fitness after selec- Resolving the MHC paradox: The extraordinarily tion and that g is negatively related to the invasion rate high levels of MHC polymorphism appears paradoxical. of new mutants. We know that this polymorphism is non-neutral, but we The level of intersection advantage, g, is negatively also know that the recognition sets of MHC molecules related to both the proportion of the homozygote PFDs may be characterized by a large amount of degeneracy, greater than or equal to the mean homozygote fitness which implies that many alleles may be selectively equiv- after selection (f; Figure 5) and the proportion of the alent. Here, using a novel model that allows us to pa- heterozygote PFDs greater than or equal to mean het- rameterize the amount of recognition degeneracy in erozygote fitness after selection (f; Figure 6). That is, MHC molecules, we provide a solution to this paradox. increasing g causes selection to push both heterozygote The utilization of a set-theoretic definition of fitness and homozygote fitnesses toward their maximum val- enabled us to control the amount of degeneracy among ues. For example, at m ¼ 90, .9% and ,1% of the PFDs the sets of pathogens recognized by MHC molecules. are greater than or equal to mean homozygote fitness Here we have defined recognition degeneracy (m) such after selection for g ¼ 0 and g ¼ 0.8, respectively (Figure that the proportion of pathogens bound by each MHC Heterozygote Advantage at MHC Genes 1481

