IN a recent article (Iwasa and Pomiankowski 1999),

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1 Coyright 001 by the Genetics Society of America The Evolution of X-Linked Genomic Imrinting Yoh Iwasa* and Andrew Pomiankowski *Deartment of Biology, Kyushu University, Fukuoka , Jaan and Deartment of Biology, University College London, London NW1 HE, United Kingdom Manuscrit received March 9, 001 Acceted for ublication May 3, 001 ABSTRACT We develo a quantitative genetic model to investigate the evolution of X-imrinting. The model comares two forces that select for X-imrinting: genomic conflict caused by olygamy and sex-secific selection. Genomic conflict can only exlain small reductions in maternal X gene exression and cannot exlain silencing of the maternal X. In contrast, sex-secific selection can cause extreme differences in gene exression, in either direction (lowered maternal or aternal gene exression), even to the oint of gene silencing of either the maternal or aternal coy. These conclusions assume that the Y chromosome lacks genetic activity. The resence of an active Y homologue makes imrinting resemble the autosomal attern, with active aternal alleles (X- and Y-linked) and silenced maternal alleles. This outcome is likely to be restricted as Y-linked alleles are subject to the accumulation of deleterious mutations. Exerimental evidence concerning X-imrinting in mouse and human is interreted in the light of these redictions and is shown to be far more easily exlained by sex-secific selection. This observation indicates that the aternally derived X is imrinted and codes for a slower develomental rate and consequently smaller embryo size. As male embryos (X m Y) do not inherit the X, they show growth acceleration relative to female embryos (X m X ) from the same broods. The reverse attern is seen in humans. In this case the X-linked gene(s) subject to imrinting affect cognitive erformance. XO humans (like mice) are female and can be either X m OorX O (both suffer from Turner s syndrome; Skuse et al. 1997). The origin of the single X has no effect on hysical henotye or general IQ. However, X m O individuals lack social awareness, flexi- bility, and resonsiveness, and scored much lower in formal tests of social cognitive skills comared to X O individuals (Skuse et al. 1997). These observations are consistent with maternal imrinting of an X-linked gene for social atitude, robably through effects on early brain develoment (Skuse et al. 1997). When the same test was alied to age-matched normal children, X m X girls showed higher social skills than X m Y boys, the dif- ference being similar to that seen between X O and X m O females. Here we develo the verbal arguments of Iwasa and Pomiankowski (1999), using a quantitative genetic model for the evolution of X-linked imrinting. This model allows genomic imrinting to evolve as a continu- ous change in the level of gene exression (Mochizuki et al. 1996). As well as roviding a formal theoretical treatment, we aim to extend the analysis resented in the revious article. In articular, we exlicitly consider the conflict hyothesis (Haig and Graham 1991; Moore and Haig 1991; Hurst 1997) as another force creating atterns of X-linked imrinting. The conflict IN a recent article (Iwasa and Pomiankowski 1999), we roosed the novel hyothesis that X-linked imrinting has evolved to control sex-secific gene exression in early embryos. Unlike autosomes, X chromosomes are inherited in an asymmetrical fashion. The maternal X chromosomes are equally likely to be inherited by female or male offsring, whereas the aternal X is always assed to female offsring and never to male offsring. So imrinting of X-linked genes naturally results in sexually dimorhic gene exression. This hyothesis redicts that imrinting of X-linked genes is likely to evolve when selection favors different levels of embryonic gene exression in the two sexes. Early exression is redicted to be affected because circulating sex hormones are not available as a signal of sex until develoment is reasonably advanced (Iwasa and Pomiankowski 1999). Greater gene exression in males relative to females can be achieved by X im- rinting (silencing/reducing aternal X activity). In contrast, greater gene exression in females relative to males can be achieved by X m imrinting (silencing/ reducing maternal X activity). These redictions are consistent with the atterns of gene exressions inferred from the henotyes of XO genotyes in mice and humans (summary in Iwasa and Pomiankowski 1999). In the mouse, X O female embryos (10.5 days ost coitum) were found to be much smaller than similar age X m O and X m X female embryos (Thornhill and Burgoyne 1993; Burgoyne et al. 1995). Corresonding author: Yoh Iwasa, Deartment of Biology, Kyushu University, Fukuoka , Jaan. yiwasscb@mbox.nc.kyushu-u.ac.j Genetics 158: (August 001)

