Atheists and Agnostics Are More Reflective than Religious Believers: Four Empirical Studies and a Meta-Analysis

Individual differences in the mere willingness to think analytically has been shown to predict religious disbelief. Recently, however, it has been argued that analytic thinkers are not actually less religious; rather, the putative association may be a result of religiosity typically being measured after analytic thinking (an order effect). In light of this possibility, we report four studies in which a negative correlation between religious belief and performance on analytic thinking measures is found when religious belief is measured in a separate session. We also performed a meta-analysis on all previously published studies on the topic along with our four new studies (N = 15,078, k = 31), focusing specifically on the association between performance on the Cognitive Reflection Test (the most widely used individual difference measure of analytic thinking) and religious belief. This meta-analysis revealed an overall negative correlation (r) of -.18, 95% CI [-.21, -.16]. Although this correlation is modest, self-identified atheists (N = 133) scored 18.7% higher than religiously affiliated individuals (N = 597) on a composite measure of analytic thinking administered across our four new studies (d = .72). Our results indicate that the association between analytic thinking and religious disbelief is not caused by a simple order effect. There is good evidence that atheists and agnostics are more reflective than religious believers.     

CRITICAL INTENSITY AND FLASH DURATION FOR RESPONSE TO FLICKER: WITH ANAX LARVAE

Determinations of the flicker response curve (F – log I_m) with larvae of Anax junius (dragonfly) for various ratios t_L/t_D of light time to dark time in a flash cycle provide relations between t_L/t_D and the parameters of the probability integral fundamentally describing the F – log I function, including the variability of I. These relations are quantitatively of the same form as those found for this function in the sunfish, and are therefore non-specific. Their meaning for the theory of reaction to visual flicker is discussed. The asymmetry of the Anax curve, resulting from mechanical conditions affecting the reception of light by the arthropod eye, is (as predicted) reduced by relative lengthening of the fractional light time in a cycle.     

Determination of Hepatocellular Carcinoma and Characterization of Hepatic Focal Lesions with Adaptive Multi-Exponential Intravoxel Incoherent Motion Model

PURPOSE: To distinguish hepatocellular carcinoma (HCC) from other types of hepatic lesions with the adaptive multi-exponential IVIM model. METHODS: 94 hepatic focal lesions, including 38 HCC, 16 metastasis, 12 focal nodular hyperplasia, 13 cholangiocarcinoma, and 15 hemangioma, were examined in this study. Diffusion-weighted images were acquired with 13 b values (b?=?0, 3, …, 500 s/mm²) to measure the adaptive multi-exponential IVIM parameters, namely, pure diffusion coefficient (D), diffusion fraction (f_d), pseudo-diffusion coefficient (D_i*) and perfusion-related diffusion fraction (f_i) of the ith perfusion component. Comparison of the parameters of and their diagnostic performance was determined using Mann-Whitney U test, independent-sample t test, one-way analysis of variance, Z test and receiver-operating characteristic analysis. RESULTS: D, D₁* and D₂* presented significantly difference between HCCs and other hepatic lesions, whereas f_d, f₁ and f₂ did not show statistical differences. In the differential diagnosis of HCCs from other hepatic lesions, D₂* (AUC, 0.927) provided best diagnostic performance among all parameters. Additionally, the number of exponential terms in the model was also an important indicator for distinguishing HCCs from other hepatic lesions. In the benign and malignant analysis, D gave the greatest AUC values, 0.895 or 0.853, for differentiation between malignant and benign lesions with three or two exponential terms. Most parameters were not significantly different between hypovascular and hypervascular lesions. For multiple comparisons, significant differences of D, D₁* or D₂* were found between certain lesion types. CONCLUSION: The adaptive multi-exponential IVIM model was useful and reliable to distinguish HCC from other hepatic lesions.     