Figure 6.—Heterozygote PFDs for m ¼ 20, 80, and 90 and g ¼ 0, 0.2, and 0.8. Means of PFDs are indicated by dotted lines. Mean heterozygote fitness after selection (see text) is indicated by dashed lines. f, proportion of PFD greater than or equal to mean heterozygote fitness after selection; s, standard deviation PFD. Invasion rate of new alleles is given in Figure 3. molecule is equal to m/100. Therefore, recognition that similarity among heterozygote fitnesses—and hence degeneracy is positively correlated with the degree of a high level of symmetry—is a necessary condition for functional similarity among MHC molecules. Conse- a stable polymorphism under overdominant selection quently, one might expect a negative relationship be- (see triangle inequality on p. 160, Lewontin et al. 1978). tween recognition degeneracy and polymorphism. That Thus, as m increases, so does symmetry, and selection is, if recognition degeneracy is high and each MHC weakens, polymorphism increases, and the MHC pop- molecule recognizes a large proportion of the patho- ulation approaches neutrality. However, while near gens to which the host population is susceptible, then neutrality appears to be necessary for high levels of that host population may require only low levels of MHC polymorphism under heterozygote advantage, polymorphism to provide complete protection from the complete neutrality generally results in very low levels pathogen community. By contrast, we have shown that of polymorphism (see ‘‘Neutral’’levels of polymorphism the correlation between recognition degeneracy and in appendix a). polymorphism is actually positive. So it appears that if heterozygote advantage can One could suggest that the mechanisms underlying explain the levels of polymorphism observed at certain this relationship are as follows: Low levels of m result in MHC loci, then recognition degeneracy needs to be only small subsets of the pathogen community being high. For recognition degeneracy to be high, pathogen recognized by each MHC molecule. If we assume that strains must contain many epitopes and/or the peptide- the MHC population is exposed to a pathogen commu- binding groove of MHC molecules must bind over- nity of variable virulence, then low levels of m result in lapping sets of epitopes (Figure 1). There is some higher variation in the fitnesses of both MHC alleles and evidence that both of these conditions are satisfied in genotypes. As a result of this increased fitness variation reality. For example, Doolan and colleagues have at low levels of recognition degeneracy, selection in- shown that Plasmodium falciparum may contain hun- tensity and selective asymmetry increases, and fewer dreds of epitopes capable of binding MHC molecules alleles can coexist. This result is concordant with the and activating T-cells in the human population (Doolan analytic results of Lewontin et al. (1978), who showed et al. 2003; see also Doolan et al. 1997, 2000). This 1482 R. J. Stoffels and H. G. Spencer phenomenon is not limited to multicellular pathogens. Wedekind et al. 2006) to those more complex profiles Multiple epitopes have been identified in hepatitis B that emerge under multi-strain coinfection over an virus (Nayersina et al. 1993; Rehermann et al. 1995; organism’s lifetime. Since the fitness profiles of MHC Bertoni et al. 1997), hepatitis C virus (Koziel et al. 1995; genotypes under single-strain infection imply significant Schulze zur Wiesch et al. 2005), HIV (Rowland-Jones intersection advantage, and since intersection advantage et al. 1998; Crotzer et al. 2000), Epstein–Barr virus has strong influences on polymorphism construction (Khanna et al. 1998), and influenza A virus ( Jameson under heterozygote advantage, it is clearly a parameter et al. 1998; Gianfrani et al. 2000; Boon et al. 2002). These worthy of theoretical investigation. contemporary findings challenge the traditional view of One effect of intersection advantage is to alter the strict immunodominance, whereby only a very small form of selection. In particular, as g increases, the form fraction of the potential epitopes contained in complex of selection operating at MHC genes shifts from antigenic proteins elicit T-cell activation (e.g., Yewdell balancing to directional. A simple thought experiment and Bennink 1999). illustrates why: Suppose we order the 100 weights in our Moreover, it appears that the binding groove of MHC pathogen set, V, from least to most virulent and that molecules has relatively flexible requirements for pep- there exists one allele—call this allele af —in the tide binding, and thus any given epitope may be bound population that recognizes the m most virulent patho- by many different MHC molecules (Figure 1; e.g., gens. Then, for this level of m, this allele has maximum Sinigaglia et al. 1988; Panina-Bordignon et al. 1989; fitness. Now, if g ¼ 0, then, when forming heterozy- Barber et al. 1995; Koziel et al. 1995; Sidney et al. 1995; gotes, it is possible to pair af with other alleles that Bertoni et al. 1997; Doolan et al. 1997; Khanna et al. recognize some subset of the remaining 100-m patho- 1998; Southwood et al. 1998; Crotzer et al. 2000; gens and heterozygotes will therefore be more fit than oolan ianfrani idney D et al. 2000; G et al. 2000; S et al. the fittest homozygote (afaf; see Equations 1 and 2). 2001; Diaz et al. 2005; Schulze zur Wiesch et al. 2005). Balancing selection will then emerge in the form of The mechanisms behind the flexibility of the peptide- heterozygote advantage, resulting in polymorphism. binding groove are not entirely clear. The commonly Now suppose that g ¼ 0:8; then the fitness of homozy- held view is that there are only one or two key anchor gote afaf will be 1.8 times the sum of the m most viru- pockets in the binding groove of each MHC molecule lent antigens (see Equation 2). A heterozygote that, in and that a peptide only needs to be of the right length addition to those antigens bound by af, also recognizes and have one or two matching residues in the corre- some subset of the 100-m pathogens least virulent antigens sponding position(s) to successfully bind to the groove. will not easily obtain a higher fitness than af af. Conse- The composition of these key anchor pockets may allow quently, heterozygote advantage will vanish and the the many thousands of HLA (human MHC) alleles to be population should become less polymorphic. Obviously, classified into 1 of 10 supertypes, each of which shares if g ¼ 1, then it would be impossible for any genotype to the same peptide-binding motif (Sidney et al. 1996, be more fit than afaf and selection will be directional 2005; Sette and Sidney 1998; Castelli et al. 2002; (and purifying), favoring only the afaf genotype. Burrows et al. 2003). However, the rules governing Our results confirm that, in this case, our intuition is peptide binding may be much more complex than the generally correct. Increasing g decreases both mean supertype classification scheme suggests, as the anchor heterozygote advantage and levels of polymorphism. It pockets do not completely determine the requirements would therefore be easy to conclude that the decline in for peptide binding. Indeed, it has been shown that polymorphism with increasing intersection advantage non-anchor residues may strongly influence binding is caused by declining heterozygote advantage alone. affinity of some antigen–MHC complexes (e.g., Nayersina However, this conclusion would be false, as we know et al. 1993; Chen et al.1994;Kast et al. 1994), and high- from our examination of the effects of recognition affinity binding may occur without any involvement of degeneracy that high levels of heterozygote advantage anchor residues (e.g., Scott et al. 1998). Moreover, some are not necessary for high levels of polymorphism. epitopes bind with MHC molecules from separate super- Indeed, the highest levels of polymorphism may occur types (see epitope A4 in Figure 1; Thimme et al. 2001; at the lowest levels of mean heterozygote advantage, as Sidney et al. 2005). discussed above. So, in addition to g’s effect on mean Intersection advantage: Intersection advantage, g, levels of heterozygote advantage, exactly how does represents the proportional fitness benefit that a geno- increasing g result in decreased levels of polymorphism? type obtains by having two alleles that both recognize a Before answering the above question, we need to be pathogen when infected by that pathogen. Intersection reminded that our set-theoretic model utilizes a very advantage is an important parameter in our models of large, yet finite, number of alleles; each allele is an m heterozygote advantage as it provides a simple way for combination from a finite set of pathogen weights, V the theory of MHC polymorphism to relate empirically (see the model). The finite-alleles approach is impor- derived fitness profiles of genotypes under single-strain tant as it allows determination of the preselection infection (e.g., Penn et al. 2002; McClelland et al. 2003; distribution of available fitnesses, which, in turn, affects Heterozygote Advantage at MHC Genes 1483 polymorphism construction. It turns out that g limits Again, we say an MHC molecule ‘‘recognizes’’ a patho- levels of polymorphism not only through the effect that gen strain when that strain produces at least one epitope it has on mean levels of heterozygote advantage, but also that binds to that molecule with an appropriate affinity through the effect that it has on the variance of the and/or conformation to activate T-cells. Thus, deter- distribution of available genotype fitnesses and hence mining the degree of recognition degeneracy is theo- on the degree of asymmetry in selection: Increasing the retically possible, but would be extremely laborious. variance of available genotype fitnesses enables small Second, intersection advantage may need to be low for subsets of maximally fit alleles to dominate the poly- heterozygote advantage to explain very high levels of morphism and preclude other mutants from invading. polymorphism at MHC loci. Currently, experimentally This result is consistent with the general theory of derived fitness profiles imply that intersection advantage heterozygote advantage and the maintenance of poly- may be high (Figure 2, A, C, and E; Penn et al. 2002; morphism, which has shown that variation in heterozy- McClelland et al. 2003; Wedekind et al. 2005, 2006), gote fitnesses severely limits the ability of overdominant which in turn leads to low levels of polymorphism. selection to maintain polymorphism (Lewontin et al. Therefore, the current experimental data, coupled with 1978; Marks and Spencer 1991). the model results presented here, imply that heterozygote The empirical foundation for intersection advan- advantage may not be as important to the maintenance of tage comes from experimentally derived fitness pro- polymorphism at MHC loci as is currently perceived. files under single-strain infection (Penn et al. 2002; However, both the degree of pathogen recognition McClelland et al. 2003; Wedekind et al. 2005, 2006), degeneracy (m) and intersection advantage (g) influ- which have shown that immune responses of hetero- enced polymorphism construction through the effect zygotes may be intermediate between the responses of that they had on selective symmetry or on the variance in both corresponding homozygotes. Coupled with the homozygote and heterozygote fitnesses; selective sym- general knowledge that MHC alleles are codominantly metry is positively correlated with m, but negatively expressed (Abbas and Lichtman 2006), such a re- correlated with g. Increasing the variance in fitness leads sponse pattern among genotypes may imply that geno- to heterozygote advantage being less symmetric and types containing two MHC molecules that recognize a lowers the level of polymorphism maintained. Our pathogen strain may obtain some fitness advantage over simple model may exaggerate the influence of m and g genotypes containing only one MHC molecule that on asymmetry, because we have not included a param- recognizes that strain when infected by that strain. The eter to control for background fitness in our fitness molecular mechanisms underlying this pattern are function (1), and increasing levels of background fitness currently unknown, but may have something to do with should lower variance in fitness among genotypes and the quantity of MHC molecules expressed on the make heterozygote advantage more symmetric. Never- surface of antigen-presenting cells; perhaps the magni- theless, the model presented here serves as an impor- tude of the T-cell response is directly proportional to the tant heuristic, clearly showing that the incorporation of quantities of matching MHC molecules on the surface salient features of the MHC–pathogen interaction affect of the cell (Chen et al. 1994; Tynanet al. 2005), which in the degree of symmetry in heterozygote advantage in turn may be proportional to levels of expression of each unobvious ways, which in turn has a strong influence on MHC allele. Irrespective of the mechanisms underlying the properties of polymorphism construction. what we have called intersection advantage, the results We thank Bastiaan Star for reading an earlier draft and two that we present here clearly show that the ability of anonymous reviewers for their helpful comments. This work was heterozygote advantage to maintain polymorphism at funded by The Marsden Fund of the Royal Society of New Zealand MHC genes depends crucially on the levels of intersec- (contract no. U00315). tion advantage. More specifically, as intersection advantage increases, polymorphism declines. LITERATURE CITED Conclusion: The results that we present here show that, for heterozygote advantage to lead to high levels of Abbas, A. K., and A. H. Lichtman, 2006 Basic Immunology: Functions and Disorders of the Immune System. W. B. Saunders, Philadelphia. polymorphism at the MHC, two requirements may need Barber, L. D., B. Gillececastro,L.Percival,X.B.Li,C.Clay- to be satisfied. First, the pathogen recognition sets of berger et al., 1995 Overlap in the repertoires of peptides MHC molecules should be degenerate. As discussed bound in-vivo by a group of related class-I Hla-B allotypes. Curr. Biol. 5: 179–190. above, there is some evidence that this is indeed the Bertoni, R., J. Sidney,P.Fowler,R.W.Chesnut,F.V.Chisari et al., case. However, there has been no direct examination of 1997 Human histocompatibility leukocyte antigen-binding the degree of degeneracy in pathogen recognition sets supermotifs predict broadly cross-reactive cytotoxic T lymphocyte responses in patients with acute hepatitis. J. Clin. Invest. of MHC molecules. Determining the degree of recog- 100: 503–513. nition degeneracy would require identification of the Boon, A. C. M., G. De Mutsert,Y.M.F.Graus,R.A.M.Fouchier, major pathogen strains with which a certain host MHC K. Sintnicolaas et al., 2002 The magnitude and specificity of influenza A virus-specific cytotoxic T-lymphocyte responses in locus interacts and then estimating the proportion of humans is related to HLA-A and -B phenotype. J. Virol. 76: those pathogen strains recognized by each MHC allele. 582–590. 1484 R. J. Stoffels and H. G. Spencer

