9Chromosomal inversions are associated with reproductive isolation and adaptation in insects such as Drosophila melanogaster and the malaria vectors Anopheles gambiae and Anopheles coluzzii. While methods based on read alignment have been useful in humans for detecting inversions, these methods are less successful in insects due to long repeated sequences at the breakpoints. Alternatively, inversions can be detected using principal component analysis (PCA) of single nucleotide polymorphisms (SNPs). We apply PCA-based inversion detection to a simulated data set and real data from multiple insect species, which vary in complexity from a single inversion in samples drawn from a single population to analyzing multiple overlapping inversions occurring in closely-related species, samples of which that were generated from multiple geographic locations. We show empirically that proper analysis of these data can be challenging when multiple inversions or populations are present, and that our alternative framework is more robust in these more difficult scenarios. 10 11 12 13 14 15 16 17 18 19 20 21 Chromosomal inversions play an important role in ecological adaptation by enabling the accumulation 22 of beneficial alleles (Love et al. (2016); Fuller et al. (2018); Prevosti et al. (1988)) and reproductive 23 isolation (Noor et al. (2001)). For example, the 2La inversion in the Anopheles gambiae complex has 24 been associated with thermal tolerance of larvae (Rocca et al. (2009)), enhanced desiccation resistance in 25 adult mosquitoes (Gray et al. (2009)), and susceptibility to at least one species (Plasmodium falciparum) 26 of malaria (Riehle et al. (2017)). 27 Inversion analysis contains three sub-problems: detection (is an inversion present?), localization of an 28 inversion along a chromosome arm, and determining the orientations of inversions present in each sample 29 (karyotyping). Most techniques can perform a subset of these tasks, but not all of them. For example, 30 some insects such as Drosophila melanogaster and the mosquito Anopheles gambiae have large polytene 31 chromosomes, which can be seen directly under a microscope. This enables detection and karyotyping of 32 previously characterized inversions (Lobo et al. (2010); Sharakhov et al. (2006); George et al. (2010)). 33 Computational approaches developed for model organisms such as human -or species without visible 34 chromosomes including many other insects -are generally based on sequencing large DNA fragments 35 from alternative karyotypes. Specifically, inversion breakpoints relative to a known reference genome can 36 discovered by checking for cases where either mate-pair or long-read sequence data align unexpectedly 37 (e.g., Zhu et al. (2017); Corbett-Detig et al. (2012); Hormozdiari et al. (2009); Chen et al. (2009); Suzuki 38 et al. (2014); Zhu et al. (2018)). Breakpoints in Anopheles mosquitoes are characterized by long, repeated 39 sequences (Sharakhov et al. (2006); Lobo et al. ( 2010)), however, which has prohibited break point 40 detection using ...