Beta diversity is an important component of large-scale patterns of biodiversity, but its explicit examination is more difficult than that of alpha diversity. Only recently have data sets large enough been presented to begin assessing global patterns of species turnover, especially in the fossil record. We present here an analysis of beta diversity of a Maastrichtian (71-65 million years old) assemblage of dinosaurs from the Western Interior of North America, a region that covers ≈1.5 × 10 6 km 2 , borders an epicontinental sea, and spans ≈20°of latitude. Previous qualitative analyses have suggested regional groupings of these dinosaurs and generally concluded that there were multiple distinct faunal regions. However, these studies did not directly account for sampling bias, which may artificially decrease similarity and increase turnover between regions. Our analysis used abundance-based data to account for sampling intensity and was unable to support any hypothesis of multiple distinct faunas; earlier hypothesized faunal delineations were likely a sampling artifact. Our results indicate a low beta diversity and support a single dinosaur community within the entire Western Interior region of latest Cretaceous North America. Homogeneous environments are a known driver of low modern beta diversities, and the warm equable climate of the late Cretaceous modulated by the epicontenental seaway is inferred to be an underlying influence on the low beta diversity of this ancient ecosystem.biogeography | macroecology | paleoecology | Cretaceous

Quantitative morphometric analyses, particularly ontogenetic allometry, are common methods used in quantifying shape, and changes therein, in both extinct and extant organisms. Due to incompleteness and the potential for restricted sample sizes in the fossil record, palaeobiological analyses of allometry may encounter higher rates of error. Differences in sample size between fossil and extant studies and any resulting effects on allometric analyses have not been thoroughly investigated, and a logical lower threshold to sample size is not clear. Here we show that studies based on fossil datasets have smaller sample sizes than those based on extant taxa. A similar pattern between vertebrates and invertebrates indicates this is not a problem unique to either group, but common to both. We investigate the relationship between sample size, ontogenetic allometric relationship and statistical power using an empirical dataset of skull measurements of modern Alligator mississippiensis. Across a variety of subsampling techniques, used to simulate different taphonomic and/or sampling effects, smaller sample sizes gave less reliable and more variable results, often with the result that allometric relationships will go undetected due to Type II error (failure to reject the null hypothesis). This may result in a false impression of fewer instances of positive/negative allometric growth in fossils compared to living organisms. These limitations are not restricted to fossil data and are equally applicable to allometric analyses of rare extant taxa. No mathematically derived minimum sample size for ontogenetic allometric studies is found; rather results of isometry (but not necessarily allometry) should not be viewed with confidence at small sample sizes.

Tooth counts are commonly recorded in fossil diapsid reptiles and have been used for taxonomic and phylogenetic purposes under the assumption that differences in the number of teeth are largely explained by interspecific variation. Although phylogeny is almost certainly one of the greatest factors influencing tooth count, the relative role of intraspecific variation is difficult, and often impossible, to test in the fossil record given the sample sizes available to palaeontologists and, as such, is best investigated using extant models. Intraspecific variation (largely manifested as size-related or ontogenetic variation) in tooth counts has been examined in extant squamates (lizards and snakes) but is poorly understood in archosaurs (crocodylians and dinosaurs). Here, we document tooth count variation in two species of extant crocodylians (Alligator mississippiensis and Crocodylus porosus) as well as a large varanid lizard (Varanus komodoensis). We test the hypothesis that variation in tooth count is driven primarily by growth and thus predict significant correlations between tooth count and size, as well as differences in the frequency of deviation from the modal tooth count in the premaxilla, maxilla, and dentary. In addition to tooth counts, we also document tooth allometry in each species and compare these results with tooth count change through growth. Results reveal no correlation of tooth count with size in any element of any species examined here, with the exception of the premaxilla of C. porosus, which shows the loss of one tooth position. Based on the taxa examined here, we reject the hypothesis, as it is evident that variation in tooth count is not always significantly correlated with growth. However, growth trajectories of smaller reptilian taxa show increases in tooth counts and, although current samples are small, suggest potential correlates between tooth count trajectories and adult size. Nevertheless, interspecific variation in growth patterns underscores the importance of considering and understanding growth when constructing taxonomic and phylogenetic characters, in particular for fossil taxa where ontogenetic patterns are difficult to reconstruct.

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