Borghans, J. A. M., J. B. Beltman and R. J. De Boer, 2004 MHC stein-Barr virus (EBV) oncogene latent membrane protein 1 polymorphism under host-pathogen coevolution. Immunogenet- (LMP1): evidence for HLA A2 supertype-restricted immune rec- ics 55: 732–739. ognition of EBV-infected cells by LMP1-specific cytotoxic T lym- Burrows, S. R., R. A. Elkington,J.J.Miles,K.J.Green,S.Walker phocytes. Eur. J. Immunol. 28: 451–458. et al., 2003 Promiscuous CTL recognition of viral epitopes on Kimura, M., and J. F. Crow, 1964 Number of alleles that can be multiple human leukocyte antigens: biological validation of maintained in a finite population. Genetics 49: 725–738. the proposed HLA A24 supertype. J. Immunol. 171: 1407–1412. Koziel, M. J., D. Dudley,N.Afdhal,A.Grakoui,C.M.Rice et al., Carrington, M., G. W. Nelson,M.P.Martin,T.Kissner,D.Vlahov 1995 Hla class I-restricted cytotoxic T-lymphocytes specific for et al., 1999 HLA and HIV-1: heterozygote advantage and B*35- hepatitis-C virus: identification of multiple epitopes and charac- Cw*04 disadvantage. Science 283: 1748–1752. terization of patterns of cytokine release. J. Clin. Invest. 96: 2311– Castelli, F. A., C. Buhot,A.Sanson,H.Zarour,S.Pouvelle- 2321. Moratille et al., 2002 HLA-DP4, the most frequent HLA II Lewontin, R. C., L. R. Ginzburg and S. D. Tuljapurkar, 1978 Het- molecule, defines a new supertype of peptide-binding specificity. erosis as an explanation for large amounts of genic polymor- J. Immunol. 169: 6928–6934. phism. Genetics 88: 149–169. Chen, W. S., S. Khilko,J.Fecondo,D.H.Margulies and J. McClus- Marks, R. W., and H. G. Spencer, 1991 The maintenance of single- key, 1994 Determinant selection of major histocompatibility locus polymorphism. 2. The evolution of fitnesses and allele fre- complex class I-restricted antigenic peptides is explained by class quencies. Am. Nat. 138: 1354–1371. I-peptide affinity and is strongly influenced by nondominant an- Martinsohn, J. T., A. B. Sousa,L.A.Guethlein and J. C. Howard, chor residues. J. Exp. Med. 180: 1471–1483. 1999 The gene conversion hypothesis of MHC evolution: a re- Consuegra, S., H. J. Megens,H.Schaschl,K.Leon,R.J.M.Stet view. Immunogenetics 50: 168–200. et al., 2005 Rapid evolution of the MH class I locus results in Maruyama, T., and M. Nei, 1981 Genetic variability maintained by different allelic compositions in recently diverged populations mutation and over-dominant selection in finite populations. of Atlantic salmon. Mol. Biol. Evol. 22: 1095–1106. Genetics 98: 441–459. Crotzer, V. L., R. E. Christian,J.M.Brooks,J.Shabanowitz,R.E. McClelland, E. E., D. J. Penn and W. K. Potts, 2003 Major histo- Settlage et al., 2000 Immunodominance among EBV-derived compatibility complex heterozygote superiority during coinfec- epitopes restricted by HLA-B27 does not correlate with epitope tion. Infect, Immun. 71: 2079–2086. abundance in EBV-transformed B-lymphoblastoid cell lines. Nayersina, R., P. Fowler,S.Guilhot,G.Missale,A.Cerny et al., J. Immunol. 164: 6120–6129. 1993 Hla A2 restricted cytotoxic T-lymphocyte responses to Crow, J. F., and A. M. Kimura, 1970 An Introduction to Population Ge- multiple hepatitis-B surface-antigen epitopes during hepatitis-B netics Theory. Harper & Row, New York. virus-infection. J. Immunol. 150: 4659–4671. De Boer, R. J., J. A. M. Borghans,M.Van Boven,C.Kesmir and F. J. Nikolich-Zˇugich, J., D. H. Fremont,M.J.Miley and I. Messaoudi, Weissing, 2004 Heterozygote advantage fails to explain the high 2004 The role of MHC polymorphism in anti-microbial resis- degree of polymorphism of the MHC. Immunogenetics 55: 725–731. tance. Microbes Infect. 6: 501–512. Diaz, G., B. Canas,J.Vazquez,C.Nombela and J. Arroyo, Ohta, T., 1999 Effect of gene conversion on polymorphic patterns at 2005 Characterization of natural peptide ligands from HLA- major histocompatibility complex loci. Immunol. Rev. 167: 319–325. DP2: new insights into HLA-DP peptide-binding motifs. Immu- Panina-Bordignon,P.,A.Tan,A.Termijtelen,S.Demotz,G.Corradin nogenetics 56: 754–759. et al., 1989 Universally immunogenic T-cell epitopes: promiscuous Doolan, D. L., S. L. Hoffman,S.Southwood,P.A.Wentworth, binding to human MHC class-Ii and promiscuous recognition by J. Sidney et al., 1997 Degenerate cytotoxic T cell epitopes from T-cells. Eur. J. Immunol. 19: 2237–2242. P-falciparum restricted by multiple HLA-A and HLA-B supertype Penn, D. J., K. Damjanovich and W. K. Potts, 2002 MHC heterozy- alleles. Immunity 7: 97–112. gosity confers a selective advantage against multiple-strain infec- Doolan, D. L., S. Southwood,R.Chesnut,E.Appella,E.Gomez tions. Proc. Natl. Acad. Sci. USA 99: 11260–11264. et al., 2000 HLA-DR-promiscuous T cell epitopes from Plasmo- Rehermann, B., P. Fowler,J.Sidney,J.Person,A.Redeker et al., dium falciparum pre-erythrocytic-stage antigens restricted by mul- 1995 The cytotoxic T-lymphocyte response to multiple hepati- tiple HLA class II alleles. J. Immunol. 165: 1123–1137. tis-B virus polymerase epitopes during and after acute viral-hep- Doolan,D.L.,S.Southwood,D.A.Freilich,J.Sidney,N.L.Graber atitis. J. Exp. Med. 181: 1047–1058. et al., 2003 Identification of Plasmodium falciparum antigens by an- Reusch, T. B. H., and A. Langefors, 2005 Inter- and intralocus re- tigenic analysis of genomic and proteomic data. Proc. Natl. Acad. combination drive MHC class IIB gene diversification in a teleost, Sci. USA 100: 9952–9957. the three-spined stickleback Gasterosteus aculeatus. J. Mol. Evol. Ewens, W. J., 2004 Mathematical Population Genetics. I. Theoretical In- 61: 531–545. troduction. Springer-Verlag, New York. Richman, A. D., L. G. Herrera,D.Nash and M. H. Schierup, Froeschke, G., and S. Sommer, 2005 MHC class II DRB variability 2003 Relative roles of mutation and recombination in generat- and parasite load in the striped mouse (Rhabdomys pumilio) ing allelic polymorphism at an MHC class II locus in Peromyseus in the southern Kalahari. Mol. Biol. Evol. 22: 1254–1259. maniculatus. Genet. Res. 82: 89–99. Gentle, J. E., 2003 Random Number Generation and Monte Carlo Meth- Rowland-Jones, S. L., T. Dong,K.R.Fowke,J.Kimani,P.Krausa ods. Springer-Verlag, New York. et al., 1998 Cytotoxic T cell responses to multiple conserved Gianfrani, C., C. Oseroff,J.Sidney,R.W.Chesnut and A. Sette, HIV epitopes in HIV-resistant prostitutes in Nairobi. J. Clin. 2000 Human memory CTL response specific for influenza A vi- Invest. 102: 1758–1765. rus is broad and multispecific. Hum. Immunol. 61: 438–452. Sauermann, U., P. Nurnberg,F.B.Bercovitch,J.D.Berard, Hedrick, P. W., 2002 Pathogen resistance and genetic variation at A. Trefilov et al., 2001 Increased reproductive success of MHC loci. Evolution 56: 1902–1908. MHC class II heterozygous males among free-ranging rhesus ma- Jameson, J., J. Cruz and F. A. Ennis, 1998 Human cytotoxic T-lym- caques. Hum. Genet. 108: 249–254. phocyte repertoire to influenza A viruses. J. Virol. 72: 8682–8689. Schaschl, H., P. Wandeler,F.Suchentrunk,G.Obexer-Ruff and Jeffery, K. J. M., and C. R. M. Bangham, 2000 Do infectious dis- S. J. Goodman, 2006 Selection and recombination drive the eases drive MHC diversity? Microbes Infect. 2: 1335–1341. evolution of MHC class II DRB diversity in ungulates. Heredity Jeffery, K. J. M., A. A. Siddiqui,M.Bunce,A.L.Lloyd,A.M.Vine 97: 427–437. et al., 2000 The influence of HLA class I alleles and heterozygos- Schulze zur Wiesch, J. S., G. M. Lauer,C.L.Day,A.Y.Kim,K. ity on the outcome of human T cell lymphotropic virus type T Ouchi et al., 2005 Broad repertoire of the CD4(1) Th cell infection. J. Immunol. 165: 7278–7284. response in spontaneously controlled hepatitis C virus infection Kast, W. M., R. M. P. Brandt,J.Sidney,J.W.Drijfhout,R.T.Kubo includes dominant and highly promiscuous epitopes. J. Immu- et al., 1994 Role of Hla-a motifs in identification of potential Ctl nol. 175: 3603–3613. epitopes in human papillomavirus type-16 E6 and E7 proteins. Scott, C. A., P. A. Peterson,L.Teyton and I. A. Wilson, J. Immunol. 152: 3904–3912. 1998 Crystal structures of two I-A(d)-peptide complexes reveal Khanna, R., S. R. Burrows,J.Nicholls and L. M. Poulsen, that high affinity can be achieved without large anchor residues. 1998 Identification of cytotoxic T cell epitopes within Ep- Immunity 8: 319–329. Heterozygote Advantage at MHC Genes 1485

