But using probable results under the null to conclude that the null is true is committing the fallacy of affirming the consequent: if A then B, we observe B, therefore A — an invalid syllogism.
Although hard sweeps on SNVs dramatically reduce K (fig. 1 C and D), they also substantially reduce S. Thus, low S and low K conditions are characteristic of a hard sweep after fixation but are hardly unexpected under the null hypothesis of neutrality.
6 for a brief discussion of models that are underidentified under the null but identified under the alternative.
The only possible exception arises when the model is exactly on the boundary of the admissibility region under the null but not under the alternative.
Nevertheless, Harvey (1989) discusses some examples in which an Ucarima model is underidentified under the null but identified under the alternative.
Resampling-based methods, such as permutation and bootstrap, can be used to estimate the distribution of the MAX3 statistic under the null, but they are computationally expensive.
For each simulation, we used MERLIN to generate a new data set with the original phenotypes but with new genotypes simulated under the null hypothesis of no linkage for all autosomal markers, retaining the same allele frequencies, marker spacing, and missing data pattern.
Clearly the test population C should not be admixed under the null hypothesis, but as we have discussed, shared demography particularly bottlenecks can also produce weighted LD.
The test does not formally depend on this assumption, since it is evaluated under the null hypothesis, but this is the alternative hypothesis for which its power is maximized.
The results for the log-likelihood values under the null model are very similar but are not shown.
