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Genomes evolve through a combination of mutation, drift, and selection, all of which act heterogeneously across genes and lineages. This leads to differences in branch-length patterns among gene trees. Genes that yield trees with the same branch-length patterns can be grouped together into clusters. Here, we propose a novel phylogenetic approach to explain the factors that influence the number and distribution of these gene-tree clusters. We apply our method to a genomic dataset from insects, an ancient and diverse group of organisms. We find some evidence that when drift is the dominant evolutionary process, each cluster tends to contain a large number of fast-evolving genes. In contrast, strong negative selection leads to many distinct clusters, each of which contains only a few slow-evolving genes. Our work, although preliminary in nature, illustrates the use of phylogenetic methods to shed light on the factors driving rate variation in genomic evolution.