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The distributions of animal populations change and evolve through time. Migratory species exploit different habitats at different times of the year. Biotic and abiotic features that determine where a species lives vary due to natural and anthropogenic factors. This spatiotemporal variation needs to be accounted for in any modeling of species' distributions. In this paper we introduce a semiparametric model that provides a flexible framework for analyzing dynamic patterns of species occurrence and abundance from broad-scale survey data. The spatiotemporal exploratory model (STEM) adds essential spatiotemporal structure to existing techniques for developing species distribution models through a simple parametric structure without requiring a detailed understanding of the underlying dynamic processes. STEMs use a multi-scale strategy to differentiate between local and global-scale spatiotemporal structure. A user-specified species distribution model accounts for spatial and temporal patterning at the local level. These local patterns are then allowed to "scale up" via ensemble averaging to larger scales. This makes STEMs especially well suited for exploring distributional dynamics arising from a variety of processes. Using data from eBird, an online citizen science bird-monitoring project, we demonstrate that monthly changes in distribution of a migratory species, the Tree Swallow (Tachycineta bicolor), can be more accurately described with a STEM than a conventional bagged decision tree model in which spatiotemporal structure has not been imposed. We also demonstrate that there is no loss of model predictive power when a STEM is used to describe a spatiotemporal distribution with very little spatiotemporal variation; the distribution of a nonmigratory species, the Northern Cardinal (Cardinalis cardinalis).

Background The COVID-19 pandemic has driven demand for forecasts to guide policy and planning. Previous research has suggested that combining forecasts from multiple models into a single "ensemble" forecast can increase the robustness of forecasts. Here we evaluate the real-time application of an open, collaborative ensemble to forecast deaths attributable to COVID-19 in the U.S. Methods Beginning on April 13, 2020, we collected and combined one- to four-week ahead forecasts of cumulative deaths for U.S. jurisdictions in standardized, probabilistic formats to generate real-time, publicly available ensemble forecasts. We evaluated the point prediction accuracy and calibration of these forecasts compared to reported deaths. Results Analysis of 2,512 ensemble forecasts made April 27 to July 20 with outcomes observed in the weeks ending May 23 through July 25, 2020 revealed precise short-term forecasts, with accuracy deteriorating at longer prediction horizons of up to four weeks. At all prediction horizons, the prediction intervals were well calibrated with 92-96% of observations falling within the rounded 95% prediction intervals. Conclusions This analysis demonstrates that real-time, publicly available ensemble forecasts issued in April-July 2020 provided robust short-term predictions of reported COVID-19 deaths in the United States. With the ongoing need for forecasts of impacts and resource needs for the COVID-19 response, the results underscore the importance of combining multiple probabilistic models and assessing forecast skill at different prediction horizons. Careful development, assessment, and communication of ensemble forecasts can provide reliable insight to public health decision makers.

Significance This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the United States. Results show high variation in accuracy between and within stand-alone models and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public-health action.

The deep image prior [26] was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to make the output match observations. This approach yields good performance on a range of image reconstruction tasks. We show that the deep image prior is asymptotically equivalent to a stationary Gaussian process prior in the limit as the number of channels in each layer of the network goes to infinity, and derive the corresponding kernel. This informs a Bayesian approach to inference. We show that by conducting posterior inference using stochastic gradient Langevin dynamics we avoid the need for early stopping, which is a drawback of the current approach, and improve results for denoising and impainting tasks. We illustrate these intuitions on a number of 1D and 2D signal reconstruction tasks.

Despite the routine nature of estimating overlapping space use in ecological research, to date no formal inferential framework for home range overlap has been available to ecologists. Part of this issue is due to the inherent difficulty of comparing the estimated home ranges that underpin overlap across individuals, studies, sites, species, and times. As overlap is calculated conditionally on a pair of home range estimates, biases in these estimates will propagate into biases in overlap estimates. Further compounding the issue of comparability in home range estimators is the historical lack of confidence intervals on overlap estimates. This means that it is not currently possible to determine if a set of overlap values is statistically different from one another. As a solution, we develop the first rigorous inferential framework for home range overlap. Our framework is based on the autocorrelated‐Kernel density estimation (AKDE) family of home range estimators, which correct for biases due to autocorrelation, small effective sample size, and irregular sampling in time. Collectively, these advances allow AKDE estimates to validly be compared even when sampling strategies differ. We then couple the AKDE estimates with a novel bias‐corrected Bhattacharyya coefficient (BC) to quantify overlap. Finally, we propagate uncertainty in the AKDE estimates through to overlap and thus are able to put confidence intervals on the BC point estimate. Using simulated data, we demonstrate how our inferential framework provides accurate overlap estimates, and reasonable coverage of the true overlap, even at small sample sizes. When applied to empirical data, we found that building an interaction network for Mongolian gazelles Procapra gutturosa based on all possible ties, vs. only those ties with statistical support, substantially influenced the network’s properties and any potential biological inferences derived from it. Our inferential framework permits researchers to calculate overlap estimates that can validly be compared across studies, sites, species, and times, and test whether observed differences are statistically meaningful. This method is available via the R package ctmm.

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Redd (nest) surveys for resident brook trout (Salvelinus fontinalis) were conducted annually in a mountain lake in northern New York for 11 years with multiple surveys conducted during the spawning season in eight of those years. Repeated surveys throughout the spawning season allowed us to fit an individually based parametric model and estimate the day of year on which spawning was initiated, reached its midpoint, and ended during each year. Spawning phenology was then assessed relative to (1) mean of maximum daily air temperature and (2) mean of maximum daily water temperature at the lake bottom during summer in each year using a linear model. Elevated temperatures in summer were correlated with a delay in spawning and a reduction in the total number of redds constructed. Increasing the summer mean of maximum daily air temperatures by 1°C delayed spawning by approximately 1 week and decreased the total number of redds constructed by nearly 65. Lake spawning brook trout select redd sites based on the presence of discharging groundwater that is relatively constant in temperature within and across years, leading to relatively consistent egg incubation times. Therefore, delayed spawning is likely to delay fry emergence, which could influence emergence synchrony with prey items. This work highlights non-lethal and sub-lethal effects of elevated summer temperatures on native resident salmonids in aquatic environments with limited thermal refugia.