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Robust ecological forecasting of tree growth under future climate conditions is critical to anticipate future forest carbon storage and flux. Here, we apply three ingredients of ecological forecasting that are key to improving forecast skill: data fusion, confronting model predictions with new data, and partitioning forecast uncertainty. Specifically, we present the first fusion of tree-ring and forest inventory data within a Bayesian state-space model at a multi-site, regional scale, focusing on Pinus ponderosa var. brachyptera in the southwestern US. Leveraging the complementarity of these two data sources, we parsed the ecological complexity of tree growth into the effects of climate, tree size, stand density, site quality, and their interactions, and quantified uncertainties associated with these effects. New measurements of trees, an ongoing process in forest inventories, were used to confront forecasts of tree diameter with observations, and evaluate alternative tree growth models. We forecasted tree diameter and increment in response to an ensemble of climate change projections, and separated forecast uncertainty into four different causes: initial conditions, parameters, climate drivers, and process error. We found a strong negative effect of fall-spring maximum temperature, and a positive effect of water-year precipitation on tree growth. Furthermore, tree vulnerability to climate stress increases with greater competition, with tree size, and at poor sites. Under future climate scenarios, we forecast increment declines of 22%-117%, while the combined effect of climate and size-related trends results in a 56%-91% decline. Partitioning of forecast uncertainty showed that diameter forecast uncertainty is primarily caused by parameter and initial conditions uncertainty, but increment forecast uncertainty is mostly caused by process error and climate driver uncertainty. This fusion of tree-ring and forest inventory data lays the foundation for robust ecological forecasting of aboveground biomass and carbon accounting at tree, plot, and regional scales, including iterative improvement of model skill.

Changing forest disturbance regimes and climate are driving accelerated tree mortality across temperate forests. However, it remains unknown if elevated mortality has induced decline of tree populations and the ecological, economic, and social benefits they provide. Here, we develop a standardized forest demographic index and use it to quantify trends in tree population dynamics over the last two decades in the western United States. The rate and pattern of change we observe across species and tree size-distributions is alarming and often undesirable. We observe significant population decline in a majority of species examined, show decline was particularly severe, albeit size-dependent, among subalpine tree species, and provide evidence of widespread shifts in the size-structure of montane forests. Our findings offer a stark warning of changing forest composition and structure across the western US, and suggest that sustained anthropogenic and natural stress will likely result in broad-scale transformation of temperate forests globally., The nature of forest disturbances are changing, yet consequences for forest dynamics remain uncertain. Using a new index, Stanke et al. show the populations of over half of the most abundant tree species in the western US have declined in the last two decades, with grim implications for how temperate forests globally will respond to sustained anthropogenic and natural stress.

A spatial regression model framework is presented to predict growing stock volume loss due to storm Adrian which caused heavy forest damage in the upper Gail valley in Carinthia, Austria, in October 2018. Model parameters were estimated using growing stock volume measured with a terrestrial laser scanner on 62 sample plots distributed across five sub-regions. Predictor variables were derived from high resolution vegetation height measurements collected during an airborne laser scanning campaign. Non-spatial and spatial candidate models were proposed and assessed based on fit to observed data and out-of-sample prediction. Spatial Gaussian processes associated model intercepts and regression coefficients were used to capture spatial dependence. Results show a spatially-varying coefficient model, which allowed the intercept and regression coefficients to vary spatially, yielded the best fit and prediction. Two approaches were considered for prediction over blowdown areas: 1) an areal approach that viewed each blowdown as a single prediction unit indexed by its centroid; and 2) a block approach where each blowdown was partitioned into smaller prediction units to better align with sample plots’ spatial support. Joint prediction was used to acknowledge spatial dependence among block units. Results demonstrated the block approach is preferable as it mitigated change-of-support issues encountered in the areal approach. Despite the small sample size, predictions for 55% of the total 564 blowdown areas, accounting for 93% of the total loss, had a coefficient of variation less than 25%. Key advantages of the proposed regression framework and chosen Bayesian inferential paradigm, were the ability to quantify uncertainty in spatial covariance parameters, propagate parameter uncertainty through to prediction, and provide statistically valid prediction point and interval estimates for individual blowdowns and collections of blowdowns at the sub-region and region scale via posterior predictive distribution summaries.

