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Without the ability to control or randomize environments (or genotypes), it is difficult to determine the degree to which observed phenotypic differences between two groups of individuals are due to genetic vs. environmental differences. However, some have suggested that these concerns may be limited to pathological cases, and methods have appeared that seem to give-directly or indirectly-some support to claims that aggregate heritable variation within groups can be related to heritable variation among groups. We consider three families of approaches: the "between-group heritability" sometimes invoked in behavior genetics, the statistic [Formula: see text] used in empirical work in evolutionary quantitative genetics, and methods based on variation in ancestry in an admixed population, used in anthropological and statistical genetics. We take up these examples to show mathematically that information on within-group genetic and phenotypic information in the aggregate cannot separate among-group differences into genetic and environmental components, and we provide simulation results that support our claims. We discuss these results in terms of the long-running debate on this topic., Competing Interests: Competing interests statement:The authors declare no competing interest.

The Caribbean was one of the last parts of the Americas to be settled by humans, but how and when the islands were first occupied remains a matter of debate. Ancient DNA can help answering these questions, but the work has been hampered by poor DNA preservation. We report the genome sequence of a 1,000-year-old Lucayan Taino individual recovered from the site of Preacher's Cave in the Bahamas. We sequenced her genome to 12.4-fold coverage and show that she is genetically most closely related to present-day Arawakan speakers from northern South America, suggesting that the ancestors of the Lucayans originated there. Further, we find no evidence for recent inbreeding or isolation in the ancient genome, suggesting that the Lucayans had a relatively large effective population size. Finally, we show that the native American components in some present-day Caribbean genomes are closely related to the ancient Taino, demonstrating an element of continuity between precontact populations and present-day Latino populations in the Caribbean., Competing Interests: Conflict of interest statement: H.S. is on the scientific advisory board of Living DNA Ltd, J.R.H. is co-founder of Encompass Bioscience Inc, and C.D.B. is founder of IdentifyGenomics, LLC, and scientific advisor for Personalis Inc, Ancestry.com Inc, and Invitae Inc. This did not affect the design, execution, or interpretation of the experiments and results presented here., (Copyright © 2018 the Author(s). Published by PNAS.)

The relative importance of different modes of evolution in shaping phenotypic diversity remains a hotly debated question. Fossil data suggest that stasis may be a common mode of evolution, while modern data suggest some lineages experience very fast rates of evolution. One way to reconcile these observations is to imagine that evolution proceeds in pulses, rather than in increments, on geological timescales. To test this hypothesis, we developed a maximum-likelihood framework for fitting Lévy processes to comparative morphological data. This class of stochastic processes includes both an incremental and a pulsed component. We found that a plurality of modern vertebrate clades examined are best fitted by pulsed processes over models of incremental change, stationarity, and adaptive radiation. When we compare our results to theoretical expectations of the rate and speed of regime shifts for models that detail fitness landscape dynamics, we find that our quantitative results are broadly compatible with both microevolutionary models and observations from the fossil record., Competing Interests: The authors declare no conflict of interest., (Copyright © 2017 the Author(s). Published by PNAS.)