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The cause, or causes, of the Pleistocene megafaunal extinctions have been difficult to establish, in part because poor spatiotemporal resolution in the fossil record hinders alignment of species disappearances with archeological and environmental data. We obtained 172 new radiocarbon dates on megafauna from Rancho La Brea in California spanning 15.6 to 10.0 thousand calendar years before present (ka). Seven species of extinct megafauna disappeared by 12.9 ka, before the onset of the Younger Dryas. Comparison with high-resolution regional datasets revealed that these disappearances coincided with an ecological state shift that followed aridification and vegetation changes during the Bølling-Allerød (14.69 to 12.89 ka). Time-series modeling implicates large-scale fires as the primary cause of the extirpations, and the catalyst of this state shift may have been mounting human impacts in a drying, warming, and increasingly fire-prone ecosystem.

 

Abstract This article investigates a form of rank deficiency in phenotypic covariance matrices derived from geometric morphometric data, and its impact on measures of phenotypic integration. We first define a type of rank deficiency based on information theory then demonstrate that this deficiency impairs the performance of phenotypic integration metrics in a model system. Lastly, we propose methods to treat for this information rank deficiency. Our first goal is to establish how the rank of a typical geometric morphometric covariance matrix relates to the information entropy of its eigenvalue spectrum. This requires clear definitions of matrix rank, of which we define three: the full matrix rank (equal to the number of input variables), the mathematical rank (the number of nonzero eigenvalues), and the information rank or “effective rank” (equal to the number of nonredundant eigenvalues). We demonstrate that effective rank deficiency arises from a combination of methodological factors—Generalized Procrustes analysis, use of the correlation matrix, and insufficient sample size—as well as phenotypic covariance. Secondly, we use dire wolf jaws to document how differences in effective rank deficiency bias two metrics used to measure phenotypic integration. The eigenvalue variance characterizes the integration change incorrectly, and the standardized generalized variance lacks the sensitivity needed to detect subtle changes in integration. Both metrics are impacted by the inclusion of many small, but nonzero, eigenvalues arising from a lack of information in the covariance matrix, a problem that usually becomes more pronounced as the number of landmarks increases. We propose a new metric for phenotypic integration that combines the standardized generalized variance with information entropy. This metric is equivalent to the standardized generalized variance but calculated only from those eigenvalues that carry nonredundant information. It is the standardized generalized variance scaled to the effective rank of the eigenvalue spectrum. We demonstrate that this metric successfully detects the shift of integration in our dire wolf sample. Our third goal is to generalize the new metric to compare data sets with different sample sizes and numbers of variables. We develop a standardization for matrix information based on data permutation then demonstrate that Smilodon jaws are more integrated than dire wolf jaws. Finally, we describe how our information entropy-based measure allows phenotypic integration to be compared in dense semilandmark data sets without bias, allowing characterization of the information content of any given shape, a quantity we term “latent dispersion”. [Canis dirus; Dire wolf; effective dispersion; effective rank; geometric morphometrics; information entropy; latent dispersion; modularity and integration; phenotypic integration; relative dispersion.] 

Recent advances in genomics and palaeontology have begun to unravel the complex evolutionary history of the gray wolf, Canis lupus . Still, much of their phenotypic variation across time and space remains to be documented. We examined the limb morphology of the fossil and modern North American gray wolves from the late Quaternary (< ca 70 ka) to better understand their postcranial diversity through time. We found that the late-Pleistocene gray wolves were characterized by short-leggedness on both sides of the Cordilleran–Laurentide ice sheets, and that this trait survived well into the Holocene despite the collapse of Pleistocene megafauna and disappearance of the ‘Beringian wolf' from Alaska. By contrast, extant populations in the Midwestern USA and northwestern North America are distinguished by their elongate limbs with long distal segments, which appear to have evolved during the Holocene possibly in response to a new level or type of prey depletion. One of the consequences of recent extirpation of the Plains ( Canis lupus nubilus ) and Mexican wolves ( C. l. baileyi ) from much of the USA is an unprecedented loss of postcranial diversity through removal of short-legged forms. Conservation of these wolves is thus critical to restoration of the ecophenotypic diversity and evolutionary potential of gray wolves in North America.