We consider alternate formulations of recently proposed hierarchical Nearest Neighbor Gaussian Process (NNGP) models (Datta et al., 2016a) for improved convergence, faster computing time, and more robust and reproducible Bayesian inference. Algorithms are defined that improve CPU memory management and exploit existing high-performance numerical linear algebra libraries. Computational and inferential benefits are assessed for alternate NNGP specifications using simulated datasets and remotely sensed light detection and ranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit (TIU) in a remote portion of Interior Alaska. The resulting data product is the first statistically robust map of forest canopy for the TIU.

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the “big data” era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online. Electronic Supplementary Material Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.

Interactions between drought and insect defoliation may dramatically alter forest function under novel climate and disturbance regimes, but remain poorly understood. We empirically tested two important hypotheses regarding tree responses to drought and insect defoliation: (a) trees exhibit delayed, persistent, and cumulative growth responses to these stressors; (b) physiological feedbacks in tree responses to these stressors exacerbate their impacts on tree growth. These hypotheses remain largely untested at a landscape scale, yet are critical for predicting forest function under novel future conditions, given the connection between tree growth and demographic processes such as mortality and regeneration. We developed a Bayesian hierarchical model to quantify the ecological memory of tree growth to past water deficits and insect defoliation events, derive antecedent variables reflecting the persistent and cumulative effects of these stressors on current growth, and test for their interactive effects. The model was applied to extensive tree growth, weather, and defoliation survey data from western and eastern regions of the Canadian boreal forest impacted by recent drought and defoliation events and characterized by contrasting tree compositions, climates, and insect defoliators. Results revealed persistent negative tree growth responses to past water (all trees) and defoliation (host trees) stress lasting 3–6 and 10–12 years, respectively, depending on study region. Accounting for the ecological memory of tree growth to water and defoliation stress allowed for detection of interactions not previously demonstrated. Contrary to expectations, we found evidence for positive interactions among non‐host trees likely due to reduced water stress following defoliation events. Regional differences in ecological memory to water stress highlight the role of climate in shaping forest responses to drought. Synthesis. Study results suggest negative feedbacks in tree responses to drought and insect attack may be weaker than predicted for defoliator‐dominated boreal forest systems. Instead, insect defoliation may offset the impacts of water deficit on boreal tree growth by reducing transpirational water demand. This offset mimics increased resistance to drought following forest thinning and may lessen growth and mortality losses due to increased aridity and more severe insect damage forecast for the boreal forest under global change.

Improved monitoring and associated inferential tools to efficiently identify declining bird populations, particularly of rare or sparsely distributed species, is key to informed conservation and management across large spatio-temporal regions. We assess abundance trends for 106 bird species in a network of eight national park forests located within the northeast USA from 2006-2019 using a novel hierarchical model. We develop a multi-species, multi-region removal sampling model that shares information across species and parks to enable inference on rare species and sparsely sampled parks and to evaluate the effects of local forest structure. Trends in bird abundance over time varied widely across parks, but species showed similar trends within parks. Three parks (Acadia, Marsh-Billings-Rockefeller, and Morristown) decreased in bird abundance across all species, while three parks (Saratoga, Roosevelt-Vanderbilt, and Weir-Farm) increased in abundance. Bird abundance peaked at medium levels of basal area and high levels of percent forest and forest regeneration, with percent forest having the largest effect. Variation in these effects across parks could be a result of differences in forest structural stage and diversity. Our novel hierarchical model enables estimates of abundance at the network, park, guild, and species levels. We found large variation in abundance trends across parks but not across bird guilds, suggesting that local forest condition may have a broad and consistent effect on the entire bird community within a given park. Management should target the three parks with overall decreasing trends in bird abundance to further identify what specific factors are driving observed declines across the bird community. Understanding how bird communities respond to local forest structure and other stressors is crucial for informed and lasting management., 39 pages, 6 figures

In the past decades, data-driven Machine Learning (ML) models have emerged as promising tools for short-term streamflow forecasts. Among other qualities, the popularity of ML for such applications is due to the methods' competitive performance compared with alternative approaches, ease of application, and relative lack of strict distributional assumptions. Despite the encouraging results, most applications of ML for streamflow forecast have been limited to watersheds where rainfall is the major source of runoff. In this study, we evaluate the potential of Random Forest (RF), a popular ML method, to make streamflow forecast at 1-day lead time at 86 watersheds in the Pacific Northwest. These watersheds span climatic conditions and physiographic settings and exhibit varied contributions of rainfall and snowmelt to their streamflow. Watersheds are classified into three hydrologic regimes: rainfall-dominated, transisent, and snowmelt-dominated based on the timing of center of annual flow volume. RF performance is benchmarked against Naive and multiple linear regression (MLR) models, and evaluated using four metrics Coefficient of determination, Root mean squared error, Mean absolute error, and Kling-Gupta efficiency. Model evaluation metrics suggest RF performs better in snowmelt-driven watersheds. Largest improvement in forecasts, compared to benchmark models, are found among rainfall-driven watersheds. We obtain Kling–Gupta Efficiency (KGE) scores in the range of 0.62–0.99. RF performance deteriorates with increase in catchment slope and increase in soil sandiness. We note disagreement between two popular measures of RF variable importance and recommend jointly considering these measures with the physical processes under study. These and other results presented provide new insights for effective application of RF-based streamflow forecasting.