The genetic mating structure of subdivided populations I. Open-mating model

The genetic mating structure of a subdivided population can describe how parental genotypes gave rise to zygotes. When parents of the same genotype are considered together as one class (“open-mating”), three independent parameters of inbreeding and mating structure are needed to describe this structure at a diallelic locus. One is Wright's fixation index F. The other two are mating structure parameters, derived herein and termed the “effective selfing” rate E and the “inbreeding assortative selfing” rate D. E is the genetically equivalent proportion of self-fertilization at a single locus, and is given by standardized second and third central moments of gene frequencies of mates. E is a summary measure of inbreeding that includes effects due to self-fertilization and mating to relatives, as well as correlations between mates induced by Wahlund effects and/or selective diversification among neighborhoods. The second parameter D measures the tendency of inbred or more homozygous individuals to effectively self more (or less) than outbred or more heterozygous individuals. D is related to the maintenance of variation of inbreeding among individuals and/or to the prevalence of spatial variation of selection. D is independent of E, but together with E controls the generational change of inbreeding, ΔF. Extensions of the model to unequal allele frequencies in male vs female mates, and to multi-allelic loci, are also examined.     

Regular measurement: A new method of biophysical experiment

A system of quantized relations between the value of the parameter (quantity) measured and the range of its experimental scattering has been revealed by analyzing the results of experiments on measuring the rates of various processes. Especially long series of stereotyped measurements under stable conditions (called regular measurements) are performed for determining the squared ratio of the standard deviation to the mean value of the quantity measured (D). Regular measurements of biochemical, chemical, and physical parameters show that the D value is related to the universal dimensionless constant D ₀, whose numerical value has been determined with considerable accuracy, and this relation is described by a simple rational equation. The simplicity of the relationship between D and D ₀ may be accounted for by the quantum behavior of the macroinstrument-object system manifested in the course of regular measurement.     

A Comparative Study of Relational Learning Capacity in Honeybees (Apis mellifera) and Stingless Bees (Melipona rufiventris)

Background

Learning of arbitrary relations is the capacity to acquire knowledge about associations between events or stimuli that do not share any similarities, and use this knowledge to make behavioural choices. This capacity is well documented in humans and vertebrates, and there is some evidence it exists in the honeybee (Apis mellifera). However, little is known about whether the ability for relational learning extends to other invertebrates, although many insects have been shown to possess excellent learning capacities in spite of their small brains.

Methodology/Principal Findings

Using a symbolic matching-to-sample procedure, we show that the honeybee Apis mellifera rapidly learns arbitrary relations between colours and patterns, reaching 68.2% correct choice for pattern-colour relations and 73.3% for colour-pattern relations. However, Apis mellifera does not transfer this knowledge to the symmetrical relations when the stimulus order is reversed. A second bee species, the stingless bee Melipona rufiventris from Brazil, seems unable to learn the same arbitrary relations between colours and patterns, although it exhibits excellent discrimination learning.

Conclusions/Significance

Our results confirm that the capacity for learning arbitrary relations is not limited to vertebrates, but even insects with small brains can perform this learning task. Interestingly, it seems to be a species-specific ability. The disparity in relational learning performance between the two bee species we tested may be linked to their specific foraging and recruitment strategies, which evolved in adaptation to different environments.     

Determining Intrachain Diffusion Coefficients for Biopolymer Dynamics from Single-Molecule Force Spectroscopy Measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.     

Incipient Genome Differentiation in Gossypium. I. Chromosomes 14, 15, 16, 19 and 20 Assessed in G. HIRSUTUM, G. RAIMONDII and G. LOBATUM by Means of Seven a-D Translocations

The genus Gossypium is favorable for study of genome divergence at several levels. Early stages of divergence have been studied among four D genomes by comparing chiasma frequencies (reciprocal exchanges) between pairs of genomes and between individual counterpart chromosomes marked by heterozygous translocations. D₅ (G. raimondii) shows barely detectable differentiation from from D_h (G. hirsutum), whereas D₇ (G. lobatum) is considerably less closely related to D_h than is D₅. Fragmentary data suggest that D_2–2 (G. harknessii) falls between D₅ and D₇ in its relationship to D_h. Since chiasma frequencies in individual chromosomes and marked regions exhibit the same order of relationships as their corresponding whole genomes, it is concluded that the genome differentiation is generalized (i.e., nucleus-wide) rather than localized in specific chromosomes or chromosome regions. Estimates of relationships based on reciprocal exchange frequencies agree with those based upon preferential synapsis in allohexaploids reported previously. Since preferential synapsis and reciprocal exchange frequencies reveal the same order of relationships, it is concluded that to some extent they reflect common underlying changes in chromosome properties, despite recent evidence that synapsis and crossing over are under independent genetic control.     

