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Journal of Integrative Neuroscience  2018, Vol. 17 Issue (1): 1-10    DOI: 10.31083/JIN-170034
Research article | Next articles
The origin of complex human diversity: Stochastic epistatic modules and the intrinsic compatibility between distributional robustness and phenotypic changeability
Shinji Ijichi1, 2, *(), Naomi Ijichi2, Yukina Ijichi2, Chikako Imamura3, Hisami Sameshima1, Yoichi Kawaike1, Hirofumi Morioka1
1 Health Service Center, Kagoshima University, 1-21-24 Korimoto, Kagoshima 890-8580, Japan
2 Institute for Externalization of Gifts and Talents, 7421-1 Shimofukumoto, Kagoshima 891-0144, Japan
3 Support Center for Students with Disabilities, Kagoshima University, 1-21-30 Korimoto, Kagoshima 890-0065, Japan
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The continuing prevalence of a highly heritable and hypo-reproductive extreme tail of a human neurobehavioral quantitative diversity suggests the reproductive majority retains the genetic mechanisms for extremes. From the perspective of stochastic epistasis, the effect of an epistatic modifier variant can randomly vary in both phenotypic value and effect direction among carriers depending on the genetic identity and the modifier carriers are ubiquitous in the population. The neutrality of the mean genetic effect in carriers ensures the survival of the variant under selection pressures. Functionally or metabolically related modifier variants make an epistatic network module and dozens of modules may be involved in the phenotype. To assess the significance of stochastic epistasis, a simplified module-based model was simulated. The individual repertoire of the modifier variants in a module also contributes in genetic identity, which determines the genetic contribution of each carrier modifier. Because the entire contribution of a module to phenotypic outcome is unpredictable in the model, the module effect represents the total contribution of related modifiers as a stochastic unit in simulations. As a result, the intrinsic compatibility between distributional robustness and quantitative changeability could mathematically be simulated using the model. The artificial normal distribution shape in large-sized simulations was preserved in each generation even if the lowest fitness tail was non-reproductive. The robustness of normality across generations is analogous to the real situation of complex human diversity, including neurodevelopmental conditions. The repeated regeneration of a non-reproductive extreme tail may be essential for survival and change of the reproductive majority, implying extremes for others. Further simulation to illustrate how the fitness of extreme individuals can be low across generations may be necessary to increase the plausibility of this stochastic epistasis model.

Key words:  Neurodevelopmental conditions      autism      schizophrenia      stochastic variation      complex trait      population diversity      quantitative change     
Submitted:  23 January 2017      Accepted:  05 April 2017      Published:  15 February 2018     
*Corresponding Author(s):  Shinji Ijichi     E-mail:

Cite this article: 

Shinji Ijichi, Naomi Ijichi, Yukina Ijichi, Chikako Imamura, Hisami Sameshima, Yoichi Kawaike, Hirofumi Morioka. The origin of complex human diversity: Stochastic epistatic modules and the intrinsic compatibility between distributional robustness and phenotypic changeability. Journal of Integrative Neuroscience, 2018, 17(1): 1-10.

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Fig. 1.  Population size-dependent stability of the simulated phenotypic diversity. A simulation is illustrated as a sequence of boxplot diagrams. The phenotypic values (Xo) were automatically calculated using the formula (y-axis title) for each generation (G1 - G100) as described in Methods. Simulations were repeated five times with the population size varying from 10 to 500, and a representative simulation for each population size is shown. Small arrow heads indicate generations whose population was not normally distributed by an assessment of the absolute value for skewness and/or kurtosis ($\geqq$ 2.0). The module number was fixed (m = 10) for these representative simulations.

Fig. 2.  Conditional effects of each coefficient of the formula (y-axis title). A simulation is illustrated as a sequence of boxplot diagrams. The phenotypic values ($Xo$) were automatically calculated using the formula for each generation ($G1-G100$) as described in Methods. Simulations for each condition were repeated five times and three representative simulations are given for each condition (300 boxplots per condition) with $a$ = 0.5, $b$ = 0.5, and $c$ = 0 for the condition a + b $\leqq$ 1 and $c = 0, a = 0.5, b = 0.5$, and $c = 0.1$ for the condition $a + b$ $\leqq$ 1, $a + b$ $ > $ |c|, and $c \neq $ 0, $a = 0.5, b = 0.5$, and $c$ = 1.0 for the condition $a + b \leqq$ 1, $a + b \leqq$ |c|, and $c \neq $ 0, and $a = 0.53, b = 0.53$, and $c = 1.0$ for the condition $a + b > $ 1 and $c \neq $ 0, respectively. To exclude the contamination of the population size effect, the population size was fixed (n = 1, 000). The module number was also fixed ($m$ = 10).

Fig. 3.  Phenotypic changeability in a selection pressure where the lowest extremes in the population cannot leave offspring. A simulation is illustrated as a line graph (the mean value $ \pm $ one standard deviation). The phenotypic values ($Xo$) were automatically calculated using the formula (y-axis title) for each generation ($G1-G100$) as described in Methods. The percentage of nonreproductive extreme cases is shown at the right end of the simulation (from 0.2% to 10% with a minus symbol). To exclude the contamination of population size effect, the population size was fixed (n=1,000).

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