Sette, A., and J. Sidney, 1998 HLA supertypes and supermotifs: a Takahata, N., Y. Satta and J. Klein, 1992 Polymorphism and bal- functional perspective on HLA polymorphism. Curr. Opin. Im- ancing selection at major histocompatibility complex loci. Genet- munol. 10: 478–482. ics 130: 925–938. Sidney, J., M. F. Delguercio,S.Southwood,V.H.Engelhard, Tang, J. M., C. Costello,I.P.M.Keet,C.Rivers,S.Leblanc et al., ppella E. A et al., 1995 Several Hla alleles share overlapping 1999 HLA class I homozygosity accelerates disease progression peptide specificities. J. Immunol. 154: 247–259. in human immunodeficiency virus type I infection. Aids Res. Sidney, J., H. M. Grey,R.T.Kubo and A. Sette, 1996 Practical, bio- Hum. Retroviruses 15: 317–324. chemical and evolutionary implications of the discovery of HLA Thimme, R., K. M. Chang,J.Pemberton,A.Sette and F. V. Chisari, class I supermotifs. Immunol. Today 17: 261–266. 2001 Degenerate immunogenicity of an HLA-A2-restricted Sidney, J., S. Southwood,D.L.Mann,M.A.Fernandez-Vina,M.J. Newman et al., 2001 Majority of peptides binding HLA-A*0201 hepatitis B virus nucleocapsid cytotoxic T-lymphocyte epitope with high affinity crossreact with other A2-supertype molecules. that is also presented by HLA-B51. J. Virol. 75: 3984–3987. hursz homas reenwood ill Hum. Immunol. 62: 1200–1216. T , M. R., H. C. T ,B.M.G and A. V. S. H , Sidney, J., S. Southwood and A. Sette, 2005 Classification of A1- 1997 Heterozygote advantage for HLA class-II type in hepatitis and A24-supertype molecules by analysis of their MHC-peptide B virus infection. Nat. Genet. 17: 11–12. binding repertoires. Immunogenetics 57: 393–408. Trachtenberg, E., B. Korber,C.Sollars,T.B.Kepler,P.T.Hraber Sinigaglia, F., M. Guttinger,J.Kilgus,D.M.Doran,H.Matile et al., 2003 Advantage of rare HLA supertype in HIV disease pro- et al., 1988 A malaria T-cell epitope recognized in association gression. Nat. Med. 9: 928–935. with most mouse and human MHC class-Ii molecules. Nature Tynan, F. E., D. Elhassen,A.W.Purcell,J.M.Burrows,N.A.Borg 336: 778–780. et al., 2005 The immunogenicity of a viral cytotoxic T cell epi- outhwood idney ondo el uercio ppella S , S., J. S ,A.K ,M.F.D G ,E.A tope is controlled by its MHC-bound conformation. J. Exp. et al., 1998 Several common HLA-DR types share largely overlap- Med. 202: 1249–1260. ping peptide binding repertoires. J. Immunol. 160: 3363–3373. Wedekind, C., M. Walker and T. J. Little, 2005 The course of ma- Spencer, H. G., and R. W. Marks, 1988 The maintenance of single- laria in mice: major histocompatibility complex (MHC) effects, locus polymorphism. I. Numerical studies of a viability selection but no general MHC heterozygote advantage in single-strain in- model. Genetics 120: 605–613. pencer arks fections. Genetics 170: 1427–1430. S , H. G., and R. W. M , 1992 The maintenance of single- edekind alker ittle locus polymorphism. IV. Models with mutation from existing al- W , C., M. W and T. J. L , 2006 The separate and leles. Genetics 130: 211–221. combined effects of MHC genotype, parasite clone, and host gen- Spencer, H. G., and R. W. Marks, 1993 The evolutionary construc- der on the course of malaria in mice. BMC Genet. 7: 55. tion of molecular polymorphisms. N.Z. J. Bot. 31: 249–256. Yewdell, J. T., and J. R. Bennink, 1999 Immunodominance in ma- Takahata, N., and M. Nei, 1990 Allelic genealogy under over- jor histocompatibility complex class I-restricted T lymphocyte re- dominant and frequency-dependent selection and polymor- sponses. Annu. Rev. Immunol. 17: 51–88. phism of major histocompatibility complex loci. Genetics 124: 967–978. Communicating editor: M. W. Feldman APPENDIX A Spencer G. H. and Stoffels J. R. 1486

