Evaluating probabilistic ecological forecasts

Probabilistic near-term forecasting facilitates evaluation of model predictions against observations and is of pressing need in ecology to inform environmental decision-making and effect societal change. Despite this imperative, many ecologists are unfamiliar with the widely used tools for evaluating probabilistic forecasts developed in other fields. We address this gap by reviewing the literature on probabilistic forecast evaluation from diverse fields including climatology, economics, and epidemiology. We present established practices for selecting evaluation data (end-sample hold out), graphical forecast evaluation (times-series plots with uncertainty, probability integral transform plots), quantitative evaluation using scoring rules (log, quadratic, spherical, and ranked probability scores), and comparing scores across models (skill score, Diebold-Mariano test). We cover common approaches, highlight mathematical concepts to follow, and note decision points to allow application of general principles to specific forecasting endeavors. We illustrate these approaches with an application to a long-term rodent population time series currently used for ecological forecasting and discuss how ecology can continue to learn from and drive the cross-disciplinary field of forecasting science.

Monitoring tropical forest succession at landscape scales despite uncertainty in Landsat time series

Forecasting rates of forest succession at landscape scales will aid global efforts to restore tree cover to millions of hectares of degraded land. While optical satellite remote sensing can detect regional land cover change, quantifying forest structural change is challenging. We developed a state-space modeling framework that applies Landsat satellite data to estimate variability in rates of natural regeneration between sites in a tropical landscape. Our models work by disentangling measurement error in Landsat-derived spectral reflectance from process error related to successional variability. We applied our modeling framework to rank rates of forest succession between 10 naturally regenerating sites in Southwestern Panama from about 2001 to 2015 and tested how different models for measurement error impacted forecast accuracy, ecological inference, and rankings of successional rates between sites. We achieved the greatest increase in forecasting accuracy by adding intra-annual phenological variation to a model based on Landsat-derived normalized difference vegetation index (NDVI). The best-performing model accounted for inter- and intra-annual noise in spectral reflectance and translated NDVI to canopy height via Landsat-lidar fusion. Modeling forest succession as a function of canopy height rather than NDVI also resulted in more realistic estimates of forest state during early succession, including greater confidence in rank order of successional rates between sites. These results establish the viability of state-space models to quantify ecological dynamics from time series of space-borne imagery. State-space models also provide a statistical approach well-suited to fusing high-resolution data, such as airborne lidar, with lower-resolution data that provides better temporal and spatial coverage, such as the Landsat satellite record. Monitoring forest succession using satellite imagery could play a key role in achieving global restoration targets, including identifying sites that will regain tree cover with minimal intervention.

Spatio-Temporal Modeling for Forecasting High-Risk Freshwater Cyanobacterial Harmful Algal Blooms in Florida

Due to the occurrence of more frequent and widespread toxic cyanobacteria events, the ability to predict freshwater cyanobacteria harmful algal blooms (cyanoHAB) is of critical importance for the management of drinking and recreational waters. Lake system specific geographic variation of cyanoHABs has been reported, but regional and state level variation is infrequently examined. A spatio-temporal modeling approach can be applied, via the computationally efficient Integrated Nested Laplace Approximation (INLA), to high-risk cyanoHAB exceedance rates to explore spatio-temporal variations across statewide geographic scales. We explore the potential for using satellite-derived data and environmental determinants to develop a short-term forecasting tool for cyanobacteria presence at varying space-time domains for the state of Florida. Weekly cyanobacteria abundance data were obtained using Sentinel-3 Ocean Land Color Imagery (OLCI), for a period of May 2016-June 2019. Time and space varying covariates include surface water temperature, ambient temperature, precipitation, and lake geomorphology. The hierarchical Bayesian spatio-temporal modeling approach in R-INLA represents a potential forecasting tool useful for water managers and associated public health applications for predicting near future high-risk cyanoHAB occurrence given the spatio-temporal characteristics of these events in the recent past. This method is robust to missing data and unbalanced sampling between waterbodies, both common issues in water quality datasets.

