Homology is what is perceived as the same trait in different taxa and is a true representation of inheritance and phylogeny at the organismal level (e.g., it is the perceived phenotype, not the processes responsible for generating it). Homoplasy is the diametric opposite of homology - underlying similarity that does not result from inheritanceThey're talking in the paper about phenotypic homoplasy, but the definitions apply to molecular homoplasy as well. If you take away all the evidence of homoplasy, you have nothing but homology and a perfect nested hierarchy as evidence of evolution. Likewise, if there is no homology, then there's no way to define homoplasy, which is only recognizable in contrast to homology. Thus certain ideas about common descent cannot be correct by definition.
On the other hand, I wish the paper had dealt more with molecular and genomic homoplasy, but that was not their subject. In any event, I'm sure this will be a very interesting read.
Wake et al. 2011. Homoplasy: From Detecting Pattern to Determining Process and Mechanism of Evolution. Science 331:1032-1035.
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