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The structure of hadronic form factors at high energies and their deviations from perturbative quantum chromodynamics provide insight on nonperturbative dynamics. Using an approach that is consistent with dispersion relations, we construct a model that simultaneously accounts for the pion wave function, gluonic exchanges, and quark Reggeization. In particular, we find that quark Reggeization can be investigated at high energies by studying scaling violation of the form factor. Published by the American Physical Society2025 

Infections by maternally inherited bacterial endosymbionts, especially Wolbachia, are common in insects and other invertebrates but infec- tion dynamics across species ranges are largely under studied. Specifically, we lack a broad understanding of the origin of Wolbachia infec- tions in novel hosts, and the historical and geographical dynamics of infections that are critical for identifying the factors governing their spread. We used Genotype-by-Sequencing data from previous population genomics studies for range-wide surveys of Wolbachia pres- ence and genetic diversity in North American butterflies of the genus Lycaeides. As few as one sequence read identified by assembly to a Wolbachia reference genome provided high accuracy in detecting infections in host butterflies as determined by confirmatory PCR tests, and maximum accuracy was achieved with a threshold of only 5 sequence reads per host individual. Using this threshold, we detected Wolbachia in all but 2 of the 107 sampling localities spanning the continent, with infection frequencies within populations ranging from 0% to 100% of individuals, but with most localities having high infection frequencies (mean 1⁄4 91% infection rate). Three major lineages of Wolbachia were identified as separate strains that appear to represent 3 separate invasions of Lycaeides butterflies by Wolbachia. Overall, we found extensive evidence for acquisition of Wolbachia through interspecific transfer between host lineages. Strain wLycC was confined to a single butterfly taxon, hybrid lineages derived from it, and closely adjacent populations in other taxa. While the other 2 strains were detected throughout the rest of the continent, strain wLycB almost always co-occurred with wLycA. Our demographic modeling suggests wLycB is a recent invasion. Within strain wLycA, the 2 most frequent haplotypes are confined almost exclusively to separate butterfly taxa with haplotype A1 observed largely in Lycaeides melissa and haplotype A2 observed most often in Lycaeides idas localities, consistent with either cladogenic mode of infection acquisition from a common ancestor or by hybridization and accompanying mutation. More than 1 major Wolbachia strain was observed in 15 localities. These results demonstrate the utility of using resequencing data from hosts to quan- tify Wolbachia genetic variation and infection frequency and provide evidence of multiple colonizations of novel hosts through hybridiza- tion between butterfly lineages and complex dynamics between Wolbachia strains.