Semiarid and savanna‐type (SAST) ecosystems in East Africa have unique plant species compositions and characteristics that make quantifying this biome's seasonality and interannual variability difficult. Phenoregion classification offers a way to use seasonality of vegetation growth to help understand the phenological spatial patterns of complex landscapes. Here, we used Normalized Difference Vegetation Index (NDVI) time series from Landsat 8 to map phenoregions in scenes centered around national parks from Mt. Kenya National Park (Kenya) to Limpopo National Park (Mozambique). We then assessed whether landscape‐scale controls on phenology are consistent across the region or whether they vary across this latitudinal gradient. We compared our phenoregion maps to MODIS Land Cover and geology, and we used multinomial logistic regression to determine the role that elevation, slope, aspect, and geology play in driving phenological differences. The sites' phenoregions showed no unique land cover composition, suggesting that MODIS land cover does not capture the subtle variations identified in phenoregion analysis. Multinomial logistic regression showed that geographic trend (x‐ and y‐directions) was a strong predictor in four of the five landscapes and that, depending on the scene, geology, elevation, or aspect was a strong secondary predictor. Using seasonality of the NDVI time series to generate phenoregions provides different and, in some cases, more ecologically relevant information, compared to vegetation maps that use only land cover from a single season or time period to generate ecoregions. With a significant population of humans and animals that live in and depend on SAST ecosystems, it is important to better understand vegetation processes and factors that affect them as climate change becomes an increasingly pertinent issue in dry systems.

Author(s): Read, QD; Zarnetske, PL; Record, S; Dahlin, KM; Costanza, JK; Finley, AO; Gaddis, KD; Grady, JM; Hobi, ML; Latimer, AM; Malone, SL; Ollinger, SV; Pau, S; Wilson, AM | Abstract: Aim: We may be able to buffer biodiversity against the effects of ongoing climate change by prioritizing the protection of habitat with diverse physical features (high geodiversity) associated with ecological and evolutionary mechanisms that maintain high biodiversity. Nonetheless, the relationships between biodiversity and habitat vary with spatial and biological context. In this study, we compare how well habitat geodiversity (spatial variation in abiotic processes and features) and climate explain biodiversity patterns of birds and trees. We also evaluate the consistency of biodiversity–geodiversity relationships across ecoregions. Location: Contiguous USA. Time period: 2007–2016. Taxa studied: Birds and trees. Methods: We quantified geodiversity with remotely sensed data and generated biodiversity maps from the Forest Inventory and Analysis and Breeding Bird Survey datasets. We fitted multivariate regressions to alpha, beta and gamma diversity, accounting for spatial autocorrelation among Nature Conservancy ecoregions and relationships among taxonomic, phylogenetic and functional biodiversity. We fitted models including climate alone (temperature and precipitation), geodiversity alone (topography, soil and geology) and climate plus geodiversity. Results: A combination of geodiversity and climate predictor variables fitted most forms of bird and tree biodiversity with ln10% relative error. Models using geodiversity and climate performed better for local (alpha) and regional (gamma) diversity than for turnover-based (beta) diversity. Among geodiversity predictors, variability of elevation fitted biodiversity best; interestingly, topographically diverse places tended to have higher tree diversity but lower bird diversity. Main conclusions: Although climatic predictors tended to have larger individual effects than geodiversity, adding geodiversity improved climate-only models of biodiversity. Geodiversity was correlated with biodiversity more consistently than with climate across ecoregions, but models tended to have a poor fit in ecoregions held out of the training dataset. Patterns of geodiversity could help to prioritize conservation efforts within ecoregions. However, we need to understand the underlying mechanisms more fully before we can build models transferable across ecoregions.

