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Bringing Bayesian models to life

Bringing Bayesian Models to Life empowers the reader to extend, enhance, and implement statistical models for ecological and environmental data analysis. We open the black box and show the reader how to connect modern statistical models to computer algorithms. These algorithms allow the user to fit models that answer their scientific questions without needing to rely on automated Bayesian software. We show how to handcraft statistical models that are useful in ecological and environmental science including: linear and generalized linear models, spatial and time series models, occupancy and capture-recapture models, animal movement models, spatio-temporal models, and integrated population-models.

Book

Evolutionary ecology of masting: Mechanisms, models, and climate change

Many perennial plants show mast seeding, characterized by synchronous and highly variable reproduction across years. We propose a general model of masting, integrating proximate factors (environmental variation, weather cues, and resource budgets) with ultimate drivers (predator satiation and pollination efficiency). This general model shows how the relationships between masting and weather shape the diverse responses of species to climate warming, ranging from no change to lower interannual variation or reproductive failure. The role of environmental prediction as a masting driver is being reassessed; future studies need to estimate prediction accuracy and the benefits acquired. Since reproduction is central to plant adaptation to climate change, understanding how masting adapts to shifting environmental conditions is now a central question.

Trends in Ecology and Evolution

Bayesian networks facilitate updating of species distribution and habitat suitability models

Managers often rely on predictions of species distributions and habitat suitability to inform conservation and management decisions. Although numerous approaches are available to develop models to make these predictions, few approaches exist to update existing models as new data accumulate. There is a need for updatable models to ensure good modeling practices in an aim to keep pace with change in the environment and change in data availability to continue to use the best-available science to inform decisions. We demonstrated a workflow to deliver predictive models to user groups within Bayesian networks, allowing models to be used to make predictions across new sites and to be easily updated with new data. To demonstrate this workflow, we focus on species distribution and habitat suitability models given their importance to informing conservation strategies across the globe. In particular, we followed a standard process of collating species encounter data available in online databases and ancillary covariate data to develop a habitat suitability model. We then used this model to parameterize a Bayesian network and updated the model with new data to predict species presence in a new focal ecoregion. We found the network updated relatively quickly as new data were incorporated, and the overall error rate generally decreased with each model update. Our approach allows for the formal incorporation of new data into predictions to help ensure model predictions are based on all relevant data available, regardless of whether they were collected after initial model development. Although our focus is on species distribution and habitat suitability models to inform conservation efforts, the workflow we describe herein can easily be applied to any use case where model uncertainty reduction and increased model prediction accuracy are desired via model updating as new data become available. Thus, our paper describes a generalizable workflow to implement model updating, which is widely recognized as a good modeling practice but is also underutilized in applied ecology.

Oregon, Washington

The bee microbiome: Impact on bee health and model for evolution and ecology of host-microbe interactions

As pollinators, bees are cornerstones for terrestrial ecosystem stability and key components in agricultural productivity. All animals, including bees, are associated with a diverse community of microbes, commonly referred to as the microbiome. The bee microbiome is likely to be a crucial factor affecting host health. However, with the exception of a few pathogens, the impacts of most members of the bee microbiome on host health are poorly understood. Further, the evolutionary and ecological forces that shape and change the microbiome are unclear. Here, we discuss recent progress in our understanding of the bee microbiome, and we present challenges associated with its investigation. We conclude that global coordination of research efforts is needed to fully understand the complex and highly dynamic nature of the interplay between the bee microbiome, its host, and the environment. High-throughput sequencing technologies are ideal for exploring complex biological systems, including host-microbe interactions. To maximize their value and to improve assessment of the factors affecting bee health, sequence data should be archived, curated, and analyzed in ways that promote the synthesis of different studies. To this end, the BeeBiome consortium aims to develop an online database which would provide reference sequences, archive metadata, and host analytical resources. The goal would be to support applied and fundamental research on bees and their associated microbes and to provide a collaborative framework for sharing primary data from different research programs, thus furthering our understanding of the bee microbiome and its impact on pollinator health.

mBio

A system dynamics model to understand the integrated ecological and human dimension aspects of wildlife health and disease management

