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Abstract Terrestrial carnivorans, with their diverse diets and unique adaptations such as the carnassial tooth, offer insights into the connections between functional traits and the climatic and environmental conditions they inhabit. They shed light on functional trait‐environment relationships at the highest trophic levels across a broad range of environmental conditions. In this study, we evaluate the relationship between relative blade length (RBL) of the lower carnassial tooth, a key dietary adaptation among terrestrial carnivorans for slicing and grinding food items, and climate. We propose RBL as an ecometric trait and test the hypothesis that community‐level RBL is correlated with climate and mediated by environmental effects on food availability. Our findings show that communities with higher mean and broader variance of RBL are typically located in warmer and wetter climates, suggesting a relationship between carnivoran dietary diversity and climate. Conversely, communities with a lower mean and narrower variance of RBL predominantly occupy cooler, drier places. This indicates that community‐level carnivoran dietary traits have the potential to serve as indicators of environmental conditions. Given the robust fossil record associated with carnivorans, we also show how RBL can be used as a proxy for reconstructing paleoclimates by examining trait change at seven sites in North America to estimate changes in temperature and precipitation over time in relation to changes in carnivoran community assembly. Understanding the nature of trait‐environment relationships can help us anticipate biological impacts of ongoing environmental change and the geographic regions at the greatest risk of ecological disruption. 

The highest species richness and ecological diversity of extant squamates are in the tropics. Both their taxic richness and functional traits are predictably correlated to environmental factors, and the utility of these measures in the squamate fossil record is an emergent tool for paleoenvironmental reconstruction. Ongoing field research in the early Miocene (approx. 20–19 Mya) Tinderet sequence of western Kenya has produced a diverse record of squamates which provides environmental data for hominoid-bearing localities. The record consists of chamaeleonid, agamid, varanid, and amphisbaenid lizards as well as snake lineages including pythonids, colubroids, elapoids, and a newly discovered taxon sharing unique vertebral apomorphies with extant tropical South American Anilius scytale. Combined with additional fossils from the Eocene of North Africa, the new Tinderet taxon demonstrates an unambiguous past record of an extant neotropical snake lineage in Africa and falsifies previous vicariance hypotheses to explain the biogeographic histories of basal divisions within snakes. Recent stable isotopic and phytolith studies of Early to Middle Miocene eastern African fossil localities have indicated heterogenous environments, including C4 grasses and wood- to scrubland, associated with vertebrate faunas. The composition of squamate faunas is generally consistent with these reconstructions, with the new taxon providing precise evidence for precipitation. Comparing climate parameters of habitats for Anilius and other extant ecological analogues equivalent to those reconstructed for the eastern African Early Miocene indicates annual precipitation between 1500–2500 mm/year, consistent with wet tropical seasonal forests and rain forests. 

Abstract We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the inverse penalization strength. 

Understanding the relationships between functional traits and environment is increasingly important for assessing ecosystem health and forecasting biotic responses to future environmental change. Taxon-free analyses of functional traits (ecometrics) allow for testing the performance of such traits through time, utilizing both the fossil record and paleoenvironmental proxies. Here, we test the role of body size as a functional trait with respect to climate, using turtles as a model system. We examine the influence of mass-specific metabolic rate as a functional factor in the sorting of body size with environmental temperature and investigate the utility of community body size composition as an ecometric correlated to climate variables. We then apply our results to the fossil record of the Plio-Pleistocene Shungura Formation in Ethiopia. Results show that turtle body sizes scale with mass-specific metabolic rate for larger taxa, but not for the majority of species, indicating that metabolism is not a primary driver of size. Body size ecometrics have stronger predictive power at continental than at global scales, but without a single, dominant predictive functional relationship. Application of ecometrics to the Shungura fossil record suggests that turtle paleocommunity ecometrics coarsely track independent paleoclimate estimates at local scales. We hypothesize that both human disruption and biotic interactions limit the ecometric fit of size to climate in this clade. Nonetheless, examination of the consistency of trait–environment relationships through deep and shallow time provides a means for testing anthropogenic influences on ecosystems. 

The late Quaternary is characterized by the extinction of many terrestrial megafauna, which included tortoises (Family: Testudinidae). However, limited information is available on how extinction shaped the phenotype of surviving taxa. Here, based on a global dataset of straight carapace length, we investigate the temporal variation, spatial distribution and evolution of tortoise body size over the past 23 million years, thereby capturing the effects of Quaternary extinctions in this clade. We found a significant change in body size distribution characterized by a reduction of both mean body size and maximum body size of extant tortoises relative to fossil taxa. This reduction of body size occurred earlier in mainland (Early Pleistocene 2.588–0.781 Ma) than in island tortoises (Late Pleistocene/Holocene 0.126–0 Ma). Despite contrasting body size patterns between fossil and extant taxa on a spatial scale, tortoise body size showed limited variation over time until this decline. Body size is a fundamental functional trait determining many aspects of species ecologies, with large tortoises playing key roles as ecosystem engineers. As such, the transition from larger sized to smaller sized classes indicated by our findings likely resulted in the homogenization of tortoises' ecological functions and diminished the role of tortoises in structuring the vegetation community. 

Abstract Mammalian megafauna have been critical to the functioning of Earth’s biosphere for millions of years. However, since the Plio-Pleistocene, their biodiversity has declined concurrently with dramatic environmental change and hominin evolution. While these biodiversity declines are well-documented, their implications for the ecological function of megafaunal communities remain uncertain. Here, we adapt ecometric methods to evaluate whether the functional link between communities of herbivorous, eastern African megafauna and their environments (i.e., functional trait-environment relationships) was disrupted as biodiversity losses occurred over the past 7.4 Ma. Herbivore taxonomic and functional diversity began to decline during the Pliocene as open grassland habitats emerged, persisted, and expanded. In the mid-Pleistocene, grassland expansion intensified, and climates became more variable and arid. It was then that phylogenetic diversity declined, and the trait-environment relationships of herbivore communities shifted significantly. Our results divulge the varying implications of different losses in megafaunal biodiversity. Only the losses that occurred since the mid-Pleistocene were coincident with a disturbance to community ecological function. Prior diversity losses, conversely, occurred as the megafaunal species and trait pool narrowed towards those adapted to grassland environments. 

East Africa is a global biodiversity hotspot and exhibits distinct longitudinal diversity gradients from west to east in freshwater fishes and forest mammals. The assembly of this exceptional biodiversity and the drivers behind diversity gradients remain poorly understood, with diversification often studied at local scales and less attention paid to biotic exchange between Afrotropical regions. Here, we reconstruct a river system that existed for several millennia along the now semiarid Kenya Rift Valley during the humid early Holocene and show how this river system influenced postglacial dispersal of fishes and mammals due to its dual role as a dispersal corridor and barrier. Using geomorphological, geochronological, isotopic, and fossil analyses and a synthesis of radiocarbon dates, we find that the overflow of Kenyan rift lakes between 12 and 8 ka before present formed a bidirectional river system consisting of a “Northern River” connected to the Nile Basin and a “Southern River,” a closed basin. The drainage divide between these rivers represented the only viable terrestrial dispersal corridor across the rift. The degree and duration of past hydrological connectivity between adjacent river basins determined spatial diversity gradients for East African fishes. Our reconstruction explains the isolated distribution of Nilotic fish species in modern Kenyan rift lakes, Guineo-Congolian mammal species in forests east of the Kenya Rift, and recent incipient vertebrate speciation and local endemism in this region. Climate-driven rearrangements of drainage networks unrelated to tectonic activity contributed significantly to the assembly of species diversity and modern faunas in the East African biodiversity hotspot.