Determining Intrachain Diffusion Coefficients for Biopolymer Dynamics from Single-Molecule Force Spectroscopy Measurements

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.     

Explanation and Falsification in Phylogenetic Inference: Exercises in Popperian Philosophy

Deduction leads to causal explanation in phylogenetic inference when the evidence, the systematic character, is conceptualized as a transformation series. Also, the deductive entailment of modus tollens is satisfied when those kinds of events are operationalized as patristic difference. Arguments to the contrary are based largely on the premise that character-states are defined intensionally as objects, in terms of similarity relations. However, such relations leave biologists without epistemological access to the causal explanation and explanatory power of historical statements. Moreover, the prediction-making to which those kinds of relations are limited in practice can lead to a category error—the mental conversion of an abstraction (the classes defined in terms of similarity relations) into a thing (such as an historical individual). The latter practices and problems characterize pattern cladistics, taxa being interpreted as homeostatic property cluster natural kinds, and other instrumentalist research programs.     

CRITICAL ILLUMINATION AND FLICKER FREQUENCY,AS A FUNCTION OF FLASH DURATION: FOR THE SUNFISH

From the relations between critical illumination in a flash (I_m) and the flash frequency (F) for response of the sunfish to visual flicker when the proportion of light time to dark time (t_L/t_D) in a flicker cycle is varied at one temperature (21.5°) the following results are obtained: At values of t_L/t_D between 1/9 and 9/1 the F - log I_m curves are progressively shifted toward higher intensities and lower F_max.. F_max. is a declining rectilinear function of the percentage of the flash cycle time occupied by light. The rod and the cone portions of the flicker curve are not shifted to the same extent. The cone portion and the rod region of the curve are each well described by a probability integral. In terms of F as 100 F/F_max. the standard deviation of the underlying frequency distribution of elemental contributions, summed to produce the effect proportional to F, is independent of t_L/t_D. The magnitude of log I_m at the inflection point (r''), however, increases rectilinearly with the percentage light time in the cycle. The proportionality between I_m and σ_II1 is independent of t_L/t_D. These effects are interpreted as consequences of the fact that the number of elements of excitation available for discrimination of flicker is increased by increasing the dark interval in a flash cycle. Decreasing the dark interval has therefore the same kind of effect as reducing the visual area, and not that produced by decreasing the temperature.     

Fluctuation of the lysozyme structure

The kinetics of hydrogen-deuterium exchange in hen egg-white lysozyme (muramidase) has been followed in aqueous solutions of various pH values and in solutions with various concentrations of lithium chloride, by an infrared absorption measurement. It was found that, in every case, 34% of the total peptide hydrogen atoms exchange relatively slowly with a rate of a first-order reaction. This amount corresponds to 44 peptide groups per molecule, and this is equal to the number of peptide NH-groups which are found to be involved in hydrogen bonds with the carbonyls of other peptide groups in the lysozyme molecule in the crystalline state. Each rate constant determined is in good agreement with the value expected from two simple assumptions. (1) The scheme of the isotope exchange reaction is N ? D → D^∗ (? N^∗), where N is the native form of the molecule, D a denatured (unfolded) form, and ∗ indicates the deuterated products. (2) The N ? D fluctuation rate is much higher than the rate of the isotope exchange reaction D → D^∗. It has been shown that the N ? D transition postulated here is the same as that which can be followed by circular dichroism measurement and by some other physical measurements. The effect of lithium chloride on the exchange reaction rate is solely attributable to the change in the N ? D equilibrium caused by the salt, whereas the effect of pH (in the 5 to 8 range) is wholly ascribed to the catalytic action of the OH⁻ anion on the D → D^∗ reaction rate. From the deuterium exchange rate observed, an effective value of the mole fraction of the D form is estimated to be 3 × 10⁻⁶in the solution with no lithium chloride at 20 °C and of pH = 5 to 8.     