Chronic wasting disease (CWD) presents an ongoing challenge for the management of deer populations and sustaining harvest opportunities across North America. Existing disease models often fail to fully capture the complex interplay between disease dynamics, host ecology, and socio-economic factors. We developed a comprehensive system dynamics (SD) model that integrates demographic, epidemiological, ecological, and socio-economic processes within a single model to more fully characterize the complex network of causal feedbacks throughout the system. The model was calibrated using a Bayesian approach that incorporates prior knowledge to generate biologically interpretable outcomes, even with sparse data. For estimating the joint posterior distribution of model parameters, we leveraged time series of deer abundance, harvest composition, genetic profiles, CWD surveillance, and hunter demographics and behavior. Model outputs reproduced key system behaviors, including observed CWD prevalence trends, deer population dynamics, and hunter license purchasing patterns. Model predictions were most sensitive to parameters governing initial deer population size and recruitment. While model predictions generally aligned with observed data, discrepancies in early CWD detection and overestimation of the reactivation of long-inactive hunters reflect data limitations and modeling challenges. Key results suggest that indirect transmission is necessary to explain observed prevalence, that transmission is moderately density-dependent, and that observed population-level genetic shifts driven by CWD may play a role in transmission and progression. The SD modelling approach enabled estimation of difficult-to-measure parameters and identified potential leverage points for management—such as prioritizing increasing participation in antlerless harvest of existing hunters over the recruitment of new hunters. This integrated modeling approach offers a flexible foundation for adaptive wildlife disease management and emphasizes the value of unifying biological and human dimension processes to better inform effective, evidence-based policy.

BioRxiv

Mapping and monitoring Mount Graham red squirrel habitat with Lidar and Landsat imagery

The Mount Graham red squirrel ( Tamiasciurus hudsonicus grahamensis ) is an endemic subspecies located in the Pinaleño Mountains of southeast Arizona. Living in a conifer forest on a sky-island surrounded by desert, the Mount Graham red squirrel is one of the rarest mammals in North America. Over the last two decades, drought, insect infestations, and fire destroyed much of its habitat. A federal recovery team is working on a plan to recover the squirrel and detailed information is necessary on its habitat requirements and population dynamics. Toward that goal I developed and compared three probabilistic models of Mount Graham red squirrel habitat with a geographic information system and logistic regression. Each model contained the same topographic variables (slope, aspect, elevation), but the Landsat model contained a greenness variable (Normalized Difference Vegetation Index) extracted from Landsat, the Lidar model contained three forest-inventory variables extracted from lidar, while the Hybrid model contained Landsat and lidar variables. The Hybrid model produced the best habitat classification accuracy, followed by the Landsat and Lidar models, respectively. Landsat-derived forest greenness was the best predictor of habitat, followed by topographic (elevation, slope, aspect) and lidar (tree height, canopy bulk density, and live basal area) variables, respectively. The Landsat model's probabilities were significantly correlated with all 12 lidar variables, indicating its utility for habitat mapping. While the Hybrid model produced the best classification results, only the Landsat model was suitable for creating a habitat time series or habitat–population function between 1986 and 2013. The techniques I highlight should prove valuable in the development of Landsat- or lidar-based habitat models range wide.

Arizona

An aridity threshold model of fire sizes and annual area burned in extensively forested ecoregions of the western USA

Wildfire occurrence varies among regions and through time due to the long-term impacts of climate on fuel structure and short-term impacts on fuel flammability. Identifying the climatic conditions that trigger extensive fire years at regional scales can enable development of area burned models that are both spatially and temporally robust, which is crucial for understanding the impacts of past and future climate change. We identified region-specific thresholds in fire-season aridity that distinguish years with limited, moderate, and extensive area burned for 11 extensively forested ecoregions in the western United States. We developed a new area burned model using these relationships and demonstrate its application in the Southern Rocky Mountains using climate projections from five global climate models (GCMs) that bracket the range of projected changes in aridity. We used the aridity thresholds to classify each simulation year as having limited, moderate, or extensive area burned and defined fire-size distributions from historical fire records for these categories. We simulated individual fires from a regression relating fire season aridity to the annual number of fires and drew fire sizes from the corresponding fire-size distributions. We project dramatic increases in area burned after 2020 under most GCMs and after 2060 with all GCMs as the frequency of extensive fire years increases. Our adaptable model can readily incorporate new observations (e.g., extreme fire years) to directly address the non-stationarity of fire-climate relationships as climatic conditions diverge from past observations. Our aridity threshold fire model provides a simple yet spatially robust approach to project regional changes in area burned with broad applicability to ecosystem and vegetation simulation models.