6 Selected polymorphism statistics for simulations with mL ¼ 10 without genetic drift

g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.009 0.0059 12.450 1.040 18.950 1.151 24.150 1.290 29.700 1.677 41.800 1.857 10.350 1.038 16.350 1.113 19.750 1.063 20.850 1.266 19.700 1.822 H 0.0023 0.0017 0.874 0.010 0.918 0.004 0.933 0.005 0.944 0.004 0.959 0.003 0.853 0.012 0.899 0.007 0.913 0.007 0.918 0.007 0.895 0.010 mean(sij) 0.183 0.007 0.148 0.005 0.117 0.004 0.072 0.002 0.011 0.000 0.158 0.007 0.122 0.004 0.092 0.004 0.055 0.002 0.014 0.001 mean(hij) 0.686 0.021 0.530 0.020 0.375 0.011 0.210 0.007 0.052 0.004 0.444 0.018 0.334 0.016 0.234 0.010 0.129 0.006 0.028 0.003 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.016 8.600 0.893 12.450 1.040 14.600 1.068 15.200 1.346 10.650 1.250 4.250 0.510 5.450 0.689 6.100 0.665 4.500 0.689 2.950 0.643 H 0.002 0.824 0.015 0.869 0.011 0.881 0.011 0.875 0.011 0.799 0.028 0.644 0.037 0.676 0.056 0.672 0.051 0.611 0.075 0.410 0.099 mean(sij) 0.129 0.007 0.096 0.004 0.071 0.003 0.041 0.002 0.013 0.001 0.058 0.004 0.042 0.003 0.031 0.002 0.017 0.001 0.004 0.001 mean(hij) 0.271 0.014 0.201 0.012 0.139 0.008 0.074 0.005 0.015 0.003 0.055 0.009 0.035 0.008 0.022 0.006 0.013 0.004 0.003 0.001 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 1.2 0.027 18.350 1.209 26.600 1.592 36.250 1.400 44.950 2.419 83.150 3.640 15.200 1.195 21.750 1.456 26.800 1.549 28.100 2.165 30.250 1.497 H 0.0188 0.0045 0.909 0.007 0.935 0.004 0.952 0.003 0.957 0.004 0.972 0.001 0.891 0.009 0.920 0.005 0.935 0.004 0.932 0.007 0.924 0.006 mean(sij) 0.169 0.008 0.146 0.008 0.110 0.003 0.064 0.002 0.008 0.000 0.145 0.007 0.117 0.005 0.083 0.004 0.047 0.002 0.010 0.000 mean(hij) 0.690 0.023 0.518 0.012 0.363 0.009 0.194 0.008 0.044 0.002 0.446 0.019 0.328 0.010 0.231 0.008 0.120 0.007 0.024 0.002 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 1.209 12.550 1.151 16.650 1.358 19.350 1.242 18.550 1.867 14.750 1.145 5.850 0.795 6.300 0.668 7.500 0.927 6.600 1.243 4.050 0.674 H 0.0196 0.867 0.015 0.894 0.007 0.911 0.007 0.895 0.014 0.847 0.016 0.697 0.051 0.718 0.030 0.740 0.044 0.663 0.087 0.510 0.084 mean(sij) 0.119 0.007 0.090 0.004 0.061 0.003 0.035 0.002 0.009 0.001 0.055 0.004 0.040 0.003 0.026 0.002 0.015 0.001 0.004 0.000 mean(hij) 0.270 0.016 0.196 0.008 0.139 0.006 0.070 0.006 0.013 0.001 0.051 0.009 0.035 0.006 0.025 0.005 0.012 0.003 0.002 0.001 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 3.3 0.1984 24.900 1.621 31.850 1.493 45.750 2.332 61.850 3.501 143.550 6.608 20.500 1.655 26.550 1.673 33.400 2.003 38.600 3.171 36.250 3.239 H 0.1754 0.028 0.930 0.007 0.944 0.003 0.957 0.003 0.965 0.002 0.977 0.001 0.916 0.009 0.929 0.005 0.942 0.004 0.943 0.006 0.928 0.008 mean(sij) 0.161 0.007 0.144 0.005 0.105 0.004 0.057 0.001 0.006 0.000 0.137 0.007 0.115 0.005 0.077 0.003 0.040 0.001 0.008 0.000 mean(hij) 0.689 0.021 0.505 0.010 0.339 0.007 0.173 0.008 0.035 0.002 0.445 0.018 0.321 0.008 0.214 0.006 0.105 0.007 0.019 0.002 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 3.499 16.700 1.408 20.650 1.234 24.500 1.618 23.850 2.580 17.550 2.121 7.400 1.049 7.550 0.859 8.200 1.051 6.350 1.373 4.500 0.847 H 0.1667 0.894 0.013 0.905 0.007 0.920 0.005 0.906 0.013 0.856 0.019 0.744 0.043 0.750 0.028 0.758 0.030 0.628 0.076 0.506 0.080 mean(sij) 0.112 0.006 0.088 0.004 0.056 0.002 0.031 0.002 0.007 0.000 0.051 0.004 0.037 0.002 0.024 0.002 0.014 0.001 0.003 0.001 mean(hij) 0.271 0.015 0.192 0.007 0.127 0.005 0.060 0.006 0.010 0.001 0.053 0.009 0.035 0.005 0.022 0.003 0.009 0.003 0.001 0.001