2 180 Y. Iwasa and A. Pomiankowski hyothesis rooses that aternally exressed alleles demand greater nutrient resources from the mother because they have lower relatedness among sibs than do maternally inherited alleles. The strength of this effect varies with the degree of olygamy. The conflict hyothesis was originally develoed to exlain atterns of autosomal imrinting, but it should aly equally to X-linked genes. In our model, we make a quantitative assessment of how X-linked imrinting is affected by sex-secific selection and conflict due to different degrees of relatedness among sibs. In our model we consider models where there is dosage comensation or where the imrinted X-linked gene escaes from dosage comensation, and we also analyze models in which an active Y-linked homologue of the imrinted X-linked gene is resent or absent. However, we do not directly model the evolution of dosage comensation. Nor do we model forces such as deleterious mutation ressure that are imortant in the evolution of Y-linked genes (Graves and Schmidt 199; Charlesworth 1996). The imortance of this is raised in the discussion. THE MODEL Figure 1. The transmission of X and Y chromosomes is asymmetric. While X m is inherited by both sexes of offsring, only females inherit X and only males inherit Y. Selection is calculated by the fitness functions (φ I, φ II, φ III, and ) associated with each attern of inheritance. Due to the asymmetric inheritance of the sex chromosomes (Iwasa and Pomiankowski 1999), there are different selective ressures on m,, and y. Selection on m has two comonents deendent on whether the off- sring is male or female, whereas selection on has only a single comonent as it is always inherited by a female. Likewise, selection on y has a single comonent as it is always inherited by a male. Selection occurs in both sexes, so we need to define sex-secific fitness functions (Figure 1). We calculate the evolutionary change in m and in each sex (see aendix a). For an X-linked gene ossessed by a fe- male in the current generation, we calculate the ex- ected number of coies in females in the following generation (i.e., her daughters) and the exected number of coies in males in the following generation (i.e., her sons). We call these the mother-to-daughter fitness (denote by φ I ) and the mother-to-son fitness (denote by φ II ), resectively. For an X-linked gene ossessed by a male in the current generation, we calculate the ex- ected number of coies in females in the following generation (i.e., his daughters), which is the father-to- daughter fitness (denoted by φ III ). There is no father- to-son fitness for X-linked genes as aternal X-linked genes are only assed on to daughters, never to sons. The father-to-son fitness alies to Y-linked genes (de- noted by ), which are assed exclusively through the male lineage. Evolutionary dynamics: We study the evolution of gene exression of an X-linked gene. The gene involved has embryonic exression that affects the suly of maternal resources. It is assumed to be subject to genomic imrinting and thus has two different levels of exression, deending on arental origin. We use a quantita- tive genetic model that was used reviously to analyze autosomal genomic imrinting (Mochizuki et al. 1996). The basic underlying assumtion is weak selection; that is, there is only a small change in fitness over the range of the trait (Iwasa et al. 1991). Unlike other formalism of quantitative genetics (e.g., Lande 1976), it does not require normality in the distribution of genetic values. The regulatory art of the gene is reresented by (, m) in which is the exression of the allele when inherited from the father and m is the exression of the allele when inherited from the mother. There is a corresonding coy of the gene on the Y chromosome. The exression of the Y coy is denoted by y. If the Y coy is inactive, y 0. A female embryo receives two X chromosomes, one from the egg ( 1, m 1 ) and the other from the serm (, m ). In female mammals, most X-linked genes undergo dosage comensation by random X inactivation (Graves and Schmidt 199). The maternal X is silenced in one-half of the cells, and the aternal X is silenced in the other one-half. Assuming random X inactivation, the gene exression in female offsring is z (m 1 )/. In contrast, a male embryo receives an X only from the egg ( 1, m 1 ). This X is active in all cells. In addition, the male receives a Y chromosome, so the gene exression in male embryos is z m 1 y.

