The foundations of the polygenic CDCV model of SZ

Early studies into the familiality of SZ proposed either single-gene recessive, single-gene dominant with incomplete penetrance or two-locus modes of inheritance (reviewed in O'Rourke et al. Reference O'Rourke, Gottesman, Suarez, Rice and Reich1982; Riley et al. Reference Riley, Asherson, McGuffin, Hirsch and and Weinberger2003). It is informative to reconsider why these models were rejected and replaced with a polygenic model. In many cases, the arguments presented rely on assumptions that seemed reasonable at the time, but that we now know do not hold.

Several observations have led to the proposal of a polygenic basis for SZ. First, there are few examples of pedigrees where SZ segregates in a clearly Mendelian manner with classical segregation ratios (Gregory, Reference Gregory1960; Gottesman & Shields, Reference Gottesman and Shields1967). The observed segregation ratios, averaged across the population, are not consistent with a single-locus, simple mode of Mendelian inheritance. A polygenic model was also presumed to be more consistent with the continuing high prevalence of the disorder, supposedly by reducing the visibility of each risk allele to negative selection. Several studies that analysed the inheritance of SZ from familial relative risk data (O'Rourke et al. Reference O'Rourke, Gottesman, Suarez, Rice and Reich1982; McGue et al. Reference McGue, Gottesman and Rao1985; Risch, Reference Risch1990 a) or by segregation analysis (Tsuang et al. Reference Tsuang, Bucher and Fleming1982; Risch & Baron, Reference Risch and Baron1984) also clearly rejected the hypothesis that all cases of SZ are caused by mutation at a single locus. However, they could not distinguish between (a) genetic (locus and/or allelic) heterogeneity, (b) oligogenic inheritance, with a single gene of major effect and a few modifying loci, or (c) polygenic inheritance. Arguments against Mendelian inheritance at one or a few loci were reinforced by the subsequent failure of linkage studies across multiple, unrelated families to generate consistent results. The reasonable alternative explanation for this inconsistency – that the disorder is highly heterogeneous – was dismissed for several reasons.

In an influential paper, Risch (Reference Risch1990 a) argued directly against heterogeneous Mendelian inheritance on the basis that, if that were the case, then distinct clinical presentations would be expected to segregate in different families: ‘if it is allelic heterogeneity, then all related individuals carrying the same allele should show a similar clinical picture’. In fact, we now know that the opposite holds; individual mutations can result in very different phenotypes in different people, and even in distinct clinical diagnoses (e.g. autism, bipolar disorder, epilepsy, SZ) (Table 1). Risch also argued that, if modes of inheritance were different between pedigrees, this would be obvious. However, because of the large decrease in fitness associated with SZ, large multiplex pedigrees are rare and, as penetrance is incomplete, deduction and comparison of modes of inheritance across pedigrees is extremely difficult. Nevertheless, there are now numerous examples of multiplex pedigrees with a better fit to either recessive or dominant inheritance (reviewed by Riley et al. Reference Riley, Asherson, McGuffin, Hirsch and and Weinberger2003). Finally, Risch suggested that the results from the linkage scans that had been conducted on SZ at that time were too inconsistent for heterogeneity to explain them; the lack of replication was taken as evidence instead that the findings were false positives. That a large number of loci might be mutable to cause SZ was thus dismissed as implausible, a priori.

Table 1. Mutations implicated in schizophrenia (SZ). Particular aberrations are included if they have been seen independently multiple times (assuming the possibility of broad phenotypic expression) or if they have strong supporting biological evidence. Only protein-coding genes are listed

ADHD, Attention deficit hyperactivity disorder; ANX, anxiety disorder; ASD, autism spectrum disorder; BD, bipolar disorder; E, epilepsy; ID, intellectual disability; MD, major depression; MR, mental retardation; OCD, obsessive–compulsive disorder; PD, Parkinson's disease; TS, Gilles de la Tourette's syndrome; VCFS, velocardiofacial syndrome.