Mean (left value) 695% confidence interval (right value). nA, number of alleles; H, heterozygosity; mean(sij), mean selection strength experienced by genotypes; mean(hij), mean proportionate heterozygote advantage relative to fittest homozygote. Expected number of alleles and heterozygosity under neutrality are presented for each population size on the left (95% confidence intervals for computational estimates only). Neutral expectations were calculated both computationally (see text) and analytically (heterozygosity from Kimura and Crow 1964; expected number of alleles from Ewens 2004). APPENDIX B

6 Selected polymorphism statistics for simulations with mL ¼ 10 with genetic drift

g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.009 0.0059 6.300 0.429 7.000 0.348 6.950 0.333 6.200 0.524 4.950 0.362 5.650 0.477 5.900 0.491 5.950 0.333 5.300 0.288 3.750 0.399 H 0.0023 0.0017 0.790 0.016 0.821 0.010 0.822 0.006 0.809 0.012 0.730 0.022 0.753 0.026 0.785 0.019 0.789 0.012 0.766 0.017 0.627 0.044 mean(sij) 0.228 0.013 0.177 0.008 0.140 0.005 0.098 0.004 0.036 0.002 0.200 0.014 0.158 0.011 0.114 0.005 0.079 0.005 0.029 0.001 mean(hij) 0.547 0.028 0.443 0.012 0.330 0.014 0.180 0.009 0.047 0.004 0.328 0.037 0.283 0.025 0.200 0.013 0.111 0.008 0.024 0.005 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.016 4.850 0.384 5.100 0.374 4.800 0.305 4.450 0.265 3.250 0.314 2.700 0.321 2.500 0.333 2.700 0.250 2.350 0.294 1.850 0.294 H 0.002 0.721 0.035 0.754 0.018 0.723 0.019 0.697 0.027 0.544 0.038 0.370 0.072 0.383 0.093 0.355 0.088 0.266 0.101 0.118 0.092 mean(sij) 0.163 0.013 0.119 0.007 0.091 0.006 0.059 0.003 0.024 0.002 0.104 0.028 0.060 0.013 0.041 0.005 0.021 0.004 0.008 0.003 eeoyoeAvnaea H ee 1487 Genes MHC at Advantage Heterozygote mean(hij) 0.209 0.025 0.168 0.010 0.104 0.010 0.065 0.006 0.013 0.003 0.017 0.033 0.008 0.013 0.005 0.011 0.003 0.005 0.002 0.003 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 1.2 0.027 10.000 0.779 12.300 0.923 13.550 0.810 14.500 0.823 12.250 0.548 8.550 0.482 10.600 0.731 11.350 0.656 10.750 0.764 7.900 0.602 H 0.0188 0.0045 0.861 0.012 0.891 0.009 0.903 0.006 0.910 0.007 0.899 0.005 0.839 0.011 0.876 0.007 0.884 0.007 0.878 0.008 0.819 0.021 mean(sij) 0.200 0.008 0.163 0.008 0.123 0.004 0.078 0.003 0.020 0.001 0.170 0.009 0.131 0.006 0.097 0.004 0.063 0.004 0.020 0.001 mean(hij) 0.612 0.029 0.495 0.016 0.344 0.012 0.192 0.009 0.053 0.004 0.389 0.024 0.308 0.008 0.212 0.009 0.122 0.006 0.025 0.004 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 1.209 7.150 0.537 8.100 0.650 8.650 0.433 7.800 0.579 5.600 0.521 3.700 0.351 4.350 0.498 3.650 0.384 3.300 0.405 2.500 0.415 H 0.0196 0.810 0.018 0.825 0.016 0.836 0.012 0.827 0.014 0.710 0.046 0.549 0.068 0.615 0.049 0.556 0.058 0.475 0.063 0.281 0.113 mean(sij) 0.143 0.010 0.112 0.008 0.079 0.005 0.045 0.002 0.019 0.002 0.100 0.019 0.068 0.009 0.048 0.009 0.028 0.005 0.012 0.005 mean(hij) 0.216 0.021 0.173 0.011 0.115 0.010 0.064 0.007 0.009 0.004 0.006 0.019 0.007 0.010 0.001 0.012 0.002 0.006 0.006 0.005 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 3.3 0.1984 14.600 1.009 18.100 1.255 21.950 1.010 24.950 0.859 24.650 1.104 12.700 1.055 15.700 0.965 17.000 1.272 17.600 0.989 14.050 1.243 H 0.1754 0.028 0.896 0.008 0.915 0.009 0.933 0.004 0.941 0.002 0.945 0.002 0.874 0.011 0.900 0.008 0.904 0.012 0.913 0.007 0.871 0.013 mean(sij) 0.179 0.010 0.146 0.006 0.114 0.005 0.069 0.002 0.012 0.000 0.164 0.010 0.125 0.007 0.093 0.005 0.054 0.002 0.015 0.001 mean(hij) 0.608 0.026 0.490 0.014 0.343 0.009 0.192 0.006 0.049 0.004 0.382 0.021 0.300 0.013 0.199 0.014 0.113 0.006 0.021 0.003 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 3.499 9.800 0.906 11.700 0.842 12.500 0.578 11.600 0.904 8.250 0.777 4.800 0.562 5.550 0.611 5.100 0.650 4.150 0.433 3.150 0.384 H 0.1667 0.849 0.015 0.873 0.010 0.877 0.007 0.850 0.014 0.771 0.031 0.625 0.046 0.679 0.074 0.634 0.055 0.560 0.055 0.288 0.101 mean(sij) 0.136 0.011 0.099 0.005 0.074 0.005 0.043 0.003 0.016 0.001 0.104 0.019 0.063 0.010 0.045 0.009 0.032 0.006 0.018 0.005 mean(hij) 0.231 0.019 0.183 0.011 0.116 0.007 0.053 0.006 0.007 0.003 0.017 0.023 0.008 0.015 0.001 0.012 0.007 0.006 0.014 0.005

