Upsilon 2000 V5.0 Serial Number ⏵
Upsilon 2000 V5.0 Serial Number
one fundamental principle of qtl mapping is that a significant association of a marker with a trait is not a sufficient condition for a causal variant to be within the genotyped markers. it is also necessary that the polymorphisms are in high ld with the causal variant. in addition to the low ld between markers and causal variants, even though the genotypes are measured, they can still be inaccurate due to various noise sources including missing data. the presence of ld between markers and causal variants can contribute to marker-causal variant association through a number of means, including (i) attenuation of the genotype effect due to ld between the marker and causal variant; (ii) the genotype effect of the causal variant being a function of the ld between the marker and the causal variant; and (iii) the genotype effect of the causal variant being a function of the ld between the marker and the causal variant.
in order to assess the impact of the number of causal variants on the heritability estimates in a random mating population (after correcting for multiple testing), we simulated data with = 0, 10, 20, 50, 100, and 200 causal variants. in order to compare heritability estimates for each model we used the design matrix with all possible combinations of causal and non-causal snps. we compared the residual variance under the car and icarh models (fig. 5a). both models had similar residual variances across all of the simulation replicates, indicating that for the range of variants simulated, there was no systematic bias in the residual variance. the average (s.e.) ({hat{h}}_{{{{{{rm{reml}}}}}}}^{2}) was, however, more accurate than the average (s.) ({hat{h}}_{{{{{{rm{he}}}}}}}^{2}). further, the difference between ({hat{h}}_{{{{{{rm{reml}}}}}}}^{2}) and ({hat{h}}_{{{{{{rm{he}}}}}}}^{2}) increased as the number of causal variants increased, indicating that this bias is larger for larger numbers of causal variants. however, the difference between the two models’ bias was not proportional to the number of causal variants. as expected, ({hat{h}}_{{{{{{rm{reml}}}}}}}^{2}) was more accurate than ({hat{h}}_{{{{{{rm{he}}}}}}}^{2}) regardless of the number of causal variants simulated.
a previous analysis of this dataset suggested that the causal variants would exhibit only moderate heterogeneity in effect. the causal variant should therefore be relatively common in order to explain the heritability of the trait.
to investigate the qualitative impact of heterogeneity, we calculated a 95th percentile of the distribution of each of the 2,000 causal variants’ effect sizes per causal allele across the base scenario, and divided the base scenarios into two groups based on whether the 95th percentiles were above or below this value. to investigate the quantitative impact, we calculated the empirical distribution of causal variant mafs across the base scenario and calculated the 95th percentile of these mafs across the base scenarios. it is unclear how the length of the simulation and the finite size of the dataset affect these percentiles, so it is not possible to make precise quantitative statements about the impact of the heterogeneity of variant effect sizes on the likelihood of a variant having an effect on the trait. however, we do infer the following qualitative points in regard to heterogeneity:
our implementation is written in r. we use the numeric application programming interface (api) to handle large matrix and computational data structures. the low-level data structures are stored using memory mapped files (mmfs), and a variety of sparse matrix formats are used. nearly all real analysis is done using matrices. if and when convenient, data may be cast as a vectorized matrix or a plain old matrix (poam). where appropriate, we also use plain-text objects (pos) that are vectors of character arrays that hold models, results and code. most dynamic data is kept in memory and will be lost if not properly saved when updating or replacing a model, results, or code. the high level structures, although also relatively small, are also stored in plain-text objects (pos) as well as various data frames. the r environment is bundled in the “car” package at cran ( https://cran.r-project.org/web/packages/car/car.pdf ).
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