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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. 

Abstract There are multiple protocols for determining total nitrogen (TN) in water, but most can be grouped into direct approaches (TN‐d) that convert N forms to nitrogen‐oxides (NO_x) and combined approaches (TN‐c) that combine Kjeldahl N (organic N +NH₃) and nitrite+nitrate (NO₂+NO₃‐N). TN concentrations from these two approaches are routinely treated as equal in studies that use data derived from multiple sources (i.e., integrated data sets) despite the distinct chemistries of the two methods. We used two integrated data sets to determine if TN‐c and TN‐d results were interchangeable. Accuracy, determined as the difference between reported concentrations and the most probable value (MPV) of reference samples, was high and similar in magnitude (within 3.5–4.5% of the MPV) for both methods, although the bias was significantly smaller at low concentrations for TN‐d. Detection limits and data flagged as below detection suggested greater sensitivity for TN‐d for one data set, while patterns from the other data set were ambiguous. TN‐c results were more variable (less precise) by many measures, although TN‐d data included a small fraction of notably inaccurate results. Precision of TN‐c was further compromised by propagated error, which may not be acknowledged or detectable in integrated data sets unless complete metadata are available and inspected. Finally, concurrent measures of TN‐c and TN‐d in lake samples were extremely similar. Overall, TN‐d tended to be slightly more accurate and precise, but similarities in accuracy and the near 1 : 1 relationship for concurrent TN‐d and TN‐c measurements support careful use of data interchangeably in analyses of heterogeneous, integrated data sets. 

Abstract Although ecosystems respond to global change at regional to continental scales (i.e., macroscales), model predictions of ecosystem responses often rely on data from targeted monitoring of a small proportion of sampled ecosystems within a particular geographic area. In this study, we examined how the sampling strategy used to collect data for such models influences predictive performance. We subsampled a large and spatially extensive data set to investigate how macroscale sampling strategy affects prediction of ecosystem characteristics in 6,784 lakes across a 1.8‐million‐km²area. We estimated model predictive performance for different subsets of the data set to mimic three common sampling strategies for collecting observations of ecosystem characteristics: random sampling design, stratified random sampling design, and targeted sampling. We found that sampling strategy influenced model predictive performance such that (1) stratified random sampling designs did not improve predictive performance compared to simple random sampling designs and (2) although one of the scenarios that mimicked targeted (non‐random) sampling had the poorest performing predictive models, the other targeted sampling scenarios resulted in models with similar predictive performance to that of the random sampling scenarios. Our results suggest that although potential biases in data sets from some forms of targeted sampling may limit predictive performance, compiling existing spatially extensive data sets can result in models with good predictive performance that may inform a wide range of science questions and policy goals related to global change.