Ecological Modelling

Evaluating effects of potential changes in streamflow regime on fish and aquatic-invertebrate assemblages in the New Jersey Pinelands

Changes in water demand associated with population growth and changes in land-use practices in the Pinelands region of southern New Jersey will have a direct effect on stream hydrology. The most pronounced and measurable hydrologic effect is likely to be flow reductions associated with increasing water extraction. Because water-supply needs will continue to grow along with population in the Pinelands area, the goal of maintaining a sustainable balance between the availability of water to protect existing aquatic assemblages while conserving the surficial aquifer for long-term support of human water use needs to be addressed. Although many aquatic fauna have shown resilience and resistance to short-term changes in flows associated with water withdrawals, sustained effects associated with ongoing water-development processes are not well understood. In this study, the U.S. Geological Survey sampled forty-three 100-meter-long stream reaches during high- and low-flow periods across a designed hydrologic gradient ranging from small- (4.1 square kilometers (1.6 square miles)) to medium- (66.3 square kilometers (25.6 square miles)) sized Pinelands stream basins. This design, which uses basin size as a surrogate for water availability, provided an opportunity to evaluate the possible effects of potential variation in stream hydrology on fish and aquatic-invertebrate assemblage response in New Jersey Pinelands streams where future water extraction is expected based on known build-out scenarios. Multiple-regression models derived from extracted non-metric multidimensional scaling axis scores of fish and aquatic invertebrates indicate that some variability in aquatic-assemblage composition across the hydrologic gradient is associated with anthropogenic disturbance, such as urbanization, changes in stream chemistry, and concomitant changes in high-flow runoff patterns. To account for such underlying effects in the study models, any flow parameter or assemblage attribute that was found to be significantly correlated (|rho| = 0.5000) to known anthropogenic drivers (for example, the amount of urbanization in the basin) was eliminated from analysis. A reduced set of low- and annual-flow hydrologic variables, found to be unrelated to anthropogenic influences, was used to develop assemblage-response models. Many linear (monotonic) and curvilinear bivariate flow-ecology response models were developed for fish and invertebrate assemblages. For example, the duration and magnitude of low-flow events were significant predictors of invertebrate-assemblage complexity (for example, invertebrate-species richness, Plecoptera richness, and Ephemeroptera abundance); however, response models between flow attributes and fish-assemblage structure were, in all cases, more poorly fit. Annual flow variability also was important, especially variability across mean minimum monthly flows and annual mean streamflow. In general, all response models followed upward or downward trends that would be expected given hydrologic changes in Pinelands streams. This study demonstrates that the structural and functional response of aquatic assemblages of the Pinelands ecosystem resulting from changes in water-use practices associated with population growth and increased water extraction may be predictable.

Scientific Investigations Report

Multistate modeling of habitat dynamics: Factors affecting Florida scrub transition probabilities

Many ecosystems are influenced by disturbances that create specific successional states and habitat structures that species need to persist. Estimating transition probabilities between habitat states and modeling the factors that influence such transitions have many applications for investigating and managing disturbance-prone ecosystems. We identify the correspondence between multistate capture-recapture models and Markov models of habitat dynamics. We exploit this correspondence by fitting and comparing competing models of different ecological covariates affecting habitat transition probabilities in Florida scrub and flatwoods, a habitat important to many unique plants and animals. We subdivided a large scrub and flatwoods ecosystem along central Florida's Atlantic coast into 10-ha grid cells, which approximated average territory size of the threatened Florida Scrub-Jay (Aphelocoma coerulescens), a management indicator species. We used 1.0-m resolution aerial imagery for 1994, 1999, and 2004 to classify grid cells into four habitat quality states that were directly related to Florida Scrub-Jay source-sink dynamics and management decision making. Results showed that static site features related to fire propagation (vegetation type, edges) and temporally varying disturbances (fires, mechanical cutting) best explained transition probabilities. Results indicated that much of the scrub and flatwoods ecosystem was resistant to moving from a degraded state to a desired state without mechanical cutting, an expensive restoration tool. We used habitat models parameterized with the estimated transition probabilities to investigate the consequences of alternative management scenarios on future habitat dynamics. We recommend this multistate modeling approach as being broadly applicable for studying ecosystem, land cover, or habitat dynamics. The approach provides maximum-likelihood estimates of transition parameters, including precision measures, and can be used to assess evidence among competing ecological models that describe system dynamics. ?? 2010 by the Ecological Society of America.