5 Selected polymorphism statistics for simulations with mL ¼ 10 without genetic drift

g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.1246 0.0069 17.800 1.070 25.350 1.533 34.400 1.460 41.550 2.246 71.750 2.735 14.800 1.134 21.000 1.408 25.650 1.445 26.550 2.078 27.850 1.500 H 0.0211 0.002 0.908 0.007 0.935 0.004 0.952 0.003 0.957 0.004 0.973 0.001 0.891 0.009 0.920 0.005 0.935 0.004 0.932 0.007 0.924 0.006 mean(sij) 0.169 0.008 0.145 0.008 0.109 0.003 0.064 0.002 0.008 0.000 0.145 0.007 0.116 0.006 0.083 0.004 0.047 0.002 0.010 0.000 mean(hij) 0.692 0.023 0.519 0.012 0.365 0.009 0.194 0.008 0.044 0.002 0.447 0.019 0.330 0.010 0.232 0.007 0.121 0.007 0.025 0.002 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.163 12.400 1.123 16.000 1.198 18.900 1.279 18.000 1.865 14.100 1.189 5.600 0.731 6.250 0.680 7.350 0.891 6.400 1.141 4.000 0.636 H 0.0196 0.867 0.014 0.894 0.007 0.912 0.007 0.895 0.014 0.848 0.015 0.697 0.051 0.718 0.030 0.741 0.044 0.664 0.088 0.512 0.082 mean(sij) 0.119 0.007 0.090 0.004 0.061 0.003 0.035 0.002 0.009 0.001 0.054 0.004 0.040 0.003 0.026 0.002 0.015 0.001 0.004 0.000 mean(hij) 0.271 0.016 0.197 0.008 0.140 0.006 0.070 0.006 0.013 0.001 0.053 0.010 0.035 0.006 0.025 0.005 0.012 0.003 0.002 0.001 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 2.87 0.0787 24.100 1.595 30.700 1.423 42.900 2.156 58.250 3.577 120.500 5.287 20.000 1.571 25.850 1.598 32.000 1.886 36.500 2.902 33.100 2.660 H 0.1673 0.0118 0.930 0.007 0.944 0.003 0.957 0.003 0.965 0.002 0.977 0.001 0.916 0.009 0.929 0.005 0.942 0.004 0.943 0.006 0.928 0.008 mean(sij) 0.161 0.007 0.144 0.005 0.105 0.004 0.057 0.002 0.006 0.000 0.137 0.007 0.115 0.005 0.076 0.003 0.040 0.001 0.008 0.000 mean(hij) 0.691 0.021 0.506 0.010 0.340 0.007 0.173 0.008 0.035 0.002 0.446 0.018 0.322 0.008 0.215 0.006 0.106 0.007 0.019 0.002 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 3.039 16.500 1.375 20.300 1.156 23.650 1.395 22.750 2.471 16.750 2.025 7.350 1.038 7.450 0.823 8.100 1.024 6.200 1.353 4.250 0.751 H 0.1667 0.894 0.013 0.905 0.007 0.920 0.005 0.906 0.013 0.857 0.018 0.743 0.043 0.750 0.028 0.759 0.031 0.630 0.077 0.504 0.082 mean(sij) 0.112 0.006 0.088 0.004 0.056 0.002 0.030 0.002 0.007 0.000 0.051 0.004 0.037 0.002 0.024 0.002 0.014 0.001 0.003 0.001 mean(hij) 0.272 0.015 0.193 0.007 0.128 0.005 0.060 0.006 0.010 0.001 0.053 0.009 0.035 0.005 0.022 0.003 0.010 0.003 0.001 0.001 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 22.725 0.6568 28.600 2.028 40.000 1.564 49.850 2.703 71.550 4.115 232.600 36.877 24.450 2.107 32.300 1.659 36.850 2.521 42.750 3.394 38.450 3.290 H 0.6336 0.0231 0.939 0.006 0.953 0.002 0.961 0.003 0.969 0.002 0.979 0.001 0.928 0.008 0.943 0.003 0.947 0.005 0.949 0.004 0.921 0.009 mean(sij) 0.162 0.006 0.140 0.004 0.104 0.004 0.052 0.001 0.005 0.000 0.136 0.005 0.109 0.004 0.075 0.003 0.036 0.001 0.007 0.000 mean(hij) 0.678 0.015 0.501 0.010 0.320 0.009 0.162 0.006 0.027 0.002 0.436 0.010 0.323 0.009 0.202 0.008 0.098 0.005 0.014 0.002 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 23.567 20.450 1.894 25.350 1.321 27.350 1.828 27.100 2.375 17.000 2.046 9.200 0.981 10.100 0.887 8.950 1.291 7.550 1.235 3.900 0.942 H 0.6667 0.910 0.009 0.926 0.007 0.925 0.007 0.916 0.009 0.834 0.028 0.787 0.029 0.810 0.025 0.756 0.044 0.663 0.070 0.468 0.114 mean(sij) 0.108 0.004 0.081 0.003 0.054 0.003 0.027 0.001 0.006 0.001 0.047 0.003 0.032 0.002 0.022 0.002 0.013 0.001 0.002 0.000 mean(hij) 0.266 0.008 0.196 0.007 0.119 0.007 0.056 0.004 0.007 0.001 0.051 0.005 0.038 0.005 0.020 0.004 0.008 0.003 0.001 0.000