3 Evolution of X-Imrinting 1803 Summing across the sexes (with a two-thirds female to one-third male weighting for X-linked genes), we have a simle result for the er generation change in the mean traits (under the weak selection assumtion), m 1 3 G m m, 1 3 G, y G y y, (1a) trait values (, m). a is the conversion coefficient from gene exression into resources. The second factor in Equation a, (1 s), is the fraction of female offsring. The third factor of 1 is the relatedness, indicating the robability of an X-linked allele in the mother being transmitted to her daughter. The final factor is the survivorshi of daughters that carry the focal allele (, m). The mother-to-son fitness is calculated in a similar way, in which G i is the genetic variation and i the selection gradient acting on trait i (i m,, y). Using the defini- tions of fitness above, the selection gradients are m m ln φ I m ln φ II, φ II Ns 1 W mal(m y), (3) where the number of offsring N is given by Equation b. The fraction of males is s, and their survivorshi is W mal (m y). ln φ III, y y ln. (1b) To define the other two fitness functions (φ III and ), we need to consider a third selective force. Females The details of these derivations are given in aendix a. mate with a variable number of males throughout their To model multile mating by females, we assume reroductive life. Here we consider the simle case in that a fraction g of females accet two males as mates which 1 g females mate with a single male, while g (olygamy). The two males are assumed to be unrelated females mate with two males, each having the same and each is assumed to contribute equally to the rogrobability of fathering offsring. First we note that eny of the female. The remaining 1 g females mate female olygamy does not affect the transmission of the with a single male (monogamy). We call g the female female s genes to the next generation. Hence neither olygamy rate. The model is not suosed to reflect φ I nor φ II are affected by g. In contrast, the fatherthe details of mammalian mating systems in the wild, to-daughter fitness is which are far more comlex. It is adoted for its simle reresentation of multile mating. φ III M 1 g 1 g N mono g 1 g N oly 1 (1 s)w fem m Fitness: To further secify the evolutionary dynamics,. we need to consider how selection is generated. The (4a) amount of resources allocated to an embryo is roor- M is the exected number of females mating with the tional to its gene exression, z. The survivorshi of an male. (1 g)/(1 g) is the fraction of matings with a embryo is taken to be an increasing function of gene monogamous female, and g/(1 g) is the fraction of exression and is different in male and female embryos matings with a olygamous female. N mono and N oly are W mal (z) and W fem (z). The mother has limited resources, the exected numbers of offsring roduced by monog- T, that can be used for reroduction. So, as the average amous and olygamous females, resectively, resource demand er embryo increases, the total number of embryos roduced declines. N mono T a These two forces are the main comonents of the (1 s)m s(m y), (4b) fitness functions. First consider the mother-to-daughter fitness φ I. To model the trade-off between gene exression and number of offsring roduced, we use a re- source division model (Mochizuki et al. 1996), N oly T a 1 s m m s(m y). (4c) Once again, N φ mono and N oly reflect the average gene I N(1 s) 1 W fem m. (a) exression of embryos, which varies with female olygamy. From the ersective of the focal aternal allele The first factor, N, is the exected number of offsring, (, m), if the female is olygamous, one-half of her offsring will be sired by another male. This reduces N T a m m m y (1 s)m s 4. the relatedness by 1, indicating the robability of an (b) The denominator of N is the average embryo gene ex- ression. This is determined by the sex ratio of offsring s, the fraction of male offsring. The focal allele (, m) is equally reresented in male and female offsring (following Mendelian inheritance). Its homologue is a random samle from the oulation, which has mean X-linked allele in the father being transmitted to his daughter if the female is olygamous. In a similar way, the male-to-son fitness is likewise affected by the degree of olygamy, M 1 g 1 g N mono g 1 g N oly 1 sw mal(m y), with (5a)

