We introduce two algorithms for reconstructing semi-directed level-1 phylogenetic networks from their complete set of 4-leaf subnetworks, known as quarnets. The first algorithm, the sequential method, begins with a single quarnet and adds on one leaf at a time until all leaves have been placed. The second algorithm, the cherry-blob method, functions similarly to cherry-picking algorithms for phylogenetic trees by identifying exterior network structures from the quarnets.

Female preference is widely described in various taxa, and the underlying mechanisms shaping preferences remain a major focus of sexual selection studies, particularly in species where males contribute minimally to offspring. Female preference is associated with maintaining male secondary sexual traits (SST). However, how male SST impact female preference is less‐understood. We hypothesized the strength of female preference should scale with the expression of male SST. To test this prediction, we compared female preference for male body size (an easily quantifiable trait that scales with other SST) in three species of Limia (Poeciliidae) varying in secondary sexual traits: L. perugiae, L. dominicensis and L. zonata. The degree of SST was assessed based on the amount of ornamentation and the presence of courtship in the species. Limia perugiae, L. dominicensis and L. zonata were designated as possessing high, intermediate and low male SST, respectively. Female preference was quantified as the relative amount of time females associated with males of various size classes: small, intermediate and large. Therefore, we predicted because L. perugiae males have the most SST, females would associate more strongly with large males. Limia perugiae females were the only species to display female preference in relation to male body size, but they preferred small males. Although preference was observed, the direction of preference was unexpected. Moreover, the lack of preference for large male size and thereby other SST in the species suggests pre‐copulatory female preference is unimpacted by male SST. We suggest cryptic female choice (i.e. preference enacted during or after copulation) may maintain costly male traits. However, future work remains necessary. The present study provides foundational behavioural work on Limia and examines the ubiquity of the evolution of female preference in poeciliids.