Proliferation of spatially indexed data (i.e., variable measurements are associated with a spatial location) has spurred considerable development in statistical modeling. Key texts in this field include Cressie (1993), Cressie and Wikle (2011), Chiles and Delfiner (1999), Moller and Waagepetersen (2003), Schabenberger and Gotway (2004), Wackernagel (2003), Diggle and Ribeiro (2007), and Banerjee et al. (2014). The statistical literature acknowledges that spatial (and temporal) associations are captured most effectively using models that build dependencies in different stages or hierarchies. As illustrated in Sect. 6.2, hierarchical models are especially advantageous with data sets that have several lurking sources of uncertainty and dependence.

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This manuscript develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a Vegetation Index data set with spatially dependent observations numbering in the millions., Comment: 22 pages, 12 figures

Before considering more advanced models which might be used in lieu of standard non-Bayesian approaches such as linear regression or Poisson regression, we start with some relatively simple Bayesian models. These will set the stage for the more sophisticated models covered in later chapters.

Selecting a prior distribution is integral to Bayesian analyses. In this chapter, we discuss several approaches to specifying priors. First, we discuss the concept of “noninformative” priors. Next we introduce improper priors. Following this, we define conjugate priors. We conclude with a brief discussion of how a scientist might specify an informative prior.

We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the regions in the partition using a sparsity-inducing directed acyclic graph (DAG). We extend the model over the DAG to a well-defined spatial process, which we call the meshed Gaussian process (MGP). A major contribution is the development of an MGPs on tessellated domains, accompanied by a Gibbs sampler for the efficient recovery of spatial random effects. In particular, the cubic MGP (Q-MGP) can harness high-performance computing resources by executing all large-scale operations in parallel within the Gibbs sampler, improving mixing and computing time compared to sequential updating schemes. Unlike some existing models for large spatial data, a Q-MGP facilitates massive caching of expensive matrix operations, making it particularly apt in dealing with spatiotemporal remote-sensing data. We compare Q-MGPs with large synthetic and real world data against state-of-the-art methods. We also illustrate using Normalized Difference Vegetation Index data from the Serengeti park region to recover latent multivariate spatiotemporal random effects at millions of locations. The source code is available at github.com/mkln/meshgp. Supplementary materials for this article are available online.

Effective Bayesian inference requires familiarity with probability distributions. In fact, as will be seen in subsequent chapters, the most important choices in Bayesian inference usually involve the choices of distributions to represent the state of knowledge before data is collected (prior distribution) and the sampling distribution, also referred to as the data model, for the observable data. Hence in this chapter we will review some commonly used probability distributions. Readers already knowledgeable about probability distributions should skim this chapter to insure that they are comfortable with our notation and terminology.

During the course of a scientific investigation, it is common to consider more than one model to explain or predict the phenomenon of interest. In some cases, it might be wise to cull the candidate models to a manageable number, and then use model averaging methods. However, often a scientist needs/wants to select a single model. In this chapter we consider the situation in which a scientist would like to select one of the candidate models to use for inference. Model selection shares many concepts with hypothesis testing, and so we begin this chapter with a discussion of hypothesis testing.

Monitoring wildlife abundance across space and time is an essential task to study their population dynamics and inform effective management. Acoustic recording units are a promising technology for efficiently monitoring bird populations and communities. We present an integrated modeling framework that combines high-quality but temporally sparse bird point count survey data with acoustic recordings. Using simulations, we compare the accuracy and precision of abundance estimates using differing amounts of acoustic vocalizations obtained from a clustering algorithm, point count data, and a subset of manually validated acoustic vocalizations. We also use our modeling framework in a case study to estimate abundance of the Eastern Wood-Pewee (Contopus virens) in Vermont, U.S.A. The simulation study reveals that combining acoustic and point count data via an integrated model improves accuracy and precision of abundance estimates compared with models informed by either acoustic or point count data alone. Combining acoustic data with only a small number of point count surveys yields estimates of abundance without the need for validating any of the identified vocalizations from the acoustic data. Within our case study, the integrated models provided moderate support for a decline of the Eastern Wood-Pewee in this region. Our integrated modeling approach combines dense acoustic data with few point count surveys to deliver reliable estimates of species abundance without the need for manual identification of acoustic vocalizations or a prohibitively expensive large number of repeated point count surveys. Our proposed approach offers an efficient monitoring alternative for large spatio-temporal regions when point count data are difficult to obtain or when monitoring is focused on rare species with low detection probability., Comment: 25 pages, 4 figures