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Abstract The isodynamic points of a plane triangle are known to be the only pair of its centers invariant under the action of the Möbius group$${\mathcal {M}}$$ $M$on the set of triangles, Kimberling (Encyclopedia of Triangle Centers,http://faculty.evansville.edu/ck6/encyclopedia). Generalizing this classical result, we introduce below theisodynamicmap associating to a univariate polynomial of degree$$d\ge 3$$ $d\ge 3$with at most double roots a polynomial of degree (at most)$$2d-4$$ $2d-4$such that this map commutes with the action of the Möbius group$${\mathcal {M}}$$ $M$on the zero loci of the initial polynomial and its image. The roots of the image polynomial will be called theisodynamic pointsof the preimage polynomial. Our construction naturally extends from univariate polynomials to binary forms and further to their ratios. 

Abstract Hybridization is a common process that has broadly impacted the evolution of multicellular eukaryotes; however, how ecological factors influence this process remains poorly understood. Here, we report the findings of a 3-year recapture study of the Bryant’s woodrat (Neotoma bryanti) and desert woodrat (Neotoma lepida), two species that hybridize within a creosote bush (Larrea tridentata) shrubland in Whitewater, CA, USA. We used a genotype-by-sequencing approach to characterize the ancestry distribution of individuals across this hybrid zone coupled with Cormack–Jolly–Seber modeling to describe demography. We identified a high frequency of hybridization at this site with ~40% of individuals possessing admixed ancestry, which is the result of multigenerational backcrossing and advanced hybrid-hybrid crossing. F1, F2, and advanced generation hybrids had apparent survival rates similar to parental N. bryanti, while parental and backcross N. lepida had lower apparent survival rates and were far less abundant. Compared to bimodal hybrid zones where hybrids are often rare and selected against, we find that hybrids at Whitewater are common and have comparable survival to the dominant parental species, N. bryanti. The frequency of hybridization at Whitewater is therefore likely limited by the abundance of the less common parental species, N. lepida, rather than selection against hybrids. 

Adaptive radiation is an important mechanism of organismal diversification and can be triggered by new ecological opportunities. Although poorly studied in this regard, parasites are an ideal group in which to study adaptive radiations because of their close associations with host species. Both experimental and comparative studies suggest that the ectoparasitic wing lice of pigeons and doves have adaptively radiated, leading to differences in body size and overall coloration. Here, we show that long-distance dispersal by dove hosts was central to parasite diversification because it provided new ecological opportunities for parasites to speciate after host-switching. We further show that among extant parasite lineages host-switching decreased over time, with cospeciation becoming the more dominant mode of parasite speciation. Taken together, our results suggest that host dispersal, followed by host-switching, provided novel ecological opportunities that facilitated adaptive radiation by parasites. 

Abstract Little is known about the tolerances of mammalian herbivores to plant specialized metabolites across landscapes.We investigated the tolerances of two species of herbivorous woodrats,Neotoma lepida(desert woodrat) andNeotoma bryanti(Bryant's woodrat) to creosote bushLarrea tridentata, a widely distributed shrub with a highly toxic resin. Woodrats were sampled from 13 locations both with and without creosote bush across a 900 km transect in the US southwest. We tested whether these woodrat populations consume creosote bush using plant metabarcoding of faeces and quantified their tolerance to creosote bush through feeding trials using chow amended with creosote resin.Toxin tolerance was analysed in the context of population structure across collection sites with microsatellite analyses. Genetic differentiation among woodrats collected from different locations was minimal within either species. Tolerance differed substantially between the two species, withN. lepidapersisting 20% longer thanN. bryantiin feeding trials with creosote resin. Furthermore, in both species, tolerance to creosote resin was similar among woodrats near or within creosote bush habitat. In both species, woodrats collected >25 km from creosote had markedly lower tolerances to creosote resin compared to animals from within the range of creosote bush.The results imply that mammalian herbivores are adapted to the specialized metabolites of plants in their diet, and that this tolerance can extend several kilometres outside of the range of dietary items. That is, direct ecological exposure to the specialized chemistry of particular plant species is not a prerequisite for tolerance to these compounds. These findings lay the groundwork for additional studies to investigate the genetic mechanisms underlying toxin tolerance and to identify how these mechanisms are maintained across landscape‐level scales in mammalian herbivores. Read the freePlain Language Summaryfor this article on the Journal blog. 

We show that, in a many‐body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time‐domain formulation is complementary to the formulation of the many‐body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one‐dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations.image