The effects of rearing density on growth,size heterogeneity and inter-individual variation of feed intake in monosex male Nile tilapia Oreochromis niloticus L.

The growth dispersion of farmed fish is a subject of increasing interest and one of the most important factors in stocking density. On a duration of 60 days, the effect of stocking density on the growth, coefficient of variation and inter-individual variation of feed intake (CV_FI) of juvenile Nile tilapia Oreochromis niloticus L. (14.9 ± 1.2 g) were studied in an experimental tank-based flow-through system. Groups of fish were stocked at four stocking densities: 200, 400, 600 and 800 fish/m³, corresponding to a density of ∼3, 6, 9 and 12 kg/m³ and referred to as D₁, D₂, D₃ and D₄, respectively. Each treatment was applied to triplicate groups in a completely randomized design. No treatment-related mortality was observed. The fish densities increased throughout the experiment from 3 to 23.5, 6 to 43.6, 9 to 56.6 and 12 to 69 kg/m³. Results show that mass gain and specific growth rate (SGR, %M/day) were negatively correlated with increased stocking density. Groups of the D₁ treatment reached a mean final body mass (FBM) of 119.3 g v. 88.9 g for the D₄ groups. Feed conversion ratios (FCRs) were 1.38, 1.54, 1.62 and 1.91 at D₁, D₂, D₃ and D₄ treatments, respectively. Growth heterogeneity, expressed by the inter-individual variations of fish mass (CV_M), was significantly affected by time (P < 0.001), stocking density (P < 0.001) and their interaction (P < 0.05). The difference in CV_M was particularly conspicuous towards the end of the experiment and was positively correlated with stocking density. Similarly, radiographic study shows that CV_FI was also found to be significantly greater for groups reared at high stocking densities (D₃ and D₄) than the other treatments (D₁ and D₂). These differences in both CV_M and CV_FI related to the stocking density need to be taken into account by husbandry practices to assure the production of more homogeneous fish size. A simple economic analysis indicates a parabolic relationship between profit and density with optimal final density at the peak of the curve. Given reasonable assumptions about production costs, the optimal final density (D_opt) is 73.7 kg/m³. A sensitivity analysis shows that changes in the fixed cost have no effects on the optimal final density. However, small change in variable costs, such as feed and juvenile costs, may have substantial effect on the optimal density.     

Macromolecular composition of bacteria

Equations are presented that describe the macromolecular composition in exponential bacterial cultures as functions of five parameters: doubling time of the culture (τ), protein per origin of replication (P₀), chromosome replication time (C-period), peptide chain elongation rate (c_p), and the time between termination of replication and cell division (D-period). Implicit in the value for some of these parameters is a specific macromolecular control system: the control of the growth rate (τ), the timing of initiation of rounds of chromosome replication (P₀), and the regulation of cell division (D). The utility of these relations is illustrated by using updated measurements of the macromolecular composition of E. coli B/r to calculate values for the fundamental parameters and to predict the composition of a mutant which has a defect in the control of DNA replication. Furthermore, the meaning of several often-cited physiological parameters (RNA/protein, RNA/cell and RNA/genome) is examined. The relations presented here show that these parameters and their variation with growth rate are not directly relevant to arguments about control of ribosome synthesis or culture growth.     

On the acquisition and analysis of microscale thermophoresis data

A comprehensive understanding of the molecular mechanisms underpinning cellular functions is dependent on a detailed characterization of the energetics of macromolecular binding, often quantified by the equilibrium dissociation constant, K_D. While many biophysical methods may be used to obtain K_D, the focus of this report is a relatively new method called microscale thermophoresis (MST). In an MST experiment, a capillary tube filled with a solution containing a dye-labeled solute is illuminated with an infrared laser, rapidly creating a temperature gradient. Molecules will migrate along this gradient, causing changes in the observed fluorescence. Because the net migration of the labeled molecules will depend on their liganded state, a binding curve as a function of ligand concentration can be constructed from MST data and analyzed to determine K_D. Herein, simulations demonstrate the limits of K_D that can be measured in current instrumentation. They also show that binding kinetics is a major concern in planning and executing MST experiments. Additionally, studies of two protein–protein interactions illustrate challenges encountered in acquiring and analyzing MST data. Combined, these approaches indicate a set of best practices for performing and analyzing MST experiments. Software for rigorous data analysis is also introduced.     

