**3.1 Mutation-selection balance is the only plausible mechanism for the persistence**

From an evolutionary viewpoint, four explanations are possible for the persistence: (i) ancestral neutrality, (ii) negative frequency-dependent selection, (iii) heterozygote advantage (balancing selection or pleiotropy), and (iv) mutation-selection balance.

'Ancestral neutrality' assumes that reproductive fitness of affected individuals and/or their relatives was higher in ancient environments and that selection coefficients of pathogenic alleles were close to zero. Because the effective population size in ancient times might be much smaller than now, pathogenic but neutral or almost neutral alleles could be fixed by genetic drift. While this hypothesis explains that schizophrenia has not been extinct in the long human history, ancestral neutrality itself provides no explanation for the apparently stable prevalence of the disease across generations today; although 'ancestral neutrality' might be plausible, it needs another mechanism to account for the persistence in modern environments, where the effective population size has been expanded and the influence of negative selection pressure may be much stronger than ever before.

Impact of Epidemiology on Molecular Genetics of Schizophrenia 117

mutation in the mtDNA which occurs at a rate of 4 2 8.8 10 ~ 1.3 10 per locus per

As is shown in the previous section, putative pathogenic genes, if located in the mtDNA, are sustained by mutation-selection balance with heterozygote advantage. On the other hand, if located in the ncDNA, they should be sustained by mutation-selection balance without heterozygote advantage. In this section, we introduce our previous work (Doi et al., 2009), in which we carefully re-examined the necessary conditions for putative nuclear susceptibility genes for schizophrenia and deduced a criterion (persistence criterion, or 'P-criterion') that every nuclear susceptibility gene should fulfill for persistence of the disease, and present its

We assume here a random-mating human population with a sufficiently large effective population size at equilibrium, where negative selection pressures on the susceptibility alleles for schizophrenia are predominant and the effect of genetic drift is negligibly small. The prevalence *p* of schizophrenia in this ideal human population is assumed to be stable across generations by mutation-selection balance. Therefore, the gene frequency in the general population (*mG*) is given in terms of the gene frequencies in the affected population

We assume here that the total of the population frequencies of the pathogenic alleles at *each risk locus* is preserved by mutation-selection balance. Therefore, *mG* ,the cross-generational reduction of the frequency of a pathogenic allele should not be more than the rate of mutations that produce pathogenic variants at the locus. On the other hand, since mutations at the locus include mutations of two directions that produce pathogenic or non-pathogenic

*dm m A U* ) (1)

) should be greater than the rate of mutations that

*mG* . (2)

(1 ) *m pm p m GA U* , or (1 ) *m m pd A G* .

We assume the multifactorial threshold model, in which quantitative traits such as liability to the disease are determined by multiple genetic and non-genetic factors including a

**4. Persistence criterion for nuclear susceptibility genes for schizophrenia** 

generation ( <sup>3</sup> 4.3 10 on average) (Sigurđardóttir et al., 2000).

applications to association studies for schizophrenia.

At first we describe our three basic assumptions.

(*mA*) and in the unaffected population (*mU*):

variants, the mutation rate at the locus (

**4.1.3 Multifactorial threshold model** 

Thus we have:

produce pathogenic variants at the locus.

**4.1.2 Mutation-selection balance in each risk locus** 

**4.1 Three basic assumptions** 

**4.1.1 An ideal human population** 

'Negative frequency-dependent selection' explains the persistence only when the fitness of the affected individuals increases as the prevalence in the general population decreases, which seems not to be the case with schizophrenia.

Thus, the remaining possibility for persistence mechanism is mutation-selection balance with or without heterozygote advantage.

#### **3.2 Heterozygote advantage works in the mitochondrial genome model but not in the nuclear genome model for schizophrenia**

'Heterozygote advantage' assumes that the susceptibility alleles increase the fitness of the unaffected gene carriers, thereby sustaining the gene frequencies. This line of explanations may include: (i) physiological advantage (resistance to shock, infections, and poor nutrition etc.), (ii) a higher sexual activity and/or attractiveness, and (iii) creative intelligence or a higher trait creativity including 'everyday creativity'.

This hypothesis needs two lines of confirmation: (a) that unaffected gene carriers have such advantages, and (b) that such advantages really contribute to sufficiently increase their reproductive fitness.

It seems to gain the confirmation (a). For example, Erlenmeyer-Kimling (1968) reported an increased survival rate of *female* children of parents with schizophrenia, proposing a possible physiological advantage associated with schizophrenia. Kinney et al. (2001), in a well-designed and methodologically sophisticated study, showed that an advantage of everyday creativity was linked to a subtle clinical picture (schizotypal signs) in a nonpsychotic sample of schizophrenia offspring.

However, it lacks the confirmation (b) in the nuclear genome model. This hypothesis, although theoretically plausible and fascinating, has not been supported by most epidemiological studies, which show a decreased reproductive fitness of unaffected siblings of patients with schizophrenia. Although recent large-sampled epidemiological studies (Bassett et al., 1996; McGrath et al., 1999; Haukka et al., 2003; Svensson et al., 2007) have consistently shown that the reproductive fitness of unaffected *female* siblings of patients with schizophrenia is slightly but significantly increased (1.02-1.08), it is not large enough to compensate for the gene loss due to the decreased reproductive fitness of patients (0.2-0.3 in males and 0.4-0.5 in females) and their unaffected male siblings (0.9-1.0) in the nuclear genome model. On the other hand, the latest meta-analysis (Bundy et al., 2011) shows no significant difference between the fertility of parents of patients with schizophrenia and healthy controls, although there is a trend towards parents having more offspring. Therefore, heterozygote advantage seems not to work in the nuclear genome model.

On the other hand, it works in the mitochondrial genome model because mitochondrial DNA (mtDNA) is transmitted to the next generation only through females. Indeed, we can see that this slightly elevated reproductive fitness of the unaffected female siblings, coupled with the less pronounced decreased reproductive fitness of female patients, is sufficient to compensate for the gene loss; when we calculate , the cross-generational reduction of the frequency of females with a putative pathogenic mtDNA in the general population, using the data in the largest-sampled cohort study to date (Haukka et al., 2003), we have <sup>3</sup> 5.06 10 (**Note**). This figure implies that the gene loss can be balanced by *de novo*

mutation in the mtDNA which occurs at a rate of 4 2 8.8 10 ~ 1.3 10 per locus per generation ( <sup>3</sup> 4.3 10 on average) (Sigurđardóttir et al., 2000).