4 1804 Y. Iwasa and A. Pomiankowski N mono T a (1 s)m s(m y), (5b) N oly T a (1 s)m s m y y. (5c) EVOLUTIONARY EQUILIBRIUM Selection gradients: The selection gradients can now be calculated by substituting the fitness terms above Figure. Sex-secific survivorshi functions for male and female embryos are functions of gene exression. Equations into Equation 1. Setting the mean gene exression in for W mal (Z m ) and W fem (Z f ) are given in the text. In this examle, a female embryo to Z f (m )/ and that in a male the rate of increase in survivorshi and fitness asymtote are embryo to Z m m y, the selection gradient with re- higher for males (a m 1, a f 0., b m 1.8, b f 1). sect to is (1 s)(1 g/)/ (1 s)z f sz m ln W fem m. (6a) In a similar way, m The ratio of male to female gene exression is Z m Z f a m(1 g/) a f (1 g/4). (10) (1 s)/ This result nicely encasulates the two forces oerating (1 s)z f sz m m ln W fem m on genomic imrinting. First, it shows that the maleto-female ratio of gene exression decreases with female olygamy g. This is so because aternally inherited genes m ln W mal(m y), (6b) s(1 g/) (1 s)z f sz m y ln W mal(m y). (6c) tend to be resource demanding (Moore and Haig 1991), so female embryos are selected to have higher gene exression than males because only females inherit the aternal X. A second factor, sex-secific selec- y tion, is also imortant and can work in either direction. To calculate the terms on the right-hand side of Equaa m a f, this acts to increase the Z m /Z f ratio, whereas If there is selection for greater gene exression in males, tion 6, we need to secify the functional form of the fitness functions. For examle, the reverse occurs if a f a m. Gene silencing: The interaction between olygamy and sex-secific selection determines whether genomic im- W fem (Z f ) b f ex a f Z f and W mal(z m ) b m ex a m Z m. rinting causes greater gene exression from X or X m. (7) We can define the equilibrium ratio of aternal to maternal gene exression by substituting Z f (m )/ and The grahs of these functions have S-shaed curves Z m m into Equation 9, (Figure ). a f and a m give the rate of increase and b f and b m give the asymtotic values of the curves. Inactive Y coy: We first focus on the case in which the Y coy is inactive (i.e., y 0 and Z m m). At equilibrium and 0 and m 0, (1 s)(1 g/) a f, (1 s)z f sz m Z f 1 s (1 s)(1 g/) ((1 s)z f sz m ) a m. (8) Z m m m a f(4 g) a m (1 g/) a m (1 g/) (11) The two forces that affect imrinting can be examined by exclusion. The effect of olygamy can be seen by setting a f a m (no sex-secific selection), 4 g 1 g/. (1) 1 g/ Rearranging and assuming that the sex ratio is even (s 0.5), When females mate with only one male (g 0), aternal and maternal X gene exressions are equal. As the robability of olygamy g increases, so does the relative ex- Z f a f 1 g/ a m 1 g/4 a f 1 g/, ression of the aternal allele. This does not lead to silencing of the maternal coy. In the resent model, Z m the maximum rate of olygamy is g 1 (all females a m 1 g/4 a m 1 g/4 a f 1 g/. (9) mate with two males), which generates about twice as

5 Evolution of X-Imrinting 1805 large as m. This differs from autosomal gene imrinting, which leads to maternal silencing for any g 0(Mochizuki et al. 1996). The intuitive reason for this difference is that, if m 0, there is no gene exression in males. For most slowly changing selection functions, selection for some gene exression in the male embryo will revent maternal gene silencing. The effect of sex-secific selection can be investigated in a similar way by excluding the effect of olygamy. Making all matings monogamous (g 0), m 4a f a m a m. (13) In the absence of sex-secific selection (a m a f ), aternal and maternal X gene exressions are equal. If selec- tion on males is stronger than selection on females (a m a f ), maternal gene exression is greater than aternal gene exression. Paternal gene silencing is achieved if this selection difference is reasonably strong (a m 4a f ). At this equilibrium, male gene exression is constrained to be no more than twice female gene exression (as Z m m and Z f m/). If selection oerates more strongly on females (a f a m ), aternal gene exression evolves to be greater than maternal gene exression, but the rate of increase is lower than with stronger selection on males. However, even if a f a m, some weak gene exression is exected from the maternal coy. Maternal gene silencing occurs only when male fitness is indeendent of gene exression and a m 0. Active Y coy: We now allow evolution of y, the quanti- tative exression of the Y coy. The existence of an active homologue on the Y chromosome changes the evolutionary outcome, making it similar to that seen with autosomal imrinting. First consider the case in which g 0 and females are monogamous. Given the dynamics in Equation 1, equilibrium requires that the three selection differentials in Equation 6 must equal 0. Among these three, only two are indeendent. So for g 0, there is a line of equilibria in three-dimensional sace (, m, y, see aendix b). The two equations secifying Z f and Z m are the same as Equation 9. But now there are many combinations of ositive values of, m, and y that satisfy Z f (m )/ and Z m m y. The dynamics cause convergence of the oulation mean values to a oint on the line of equilibria, but the dynamics then are neutrally stable. This result holds even if there is sexsecific selection. If a m a f, this changes the location of the line of equilibrium in three-dimensional sace (see Equation B1). These results hold for female monogamy (g 0). If females have some ositive robability of acceting a second male (g 0), then the line of equilibria disaears. The only stable