The Effect of Implicitly Incentivized Faking on Explicit and Implicit Measures of Doping Attitude: When Athletes Want to Pretend an Even More Negative Attitude to Doping

The Implicit Association Test (IAT) aims to measure participants’ automatic evaluation of an attitude object and is useful especially for the measurement of attitudes related to socially sensitive subjects, e.g. doping in sports. Several studies indicate that IAT scores can be faked on instruction. But fully or semi-instructed research scenarios might not properly reflect what happens in more realistic situations, when participants secretly decide to try faking the test. The present study is the first to investigate IAT faking when there is only an implicit incentive to do so. Sixty-five athletes (22.83 years ± 2.45; 25 women) were randomly assigned to an incentive-to-fake condition or a control condition. Participants in the incentive-to-fake condition were manipulated to believe that athletes with lenient doping attitudes would be referred to a tedious 45-minute anti-doping program. Attitudes were measured with the pictorial doping brief IAT (BIAT) and with the Performance Enhancement Attitude Scale (PEAS). A one-way MANOVA revealed significant differences between conditions after the manipulation in PEAS scores, but not in the doping BIAT. In the light of our hypothesis this suggests that participants successfully faked an exceedingly negative attitude to doping when completing the PEAS, but were unsuccessful in doing so on the reaction time-based test. This study assessed BIAT faking in a setting that aimed to resemble a situation in which participants want to hide their attempts to cheat. The two measures of attitude were differentially affected by the implicit incentive. Our findings provide evidence that the pictorial doping BIAT is relatively robust against spontaneous and naïve faking attempts. (B)IATs might be less prone to faking than implied by previous studies.     

Metabolism and binding properties of 24,24-difluoro-25-hydroxyvitamin D3

To evaluate possible functional roles for 24,25-dihydroxyvitamin D₃, 24,24-difluoro-25-hydroxyvitamin D₃ has been synthesized and shown to be equally as active as 25-hydroxyvitamin D₃ in all known functions of vitamin D. The use of the difluoro compound for this purpose is based on the assumption that the C-F bonds are stable in vivo and that the fluorine atom does not act as hydroxyl in biological systems. No 24,25-dihydroxyvitamin D₃ was detected in the serum obtained from vitamin D-deficient rats that had been given 24,24-difluoro-25-hydroxyvitamin D₃, while large amounts were found when 25-hydroxyvitamin D₃ was given. Incubation of the 24,24-difluoro compound with kidney homogenate prepared from vitamin D-replete chickens failed to produce 24,25-dihydroxyvitamin D₃, while the same preparations produced large amounts of 24,25-dihydroxyvitamin D₃ from 25-hydroxyvitamin D₃. Kidney homogenate prepared from vitamin D-deficient chickens produced 24,24-difluoro-1,25-dihydroxyvitamin D₃ from 24,24-difluoro-25-hydroxyvitamin D₃ and 1,25-dihydroxyvitamin D₃ from 25-hydroxyvitamin D₃. In binding to the plasma transport protein for vitamin D compounds, 24,24-difluoro-25-hydroxyvitamin D₃ is less active than 25-hydroxyvitamin D₃ and 24R,25-dihydroxyvitamin D₃. In binding to the chick intestinal cytosol receptor, 24,24-difluoro-25-hydroxyvitamin D₃ is more active than 25-hydroxyvitamin D₃ which is itself more active than 24R,25-dihydroxyvitamin D₃. The 24,24-difluoro-1,25-dihydroxyvitamin D₃ is equal to 1,25-dihydroxyvitamin D₃, and both are 10 times more active than 1,24R,25-trihydroxyvitamin D₃ in this system. These results provide strong evidence that the C-24 carbon of 24,24-difluoro-25-hydroxyvitamin D₃ cannot be hydroxylated in vivo, and, further, the 24-F substitution acts similar to H and not to OH in discriminating binding systems for vitamin D compounds.     

