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We show how using simple regression models in conjunction with external data such as average trait values can improve the power of genome-wide association studies.
Average trait values of four environments were used.
Average trait values for each genotypic class (i.e., 1, 3, 6, or 12) were also used as observed values to test for non-additivity against a null model.
In the standard BayesTraits approach Model A and Model B are compared in order to test the hypothesis that tips further from the root have different average trait values from tips nearer the root due to directional selection [42].
By manipulating the nutritional environment that populations experienced, we have documented a shift in average trait values but not the relationships between traits in a way that is consistent with the predictions of short term or weak selection.
Specifically we tested the theoretical life-history prediction that the nature of specific trade-offs will remain the same across the different treatments even if average trait values change.
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The average trait value of each accession was used in data analyses of GWAS.
The evolutionary response is symbolized as R, and is calculated as the average trait value in the current generation (offspring) subtracted from the average trait value in the previous generation (parents).
Both figures plot average trait value between the two parents (mid-parent trait value) and the trait values for each resulting offspring.
We calculated the average phenotypic score and variance associated with it in this generation and determined the evolutionary response (R) to selection as the average trait value in the current generation subtracted from the average trait value in the previous generation prior to selection.
Note that the inclusion of random environmental effects need not change the average trait value across generations; however, the heritability is drastically reduced leading to a dampened response to selection.
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