equilibrium occurs when the a- ternally inherited alleles are active ( 0, y 0) and the maternally inherited allele is silenced (m 0, see aendix b for roof). At this equilibrium, y 0, so substituting m 0 and s 0.5 (one-to-one sex ratio), Z f a f a f a m 1 g/ and Z m y a m a f a m 1 g/. (14) In the absence of sex-secific selection (a m a f ), both male and female embryos increase gene exression with the olygamy rate g. The increase is the same in both sexes because olygamy reduces the relatedness of X and Y-linked genes among sibs at an identical rate (unless the sex ratio is not 1:1). The single stable equilibrium with 0, m 0, and y 0 holds irresective of sex-secific selection. Both with a m a f and a m a f, the maternal X is silenced. This haens because evolves to fulfill selection on female exression and y evolves to fulfill selection on male exression. Sex-secific selection only changes the relative exression of these two genes, Z m Z f y a m a f. (15) This ratio is indeendent of g and deends entirely on the relative strength of selection on the two sexes. In many cases where there is an active Y-linked homo- logue, the X-linked genes in the female do not undergo dosage comensation by X inactivation (Disteche 1995). All the revious calculations remain the same excet that the fitness functions and selection gradients change to reflect the lack of X inactivation in females (see aendix c). This does not change the results in (14) and (15), excet that Z f rather than Z f /. Although the results for an active Y coy may look strange, they are equivalent to those found with autosomal imrinting (Moore and Haig 1991). An imrinted autosomal locus has exression levels m and when maternally or aternally inherited, resectively (Mochi- zuki et al. 1996). Under female monogamy, there is no genetic conflict and natural selection works only on the sum m, the exression level in females and males. The otimal exression, Z m, defines a line of equilibria in two-dimensional sace (, m). This line disaears when g 0. Polygamy causes a conflict be- tween aternal and maternal coies, resulting in the evolution of higher and lower m, ending with silencing of the maternally inherited allele (Mochizuki et al. 1996). DISCUSSION In this article we formalized the analysis of X chromo- some imrinting resented by Iwasa and Pomiankowski (1999). We used a quantitative genetic model to

6 1806 Y. Iwasa and A. Pomiankowski allow continuous change in the level of gene exression in females, this results in higher exression from m, the (Iwasa et al. 1991; Mochizuki et al. 1996). An alternative maternal coy, than from, the aternal coy (see Equamodeling strategy is to let imrinting evolve in an all- tion 13). This reversed attern of imrinting cannot or-nothing fashion using a major gene model (Ander- easily be exlained by the conflict hyothesis (Iwasa son and Sencer 1999). The modeling assumes that and Pomiankowski 1999). If the difference in sex-segene exression in the embryo affects the suly of cific selection is moderately large (a m 4a f ), the X resources received by the embryo from the mother. gene is silenced. The modeling allows us to lace a number of verbal When selection favors higher gene exression in feredictions on a more secure footing. It also ermits a males than in males, higher gene exression is redicted quantitative comarison of sex-secific selection and from than from m. The degree of imrinting reflects genomic conflict as causes of X-linked imrinting at- the difference in sex-secific selection. If selection is terns. Evolutionary outcomes differ deending on the considerably stronger on females, then the ratio of lack or resence of an active Y-linked coy, so we discuss to m can be very large. Ultimately, gene silencing of these in turn. m can occur, but only if selection favors no gene exres- Inactive Y coy: Most X-linked genes in human and sion in males. The difference is exression between mouse lack Y-linked homologues (Graves and Schmidt and m does not increase as quickly when selection favors 199). These genes are generally subject to X inactiva- higher exression in females (comared to selection tion, which standardizes dosage across the sexes (Graves favoring higher exression in males). This is a reflection and Schmidt 199). To reflect this, we first consider of the asymmetric inheritance of the X chromosomes. the evolution of X-linked imrinting when the gene Imrinting of X reduces gene exression in females involved lacks a Y-linked homologue and undergoes only, whereas imrinting of X m reduces gene exression random X inactivation. both in males and to a lesser extent in females. The conflict hyothesis redicts that genomic im- Active Y coy: The conclusions above assume that the rinting arises because of differential selection on ater- Y chromosome lacks genetic activity. This assumtion nal and maternal coies, which is generated by olygmust have been invalid rior to the degeneration of the amy (Haig and Graham 1991; Moore and Haig 1991). mammalian Y chromosome. It also