Combining sap flow and trunk diameter measurements to assess water needs in mature olive orchards

Sap flux (Q) and trunk diameter variation (TDV) are among the most useful plant-based measurements to detect water stress and to evaluate plant water consumption. The usefulness of both methods decreases, however, when applied to species that, like olive, have an outstanding tolerance to drought and a remarkable capacity to take up water from drying soils. Evidence shows that this problem is greater in old, big trees with heavy fruit load. Our hypothesis is that the analysis of simultaneous measurements of Q and TDV made in the same trees is more useful for assessing irrigation needs in old olive orchards than the use of any of these two methods alone. To test our hypothesis, we analysed relations between Q, TDV, midday stem water potential (Ψ_stem), relative extractable water and atmospheric demand in an olive orchard of 38-year-old ‘Manzanilla’ trees with heavy fruit load. Measurements were made during one irrigation season (May-October), in fully irrigated trees (FI, 107% of the crop evapotranspiration, ET_c, supplied by irrigation), and in trees under two levels of deficit irrigation (DI60, 61% ET_c; DI30, 29% ET_c). Time courses of Q and TDV measured on days of contrasting weather and soil water conditions were analysed to evaluate the usefulness of both methods to assess the crop water status. We calculated the daily tree water consumption (E_p) from Q measurements. For both DI treatments we calculated a signal intensity by dividing daily E_p values of each DI tree by those of the FI tree (SI−Ep). We did the same with the maximum daily shrinkage (MDS) values (S_I−MDS). Neither SI−Ep nor S_I−MDS rendered useful information for assessing the crop water needs. On the contrary, the daily difference for maximum trunk diameter (MXTD) between each of the DI trees and the FI tree (D_MXTD) clearly indicated the onset and severity of water stress. A similar analysis with the E_p values, from which DEp values were derived, showed the effect of water stress on the water consumption of the trees. We concluded that the simultaneous use of D_MXTD and DEp values provides more detailed information to assess water needs in mature olive orchards than the use of Q or TDV records alone.     

Genomic Scans of Zygotic Disequilibrium and Epistatic SNPs in HapMap Phase III Populations

Previous theory indicates that zygotic linkage disequilibrium (LD) is more informative than gametic or composite digenic LD in revealing natural population history. Further, the difference between the composite digenic and maximum zygotic LDs can be used to detect epistatic selection for fitness. Here we corroborate the theory by investigating genome-wide zygotic LDs in HapMap phase III human populations. Results show that non-Africa populations have much more significant zygotic LDs than do Africa populations. Africa populations (ASW, LWK, MKK, and YRI) possess more significant zygotic LDs for the double-homozygotes (D_AABB) than any other significant zygotic LDs (D_AABb, D_AaBB, and D_AaBb), while non-Africa populations generally have more significant D_AaBb’s than any other significant zygotic LDs (D_AABB, D_AABb, and D_AaBB). Average r-squares for any significant zygotic LDs increase generally in an order of populations YRI, MKK, CEU, CHB, LWK, JPT, CHD, TSI, GIH, ASW, and MEX. Average r-squares are greater for D_AABB and D_AaBb than for D_AaBB and D_AABb in each population. YRI and MKK can be separated from LWK and ASW in terms of the pattern of average r-squares. All population divergences in zygotic LDs can be interpreted with the model of Out of Africa for modern human origins. We have also detected 19735-95921 SNP pairs exhibiting strong signals of epistatic selection in different populations. Gene-gene interactions for some epistatic SNP pairs are evident from empirical findings, but many more epistatic SNP pairs await evidence. Common epistatic SNP pairs rarely exist among all populations, but exist in distinct regions (Africa, Europe, and East Asia), which helps to understand geographical genomic medicine.