¹ Knight et al. (Reference Knight, Pickard, Maclean, Malloy, Soares, McRae, Condie, White, Hawkins, McGhee, van Beck, Macintyre, Starr, Deary, Visscher, Porteous, Cannon, St Clair, Muir and Blackwood2009), ² Friedman et al. (Reference Friedman, Vrijenhoek, Markx, Janssen, van der Vliet, Faas, Knoers, Cahn, Kahn, Edelmann, Davis, Silverman, Brunner, van Kessel, Wijmenga, Ophoff and Veltman2008), ³ International Schizophrenia Consortium (2008), ⁴ Elia et al. (Reference Elia, Gai, Xie, Perin, Geiger, Glessner, D'Arcy, Deberardinis, Frackelton, Kim, Lantieri, Muganga, Wang, Takeda, Rappaport, Grant, Berrettini, Devoto, Shaikh, Hakonarson and White2009), ⁵ Bakkaloglu et al. (Reference Bakkaloglu, O'Roak, Louvi, Gupta, Abelson, Morgan, Chawarska, Klin, Ercan-Sencicek, Stillman, Tanriover, Abrahams, Duvall, Robbins, Geschwind, Biederer, Gunel, Lifton and State2008), ⁶ Verkerk et al. (Reference Verkerk, Mathews, Joosse, Eussen, Heutink and Oostra2003), ⁷ Millar et al. (Reference Millar, Wilson-Annan, Anderson, Christie, Taylor, Semple, Devon, Clair, Muir, Blackwood and Porteous2000), ⁸ Song et al. (Reference Song, Li, Feng, Heston, Scaringe and Sommer2008), ⁹ Chubb et al. (Reference Chubb, Bradshaw, Soares, Porteous and Millar2008), ¹⁰ Walsh et al. (Reference Walsh, McClellan, McCarthy, Addington, Pierce, Cooper, Nord, Kusenda, Malhotra, Bhandari, Stray, Rippey, Roccanova, Makarov, Lakshmi, Findling, Sikich, Stromberg, Merriman, Gogtay, Butler, Eckstrand, Noory, Gochman, Long, Chen, Davis, Baker, Eichler, Meltzer, Nelson, Singleton, Lee, Rapoport, King and Sebat2008), ¹¹ Pickard et al. (Reference Pickard, Malloy, Christoforou, Thomson, Evans, Morris, Hampson, Porteous, Blackwood and Muir2006), ¹² Pickard et al. (Reference Pickard, Malloy, Porteous, Blackwood and Muir2005), ¹³ Rujescu et al. (Reference Rujescu, Ingason, Cichon, Pietilainen, Barnes, Toulopoulou, Picchioni, Vassos, Ettinger, Bramon, Murray, Ruggeri, Tosato, Bonetto, Steinberg, Sigurdsson, Sigmundsson, Petursson, Gylfason, Olason, Hardarsson, Jonsdottir, Gustafsson, Fossdal, Giegling, Moller, Hartmann, Hoffmann, Crombie, Fraser, Walker, Lonnqvist, Suvisaari, Tuulio-Henriksson, Djurovic, Melle, Andreassen, Hansen, Werge, Kiemeney, Franke, Veltman, Buizer-Voskamp, Sabatti, Ophoff, Rietschel, Nothen, Stefansson, Peltonen, St Clair, Stefansson and Collier2009), ¹⁴ Kamiya et al. (Reference Kamiya, Tan, Kubo, Engelhard, Ishizuka, Kubo, Tsukita, Pulver, Nakajima, Cascella, Katsanis and Sawa2008), ¹⁵ Millar et al. (Reference Millar, Pickard, Mackie, James, Christie, Buchanan, Malloy, Chubb, Huston, Baillie, Thomson, Hill, Brandon, Rain, Camargo, Whiting, Houslay, Blackwood, Muir and Porteous2005), ¹⁶ Steinlechner et al. (Reference Steinlechner, Stahlberg, Volkel, Djarmati, Hagenah, Hiller, Hedrich, Konig, Klein and Lencer2007), ¹⁷ Funayama et al. (Reference Funayama, Li, Tsoi, Lam, Ohi, Yazawa, Uyama, Djaldetti, Melamed, Yoshino, Imamichi, Takashima, Nishioka, Sato, Tomiyama, Kubo, Mizuno and Hattori2008), ¹⁸ Cheng & Chen (Reference Cheng and Chen2007), ¹⁹ Verma et al. (Reference Verma, Chauhan, Saleem, Gandhi, Jain and Brahmachari2004), ²⁰ Need et al. (Reference Need, Ge, Weale, Maia, Feng, Heinzen, Shianna, Yoon, Kasperaviciute, Gennarelli, Strittmatter, Bonvicini, Rossi, Jayathilake, Cola, McEvoy, Keefe, Fisher, St Jean, Giegling, Hartmann, Moller, Ruppert, Fraser, Crombie, Middleton, St Clair, Roses, Muglia, Francks, Rujescu, Meltzer and Goldstein2009), ²¹ Xu et al. (Reference Xu, Roos, Levy, van Rensburg, Gogos and Karayiorgou2008), ²² Kirov et al. (Reference Kirov, Grozeva, Norton, Ivanov, Mantripragada, Holmans, Craddock, Owen and O'Donovan2009), ²³ Brunetti-Pierri et al. (Reference Brunetti-Pierri, Berg, Scaglia, Belmont, Bacino, Sahoo, Lalani, Graham, Lee, Shinawi, Shen, Kang, Pursley, Lotze, Kennedy, Lansky-Shafer, Weaver, Roeder, Grebe, Arnold, Hutchison, Reimschisel, Amato, Geragthy, Innis, Obersztyn, Nowakowska, Rosengren, Bader, Grange, Naqvi, Garnica, Bernes, Fong, Summers, Walters, Lupski, Stankiewicz, Cheung and Patel2008), ²⁴ Mefford et al. (Reference Mefford, Sharp, Baker, Itsara, Jiang, Buysse, Huang, Maloney, Crolla, Baralle, Collins, Mercer, Norga, de Ravel, Devriendt, Bongers, de Leeuw, Reardon, Gimelli, Bena, Hennekam, Male, Gaunt, Clayton-Smith, Simonic, Park, Mehta, Nik-Zainal, Woods, Firth, Parkin, Fichera, Reitano, Lo Giudice, Li, Casuga, Broomer, Conrad, Schwerzmann, Raber, Gallati, Striano, Coppola, Tolmie, Tobias, Lilley, Armengol, Spysschaert, Verloo, De Coene, Goossens, Mortier, Speleman, van Binsbergen, Nelen, Hochstenbach, Poot, Gallagher, Gill, McClellan, King, Regan, Skinner, Stevenson, Antonarakis, Chen, Estivill, Menten, Gimelli, Gribble, Schwartz, Sutcliffe, Walsh, Knight, Sebat, Romano, Schwartz, Veltman, de Vries, Vermeesch, Barber, Willatt, Tassabehji and Eichler2008), ²⁵ Kirov et al. (Reference Kirov, Gumus, Chen, Norton, Georgieva, Sari, O'Donovan, Erdogan, Owen, Ropers and Ullmann2008), ²⁶ Xu et al. (Reference Xu, Woodroffe, Rodriguez-Murillo, Roos, van Rensburg, Abecasis, Gogos and Karayiorgou2009), ²⁷ Vrijenhoek et al. (Reference Vrijenhoek, Buizer-Voskamp, van der Stelt, Strengman, Sabatti, Geurts van Kessel, Brunner, Ophoff and Veltman2008), ²⁸ Ballif et al. (Reference Ballif, Theisen, Coppinger, Gowans, Hersh, Madan-Khetarpal, Schmidt, Tervo, Escobar, Friedrich, McDonald, Campbell, Ming, Zackai, Bejjani and Shaffer2008), ²⁹ Pickard et al. (Reference Pickard, Hollox, Malloy, Porteous, Blackwood, Armour and Muir2004), ³⁰ Shi et al. (Reference Shi, He, Zhang, Tang, Zhang, Zhao, Zhang, Li, Xi, Fang, Zhao, Feng and He2008), ³¹ Tyson et al. (Reference Tyson, Harvard, Locker, Friedman, Langlois, Lewis, Van Allen, Somerville, Arbour, Clarke, McGilivray, Yong, Siegel-Bartel and Rajcan-Separovic2005), ³² Guilmatre et al. (Reference Guilmatre, Dubourg, Mosca, Legallic, Goldenberg, Drouin-Garraud, Layet, Rosier, Briault, Bonnet-Brilhault, Laumonnier, Odent, Le Vacon, Joly-Helas, David, Bendavid, Pinoit, Henry, Impallomeni, Germano, Tortorella, Di Rosa, Barthelemy, Andres, Faivre, Frebourg, Saugier Veber and Campion2009), ³³ Marshall et al. (Reference Marshall, Noor, Vincent, Lionel, Feuk, Skaug, Shago, Moessner, Pinto, Ren, Thiruvahindrapduram, Fiebig, Schreiber, Friedman, Ketelaars, Vos, Ficicioglu, Kirkpatrick, Nicolson, Sloman, Summers, Gibbons, Teebi, Chitayat, Weksberg, Thompson, Vardy, Crosbie, Luscombe, Baatjes, Zwaigenbaum, Roberts, Fernandez, Szatmari and Scherer2008), ³⁴ Park et al. Reference Park, Moeschler, Berg and Wurster-Hill1991), ³⁵ Glessner et al. (Reference Glessner, Wang, Cai, Korvatska, Kim, Wood, Zhang, Estes, Brune, Bradfield, Imielinski, Frackelton, Reichert, Crawford, Munson, Sleiman, Chiavacci, Annaiah, Thomas, Hou, Glaberson, Flory, Otieno, Garris, Soorya, Klei, Piven, Meyer, Anagnostou, Sakurai, Game, Rudd, Zurawiecki, McDougle, Davis, Miller, Posey, Michaels, Kolevzon, Silverman, Bernier, Levy, Schultz, Dawson, Owley, McMahon, Wassink, Sweeney, Nurnberger, Coon, Sutcliffe, Minshew, Grant, Bucan, Cook, Buxbaum, Devlin, Schellenberg and Hakonarson2009), ³⁶ Stefansson et al. (Reference Stefansson, Rujescu, Cichon, Pietilainen, Ingason, Steinberg, Fossdal, Sigurdsson, Sigmundsson, Buizer-Voskamp, Hansen, Jakobsen, Muglia, Francks, Matthews, Gylfason, Halldorsson, Gudbjartsson, Thorgeirsson, Sigurdsson, Jonasdottir, Bjornsson, Mattiasdottir, Blondal, Haraldsson, Magnusdottir, Giegling, Moller, Hartmann, Shianna, Ge, Need, Crombie, Fraser, Walker, Lonnqvist, Suvisaari, Tuulio-Henriksson, Paunio, Toulopoulou, Bramon, Di Forti, Murray, Ruggeri, Vassos, Tosato, Walshe, Li, Vasilescu, Muhleisen, Wang, Ullum, Djurovic, Melle, Olesen, Kiemeney, Franke, Sabatti, Freimer, Gulcher, Thorsteinsdottir, Kong, Andreassen, Ophoff, Georgi, Rietschel, Werge, Petursson, Goldstein, Nothen, Peltonen, Collier, St Clair and Stefansson2008), ³⁷ Bucan et al. (Reference Bucan, Abrahams, Wang, Glessner, Herman, Sonnenblick, Alvarez Retuerto, Imielinski, Hadley, Bradfield, Kim, Gidaya, Lindquist, Hutman, Sigman, Kustanovich, Lajonchere, Singleton, Kim, Wassink, McMahon, Owley, Sweeney, Coon, Nurnberger, Li, Cantor, Minshew, Sutcliffe, Cook, Dawson, Buxbaum, Grant, Schellenberg, Geschwind and Hakonarson2009), ³⁸ Rodriguez-Santiago et al. (Reference Rodriguez-Santiago, Brunet, Sobrino, Serra-Juhe, Flores, Armengol, Vilella, Gabau, Guitart, Guillamat, Martorell, Valero, Gutierrez-Zotes, Labad, Carracedo, Estivill and Perez-Jurado2009), ³⁹ van Bon et al. (Reference van Bon, Mefford, Menten, Koolen, Sharp, Nillesen, Innis, de Ravel, Mercer, Fichera, Stewart, Connell, Ounap, Lachlan, Castle, Van der Aa, van Ravenswaaij, Nobrega, Serra-Juhe, Simonic, de Leeuw, Pfundt, Bongers, Baker, Finnemore, Huang, Maloney, Crolla, van Kalmthout, Elia, Vandeweyer, Fryns, Janssens, Foulds, Reitano, Smith, Parkel, Loeys, Woods, Oostra, Speleman, Pereira, Kurg, Willatt, Knight, Vermeesch, Romano, Barber, Mortier, Perez-Jurado, Kooy, Brunner, Eichler, Kleefstra and de Vries2009), ⁴⁰ Miller et al. (Reference Miller, Shen, Weiss, Korn, Anselm, Bridgemohan, Cox, Dickinson, Gentile, Harris, Hegde, Hundley, Khwaja, Kothare, Luedke, Nasir, Poduri, Prasad, Raffalli, Reinhard, Smith, Sobeih, Soul, Stoler, Takeoka, Tan, Thakuria, Wolff, Yusupov, Gusella, Daly and Wu2009), ⁴¹ Weiss et al. (Reference Weiss, Shen, Korn, Arking, Miller, Fossdal, Saemundsen, Stefansson, Ferreira, Green, Platt, Ruderfer, Walsh, Altshuler, Chakravarti, Tanzi, Stefansson, Santangelo, Gusella, Sklar, Wu and Daly2008), ⁴² Mefford et al. (Reference Mefford, Cooper, Zerr, Smith, Baker, Shafer, Thorland, Skinner, Schwartz, Nickerson and Eichler2009), ⁴³ Hannes et al. (Reference Hannes, Sharp, Mefford, de Ravel, Ruivenkamp, Breuning, Fryns, Devriendt, Van Buggenhout, Vogels, Stewart, Hennekam, Cooper, Regan, Knight, Eichler and Vermeesch2009).