remains invalid for a If a female mates with several males throughout her number of X-linked genes that retain Y-linked homoreroductive life, the average relatedness of aternally logues (Jegalian and Page 1998). With these limitations inherited genes among sibs will be less than that of in mind, we modeled the evolution of X-imrinting when maternally inherited genes. This logic alies equally a fully active Y-linked homologue also contributes to gene to X-linked genes as to autosomal genes. It redicts that, exression. under olygamy, selection will cause the evolution of When there is an active Y coy, the evolutionary outhigher, the gene exression from X (aternally inhercome of X-imrinting more closely resembles atterns ited X), than m, the gene exression from X m (materseen with autosome imrinting. If there is comlete nally inherited X). monogamy and no sex-secific selection, there are mul- With autosomal imrinting, even the smallest degree tile equilibria. Many combinations of, m, and y can of olygamy leads to silencing of the maternal coy, with gene exression only from the aternal coy satisfy the gene exression of males and females. For- (Mochizuki et al. 1996). However, silencing of maternal mally there is a line of equilibria in three-dimensional alleles is not an outcome with X-linkage (see Equation sace (, m, y). A similar set of multile equilibria are 1). Due to the asymmetric inheritance of the X chrobut limited to two dimensions (, m). seen with autosomal imrinting (Mochizuki et al. 1996) mosomes (Figure 1), silencing of X m leads to a comlete absence of gene exression in male offsring. This acts as If there is any degree of olygamy, the line of equilib- a check on the evolution of maternal silencing (m 0). rium breaks down to a single stable equilibrium. This In our model, the most extreme difference in gene occurs when the aternally inherited alleles are active exression generated by olygamy was about twice as ( 0, y 0) and the maternally inherited allele is large as m. Although the quantitative value of this result silenced (m 0). As the aternal X is inherited solely is contingent on our model of olygamy and selection, by daughters and the aternal Y solely by sons, these other models are likely to give similar outcomes. The two genes can evolve to indeendent states that satisfy general oint is that genomic conflict does not result selection on the two sexes of offsring. in extreme differences in gene exression between X m The single equilibrium with maternal gene silencing and X and cannot exlain X m silencing when quantitamerely also holds when there is sex-secific selection. This tive variation in gene exression is ossible. changes the exact equilibrium values of and This outcome is in contrast to that with sex-secific y. A similar adjustment needs to be made for X-linked differences in selection, which can cause extreme differ- genes that escae X inactivation. These tend to have ences in gene exression and even gene silencing. If Y-linked homologues. This will cause a doubling of the selection favors higher gene exression in males than aternal X gene exression (as this is no longer subject

7 Evolution of X-Imrinting 1807 to dosage comensation), but it does not alter the exis- (Thornhill and Burgoyne 1993; Burgoyne et al. tence or stability of the single equilibrium. 1995). Early in develoment, the aternal X is thought The results above assume that Y-linked genes evolve to be silenced, the maternal X remains active, and a Y under the same conditions as X-linked or autosomal effect is resent (m 0, 0, y 0). This attern genes. This is not likely to be the case as most Y-linked does not directly fit either hyothesis. The attern cannot genes are subject to the build u of deleterious mutations be exlained by the conflict hyothesis, which regenes because they do not undergo regular recombina- dicts greater aternal gene exression. However, the tion (Graves and Schmidt 199; Charlesworth 1996). attern is consistent with selection for greater gene ex- The analysis resented above relates to the secial condi- ression in males, a m a f, if we assume that the Y effect tion in which the oulation of Y-linked genes is not is a small fixed effect. If this is the case, the Y rovides subject to deleterious mutation. The effect of deleteri- insufficient exression for the male and so needs to be ous mutations was analyzed by Mochizuki et al. (1996) augmented by the maternal X. for autosomal imrinting. Their conclusion was that The few data available on X-imrinting aear to be deleterious mutation ressure acts to sto the evolution far more easily exlained by sex-secific selection than of gene silencing by imrinting, as monoallelic exres- by the conflict hyothesis. The data suggest that selection sion leads to severe fitness loss when the single exressed generated by olygamy for greater aternal gene gene carries an inactivating mutation. exression is easily outweighed by selection for sexual General discussion: As in our revious article (Iwasa dimorhism. However, our