Predicting responses to climate change using a joint species, spatially dependent physiologically guided abundance model.

Predicting the effects of warming temperatures on the abundance and distribution of organisms under future climate scenarios often requires extrapolating species-environment correlations to climatic conditions not currently experienced by a species, which can result in unrealistic predictions. For poikilotherms, incorporating species' thermal physiology to inform extrapolations under novel thermal conditions can result in more realistic predictions. Furthermore, models that incorporate species and spatial dependencies may improve predictions by capturing correlations present in ecological data that are not accounted for by predictor variables. Here, we present a joint species, spatially dependent physiologically guided abundance (jsPGA) model for predicting multispecies responses to climate warming. The jsPGA model uses a basis function approach to capture both species and spatial dependencies. We apply the jsPGA model to predict the response of eight fish species to projected climate warming in thousands of lakes in Minnesota, USA. By the end of the century, the cold-adapted species was predicted to have high probabilities of extirpation across its current range-with 10% of lakes currently inhabited by this species having an extirpation probability >0.90. The remaining species had varying levels of predicted changes in abundance, reflecting differences in their thermal physiology. Though the model did not identify many strong species dependencies, the variation in estimated spatial dependence across species suggested that accounting for both dependencies was important for predicting the abundance of these fishes. The jsPGA model provides a new tool for predicting changes in the abundance, distribution, and extirpation probability of poikilotherms under novel thermal conditions.

Predicting climate change impacts on poikilotherms using physiologically guided species abundance models.

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.

Ecological prediction at macroscales using big data: Does sampling design matter?

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-km2 area. 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.

Identifying and characterizing extrapolation in multivariate response data.

Faced with limitations in data availability, funding, and time constraints, ecologists are often tasked with making predictions beyond the range of their data. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the data. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are common in ecological investigations. In this paper, we extend previous work that identified extrapolation by applying the predictive variance from the univariate setting to the multivariate case. We propose using the trace or determinant of the predictive variance matrix to obtain a scalar value measure that, when paired with a selected cutoff value, allows for delineation between prediction and extrapolation. We illustrate our approach through an analysis of jointly modeled lake nutrients and indicators of algal biomass and water clarity in over 7000 inland lakes from across the Northeast and Mid-west US. In addition, we outline novel exploratory approaches for identifying regions of covariate space where extrapolation is more likely to occur using classification and regression trees. The use of our Multivariate Predictive Variance (MVPV) measures and multiple cutoff values when exploring the validity of predictions made from multivariate statistical models can help guide ecological inferences.

Alternating Gaussian Process Modulated Renewal Processes for Modeling Threshold Exceedances and Durations.

It is often of interest to model the incidence and duration of threshold exceedance events for an environmental variable over a set of monitoring locations. Such data arrive over continuous time and can be considered as observations of a two-state process yielding, sequentially, a length of time in the below threshold state followed by a length of time in the above threshold state, then returning to the below threshold state, etc. We have a two-state continuous time Markov process, often referred to as an alternating renewal process. The process is observed over a truncated time window and, within this window, time in each state is modeled using a distinct cumulative intensity specification. Initially, we model each intensity over the window using a parametric regression specification. We extend the regression specification adding temporal random effects to enrich the model, using a realization of a log Gaussian process over time. With only one type of renewal, this specification is referred to as a Gaussian process modulated renewal process. Here, we introduce Gaussian process modulation to the intensity for each state. Model fitting is done within a Bayesian framework. We clarify that fitting with a customary log Gaussian process specification over a lengthy time window is computationally infeasible. The nearest neighbor Gaussian process (NNGP), which supplies sparse covariance structure, is adopted to enable tractable computation. We also propose methods for both generating data under our models and for conducting model comparison. The model is applied to hourly ozone data for four monitoring sites in different locations across the United States for the ozone season of 2014. For each site, we obtain estimated profiles of up-crossing and down-crossing intensity functions through time. In addition, we obtain inference regarding the number of exceedances, the distribution of the duration of exceedance events, and the proportion of time in the above and below threshold state for any time interval.

Asymmetric biotic interactions and abiotic niche differences revealed by a dynamic joint species distribution model.

A species' distribution and abundance are determined by abiotic conditions and biotic interactions with other species in the community. Most species distribution models correlate the occurrence of a single species with environmental variables only, and leave out biotic interactions. To test the importance of biotic interactions on occurrence and abundance, we compared a multivariate spatiotemporal model of the joint abundance of two invasive insects that share a host plant, hemlock woolly adelgid (HWA; Adelges tsugae) and elongate hemlock scale (EHS; Fiorina externa), to independent models that do not account for dependence among co-occurring species. The joint model revealed that HWA responded more strongly to abiotic conditions than EHS. Additionally, HWA appeared to predispose stands to subsequent increase of EHS, but HWA abundance was not strongly dependent on EHS abundance. This study demonstrates how incorporating spatial and temporal dependence into a species distribution model can reveal the dependence of a species' abundance on other species in the community. Accounting for dependence among co-occurring species with a joint distribution model can also improve estimation of the abiotic niche for species affected by interspecific interactions.