A crucial assumption in that line of reasoning was that rates of mutation are far too low to continuously replenish highly penetrant alleles, which would be expected to be rapidly selected against in the population (Gottesman & Shields, Reference Gottesman and Shields1967). That new mutations can be ignored is explicitly assumed in studies that have attempted to deduce the mode of inheritance from data on familial relative risks (O'Rourke et al. Reference O'Rourke, Gottesman, Suarez, Rice and Reich1982; McGue et al. Reference McGue, Gottesman and Rao1985; Risch, Reference Risch1990 a). In fact, we now know that the de novo mutation rate is much higher than previously expected (Crow, Reference Crow2000). Whole-genome sequencing has revealed a remarkable plethora of rare and private mutations (Ng et al. Reference Ng, Levy, Huang, Stockwell, Walenz, Li, Axelrod, Busam, Strausberg and Venter2008; Wheeler et al. Reference Wheeler, Srinivasan, Egholm, Shen, Chen, McGuire, He, Chen, Makhijani, Roth, Gomes, Tartaro, Niazi, Turcotte, Irzyk, Lupski, Chinault, Song, Liu, Yuan, Nazareth, Qin, Muzny, Margulies, Weinstock, Gibbs and Rothberg2008; Frazer et al. Reference Frazer, Murray, Schork and Topol2009) not detected by the HapMap project. In addition, copy number variants (CNVs) occur at a previously unrecognized and appreciable frequency; lower than point mutations, but affecting far more bases (Sebat et al. Reference Sebat, Lakshmi, Troge, Alexander, Young, Lundin, Maner, Massa, Walker, Chi, Navin, Lucito, Healy, Hicks, Ye, Reiner, Gilliam, Trask, Patterson, Zetterberg and Wigler2004; Lupski, Reference Lupski2007). De novo mutations in human sperm accumulate markedly with age (Crow, Reference Crow2000) and numerous studies have shown a consistent link between increasing paternal age and risk of SZ in offspring (Malaspina et al. Reference Malaspina, Harlap, Fennig, Heiman, Nahon, Feldman and Susser2001; Wohl & Gorwood, Reference Wohl and Gorwood2007). New mutations may thus explain a significant fraction of sporadic SZ cases.