interretations remain tenand Pomiankowski 1999), we can use the results here tative until more detailed genetic evidence becomes to comare the ability of conflict and sex-secific selection available. to exlain atterns of X-linked genomic im- This work was suorted in art by a Grant-in-Aid from the Ministry rinting. Both these forces can otentially contribute of Education, Science, Sorts and Culture of Jaan (Y.I.), a CREST to X-imrinting. roject (Y.I.), and a Royal Society Fellowshi (A.P.). For the majority of X-linked genes there are no Y-linked homologues (Graves and Schmidt 199). In this case, the conflict hyothesis can exlain weak im- LITERATURE CITED rinting of X m ( m), but cannot exlain silencing Anderson, R. J. E., and H. G. Sencer, 1999 Poulation models of of X m (m 0), or the reverse attern of X imrinting genomic imrinting. I. Differential variability in the sexes and ( m). In contrast, selection for sex-secific gene ex- the analogy with genetic dominance. Genetics 153: ression can otentially exlain imrinting of X m, real., 000 Distinctive atterns of memory function in subgrous Bisho, D. V. M., E. Canning, K. Elgar, E. Morris, P. A. Jacobs et verse imrinting of X, and silencing of either allele. of females with Turner syndrome: evidence for imrinted loci When there is an active Y-linked coy, the conflict hychologia on the X-chromosome affecting neurodeveloment. Neurosyothesis 38: redicts silencing of X m (m 0), with male Burgoyne, P. S., A. R. Thornhill, S. K. Boudrean, S. M. Darling, gene exression controlled by the Y coy and female C. E. Bisho et al., 1995 The genetic basis of XX-XY difference exression controlled by the aternal X. resent before gonadal sex differentiation in the mouse. Philos. How do these redictions fare in the face of the avail- Trans. R. Soc. Lond. Ser B 350: Charlesworth, B. C., 1996 The evolution of chromosomal sex able data? X-imrinting has so far been detected in determination and dosage comensation. Curr. Biol. 6: human and mouse. Unfortunately the genes involved Disteche, C. M., 1995 Escae from X inactivation in human and have not been maed, so the interretation of data mouse. Trends Genet. 11: 17. Graves, J. A. M., and M. M. Schmidt, 199 Mammalian sex chromoremains tentative. In humans, X-imrinting is thought somes: design or accident? Curr. Oin. Genet. Dev. : to contribute to the develoment of social cognitive Haig, D., and C. Graham, 1991 Genomic imrinting and the skills and memory (Skuse et al. 1997; Bisho et al. 000). strange case of the insulin-like growth factor II recetor. Cell 64: The maternal X is thought to be silenced, the aternal Hurst, L. D., 1997 Evolutionary theories of genomic imrinting, X remains active, and no Y effect is resent (m 0, in Frontiers in Molecular Biology: Imrinting, edited by 0, y 0). This creates greater gene exression in W. Reik and A. Surani. IRL Press, Oxford. Iwasa, Y., and A. Pomiankowski, 1994 The evolution of mate referfemales, which is consistent with selection for greater ences for multile handicas. Evolution 48: female gene exression, a f a m (Iwasa and Pomian- Iwasa, Y., and A. Pomiankowski, 1999 Sex secific X chromosome kowski 1999; Skuse 1999). Maternal X silencing is not exression caused by genomic imrinting. J. Theor. Biol. 197: redicted by the conflict hyothesis. At best, art of the Iwasa, Y., S. Nee and A. Pomiankowski, 1991 The evolution of costly greater aternal X exression might be attributed to mate references. Part II. The handica rincile. Evolution 45: selection due to conflict. However, the gene(s) involved does not seem to be involved in fetal-maternal resource Jegalian, K., and D. C. Page, 1998 A roosed ath by which genes common to mammalian X and Y chromosomes evolve to become accrual; rather it aears to regulate differential growth X inactivated. Nature 394: of regions in the brain (Bisho et al. 000). So there Lande, R., 1976 Natural selection and random genetic drift in he- aears to be little room for conflict in this case. notyic evolution. Evolution 30: Mochizuki, A., Y. Takeda and Y. Iwasa, 1996 Evolution of genomic The second examle of X-imrinting affects early de- imrinting: Why are so few genes imrinted? Genetics 144: 183 velomental arrest and growth rates in the mouse 195.

8 1808 Y. Iwasa and A. Pomiankowski Moore, T., and D. Haig, 1991 Genomic imrinting in mammalian Combining these two equations and taking into account develoment: a arental genetic conflict. Trends Genet. 7: Skuse, D. H., 1999 Genomic imrinting of the X chromosome: a the attern of inheritance of the X chromosomes, novel mechanism for the evolution of sexual dimorhism. Curr. Oin. Pediatr. 9: t1 t1 Skuse, D. H., R. S. James, D. V. M. Bisho, B. Coin, P. Dalton et 3 3 al., 1997 Evidence from Turner s syndrome of an imrinted X-linked locus affecting cognitive function. Nature 387: G ln φ I G ln φ Thornhill, A. R., and P. S. Burgoyne, 1993 A aternally imrinted II G ln φ III. X chromosome retards the develoment of the early mouse embryo. Develoment 118: (A3) Communicating editor: C.