The use of bifurcating trees as evolutionary models has greatly facilitated the discussion and testing of phylogenetic and evolutionary hypotheses. However, it is well known that such models poorly describe more complex evolutionary scenarios, particularly when reticulate events such as horizontal gene transfer, gene duplication, or recombination are involved (Huson and Bryant, 2006). Hybridization is of particular importance because gene flow between species can bring together adaptive variation from divergent genetic lineages for selection to act upon. Although the extent of its evolutionary significance remains controversial (Seehausen, 2004), it is increasingly seen as an important process for generating biotic diversity (Arnold, 1997, Ferguson and Sang, 2001 and Rieseberg et al., 2003) and as a comparable, or even greater, source of adaptive genetic variation than mutation (Arnold and Martin, 2009, Grant and Grant, 1996 and Kunte et al., 2011). Because hybridization is more common between closely related species, species-rich groups that are undergoing rapid adaptive radiations are those that hybridize most (Gourbière and Mallet, 2010, Price and Bouvier, 2002 and Seehausen, 2004). If hybrid speciation takes place commonly in natural populations, it might also have played a major role in the origin and divergence of both major lineages and individual species. Hybridization is often inferred from incongruence among gene trees from independent loci (Fig. 1B; Linder and Rieseberg, 2004) or from trees in which species are not monophyletic (Funk and Omland, 2003). However, it is extremely difficult to detect the signal of a basal hybrid gene flow deep in a phylogeny using DNA sequence data, because phylogenetic reconstruction errors and artefacts based on sequence data induced by phenomenon such as long-branch attraction, biased nucleotide compositional effects, saturation and perhaps even convergence due to selection, make distinguishing any weak remaining signal very difficult.

Processes other than hybridization, such as gene duplication (Small et al., 2004) and incomplete lineage sorting (Buckley et al., 2006, Holder et al., 2001, Huson et al., 2005, Joly et al., 2009, Machado et al., 2002, Sang and Zhong, 2000 and Wang et al., 1997), can also produce incongruent gene–species phylogenies (Fig. 1A). Gene duplication is of more concern for recent divergences, because duplicated genes tend to diverge rapidly, and end up becoming sub-functional, acquiring new functions, or losing function and being lost. Incomplete lineage sorting refers to the retention and incomplete random sorting of alleles at many loci independently because the intervals between divergence events were brief (Fig. 1C). This is more likely if the effective population sizes are large relative to the divergence time after a speciation event. In this case, genetic drift is unlikely to have time to bring genes to fixation before subsequent divergences (Pamilo and Nei, 1988).

Retroposons (RTs) are highly repetitive mobile sequences that transpose into eukaryotic DNA through RNA intermediates. In many species, RTs are a ubiquitously dispersed feature of the whole genome, often constituting a significant (∼ 10%) mass fraction of total DNA. RTs cause mutations both by their retro-transposition within genes and by unequal recombination, and are widely considered examples of ‘selfish’ or ‘parasitic’ DNA. RTs have proven to be excellent markers for phylogenetic analysis: their mode of evolution is predominantly homoplasy-free, because they do not insert in the same locus of two unrelated lineages, and unidirectional, because they are not precisely excised from a locus with the flanking sequences preserved (Shedlock and Okada, 2000). The use of RTs for diagnosing common ancestry is being expanded to examine the differential sorting of lineages through the course of speciation events. They have been used to show that hippopotamuses are the closest living relatives of whales (Nikaido et al., 1999 and Shimamura et al., 1997), to determine phylogenetic relationships among cichlid fishes (Takahashi et al., 2001 and Terai et al., 2003), and to elucidate the phylogeny of eight Primate species, providing the strongest evidence yet that chimps are the closest living relatives of humans (Salem et al., 2003).

Incongruent insertion patterns revealed by ancient fixed RT loci contain information that can be useful in detecting cases of incomplete lineage sorting/hybridization that are otherwise obscured by accumulated mutations, homoplasy and phylogenetic uncertainty in sequence data (Churakov et al., 2009 and Shedlock et al., 2004). Among vertebrates, birds are particularly prone to hybridization (reviewed and summarized in Mallet, 2005). Phylogenetic evidence suggests that the early diversification of neoavian orders most likely occurred in a rapid adaptive radiation more than 65 million years ago (Hackett et al., 2008, Haddrath and Baker, 2012, Matzke et al., 2012, Poe and Chubb, 2004 and Suh et al., 2011), and that rapid adaptive radiations have been abundant during both early and ongoing bird radiations (Jetz et al., 2012). Attempts to resolve the higher-level phylogenetic relationships have resulted in contradictory or unresolved relationships at deep nodes (Mayr, 2011). RTs have been useful to clarify relationships between game birds (Kriegs et al., 2007), and in a recent study, Matzke et al. (2012) used chicken repeat 1 (CR1) RT markers to elucidate the early radiation of Neoaves. Because there is a high percentage of discordant retroposons found in neoavian orders, the authors suggest a rapid ancestral radiation of Neoaves characterized by insertion polymorphism and incomplete lineage sorting (and perhaps hybridization). Phylogenetic networks have an important role to play in the representation and eventual reconstruction of evolutionary history when applied to RT-type data. Implicit models such as split networks are very useful for exploring and visualizing the different signals in a data set, whereas explicit models such as hybridization and recombination networks can be used to model reticulate evolution.

Median networks, a type of unrooted phylogenetic networks, are particularly suited to visualize conflicting data in a set of binary characters on a set of taxa, such as the presence/absence of CR1 insertion data. In a median network, every sequence of characters is represented by a node, and additional nodes represent unobserved characters (i.e. insertion patterns). Two nodes are connected by an edge only if they differ by one character (as when used to visualize haplotype relationships). We used the 12 retroposon markers used by Matzke et al. (2012) and the four conflicting markers used by Suh et al. (2011) to construct a median-joining split network as implemented in SplitsTree4, with count-splits filter. In this case, the CR1 presence/absence data are analogous to a group of haplotypes, and the network represents the relationships among them (i.e. each “haplotype” is the insertion pattern of the 16 markers for each species).