The most commonly cited evidence for a polygenic model of SZ is that the risk to relatives decreases by more than a factor of two with degree of relatedness (Gottesman & Shields, Reference Gottesman and Shields1967; Risch, Reference Risch1990 b). A monotonic decrease in risk of a factor of two is expected if all cases follow a single-gene dominant mode of inheritance (even if different genes are involved in different families, and regardless of penetrance). It has been argued that this expected relationship is independent of the mode of inheritance (Risch, Reference Risch1990 b). In fact, under a standard recessive model, for any given mutation, risk to relatives decreases much more sharply and declines rapidly to zero beyond first-degree relatives if the risk allele is rare. If an appreciable proportion of cases are caused by de novo mutation, this will also dramatically reduce the familial relative risk rates. Observed familial risk rates are in fact consistent with expectation from a heterogeneous model, if varying proportions of SZ cases fall under de novo, dominant or recessive modes of inheritance (Table 2).

Table 2. Familial recurrence risks with heterogeneous modes of Mendelian inheritance. Expected recurrence risks for various family members under a hypothetical equal distribution of cases into three different modes of inheritance: de novo, dominant and recessive

DZ, Dizygotic; FS, full sibling.

Average penetrance of 50% is assumed, based on monozygotic (MZ) twin concordance. A greater than twofold reduction in risk with increasing degrees of relatedness can readily be generated by such a distribution. This is not meant to suggest that these particular figures are correct, but rather the opposite, that frequencies in relatives cannot be used to disprove heterogeneous Mendelian inheritance. As originally pointed out by James (Reference James1971): there is ‘an infinite number of parameter sets … which lead to the same frequencies in relatives’.

Thus, despite the commonly held view to the contrary, there are no valid theoretical arguments to reject a Mendelian model of inheritance of SZ, with locus and/or allelic heterogeneity and variable penetrance, that may or may not include a role for modifying alleles. As discussed later, the weight of the empirical evidence also favours such a rare variants model.