Ecology

The South Florida Ecosystem Portfolio Model - A Map-Based Multicriteria Ecological, Economic, and Community Land-Use Planning Tool

The South Florida Ecosystem Portfolio Model (EPM) prototype is a regional land-use planning Web tool that integrates ecological, economic, and social information and values of relevance to decision-makers and stakeholders. The EPM uses a multicriteria evaluation framework that builds on geographic information system-based (GIS) analysis and spatially-explicit models that characterize important ecological, economic, and societal endpoints and consequences that are sensitive to regional land-use/land-cover (LULC) change. The EPM uses both economics (monetized) and multiattribute utility (nonmonetized) approaches to valuing these endpoints and consequences. This hybrid approach represents a methodological middle ground between rigorous economic and ecological/ environmental scientific approaches. The EPM sacrifices some degree of economic- and ecological-forecasting precision to gain methodological transparency, spatial explicitness, and transferability, while maintaining credibility. After all, even small steps in the direction of including ecosystem services evaluation are an improvement over current land-use planning practice (Boyd and Wainger, 2003). There are many participants involved in land-use decision-making in South Florida, including local, regional, State, and Federal agencies, developers, environmental groups, agricultural groups, and other stakeholders (South Florida Regional Planning Council, 2003, 2004). The EPM's multicriteria evaluation framework is designed to cut across the objectives and knowledge bases of all of these participants. This approach places fundamental importance on social equity and stakeholder participation in land-use decision-making, but makes no attempt to determine normative socially 'optimal' land-use plans. The EPM is thus a map-based set of evaluation tools for planners and stakeholders to use in their deliberations of what is 'best', considering a balancing of disparate interests within a regional perspective. Although issues of regional ecological sustainability can be explored with the EPM (for example, changes in biodiversity potential and regional habitat fragmentation), it does not attempt to define or evaluate long-term ecological sustainability as such. Instead, the EPM is intended to provide transparent first-order indications of the direction of ecological, economic, and community change, not to make detailed predictions of ecological, economic, and social outcomes. In short, the EPM is an attempt to widen the perspectives of its users by integrating natural and social scientific information in a framework that recognizes the diversity of values at stake in South Florida land-use planning. For terrestrial ecosystems, land-cover change is one of the most important direct drivers of changes in ecosystem services (Hassan and others, 2005). More specifically, the fragmentation of habitat from expanding low-density development across landscapes appears to be a major driver of terrestrial species decline and the impairment of terrestrial ecosystem integrity, in some cases causing irreversible impairment from a land-use planning perspective (Brody, 2008; Peck, 1998). Many resource managers and land-use planners have come to realize that evaluating land-use conversions on a parcel-by-parcel basis leads to a fragmented and narrow view of the regional effects of natural land-cover loss to development (Marsh and Lallas, 1995). The EPM is an attempt to integrate important aspects of the coupled natural-system/human-system view from a regional planning perspective. The EPM evaluates proposed land-use changes, both conversion and intensification, in terms of relevant ecological, economic, and social criteria that combine information about probable land-use outcomes, based on ecological and environmental models, as well as value judgments, as expressed in user-modifiable preference models. Based on on-going meetings and interviews with stakeholders and potential tool users we foc

Scientific Investigations Report

Carbon dynamics and land-use choices: building a regional-scale multidisciplinary model

Policy enabling tropical forests to approach their potential contribution to global-climate-change mitigation requires forecasts of land use and carbon storage on a large scale over long periods. In this paper, we present an integrated modeling methodology that addresses these needs. We model the dynamics of the human land-use system and of C pools contained in each ecosystem, as well as their interactions. The model is national scale, and is currently applied in a preliminary way to Costa Rica using data spanning a period of over 50 years. It combines an ecological process model, parameterized using field and other data, with an economic model, estimated using historical data to ensure a close link to actual behavior. These two models are linked so that ecological conditions affect land-use choices and vice versa. The integrated model predicts land use and its consequences for C storage for policy scenarios. These predictions can be used to create baselines, reward sequestration, and estimate the value in both environmental and economic terms of including C sequestration in tropical forests as part of the efforts to mitigate global climate change. The model can also be used to assess the benefits from costly activities to increase accuracy and thus reduce errors and their societal costs.

