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Hindlimb loss has evolved repeatedly in many different animals by means of molecular mechanisms that are still unknown. To determine the number and type of genetic changes underlying pelvic reduction in natural populations, we carried out genetic crosses between threespine stickleback fish with complete or missing pelvic structures. Genome-wide linkage(More)
The molecular mechanisms underlying major phenotypic changes that have evolved repeatedly in nature are generally unknown. Pelvic loss in different natural populations of threespine stickleback fish has occurred through regulatory mutations deleting a tissue-specific enhancer of the Pituitary homeobox transcription factor 1 (Pitx1) gene. The high prevalence(More)
We develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvabil-ity theory for the nonmodular TC commutator. These theories are used to show that each of the following sets of statements are equivalent for a variety V of algebras. (I) (a) V satisfies a nontrivial congruence identity. (b)(More)
There are approximately 400 breeds of dog worldwide, displaying significant differences in body size, coat type, leg length, head shape, and more. We have undertaken a genome wide association study (GWAS), involving hundreds of dogs to identify the genes and mutations responsible for this range of variation. A total of 835 dogs from nearly 80 breeds were(More)