Empirical data on the influence of common variants

Advances in human genomics, particularly the HapMap project and associated array-based methods for low-cost, high-throughput genotyping, offered the hope that common variants contributing a modest increase in risk could be detected by GWAS (Risch & Merikangas, Reference Risch and Merikangas1996; Reich & Lander, Reference Reich and Lander2001). Several such studies have now been published (Mah et al. Reference Mah, Nelson, Delisi, Reneland, Markward, James, Nyholt, Hayward, Handoko, Mowry, Kammerer and Braun2006; O'Donovan et al. Reference O'Donovan, Craddock, Norton, Williams, Peirce, Moskvina, Nikolov, Hamshere, Carroll, Georgieva, Dwyer, Holmans, Marchini, Spencer, Howie, Leung, Hartmann, Moller, Morris, Shi, Feng, Hoffmann, Propping, Vasilescu, Maier, Rietschel, Zammit, Schumacher, Quinn, Schulze, Williams, Giegling, Iwata, Ikeda, Darvasi, Shifman, He, Duan, Sanders, Levinson, Gejman, Cichon, Nothen, Gill, Corvin, Rujescu, Kirov, Owen, Buccola, Mowry, Freedman, Amin, Black, Silverman, Byerley and Cloninger2008; Need et al. Reference Need, Ge, Weale, Maia, Feng, Heinzen, Shianna, Yoon, Kasperaviciute, Gennarelli, Strittmatter, Bonvicini, Rossi, Jayathilake, Cola, McEvoy, Keefe, Fisher, St Jean, Giegling, Hartmann, Moller, Ruppert, Fraser, Crombie, Middleton, St Clair, Roses, Muglia, Francks, Rujescu, Meltzer and Goldstein2009), including recent ones with very large sample sizes, across which data could be pooled for meta-analysis (Purcell et al. Reference Purcell, Wray, Stone, Visscher, O'Donovan, Sullivan and Sklar2009; Shi et al. Reference Shi, Levinson, Duan, Sanders, Zheng, Pe'er, Dudbridge, Holmans, Whittemore, Mowry, Olincy, Amin, Cloninger, Silverman, Buccola, Byerley, Black, Crowe, Oksenberg, Mirel, Kendler, Freedman and Gejman2009; Stefansson et al. Reference Stefansson, Ophoff, Steinberg, Andreassen, Cichon, Rujescu, Werge, Pietilainen, Mors, Mortensen, Sigurdsson, Gustafsson, Nyegaard, Tuulio-Henriksson, Ingason, Hansen, Suvisaari, Lonnqvist, Paunio, Borglum, Hartmann, Fink-Jensen, Nordentoft, Hougaard, Norgaard-Pedersen, Bottcher, Olesen, Breuer, Moller, Giegling, Rasmussen, Timm, Mattheisen, Bitter, Rethelyi, Magnusdottir, Sigmundsson, Olason, Masson, Gulcher, Haraldsson, Fossdal, Thorgeirsson, Thorsteinsdottir, Ruggeri, Tosato, Franke, Strengman, Kiemeney, Melle, Djurovic, Abramova, Kaleda, Sanjuan, de Frutos, Bramon, Vassos, Fraser, Ettinger, Picchioni, Walker, Toulopoulou, Need, Ge, Yoon, Shianna, Freimer, Cantor, Murray, Kong, Golimbet, Carracedo, Arango, Costas, Jonsson, Terenius, Agartz, Petursson, Nothen, Rietschel, Matthews, Muglia, Peltonen, St Clair, Goldstein, Stefansson and Collier2009). Across these studies, only a few loci showed genome-wide significant association with increased risk, each with very small effect sizes [odds ratio (OR) ~1.1–1.2]. With the exception of the long-established SZ association with the human leucocyte antigen (HLA) region, there was little evidence for concordance of ‘top-ranked’ associations between the three studies. Given the large sample sizes in each study, the uncontestable primary conclusion is that the predicated large number of common risk variants of even modest effect size do not exist.

To assess more generally the possibility of a polygenic influence on risk, the authors of one of these studies (Purcell et al. Reference Purcell, Wray, Stone, Visscher, O'Donovan, Sullivan and Sklar2009) derived an aggregate score from the association results of the top 10–50% of over 74 000 single-nucleotide polymorphisms (SNPs). This score could predict about 3% of the variance in risk of SZ in a target group. At face value, these data indicate that 97% of the observed variance in risk is not due to polygenic common variants. The authors argue, however, that the variants that are having a real effect are being drowned out by the noise of the majority of false positives and use simulations to attempt to estimate the ‘true variance’ that would be explained if only we knew which SNPs to look at. These simulations are, however, based explicitly on the liability-threshold model, which, we argue below, has no biological validity. Moreover, despite the claim of dramatic convergence, the resultant seven models (out of 560 tested) give wildly different estimates of the total true variance explained (from 34% to 98%) and the number of SNPs contributing (from 6% to 100%). By default, the necessary and striking conclusion from this study is thus that not common, lowly penetrant, but rare, highly penetrant variants explain at least two-thirds and possibly as much as 97% of the phenotypic variance across the population. This conclusion has sound empirical support.

Empirical support for the rare variants model

The most compelling evidence for rare variants is that many mutations have now been shown to segregate with SZ and are thus highly likely to be causal (McClellan et al. Reference McClellan, Susser and King2007; Sebat et al. Reference Sebat, Levy and McCarthy2009). These include single-gene mutations in addition to CNVs or other cytogenetic abnormalities (Table 1). Typically, such mutations show high, but incomplete, penetrance for SZ and may lead to other psychiatric disorders such as bipolar disorder, major depression, autism or attention deficit hyperactivity disorder, and also to epilepsy and mental retardation (Table 1). These findings are consistent with studies of increased co-morbidity of autism, bipolar disorder and epilepsy within families of schizophrenics (Cardno et al. Reference Cardno, Rijsdijk, Sham, Murray and McGuffin2002; Qin et al. Reference Qin, Xu, Laursen, Vestergaard and Mortensen2005; Lichtenstein et al. Reference Lichtenstein, Yip, Bjork, Pawitan, Cannon, Sullivan and Hultman2009; Steinhausen et al. Reference Steinhausen, Foldager, Perto and Munk-Jorgensen2009) and provide additional evidence for an overlapping aetiology of these disorders.

It is important to note also several families where the appearance of a psychiatric diagnosis was not restricted to those members carrying the putative causative allele (Guilmatre et al. Reference Guilmatre, Dubourg, Mosca, Legallic, Goldenberg, Drouin-Garraud, Layet, Rosier, Briault, Bonnet-Brilhault, Laumonnier, Odent, Le Vacon, Joly-Helas, David, Bendavid, Pinoit, Henry, Impallomeni, Germano, Tortorella, Di Rosa, Barthelemy, Andres, Faivre, Frebourg, Saugier Veber and Campion2009; Xu et al. Reference Xu, Woodroffe, Rodriguez-Murillo, Roos, van Rensburg, Abecasis, Gogos and Karayiorgou2009). This apparent violation of the principle of causality could be explained by intra-familial heterogeneity in some families, where more than one highly penetrant mutation is segregating. Such a situation may be more common than expected because of assortative mating (Merikangas, Reference Merikangas1982) and a high de novo mutation rate.

Thus, mutations in many genes affecting the development or function of the nervous system may lead to the same clinical phenotype, whereas mutations in the same gene can lead to different phenotypes in different individuals (Sebat et al. Reference Sebat, Levy and McCarthy2009). With this background, it is not surprising that traditional linkage studies using single diagnostic categories or combining multiple families segregating different mutations have had few successes in identifying such mutations. This contrasts with the remarkable return, by current proportion of effort and investment, from single family and single case studies.