Journal of Environmental Management

Designing flows to enhance ecosystem functioning in heavily altered rivers

More than a century of dam construction and water development in the western United States has led to extensive ecological alteration of rivers. Growing interest in improving river function is compelling practitioners to consider ecological restoration when managing dams and water extraction. We developed an Ecological Response Model (ERM) for the Cache la Poudre River, northern Colorado, USA, to illuminate effects of current and possible future water management and climate change. We used empirical data and modeled interactions among multiple ecosystem components to capture system-wide insights not possible with the unintegrated models commonly used in environmental assessments. The ERM results showed additional flow regime modification would further alter the structure and function of Poudre River aquatic and riparian ecosystems due to multiple and interacting stressors. Model predictions illustrated that specific peak flow magnitudes in spring and early summer are critical for substrate mobilization, dynamic channel morphology, and overbank flows, with strong subsequent effects on instream and riparian biota that varied seasonally and spatially, allowing exploration of nuanced management scenarios. Instream biological indicators benefitted from higher and more stable base flows and high peak flows, but stable base flows with low peak flows were only half as effective to increase indicators. Improving base flows while reducing peak flows, as currently proposed for the Cache la Poudre River, would further reduce ecosystem function. Modeling showed that even presently depleted annual flow volumes can achieve substantially different ecological outcomes in designed flow scenarios, while still supporting social demands. Model predictions demonstrated that implementing designed flows in a natural pattern, with attention to base and peak flows, may be needed to preserve or improve ecosystem function of the Poudre River. Improved regulatory policies would include preservation of ecosystem-level, flow-related processes and adaptive management when water development projects are considered.

Colorado

Pattern-oriented modeling of agent-based complex systems: Lessons from ecology

Agent-based complex systems are dynamic networks of many interacting agents; examples include ecosystems, financial markets, and cities. The search for general principles underlying the internal organization of such systems often uses bottom-up simulation models such as cellular automata and agent-based models. No general framework for designing, testing, and analyzing bottom-up models has yet been established, but recent advances in ecological modeling have come together in a general strategy we call pattern-oriented modeling. This strategy provides a unifying framework for decoding the internal organization of agent-based complex systems and may lead toward unifying algorithmic theories of the relation between adaptive behavior and system complexity.

Science

Restoring the Florida Everglades: Insights on integrating sea level rise into decision-support tools

Although coastal ecosystems are impacted by climate change and sea-level rise, many ecological and hydrological models do not yet incorporate sea-level rise projections in their modeling outputs. Therefore, this research examined the various challenges that may prevent sea-level rise from being effectively incorporated in modeling and decision-support tools. We conducted semi-structured interviews with twenty-six professionals involved in Florida’s Everglades restoration. We applied the Diffusions of Innovations Theory to better understand factors that can impact practitioners’ adoption of newly designed decision-support tools that examine sea-level rise in the freshwater Everglades. The Diffusions of Innovations Theory provided insights into practitioners’ perceptions of these tools. We found that these practitioners have a strong interest in using dynamic decision-support tools to plan for sea-level rise impacts on Everglades restoration, particularly when they receive information at appropriate geographic and temporal scales and are given hands-on tools and training. However, challenges that prevent developing these tools include outdated data, limited organizational capacity and funding, limited use of long-term indicators, uncertainty about climate change impacts on local ecosystems, and lack of integration between hydrological and ecological models. Our research also highlights that greater availability of different types of tools can help to meet the needs of the scientific and non-scientific audiences involved in Everglades restoration.

