We developed a theoretical framework based on phylogenetic comparative methods to integrate phylogeny into three measures of biodiversity: species variability, richness, and evenness. These metrics can be used in conjunction with permutation procedures to test for phylogenetic community structure. As an illustration, we analyzed data on the composition of 58 lake fish communities in Wisconsin. The fish communities showed phylogenetic underdispersion, with communities more likely to contain closely related species. Using information about differences in environmental characteristics among lakes, we demonstrated that phylogenetic underdispersion in fish communities was associated with environmental factors. For example, lakes with low pH were more likely to contain species in the same clade of acid-tolerant species. Our metrics differ from existing metrics used to calculate phylogenetic community structure, such as net relatedness index and Faith's phylogenetic diversity. Our metrics have the advantage of providing an integrated and easy-to-understand package of phylogenetic measures of species variability, richness, and evenness with well-defined statistical properties. Furthermore, they allow the easy evaluation of contributions of individual species to different aspects of the phylogenetic organization of communities. Therefore, these metrics should aid with the incorporation of phylogenetic information into strategies for understanding biodiversity and its conservation.

Lake and stream habitats pose a variety of challenges to fishes due to differences in variables such as water velocity, habitat structure, prey community, and predator community. These differences can cause divergent selection on body size and/or shape. Here, we measured sex, age, length, and eight different morphological traits of the blackstripe topminnow, Fundulus notatus, from 19 lake and stream populations across four river drainages in central Illinois. Our goal was to determine whether size and shape differed consistently between lake and stream habitats across drainages. We also considered the effects of age and sex as they may affect size and morphology. We found large differences in body size of age 1 topminnows where stream fish were generally larger than lake fish. Body shape mainly varied as a function of sex. Adult male topminnows had larger morphological traits (with the exception of body width) than females, in particular longer dorsal and anal base lengths. Subtle effects of habitat were present. Stream fish had a longer dorsal fin base than lake fish. These phenotypic patterns may be the result of genetic and/or environmental variation. As these lakes are human-made, the observed differences, if genetic, would have had to occur relatively rapidly (within about 100 years).

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Two-component dipolar condensates are now experimentally producible, and we theoretically investigate the nature of supersolidity in this system. We predict the existence of a binary supersolid state in which the two components form a series of alternating domains, producing an immiscible double supersolid. Remarkably, we find that a dipolar component can even induce supersolidity in a nondipolar component. In stark contrast to single-component supersolids, the number of crystal sites is not strictly limited by the condensate populations, and the density is hence substantially lower. Our results are applicable to a wide range of dipole moment combinations, marking an important step towards long-lived bulk-supersolidity.

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