Conservation and production responses vary by disturbance intensity in a long-term forest management experiment

Reductions in management intensity are often proposed to support a broader range of beneficial ecosystem responses than traditional management approaches. However, few studies evaluate ecosystem responses across approaches. Also, managers lack information about how species traits mediate responses across management approaches, a potentially substantial source of spatial and temporal variation in population and community responses that if ignored may hinder effectiveness of management programs. We used data collected over eight years from a manipulative experiment to test how four forest management strategies influenced avian community composition and wood production. After harvesting, we evaluated responses to three levels of plant cover suppression (Light, Moderate, and Intensive herbicide applications) in relation to a control without herbicide. We predicted the Moderate and Intensive treatments would exert strong negative effects on leaf-gleaning insectivores, including species of conservation concern due to long-term population declines. However, given high forest productivity, we expected temporal duration of effects to be short. Richness of leaf-gleaning bird species was reduced by 20-50% during the first four years post-harvest (when herbicide treatments were on-going), but the effect size declined over the next four years once treatments were completed (13-20% reduction). Effect sizes were substantially smaller for the non-leaf-gleaner group during years 1-4 (19-27%) and disappeared during years 5-8 (2-3%). However, in our final year of observation, we did find an average of five fewer non-leaf-gleaner species on Light vs. Control units. In the last two years of observation, turnover probabilities for the leaf-gleaner species remained higher on all treatments compared to the Control (0.11-0.21), indicating that new species continued to colonize treatments. Planted conifers were 40-44% taller and 74-81% larger in diameter in the Moderate and Intensive treatments compared to the Control, leading to substantial gains in wood biomass. Current practices provided more balance between two ecosystem responses, avian diversity and wood production, compared to less intensive alternatives. When short-term negative effects occur, the spatial distribution of harvesting and regeneration regionally indicates that habitat is often available locally to support leaf-gleaning and non-leaf-gleaning bird populations while releasing other portions of the region for high priority conservation objectives including late-successional forest reserves.

Improving estimates of environmental change using multilevel regression models of Ellenberg indicator values

Ellenberg indicator values (EIVs) are a widely used metric in plant ecology comprising a semi-quantitative description of species' ecological requirements. Typically, point estimates of mean EIV scores are compared over space or time to infer differences in the environmental conditions structuring plant communities-particularly in resurvey studies where no historical environmental data are available. However, the use of point estimates as a basis for inference does not take into account variance among species EIVs within sampled plots and gives equal weighting to means calculated from plots with differing numbers of species. Traditional methods are also vulnerable to inaccurate estimates where only incomplete species lists are available.We present a set of multilevel (hierarchical) models-fitted with and without group-level predictors (e.g., habitat type)-to improve precision and accuracy of plot mean EIV scores and to provide more reliable inference on changing environmental conditions over spatial and temporal gradients in resurvey studies. We compare multilevel model performance to GLMMs fitted to point estimates of mean EIVs. We also test the reliability of this method to improve inferences with incomplete species lists in some or all sample plots. Hierarchical modeling led to more accurate and precise estimates of plot-level differences in mean EIV scores between time-periods, particularly for datasets with incomplete records of species occurrence. Furthermore, hierarchical models revealed directional environmental change within ecological habitat types, which less precise estimates from GLMMs of raw mean EIVs were inadequate to detect. The ability to compute separate residual variance and adjusted R 2 parameters for plot mean EIVs and temporal differences in plot mean EIVs in multilevel models also allowed us to uncover a prominent role of hydrological differences as a driver of community compositional change in our case study, which traditional use of EIVs would fail to reveal. Assessing environmental change underlying ecological communities is a vital issue in the face of accelerating anthropogenic change. We have demonstrated that multilevel modeling of EIVs allows for a nuanced estimation of such from plant assemblage data changes at local scales and beyond, leading to a better understanding of temporal dynamics of ecosystems. Further, the ability of these methods to perform well with missing data should increase the total set of historical data which can be used to this end.

