BackgroundIn the study of associations between genomic data and complex phenotypes there may be relationships that are not amenable to parametric statistical modeling. Such associations have been investigated mainly using single-marker and Bayesian linear regression models that differ in their distributions, but that assume additive inheritance while ignoring interactions and non-linearity. When interactions have been included in the model, their effects have entered linearly. There is a growing interest in non-parametric methods for predicting quantitative traits based on reproducing kernel Hilbert spaces regressions on markers and radial basis functions. Artificial neural networks (ANN) provide an alternative, because these act as universal approximators of complex functions and can capture non-linear relationships between predictors and responses, with the interplay among variables learned adaptively. ANNs are interesting candidates for analysis of traits affected by cryptic forms of gene action.ResultsWe investigated various Bayesian ANN architectures using for predicting phenotypes in two data sets consisting of milk production in Jersey cows and yield of inbred lines of wheat. For the Jerseys, predictor variables were derived from pedigree and molecular marker (35,798 single nucleotide polymorphisms, SNPS) information on 297 individually cows. The wheat data represented 599 lines, each genotyped with 1,279 markers. The ability of predicting fat, milk and protein yield was low when using pedigrees, but it was better when SNPs were employed, irrespective of the ANN trained. Predictive ability was even better in wheat because the trait was a mean, as opposed to an individual phenotype in cows. Non-linear neural networks outperformed a linear model in predictive ability in both data sets, but more clearly in wheat.ConclusionResults suggest that neural networks may be useful for predicting complex traits using high-dimensional genomic information, a situation where the number of unknowns exceeds sample size. ANNs can capture nonlinearities, adaptively. This may be useful when prediction of phenotypes is crucial.

The predacious mite Neoseiulus cucumeris (Oudemans) is an effective natural enemy of pest insects and mites. To identify the relative fitness of the avermectin-resistant strain of N. cucumeris, the life history parameters of avermectin resistant (R) and susceptible (S) strains of N. cucumeris were observed under experimental conditions (25 ± 1°C, 90 ± 5% RH and L: D = 14:10 h) feeding upon Tetranychus truncatus (Ehara). Fertility, net reproductive rates (R 0 /female), intrinsic rates of increase (r /day) and development durations of the two strains were compared. The abamectin resistant strain of N. cucumeris had significantly shorter developmental duration and longevity than the sensitive stain. However, the mean fecundity of the resistant strain was significantly higher than that of the susceptible strain. The net reproductive rate (R 0 =30.3833 offspring), the intrinsic rate of increase (r=0.2231 d -1 ) and the finite rate of increase (λ=1.2499 d -1 ) of the resistant strain were only slightly higher than those of the susceptible strain (R 0 =29.5333 offspring, r = 0.2130 d -1 , λ =1.2373 d -1 ); the differences were not significant. However, the mean generation time (T=15.1768 d) of the resistant strain was significantly shorter than that of the susceptible strain (T=16.0314 d).

Different data sources were used to examine hypothesized relations among neighborhood-, family-, and individual-level variables, and perceptions of neighborhood collective efficacy. Data were from 1,105 individuals (56% female, 42% African American, and 58% White) nested within 55 neighborhoods and 392 families, analyzed within a multilevel design using a 3-level model. At the neighborhood level, the study examined relations between Census, police, and neighborhood representative indicators. At the family level, the model examined the influence of marital status and family income. At the individual level, gender and age were examined. Results indicated that age at the individual level, marital status at the family level, and poverty and perceived gang activity at the neighborhood level predicted levels of neighborhood collective efficacy. The study illustrated significant variation across neighborhoods and families, and demonstrates the utility of combining different sources of neighborhood data to examine relations of interest within a multilevel framework.

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Genome-wide association studies (GWAS) have identified >300 loci associated with measures of adiposity including body mass index (BMI) and waist-to-hip ratio (adjusted for BMI, WHRadjBMI), but few have been identified through screening of the African ancestry genomes. We performed large scale meta-analyses and replications in up to 52,895 individuals for BMI and up to 23,095 individuals for WHRadjBMI from the African Ancestry Anthropometry Genetics Consortium (AAAGC) using 1000 Genomes phase 1 imputed GWAS to improve coverage of both common and low frequency variants in the low linkage disequilibrium African ancestry genomes. In the sex-combined analyses, we identified one novel locus (TCF7L2/HABP2) for WHRadjBMI and eight previously established loci at P < 5×10−8: seven for BMI, and one for WHRadjBMI in African ancestry individuals. An additional novel locus (SPRYD7/DLEU2) was identified for WHRadjBMI when combined with European GWAS. In the sex-stratified analyses, we identified three novel loci for BMI (INTS10/LPL and MLC1 in men, IRX4/IRX2 in women) and four for WHRadjBMI (SSX2IP, CASC8, PDE3B and ZDHHC1/HSD11B2 in women) in individuals of African ancestry or both African and European ancestry. For four of the novel variants, the minor allele frequency was low (<5%). In the trans-ethnic fine mapping of 47 BMI loci and 27 WHRadjBMI loci that were locus-wide significant (P < 0.05 adjusted for effective number of variants per locus) from the African ancestry sex-combined and sex-stratified analyses, 26 BMI loci and 17 WHRadjBMI loci contained ≤ 20 variants in the credible sets that jointly account for 99% posterior probability of driving the associations. The lead variants in 13 of these loci had a high probability of being causal. As compared to our previous HapMap imputed GWAS for BMI and WHRadjBMI including up to 71,412 and 27,350 African ancestry individuals, respectively, our results suggest that 1000 Genomes imputation showed modest improvement in identifying GWAS loci including low frequency variants. Trans-ethnic meta-analyses further improved fine mapping of putative causal variants in loci shared between the African and European ancestry populations.

Bayesian regularization of artificial neural networks (BRANNs) were used to predict body mass index (BMI) in mice using single nucleotide polymorphism (SNP) markers. Data from 1896 animals with both phenotypic and genotypic (12 320 loci) information were used for the analysis. Missing genotypes were imputed based on estimated allelic frequencies, with no attempt to reconstruct haplotypes based on family information or linkage disequilibrium between markers. A feed-forward multilayer perceptron network consisting of a single output layer and one hidden layer was used. Training of the neural network was done using the Bayesian regularized backpropagation algorithm. When the number of neurons in the hidden layer was increased, the number of effective parameters, γ, increased up to a point and stabilized thereafter. A model with five neurons in the hidden layer produced a value of γ that saturated the data. In terms of predictive ability, a network with five neurons in the hidden layer attained the smallest error and highest correlation in the test data although differences among networks were negligible. Using inherent weight information of BRANN with different number of neurons in the hidden layer, it was observed that 17 SNPs had a larger impact on the network, indicating their possible relevance in prediction of BMI. It is concluded that BRANN may be at least as useful as other methods for high-dimensional genome-enabled prediction, with the advantage of its potential ability of capturing non-linear relationships, which may be useful in the study of quantitative traits under complex gene action.

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