At the moment, such Mendelian cases or specific CNVs constitute a small, but growing, fraction of SZ cases. There is every reason to think, however, that these represent only the tip of the iceberg and that CNV analyses with better genome coverage and deep resequencing or whole-genome sequencing will turn up many more such cases. For example, sequencing the exons of Disrupted-in-Schizophrenia 1 (DISC1) identified five ultra-rare missense mutations in six out of 288 unrelated cases of SZ (2% overall), which were not found in 10 000 control chromosomes (Song et al. Reference Song, Li, Feng, Heston, Scaringe and Sommer2008). Bioinformatic (Chubb et al. Reference Chubb, Bradshaw, Soares, Porteous and Millar2008) and biological analyses (D. Porteous, unpublished data) suggest that these rare variants alter DISC1 function. If a conservative 2% of cases can be explained by highly penetrant mutations in this single gene, and this case is not exceptional, then single mutations could clearly numerically account for all cases of SZ. Importantly, many of the implicated genes have biologically plausible roles in neural development (Guilmatre et al. Reference Guilmatre, Dubourg, Mosca, Legallic, Goldenberg, Drouin-Garraud, Layet, Rosier, Briault, Bonnet-Brilhault, Laumonnier, Odent, Le Vacon, Joly-Helas, David, Bendavid, Pinoit, Henry, Impallomeni, Germano, Tortorella, Di Rosa, Barthelemy, Andres, Faivre, Frebourg, Saugier Veber and Campion2009; Raychaudhuri et al. Reference Raychaudhuri, Plenge, Rossin, Ng, Purcell, Sklar, Scolnick, Xavier, Altshuler and Daly2009; Sebat et al. Reference Sebat, Levy and McCarthy2009), and when mutated in mice model aspects of SZ with good construct, face and predictive validity (Waddington et al. Reference Waddington, Corvin, Donohoe, O'Tuathaigh, Mitchell and Gill2007; Carpenter & Koenig, Reference Carpenter and Koenig2008; Porteous, Reference Porteous2008). The hypothesis that they are causative, although obviously requiring case-by-case confirmation, is thus highly parsimonious and well supported by the evidence to date.

Thus, there is now very strong evidence for a major contribution of single mutations of high penetrance to the genetic architecture of SZ. This role has been incorporated into mixed models that either apportion cases to those caused by single mutations versus polygenic influences (Psychiatric GWAS Consortium Steering Committee, 2009) or presume an interaction between these factors in individuals (Frazer et al. Reference Frazer, Murray, Schork and Topol2009).

Mixed models, mutations and modifiers

On the reasonable assumption that the rare variants already identified represent only a fraction of those causing disease, and if the model of Mendelian inheritance with genetic heterogeneity is broadly consistent with the distribution of familial risks across the population, is there any reason to invoke additional factors? Analyses of GWAS data do suggest some contribution from common alleles to phenotypic variance across the population. In addition, many rare variants show incomplete penetrance and variable phenotypic expressivity that could be partly explained by an interaction with other genetic factors. These and other considerations have led to the emergence of mixed models for the genetic architecture of SZ (Fig. 1). One such model apportions cases of SZ across the population to those caused by single mutations versus those caused by polygenic effects. A second model proposes that the phenotypic expression of single mutations of high penetrance will be modified by genetic background; that is, there is an epistatic interaction, within each individual, between disease-causing and disease-modifying variants. Under this model, the ‘causal’ variant may be necessary, but not always sufficient, to generate the phenotype.

Fig. 1. Recent evolution of genetic models for schizophrenia. See text for details.

Fig. 2. A framework for the complex actiology of schizophrenia. Rare mutations in many different genes, modified by genetic background, will generate risk genotypes. Non-genetic factors will influence the trajectory of neurodevelopment and contribute to phenotypic divergence. Primary defects may trigger reactive mechanisms or have cascading effects on subsequent experience-dependent development. Phenotypic convergence may arise through overlapping primary defects or common secondary pathways. All these processes, possibly intersecting with ongoing maturation and/or stress, will ultimately result in a varied spectrum of intermediate phenotypes or symptoms in different individuals and thus in different clinical diagnoses, one category of which is schizophrenia.

We argue here that the second model is more parsimonious, more biologically plausible and has greater explanatory power. If we know that single mutations can lead to this phenotype, there is no obvious reason to invoke what is essentially a novel and highly speculative genetic mechanism to explain the fraction of cases where a mutation of major influence has not yet been identified. It has been proposed that a cumulative polygenic effect could be manifest as a distinct phenotype under a liability-threshold model (Gottesman & Shields, Reference Gottesman and Shields1967). Although this concept has been described mathematically for decades (Dempster & Lerner, Reference Dempster and Lerner1950), it remains essentially metaphorical.

This model is founded on the notion of an underlying ‘liability’ to the disorder, which is normally distributed in the population (reflecting the distribution of many common alleles), but that the risk of developing the disease depends upon exceeding some ‘threshold’ of liability. This model posits a sharp increase in risk between someone with n liability alleles on one side of the threshold and someone with n+1 liability alleles on the other (e.g. Kendler & Kidd, Reference Kendler and Kidd1986). Why this should be the case is not clear. Nor is there any empirical evidence to suggest that this mechanism ever applies, unless of course n is a very small number and segregation is essentially Mendelian.

The appeal of this model seems to arise from a conflation between a threshold event, in a developmental sense, which can explain incomplete penetrance of an all-or-none phenotype, such as cleft palate, and a threshold of cumulative genetic burden. In cleft palate, the threshold explains the bimodal phenotype distribution in people with the same underlying liability (even MZ twins). Whether or not the phenotype emerges depends on chance or other non-genetic factors, including epigenetic cascades or environmental triggers. A similar mechanism might very well be at play in the emergence of SZ (Mitchell, Reference Mitchell2007) (Fig. 2). However, this mechanism does not relate in any way to the difference in the chance of the event happening in people with different genotypes, nor is there any evidence for a sudden change from very low to very high risk at some point along a genetic continuum.