A Bayesian latent variable approach to aggregation of partial and top-ranked lists in genomic studies

In genomic research, it is becoming increasingly popular to perform meta-analysis, the practice of combining results from multiple studies that target a common essential biological problem. Rank aggregation, a robust meta-analytic approach, consolidates such studies at the rank level. There exists extensive research on this topic, and various methods have been developed in the past. However, these methods have two major limitations when they are applied in the genomic context. First, they are mainly designed to work with full lists, whereas partial and/or top-ranked lists prevail in genomic studies. Second, the component studies are often clustered, and the existing methods fail to utilize such information. To address the above concerns, a Bayesian latent variable approach, called BiG, is proposed to formally deal with partial and top-ranked lists and incorporate the effect of clustering. Various reasonable prior specifications for variance parameters in hierarchical models are carefully studied and compared. Simulation results demonstrate the superior performance of BiG compared with other popular rank aggregation methods under various practical settings. A non-small-cell lung cancer data example is analyzed for illustration.

Testing the External Validity of a Discrete Choice Experiment Method: An Application to Latent Tuberculosis Infection Treatment

OBJECTIVES

To explore the external validity and predictive power of stated preferences obtained from a discrete choice experiment (DCE) by comparing the predicted behavior of respondents to their actual choices at an individual level.

METHODS

A DCE was performed in patients before being offered treatment for latent tuberculosis infection. A mixed logit model was estimated using hierarchical Bayes. The individual-specific preference coefficients were used to calculate the expected probability of choosing the treatment by each patient. The predicted choice using this probability was compared with their actual decision. We used a receiver-operating characteristic curve and different thresholds to convert probabilities into the predicted choices. The comparability of different distributions for the random parameters was also examined.

RESULTS

Our results identified significant heterogeneity in preferences for all attributes among respondents. The best model correctly predicted actual treatment decisions for 83% of the participants. The results from using different thresholds and a receiver-operating characteristic curve also confirmed the compatibility between predicted and actual choices. We showed that individual-specific coefficients reflected respondents' actual choices more closely compared with the aggregate-level estimates.

CONCLUSIONS

The results of this study provided support for the external validity of DCEs on the basis of their power to predict actual behavior in this setting. Future investigations are, however, required to establish the external validity of DCEs in different settings.

Adult mortality in a low-density tree population using high-resolution remote sensing

We developed a statistical framework to quantify mortality rates in canopy trees observed using time series from high-resolution remote sensing. By timing the acquisition of remote sensing data with synchronous annual flowering in the canopy tree species Handroanthus guayacan, we made 2,596 unique detections of 1,006 individual adult trees within 18,883 observation attempts on Barro Colorado Island, Panama (BCI) during an 11-yr period. There were 1,057 observation attempts that resulted in missing data due to cloud cover or incomplete spatial coverage. Using the fraction of 123 individuals from an independent field sample that were detected by satellite data (109 individuals, 88.6%), we estimate that the adult population for this species on BCI was 1,135 individuals. We used a Bayesian state-space model that explicitly accounted for the probability of tree detection and missing observations to compute an annual adult mortality rate of 0.2%·yr^-1 (SE = 0.1, 95% CI = 0.06-0.45). An independent estimate of the adult mortality rate from 260 field-checked trees closely matched the landscape-scale estimate (0.33%·yr^-1 , SE = 0.16, 95% CI = 0.12-0.74). Our proof-of-concept study shows that one can remotely estimate adult mortality rates for canopy tree species precisely in the presence of variable detection and missing observations.

Predictive models for radial sap flux variation in coniferous, diffuse-porous and ring-porous temperate trees

Accurately scaling sap flux observations to tree or stand levels requires accounting for variation in sap flux between wood types and by depth into the tree. However, existing models for radial variation in axial sap flux are rarely used because they are difficult to implement, there is uncertainty about their predictive ability and calibration measurements are often unavailable. Here we compare different models with a diverse sap flux data set to test the hypotheses that radial profiles differ by wood type and tree size. We show that radial variation in sap flux is dependent on wood type but independent of tree size for a range of temperate trees. The best-fitting model predicted out-of-sample sap flux observations and independent estimates of sapwood area with small errors, suggesting robustness in the new settings. We develop a method for predicting whole-tree water use with this model and include computer code for simple implementation in other studies.

