Distinguishing phylogenetic signal from homoplasy (shared similarities among 
taxa that do not arise by common ancestry) is an implicit goal of any 
phylogenetic study. Large amounts of homoplasy can interfere with accurate tree 
inference, and it is expected that common measures of clade support, including 
bootstrap proportions and Bayesian posterior probabilities, should also be 
impacted to some degree by homoplasy. Through data simulation and analysis of 38 
empirical data sets, we show that high amounts of homoplasy will affect all 
measures of clade support in a manner that is dependent on clade size. More 
specifically, the smallest taxon bipartitions in an unrooted tree topology will 
receive higher support relative to clades of intermediate sizes, even when all 
clades are supported by the same amount of data. We determine that the ultimate 
causes of this effect are the inclusion of random trees (due to homoplasy) 
during bootstrap resampling and Markov chain Monte Carlo (MCMC) topology 
searching and the higher relative proportion of small taxon bipartitions (i.e., 
2 or 3 taxa) to larger sized bipartitions. However, the use of explicit 
model-based methods, especially Bayesian MCMC methods, effectively overcomes 
this clade size effect even when very small amounts of phylogenetic signal are 
present. We develop a post hoc statistic, the clade disparity index (CDI), to 
measure both the relative magnitude of the clade size effect and its statistical 
significance. In analyses of both simulated and empirical data, CDI values 
indicate that Bayesian MCMC analyses are substantially more likely to estimate 
clade support values that are uncorrelated with clade size than are maximum 
parsimony and maximum likelihood bootstrap analyses and thus less affected by 
homoplasy. These results may be especially relevant to "deep" phylogenetic 
problems, such as reconstructing the tree of life, as they represent the largest 
possible extremes of time and evolutionary rates, 2 factors that cause 
homoplasy.