Quantitative tests of primary homology

In systematic biology homology hypotheses are typically based on points of similarity and tested using congruence, of which the two stages have come to be distinguished as "primary" versus "secondary" homology. Primary homology is often regarded as prior to logical test, being a kind of background assumption or prior knowledge. Similarity can, however, be tested by more detailed studies that corroborate or weaken previous homology hypotheses before the test of congruence is applied. Indeed testing similarity is the only way to test the homology of characters, as congruence only tests their states. Traditional homology criteria include topology, special similarity, function, ontogeny and step-counting (for example, transformation in one step versus two via loss and gain). Here we present a method to compare quantitatively the ability of such criteria, and competing homology schema, to explain morphological observations. We apply the method to a classic and difficult problem in the homology of male spider genital sclerites. For this test case topology performed better than special similarity or function. Primary homologies founded on topology resulted in hypotheses that were globally more parsimonious than those based on other criteria, and therefore yielded a more coherent and congruent nomenclature of palpal sclerites in theridiid spiders than prior attempts. Finally, we question whether primary homology should be insulated as "prior knowledge" from the usual issues and demands that quantitative phylogenetic analyses pose, such as weighting and global versus local optima.