Correcting the problem of false incongruence due to noise imbalance in the incongruence length difference (ILD) test.

The incongruence length difference (ILD) test is prone to suggesting significant conflict between character partitions when these differ only in the amount of undirected homoplasy (noise). This has been shown to be due to nonlinearity in the relationship between tree length and noise. Here we show that by standardizing either tree length or 1-retention index on a 0-to-1 scale, and then taking the arcsine of the value, the resulting value is linearly related to noise except at extremely high noise levels. We then investigate the effect of substituting these values instead of raw tree metrics in a modified ILD test (here called arcsine-ILD) for two types of noise. We show that, using the modified metric instead of the raw length, the results of ILD tests agreed better with desirable properties.