Wood production response to climate change will depend critically on forest composition and structure

Established forests currently function as a major carbon sink, sequestering as woody biomass about 26% of global fossil fuel emissions. Whether forests continue to act as a global sink will depend on many factors, including the response of aboveground wood production (AWP; MgC ha(-1 ) yr(-1) ) to climate change. Here, we explore how AWP in New Zealand's natural forests is likely to change. We start by statistically modelling the present-day growth of 97 199 individual trees within 1070 permanently marked inventory plots as a function of tree size, competitive neighbourhood and climate. We then use these growth models to identify the factors that most influence present-day AWP and to predict responses to medium-term climate change under different assumptions. We find that if the composition and structure of New Zealand's forests were to remain unchanged over the next 30 years, then AWP would increase by 6-23%, primarily as a result of physiological responses to warmer temperatures (with no appreciable effect of changing rainfall). However, if warmth-requiring trees were able to migrate into currently cooler areas and if denser canopies were able to form, then a different AWP response is likely: forests growing in the cool mountain environments would show a 30% increase in AWP, while those in the lowland would hardly respond (on average, -3% when mean annual temperature exceeds 8.0 °C). We conclude that response of wood production to anthropogenic climate change is not only dependent on the physiological responses of individual trees, but is highly contingent on whether forests adjust in composition and structure.

Trait-mediated assembly processes predict successional changes in community diversity of tropical forests

Interspecific differences in relative fitness can cause local dominance by a single species. However, stabilizing interspecific niche differences can promote local diversity. Understanding these mechanisms requires that we simultaneously quantify their effects on demography and link these effects to community dynamics. Successional forests are ideal systems for testing assembly theory because they exhibit rapid community assembly. Here, we leverage functional trait and long-term demographic data to build spatially explicit models of successional community dynamics of lowland rainforests in Costa Rica. First, we ask what the effects and relative importance of four trait-mediated community assembly processes are on tree survival, a major component of fitness. We model trait correlations with relative fitness differences that are both density-independent and -dependent in addition to trait correlations with stabilizing niche differences. Second, we ask how the relative importance of these trait-mediated processes relates to successional changes in functional diversity. Tree dynamics were more strongly influenced by trait-related interspecific variation in average survival than trait-related responses to neighbors, with wood specific gravity (WSG) positively correlated with greater survival. Our findings also suggest that competition was mediated by stabilizing niche differences associated with specific leaf area (SLA) and leaf dry matter content (LDMC). These drivers of individual-level survival were reflected in successional shifts to higher SLA and LDMC diversity but lower WSG diversity. Our study makes significant advances to identifying the links between individual tree performance, species functional traits, and mechanisms of tropical forest succession.

Rapid shifts in dispersal behavior on an expanding range edge

Dispersal biology at an invasion front differs from that of populations within the range core, because novel evolutionary and ecological processes come into play in the nonequilibrium conditions at expanding range edges. In a world where species' range limits are changing rapidly, we need to understand how individuals disperse at an invasion front. We analyzed an extensive dataset from radio-tracking invasive cane toads (Rhinella marina) over the first 8 y since they arrived at a site in tropical Australia. Movement patterns of toads in the invasion vanguard differed from those of individuals in the same area postcolonization. Our model discriminated encamped versus dispersive phases within each toad's movements and demonstrated that pioneer toads spent longer periods in dispersive mode and displayed longer, more directed movements while they were in dispersive mode. These analyses predict that overall displacement per year is more than twice as far for toads at the invasion front compared with those tracked a few years later at the same site. Studies on established populations (or even those a few years postestablishment) thus may massively underestimate dispersal rates at the leading edge of an expanding population. This, in turn, will cause us to underpredict the rates at which invasive organisms move into new territory and at which native taxa can expand into newly available habitat under climate change.