Florida

The confluences of ideas leading to, and the flow of ideas emerging from, individual-based modeling of riverine fishes

In this review article, we trace the history of events leading to the development of individual-based models (IBMs) to represent aquatic organisms in rivers and streams. As a metaphor, we present this history as a series of confluences between individual scientists (tributaries) sharing ideas. We describe contributions of these models to science and management. One iconic feature of river IBMs is the linkage between flow and the physical habitat experienced by individual animals, and the first model that focused on this linkage is briefly described. We continue by reviewing the contributions of riverine IBMs to eight broad areas of scientific inquiry. The first four areas include research to understand 1) the effects of flow regimes on fish populations, 2) species interactions (e.g., size-mediated competition and predation), 3) fish movement and habitat selection, and 4) contaminant and water quality impacts on populations. Next, we review research using IBMs 5) to guide conservation biology of imperiled taxa through population viability analysis, including research 6) to understand river fragmentation by dams and reconnection, 7) to understand genetic outcomes for riverine metapopulations, and 8) to anticipate the future effects of temperature and climate change. This rich body of literature has contributed to both theoretical insights (e.g., about animal behavior and life history) and applied insights (e.g., population-level effects of flow regimes, temperature, and the effects of hydropower and other industries that share rivers with aquatic biota). We finish by exploring promising branches that lie ahead in the braided, downstream channel that represents future river modeling research.

Ecological Modelling

Estimation of lake-scale stock-recruitment models for Great Lakes sea lampreys

Understanding recruitment dynamics is an essential part of effective fisheries management, whether the focus is on conservation, harvest policy development, or invasive species control. We developed a model that estimates lake-wide Ricker stock-recruitment relations for invasive sea lampreys ( Petromyzon marinus ) in each of the five Laurentian Great Lakes to inform future control efforts. We fit adult-to-adult models, taking advantage of a long time series of lake-wide, adult, sea lamprey abundance estimates. We incorporated proportional contributions at age for the stock as well as additional explanatory variables sea lamprey weight, as a surrogate for fecundity, and lampricide quantity applied, as a surrogate for anthropogenic mortality, to explain residual recruitment variability. The best model incorporated equal cohort contributions from the adult stock (that matured 5, 6, and 7 years prior to recruitment), a single productivity parameter ( α "> α ) common to all five lakes, lake-specific carrying capacity parameters ( β j "> βj ), and coefficients for sea lamprey weight and lampricide quantity applied. The precision of the estimated Ricker parameters compared favorably to those estimated by adult-to-larva models, a promising development in the pursuit of sea lamprey recruitment prediction. The model should be useful to fisheries managers in the Great Lakes wishing to consider various recruitment overfishing strategies in the control of invasive sea lampreys, reaffirming that even models built on a single life stage can inform our understanding of ecological interactions and explorative management scenarios.

Great Lakes

Failure to meet the exchangeability assumption in Bayesian multispecies occupancy models: Implications for study design

Bayesian hierarchical models are ubiquitous in ecology. Random effect model structures are often employed that treat individual effects as deviations from larger population-level effects. In this way individuals are assumed to be "exchangeable" samples. Ecologists may address this exchangeability assumption intuitively, but might in certain modeling contexts ignore it altogether, including in situations where it may have large implications for study design. Multispecies occupancy models based on detection/non-detection data are an approach that can be utilized by those tasked with monitoring rare and endangered species because most literature suggests that, compared to single species occupancy models, improved parameter estimates are assured. Yet, we illustrate through a power analysis how sampling requirements to detect experimental treatment effects vary tremendously depending on whether the species exchangeability assumption is met. The degree to which species in a community respond similarly to covariates governs the ability to accurately estimate parameters using multispecies occupancy models. Detecting small or moderate changes in occupancy resulting from habitat restoration treatments may be impossible for small datasets (e.g., < 36 sampling locations, each surveyed < 8 times) even with a paired treatment-control design if the exchangeability assumption is violated. By contrast, when the assumption is met, small effects may be confidently estimated with as few as 12 sampling locations (6 pairs) and 6-8 survey events. Often, it may be impossible to know whether the exchangeability assumption is met. The statistical power needed to accurately estimate species-specific effects using detection/non-detection multispecies occupancy models depends on the unknown values of treatment effects and whether responses by species in the community diverge. When the species exchangeability assumption is violated, and at lower levels of sampling effort, multispecies occupancy models may provide worse inference than single species occupancy models.

BioRxiv