In fact, biological systems are generally highly buffered and quite robust to the cumulative effects of weak mutations (Kitano, Reference Kitano2004). Most genetic systems incorporate substantial levels of noise, as a design feature, not a ‘bug’ (Kerszberg, Reference Kerszberg2004). Intrinsic variation in the amounts or activities of individual components serves to buffer the effects of extrinsic perturbations, and also has the effect of allowing the system to absorb small changes in gene expression of many individual components. These properties hold for both metabolic (Kacser & Burns, Reference Kacser and Burns1981) and developmental (Waddington, Reference Waddington1959; Siegal & Bergman, Reference Siegal and Bergman2002) systems.

Several observations have been put forward as supporting a multifactorial threshold model in the case of SZ (Gottesman & Shields, Reference Gottesman and Shields1967). These include: (i) increasing risk with increasing familial loading (number of affected relatives); (ii) increasing risk to siblings with the severity of the disorder in the affected proband; and (iii) increased risk with bilineal inheritance (where both parents are affected). In fact, all of these observations are consistent with a heterogeneous Mendelian mode of inheritance. If some alleles have higher penetrance than others, then some pedigrees will show more affecteds than others and this will correlate with statistical risk to individual members. Similarly, if more highly penetrant alleles also have higher expressivity (and there is no reason to expect that they would not), then individual risk would also be correlated with severity in relatives. Finally, if both parents are affected due to independent risk alleles of modest to high penetrance, then their offspring will obviously be at much higher risk, especially if there are also epistatic interactions between the two alleles (Gottesman et al. Reference Gottesman, Laursen, Bertelsen and Mortensen2010).

A mixed model that apportions cases to either single-mutation or polygenic mechanisms also provides no explanation for the variability in phenotypic expression of particular mutations. The alternative mixed model incorporates a role for polygenic influences but proposes that these modify the phenotypic effects of highly penetrant mutations, rather than producing the phenotype themselves. This view is highly congruent with findings from experimental genetics, where genetic background effects are typical and can be large (Nadeau, Reference Nadeau2001; Shao et al. Reference Shao, Burrage, Sinasac, Hill, Ernest, O'Brien, Courtland, Jepsen, Kirby, Kulbokas, Daly, Broman, Lander and Nadeau2008). For example, many phenotypes in mutant mice are affected by a change in genetic background, sometimes dramatically, although the mutant phenotype usually never occurs in either background without the major mutation. Indeed, given the complexities of the phenotypes concerned, it would be astonishing if such genetic background effects were not important in human psychiatric disease (e.g. Girirajan et al. Reference Girirajan, Rosenfeld, Cooper, Antonacci, Siswara, Itsara, Vives, Walsh, McCarthy, Baker, Mefford, Kidd, Browning, Browning, Dickel, Levy, Ballif, Platky, Farber, Gowans, Wetherbee, Asamoah, Weaver, Mark, Dickerson, Garg, Ellingwood, Smith, Banks, Smith, McDonald, Hoo, French, Hudson, Johnson, Ozmore, Moeschler, Surti, Escobar, El-Khechen, Gorski, Kussmann, Salbert, Lacassie, Biser, McDonald-McGinn, Zackai, Deardorff, Shaikh, Haan, Friend, Fichera, Romano, Gecz, DeLisi, Sebat, King, Shaffer and Eichler2010).

Of course, the genetic background will be made up of all other variants, rare and common, in the genotype. We might expect the rarer variants to make a larger contribution to phenotypic variance; indeed, this seems to be the case even for many quantitative traits (Cohen et al. Reference Cohen, Kiss, Pertsemlidis, Marcel, McPherson and Hobbs2004; Ji et al. Reference Ji, Foo, O'Roak, Zhao, Larson, Simon, Newton-Cheh, State, Levy and Lifton2008; Frazer et al. Reference Frazer, Murray, Schork and Topol2009; Goldstein, Reference Goldstein2009). However, common variants (most obviously the presence or absence of a Y chromosome) may also play an important role, as outlined below.

Rare variants, common modifiers and endophenotypes

Particular common variants could directly modify the biochemical, cellular or physiological effects of specific rare variants. For example, common variants in proline dehydrogenase (oxidase) 1 (PRODH) may modify the phenotypic effects of 22q11 deletions (Guilmatre et al. Reference Guilmatre, Dubourg, Mosca, Legallic, Goldenberg, Drouin-Garraud, Layet, Rosier, Briault, Bonnet-Brilhault, Laumonnier, Odent, Le Vacon, Joly-Helas, David, Bendavid, Pinoit, Henry, Impallomeni, Germano, Tortorella, Di Rosa, Barthelemy, Andres, Faivre, Frebourg, Saugier Veber and Campion2009). Such dominance or epistatic effects would most probably be specific to particular rare variants. Common variants might also influence risk indirectly, but more generally, for example through effects on cognitive reserve (discussed later).

A genetic background effect offers one possible explanation for what might be considered the strongest evidence for a polygenic influence on SZ risk, namely that unaffected relatives of SZ patients often show intermediate values on a range of endophenotypes. The endophenotype model is based firmly on the common variants hypothesis; specifically, it suggests that different variants may contribute to different aspects of the overall phenotype (such as defects in working memory or executive function, for example) and that the combination of many such defects results in the clinical phenotype (Gottesman & Gould, Reference Gottesman and Gould2003; Braff et al. Reference Braff, Freedman, Schork and Gottesman2007). The prediction of this model is that relatives of affected individuals will carry some, but not all, of the multiple risk variants that in combination cause disease, and will thus show some of the endophenotypes of the disease, though normally at a less severe level. By contrast, the single-mutation hypothesis in its simplest form (without modifiers) predicts that unaffected relatives will not differ from the general population.

Many studies do indeed show that unaffected first-degree relatives of schizophrenics have endophenotypes that place them, on average, intermediate between cases and unrelated controls. These include studies of cognitive endophenotypes, such as working memory or executive function, and also physiological endophenotypes, such as the amplitude of various evoked potentials. How can the rare variants model explain these findings?