-I Wu Under the weak selection assumtion, the difference in mean trait value of X chromosomes in females and in APPENDIX A males ( and ) is small; hence, We develo a quantitative genetic model originally t1 develoed to study sexual selection (Iwasa et al. 1991; Iwasa and Pomiankowski 1994) and more recently 1 3 G ln φ I G ln φ II G ln φ III. (A4a) alied to study autosomal imrinting (Mochizuki et al. 1996). The model assumes weak selection (small In a similar way, changes in fitness over the range of the trait), a constant variance-covariance matrix, and similar values of and m 1 3 G m m ln φ I G m m ln φ II G m in the two sexes. These assumtions will be violated m m ln φ III, (A4b) when there is strong selection, when selection leads to changes in the variance-covariance matrix, or when y G y ln. y (A4c) values of and m are significantly different in the two sexes. These extra factors will alter the evolutionary Now we note that the mother-to-daughter fitness φ I and trajectory but should not make major differences in the the mother-to-son fitness φ II are functions of m but indelocation of equilibria. They deserve to be studied further endent of. In contrast, the father-to-daughter fitness in major gene models (e.g., Anderson and Sencer φ III is indeendent of m. Hence we have Equation 1 in 1999). the text. Note, in addition, that we assume that the To calculate changes in the mean values, m, and y, genetic covariance between m and is much smaller we have to follow inheritance and selection through than the genetic variances G m and G. Although a nonthe maternal and aternal lineages. We introduced the following notation. For generation t, let ( zero genetic covariance will change the dynamics, it will t, m t ) be the average over all females, ( not affect the location or stability of equilibria. t, m t ) be the average over all males, and y t be the average of y in males. In addition, (* t, m* t ) is the average over all maternal X chromosomes transmitted to daughters and (* t, m* t )isthe APPENDIX B average over all aternal X chromosomes transmitted When there is an active Y-linked coy and no olygto daughters. amy (g 0), there is a line of equilibria. The three These averages determine the values of, m, and y in equations m 0, 0, and y 0 given in (6) are the next generation via four fitness functions. To illusnot indeendent. Given Z f (m )/ and Z m m trate this, we concentrate on change in (we can derive the same set of equations for m). The mean female X y as in (9), and setting g 0, the line of equilibria in the exression in the next generation is (, m, y) sace is t1 * * 1 G ln φ I G ln φ III (A1) This line collases when there is some degree of olygamy (g 0). To investigate the location and stability of the equilibria, we note that 0 holds if 0 at equilibrium. If instead 0 at equilibrium, 0 must hold. In a similar way, m 0 and m 0, or m 0 and m 0; likewise y 0 and y 0, or y 0 and y 0. To find which of these relationshis hold, we note from (6) that (derived as described in the Aendix of Iwasa et al. 1991). Equation A1 indicates that the change is equal to the roduct of additive genetic variance and the selec- tion gradient. The mean male X exression in the next generation is t1 G ln φ II. (A) m a f a f a m y, a f a m a f a m y. (B1)

9 Evolution of X-Imrinting 1809 y m (1 s)(g/4) 0. (B) (1 s)z f sz m Now we can consider ossible equilibria: 1. At the equilibrium 0, m 0, y 0, it must be the case that m y 0, which is inconsistent with (B). Hence there is no equilibrium of this tye.. At the equilibrium with 0, m 0, y 0, it must be the case that m y 0. (B) requires 0, which imlies that the equilibrium is unstable against increases in. 3. At the equilibrium with 0, m 0, y 0, it must be the case that m 0. (B) requires y 0, which imlies that this equilibrium is unstable against increases in y. However, this equilibrium is ossible if the exression of y is erfectly silenced by some additional mechanism, such as the accumulation of deleterious mutations (see discussion). 4. At the equilibrium with 0, m 0, y 0, it must be the case that y 0. (B) requires m 0, so this equilibrium is stable. Hence with female olygamy (g 0), we can conclude that the only stable equilibrium is 0, m 0, y 0. APPENDIX C When there is no random X inactivation, or the gene concerned is not subject to dosage comensation, the gene exression in female is Z f m, instead of Z f (m )/. All the calculations in the text remain the same, excet for the fitness functions, which change to reflect the lack of X inactivation, φ I N(1 s) 1 W fem(m ), φ II Ns 1 W mal(m y), φ III M 1 g 1 g N mono g 1 g N oly 1 (1 s)w fem(m ), M 1 g 1 g N mono g 1 g N oly 1 sw mal(m y), N T a m m m y (1 s)m s, N mono a[(1 s)(m ) s(m y)], T N oly T a 1 s (m ) s(m y), N mono a[(1 s)(m ) s(m y)], T N oly T a (1 s)(m ) s y y m, (C1) and the selection gradients are ln φ (1 s)(1 g/) III (1 s)z f sz m ln W fem(m ). m m ln φ I m ln φ II (1 s) (1 s)z f sz m m ln W fem(m ) m lnw mal(m y), y s(1 g/) ln y (1 s)z f sz m y ln W mal (m y). (C)