Evidence of Absence Treated as Absence of Evidence: The Effects of Variation in the Number and Distribution of Gaps Treated as Missing Data on the Results of Standard Maximum Likelihood Analysis
We evaluated the effects of variation in the number and distribution of gaps (i.e., no base; coded as IUPAC \".\" or \"-\") treated as missing data (i.e., any base, coded as \"?\" or IUPAC \"N\") in standard maximum likelihood (ML) analysis. We obtained alignments with variable numbers and arrangements of gaps by aligning seven diverse empirical datasets under different gap opening costs using MAFFT. We selected the optimal substitution model for each alignment using the corrected Akaike Information Criterion (AICc) in jModelTest2 and searched for the optimal trees for each alignment using default search parameters and the selected models in GARLI. We also employed a Monte Carlo approach to randomly insert gaps (treated as missing data) into an empirical dataset to understand more precisely the effects of their variable numbers and distributions. To compare alignments quantitatively, we used several measures to quantify the number and distribution of gaps in all alignments (e.g., alignment length, total number of gaps, total number of characters containing gaps, number of gap openings). We then used these variables to derive four indices (ranging from 0 to 1) that summarize the distribution of gaps both within and among terminals, including an index that takes into account their optimization on the tree. Our most important observation is that ML scores correlate negatively with gap opening costs, and the amount of missing data. These variables also cause unpredictable effects on tree topologies. We discuss the implications of our results for the traditional and tree-alignment approaches in ML.