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Abstract Traits that independently evolve many times are important for testing hypotheses about correlated evolution and understanding the forces shaping biodiversity. However, population genetics processes can cause hemiplasies (traits determined by genes whose topologies do not match the species tree), leading to a false impression of convergence (homoplasy) and potentially misleading inferences of correlated evolution. Discerning between homoplasies and hemiplasies can be important in cases of rapid radiations and clades with many gene tree incongruences. Here, focusing on two-clawed spiders (Dionycha) and close relatives, we evaluate if the observed distribution of characters related to a web-less lifestyle could be better explained as synapomorphies, homoplasies, or hemiplasies. We find that, although there are several convergences, hemiplasies are also sometimes probable. We discuss how these hemiplasies could affect inferences about correlation and causal relationship of traits. Understanding when and where in the tree of life hemiplasy could have happened is important, preventing false inference of convergent evolution. Furthermore, this understanding can provide alternative hypotheses that can be tested with independent data. Using traits related to the climbing ability of spiders we show that, when hemiplasy is unlikely, adequate model testing can be used to better understand correlated evolution, and propose hypotheses to be tested using controlled behavioral and mechanical experiments. 

Abstract Understanding diversity has been a pursuit in evolutionary biology since its inception. A challenge arises when sexual selection has played a role in diversification. Questions of what constitutes a ‘species’, homoplasy vs. synapomorphy, and whether sexually selected traits show phylogenetic signal have hampered work on many systems. Peacock spiders are famous for sexually selected male courtship dances and peacock-like abdominal ornamentation. This lineage of jumping spiders currently includes over 90 species classified into two genera, Maratus and Saratus. Most Maratus species have been placed into groups based on secondary sexual characters, but evolutionary relationships remain unresolved. Here we assess relationships in peacock spiders using phylogenomic data (ultraconserved elements and RAD-sequencing). Analyses reveal that Maratus and the related genus Saitis are paraphyletic. Many, but not all, morphological groups within a ‘core Maratus’ clade are recovered as genetic clades but we find evidence for undocumented speciation. Based on original observations of male courtship, our comparative analyses suggest that courtship behaviour and peacock-like abdominal ornamentation have evolved sequentially, with some traits inherited from ancestors and others evolving repeatedly and independently from ‘simple’ forms. Our results have important implications for the taxonomy of these spiders, and provide a much-needed evolutionary framework for comparative studies of the evolution of sexual signal characters.