5 Selected polymorphism statistics for simulations with mL ¼ 10 with genetic drift

g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

3 Ne ¼ 10 nA 1.1246 0.0069 7.250 0.490 7.750 0.373 7.400 0.298 6.550 0.482 5.400 0.480 6.950 0.522 6.700 0.405 6.800 0.441 5.850 0.356 4.200 0.365 H 0.0211 0.002 0.834 0.009 0.846 0.010 0.839 0.007 0.815 0.013 0.756 0.018 0.819 0.014 0.820 0.009 0.813 0.013 0.788 0.013 0.664 0.032 mean(sij) 0.199 0.006 0.173 0.009 0.135 0.006 0.096 0.004 0.030 0.002 0.180 0.010 0.141 0.005 0.111 0.005 0.070 0.003 0.025 0.001 mean(hij) 0.746 0.024 0.571 0.023 0.398 0.016 0.234 0.008 0.066 0.006 0.461 0.019 0.361 0.022 0.256 0.010 0.145 0.006 0.038 0.003 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

3 3 Ne ¼ 10 Ne ¼ 10 nA 1.163 5.550 0.438 5.600 0.330 5.200 0.392 4.700 0.379 3.300 0.379 3.150 0.294 3.300 0.351 2.900 0.315 2.650 0.384 1.850 0.257 H 0.0196 0.770 0.019 0.777 0.015 0.741 0.027 0.727 0.020 0.518 0.077 0.539 0.048 0.506 0.088 0.483 0.065 0.382 0.081 0.070 0.074 mean(sij) 0.150 0.008 0.119 0.009 0.088 0.004 0.055 0.003 0.020 0.003 0.100 0.021 0.067 0.012 0.046 0.010 0.030 0.007 0.013 0.005 eeoyoeAvnaea H ee 1489 Genes MHC at Advantage Heterozygote mean(hij) 0.294 0.014 0.206 0.016 0.149 0.010 0.082 0.007 0.019 0.004 0.010 0.027 0.016 0.016 0.017 0.012 0.000 0.006 0.008 0.004 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 2.87 0.0787 12.650 0.756 14.350 0.574 16.350 0.624 16.550 0.522 14.650 0.820 10.400 0.797 12.350 0.935 12.750 0.974 12.750 0.695 9.750 0.815 H 0.1673 0.0118 0.892 0.008 0.911 0.003 0.921 0.004 0.922 0.004 0.910 0.004 0.870 0.010 0.886 0.012 0.897 0.007 0.892 0.009 0.852 0.016 mean(sij) 0.186 0.010 0.155 0.006 0.116 0.006 0.070 0.002 0.015 0.000 0.160 0.007 0.127 0.007 0.090 0.004 0.052 0.002 0.016 0.001 mean(hij) 0.703 0.023 0.539 0.013 0.371 0.012 0.202 0.010 0.055 0.004 0.446 0.017 0.335 0.019 0.238 0.011 0.123 0.008 0.030 0.003 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

4 4 Ne ¼ 10 Ne ¼ 10 nA 3.039 8.100 0.737 9.850 0.782 10.600 0.904 9.450 0.772 6.800 0.484 4.600 0.558 5.200 0.524 4.750 0.584 4.300 0.553 2.650 0.433 H 0.1667 0.824 0.012 0.855 0.012 0.865 0.016 0.856 0.011 0.757 0.020 0.654 0.039 0.701 0.035 0.642 0.054 0.574 0.077 0.264 0.114 mean(sij) 0.139 0.008 0.102 0.006 0.072 0.005 0.040 0.003 0.016 0.001 0.085 0.014 0.066 0.011 0.044 0.007 0.034 0.008 0.017 0.005 mean(hij) 0.258 0.022 0.195 0.011 0.132 0.011 0.074 0.005 0.012 0.002 0.017 0.017 0.015 0.013 0.006 0.010 0.005 0.009 0.011 0.005 g ¼ 0 g ¼ 0.2 m Neutral: computational 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 22.725 0.6568 19.550 1.159 25.000 1.821 29.350 1.572 34.800 1.236 42.700 1.689 17.050 1.020 21.300 1.216 24.300 1.609 24.250 1.706 22.500 1.338 H 0.6336 0.0231 0.914 0.006 0.930 0.005 0.940 0.003 0.949 0.003 0.956 0.002 0.893 0.010 0.914 0.007 0.922 0.007 0.923 0.005 0.884 0.010 mean(sij) 0.197 0.010 0.161 0.007 0.115 0.004 0.065 0.001 0.010 0.000 0.178 0.010 0.137 0.008 0.096 0.005 0.053 0.002 0.016 0.001 mean(hij) 0.623 0.020 0.492 0.011 0.329 0.009 0.188 0.004 0.044 0.003 0.370 0.023 0.293 0.018 0.193 0.012 0.107 0.004 0.017 0.002 g ¼ 0.4 g ¼ 0.8 m Neutral: analytic 10 30 50 70 90 10 30 50 70 90

5 5 Ne ¼ 10 Ne ¼ 10 nA 23.567 13.300 1.199 16.700 1.465 18.400 1.167 18.050 1.268 15.350 1.258 7.300 0.740 8.400 0.937 9.150 1.067 8.700 1.026 6.900 0.920 H 0.6667 0.870 0.012 0.882 0.012 0.894 0.009 0.873 0.011 0.786 0.048 0.677 0.036 0.690 0.038 0.702 0.044 0.594 0.092 0.291 0.100 mean(sij) 0.145 0.010 0.119 0.007 0.081 0.004 0.050 0.004 0.021 0.002 0.148 0.017 0.103 0.013 0.085 0.008 0.061 0.007 0.036 0.005 mean(hij) 0.229 0.014 0.153 0.013 0.105 0.007 0.045 0.006 0.000 0.003 0.067 0.019 0.040 0.014 0.041 0.010 0.039 0.008 0.031 0.006