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Poikilothermic animals comprise most species on Earth and are especially sensitive to changes in environmental temperatures. Species conservation in a changing climate relies upon predictions of species responses to future conditions, yet predicting species responses to climate change when temperatures exceed the bounds of observed data is fraught with challenges. We present a physiologically guided abundance (PGA) model that combines observations of species abundance and environmental conditions with laboratory-derived data on the physiological response of poikilotherms to temperature to predict species geographical distributions and abundance in response to climate change. The model incorporates uncertainty in laboratory-derived thermal response curves and provides estimates of thermal habitat suitability and extinction probability based on site-specific conditions. We show that temperature-driven changes in distributions, local extinction, and abundance of cold, cool, and warm-adapted species vary substantially when physiological information is incorporated. Notably, cold-adapted species were predicted by the PGA model to be extirpated in 61% of locations that they currently inhabit, while extirpation was never predicted by a correlative niche model. Failure to account for species-specific physiological constraints could lead to unrealistic predictions under a warming climate, including underestimates of local extirpation for cold-adapted species near the edges of their climate niche space and overoptimistic predictions of warm-adapted species. 

Summary Many real‐world scientific processes are governed by complex non‐linear dynamic systems that can be represented by differential equations. Recently, there has been an increased interest in learning, or discovering, the forms of the equations driving these complex non‐linear dynamic systems using data‐driven approaches. In this paper, we review the current literature on data‐driven discovery for dynamic systems. We provide a categorisation to the different approaches for data‐driven discovery and a unified mathematical framework to show the relationship between the approaches. Importantly, we discuss the role of statistics in the data‐driven discovery field, describe a possible approach by which the problem can be cast in a statistical framework and provide avenues for future work. 

Abstract Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the seasonal temperature cycle. However, an often overlooked feature of the climate seasonal cycle is the semi‐annual harmonic, which can account for a significant portion of the variance of the seasonal cycle and varies in amplitude and phase across space. Together, the spatial variation in the annual and semi‐annual harmonics can play an important role in driving processes that are tied to seasonality (e.g., ecological and agricultural processes). We propose a multivariate spatiotemporal model to quantify the spatial and temporal change in minimum and maximum temperature seasonal cycles as a function of the annual and semi‐annual harmonics. Our approach captures spatial dependence, temporal dynamics, and multivariate dependence of these harmonics through spatially and temporally varying coefficients. We apply the model to minimum and maximum temperature over North American for the years 1979–2018. Formal model inference within the Bayesian paradigm enables the identification of regions experiencing significant changes in minimum and maximum temperature seasonal cycles due to the relative effects of changes in the two harmonics.