Joined at the hip: linked characters and the problem of missing data in studies of disparity

Paleontological investigations into morphological diversity, or disparity, are often confronted with large amounts of missing data. We illustrate how missing discrete data affect disparity using a novel simulation for removing data based on parameters from published datasets that contain both extinct and extant taxa. We develop an algorithm that assesses the distribution of missing characters in extinct taxa, and simulates data loss by applying that distribution to extant taxa. We term this technique "linkage." We compare differences in disparity metrics and ordination spaces produced by linkage and random character removal. When we incorporated linkage among characters, disparity metrics declined and ordination spaces shrank at a slower rate with increasing missing data, indicating that correlations among characters govern the sensitivity of disparity analysis. We also present and test a new disparity method that uses the linkage algorithm to correct for the bias caused by missing data. We equalized proportions of missing data among time bins before calculating disparity, and found that estimates of disparity changed when missing data were taken into account. By removing the bias of missing data, we can gain new insights into the morphological evolution of organisms and highlight the detrimental effects of missing data on disparity analysis.