First, some endophenotypes, especially ones that measure cognitive abilities, may reflect a genetic background effect that modifies risk of expression of disease, rather than disease-causing genes per se. There is very good evidence that poor pre-morbid cognitive function, perhaps reflecting inefficient neural processing, is a strong independent risk factor for SZ (Woodberry et al. Reference Woodberry, Giuliano and Seidman2008). A less efficient brain (with lower ‘cognitive reserve’) may be less well buffered and more likely to be pushed into a pathophysiological state by the effects of rare variants (as seen in brain injury and dementia) (Barnett et al. Reference Barnett, Salmond, Jones and Sahakian2006). SZ patients and their relatives might therefore be expected to have an underlying deficit in cognitive performance, compared to unrelated controls.

A second explanation for observed endophenotypes in ‘unaffected’ relatives is that many of them will also carry the risk variant, as the allelic penetrance for the clinical diagnosis is typically less than 50%. If the penetrance for a particular endophenotype is higher, then many first-degree relatives will show this endophenotype, and in fact may show it at the same level as affecteds. The average across relatives will thus be intermediate between cases and controls. There is good evidence that this situation applies to some endophenotypes. In the case of the DISC1 translocation, for example, relatives who carry the translocation, but who are not diagnosed with a psychiatric disorder, show the same P300 auditory evoked potential phenotype as affecteds (Blackwood & Muir, Reference Blackwood and Muir2004). More generally, many endophenotypes are present only in relatives who have broader psychiatric symptoms or diagnosis (Saperstein et al. Reference Saperstein, Fuller, Avila, Adami, McMahon, Thaker and Gold2006; Turetsky et al. Reference Turetsky, Greenwood, Olincy, Radant, Braff, Cadenhead, Dobie, Freedman, Green, Gur, Gur, Light, Mintz, Nuechterlein, Schork, Seidman, Siever, Silverman, Stone, Swerdlow, Tsuang, Tsuang and Calkins2008; Prasad et al. Reference Prasad, Sanders, Sweeney, Montrose, Diwadkar, Dworakowski, Miewald and Keshavan2009) or in relatives who later go on to develop full-blown SZ (Erlenmeyer-Kimling et al. Reference Erlenmeyer-Kimling, Rock, Roberts, Janal, Kestenbaum, Cornblatt, Adamo and Gottesman2000; Owens & Johnstone, Reference Owens and Johnstone2006), again presumably differentiating carriers of a causal mutation from non-carriers.

Explaining the persistence of SZ

The strongest version of the rare variants model thus proposes that most, if not all, cases of SZ are dependent upon the presence of some highly penetrant mutation. This is consistent with general evidence that rare mutations are much more likely to affect protein function and to cause deleterious phenotypes (Kryukov et al. Reference Kryukov, Pennacchio and Sunyaev2007; Ng et al. Reference Ng, Levy, Huang, Stockwell, Walenz, Li, Axelrod, Busam, Strausberg and Venter2008). Conversely, mutations that have such effects are likely to be subject to strong negative selection and not rise to high allelic frequencies. To explain the high rate of the disorder thus requires both a high enough rate of new mutation and a large enough mutational target (Keller & Miller, Reference Keller and Miller2006). For this model to be true, there must therefore be many genes that, when mutated, can give rise to SZ. More than 45 distinct loci have already been implicated (Table 1) and this number is very likely to increase. A mutation-selection balance model also predicts a preponderance of mutations in larger genes and in regions with a higher than average mutation rate. These predictions are borne out by the data, with the observed length of the implicated genes over 200-fold greater than the genomic average and a significant contribution from recurrent CNVs (Table 2).

This suggests a straightforward and plausible explanation for the existence and persistence of SZ in human populations. It simply takes a lot of genes to build and wire a human brain. This may seem to contradict the assertion made earlier that neurodevelopmental systems are robust to the cumulative effects of small changes. It is important to note, however, that such systems may nevertheless be sensitive to large perturbations of particular components, especially highly connected nodes (e.g. DISC1) (Kitano, Reference Kitano2004). When early processes of brain wiring fail due to mutation in one or other of these genes, neurodevelopment may be channelled into a common, maladaptive state (Fig. 2). For now, we call this schizophrenia, but in time it may be usefully and appropriately redefined on the basis of the particular molecular pathology.

Rethinking the approach to SZ

In summary, there is every reason to expect that most, if not all, cases of SZ are dependent upon the presence of some highly penetrant mutation. The number of loci involved, the frequency of the mutations, the fractions that are dominant or recessive and their penetrance for either intermediate phenotypes or for the clinical diagnosis of SZ itself are all matters for empirical investigation. Where a polygenic effect is likely to be observed is in modifying the phenotypic expression of such mutations, rather than in generating a distinct proportion of cases. Specific epistatic interactions are very likely to be important in determining each individual's phenotype (e.g. Girirajan et al. Reference Girirajan, Rosenfeld, Cooper, Antonacci, Siswara, Itsara, Vives, Walsh, McCarthy, Baker, Mefford, Kidd, Browning, Browning, Dickel, Levy, Ballif, Platky, Farber, Gowans, Wetherbee, Asamoah, Weaver, Mark, Dickerson, Garg, Ellingwood, Smith, Banks, Smith, McDonald, Hoo, French, Hudson, Johnson, Ozmore, Moeschler, Surti, Escobar, El-Khechen, Gorski, Kussmann, Salbert, Lacassie, Biser, McDonald-McGinn, Zackai, Deardorff, Shaikh, Haan, Friend, Fichera, Romano, Gecz, DeLisi, Sebat, King, Shaffer and Eichler2010). This will undoubtedly complicate analyses of segregation, as strict Mendelian patterns of inheritance are unlikely to be the norm. In addition, there must also be a major contribution from modifying effects of environmental factors (Kinney et al. Reference Kinney, Teixeira, Hsu, Napoleon, Crowley, Miller, Hyman and Huang2009) or stochastic developmental variation (Woolf, Reference Woolf1997; Mitchell, Reference Mitchell2007) to explain phenotypic discordance of MZ twins (Fig. 2). However, none of these factors should distract from a focus on the primary, causative mutations. As in other areas of biology, mutations with the largest effects in individuals, regardless of their frequency in the population, will be the most informative as to the underlying pathogenic and pathophysiological mechanisms.