Finally, the magic of Bayesian model notation revealed
Book review of Hobbs and Hooten 2015 Bayesian models: a statistical primer for ecologists.
Ecology↗
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Results for “Ecological Modeling”
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A suggestion for computing objective function in model calibration
A parameter-optimization process (model calibration) is usually required for numerical model applications, which involves the use of an objective function to determine the model cost (model-data errors). The sum of square errors (SSR) has been widely adopted as the objective function in various optimization procedures. However, ‘square error’ calculation was found to be more sensitive to extreme or high values. Thus, we proposed that the sum of absolute errors (SAR) may be a better option than SSR for model calibration. To test this hypothesis, we used two case studies—a hydrological model calibration and a biogeochemical model calibration—to investigate the behavior of a group of potential objective functions: SSR, SAR, sum of squared relative deviation (SSRD), and sum of absolute relative deviation (SARD). Mathematical evaluation of model performance demonstrates that ‘absolute error’ (SAR and SARD) are superior to ‘square error’ (SSR and SSRD) in calculating objective function for model calibration, and SAR behaved the best (with the least error and highest efficiency). This study suggests that SSR might be overly used in real applications, and SAR may be a reasonable choice in common optimization implementations without emphasizing either high or low values (e.g., modeling for supporting resources management).
Ecological Informatics↗
Hierarchical spatial capture-recapture models: Modeling population density from stratified populations
Capture–recapture studies are often conducted on populations that are stratified by space, time or other factors. In this paper, we develop a Bayesian spatial capture–recapture (SCR) modelling framework for stratified populations – when sampling occurs within multiple distinct spatial and temporal strata. We describe a hierarchical model that integrates distinct models for both the spatial encounter history data from capture–recapture sampling, and also for modelling variation in density among strata. We use an implementation of data augmentation to parameterize the model in terms of a latent categorical stratum or group membership variable, which provides a convenient implementation in popular BUGS software packages. We provide an example application to an experimental study involving small-mammal sampling on multiple trapping grids over multiple years, where the main interest is in modelling a treatment effect on population density among the trapping grids. Many capture–recapture studies involve some aspect of spatial or temporal replication that requires some attention to modelling variation among groups or strata. We propose a hierarchical model that allows explicit modelling of group or strata effects. Because the model is formulated for individual encounter histories and is easily implemented in the BUGS language and other free software, it also provides a general framework for modelling individual effects, such as are present in SCR models.
Methods in Ecology and Evolution↗
A log-linear model approach to estimation of population size using the line-transect sampling method
The technique of estimating wildlife population size and density using the belt or line-transect sampling method has been used in many past projects, such as the estimation of density of waterfowl nestling sites in marshes, and is being used currently in such areas as the assessment of Pacific porpoise stocks in regions of tuna fishing activity. A mathematical framework for line-transect methodology has only emerged in the last 5 yr. In the present article, we extend this mathematical framework to a line-transect estimator based upon a log-linear model approach.
Ecology↗
Spatio-temporal variability in the strength, directionality, and relative importance of climate on occupancy and population densities in a philopatric mammal, the American pika (Ochotona princeps)
Species distribution models (SDMs) have been widely employed to evaluate species–environment relationships. However, when extrapolated over broad spatial scales or through time, these models decline in their predictive ability due to variation in how species respond to their environment. Many models assume species–environment relationships remain constant over space and time, hindering their ability to accurately forecast distributions. Therefore, there is growing recognition that models could be improved by accounting for spatio-temporal nonstationarity – a phenomenon wherein the factors governing ecological processes change over space or time. Here, we investigated nonstationarity in American pika ( Ochotona princeps ) relationships with climatic variables in the Rocky Mountains (USA). We first compared broad-scale differences in pika–climate patterns for occupancy and population density across the Southern, Central, and Northern Rockies. Next, we investigated within-ecoregion variation across four mountain ranges nested within the Northern Rockies. Lastly, we tested whether species–climate relationships changed over time within the Central Rockies ecoregion. Across all analyses, we found varying levels of nonstationarity among the climate metrics for both occupancy and density. Although we found general congruence in temperature metrics, which consistently had negative coefficients, and moisture metrics (e.g., relative humidity), which had positive coefficients, nonstationarity was greatest for summer and winter precipitation over both space and time. These results suggest that interpretations from one ecoregion should not be applied to other regions universally – especially when using precipitation metrics. The within-ecoregion analysis found much greater variation in the strength-of-relationship coefficients among the four mountain ranges, relative to the inter-regional analysis, possibly attributable to smaller sample sizes per mountain range. Lastly, the importance of several variables shifted through time from significant to insignificant in the temporal analysis. Our results collectively reveal the overall complexity underlying species–environment relationships. With rapidly shifting conditions globally, this work adds to the growing body of literature highlighting how issues of spatio-temporal nonstationarity can limit the accuracy, transferability, and reliability of models and that interpretations will likely be most robust at local to regional scales. Diagnosing, describing, and incorporating nonstationarity of species–climate relationships into models over space and time could serve as a pivotal step in creating more informative models.
Frontiers in Ecology and Evolution↗
Examining the occupancy–density relationship for a low-density carnivore
The challenges associated with monitoring low-density carnivores across large landscapes have limited the ability to implement and evaluate conservation and management strategies for such species. Non-invasive sampling techniques and advanced statistical approaches have alleviated some of these challenges and can even allow for spatially explicit estimates of density, one of the most valuable wildlife monitoring tools. For some species, individual identification comes at no cost when unique attributes (e.g. pelage patterns) can be discerned with remote cameras, while other species require viable genetic material and expensive laboratory processing for individual assignment. Prohibitive costs may still force monitoring efforts to use species distribution or occupancy as a surrogate for density, which may not be appropriate under many conditions. Here, we used a large-scale monitoring study of fisher Pekania pennanti to evaluate the effectiveness of occupancy as an approximation to density, particularly for informing harvest management decisions. We combined remote cameras with baited hair snares during 2013–2015 to sample across a 70 096-km 2 region of western New York, USA. We fit occupancy and Royle–Nichols models to species detection–non-detection data collected by cameras, and spatial capture–recapture (SCR) models to individual encounter data obtained by genotyped hair samples. Variation in the state variables within 15-km 2 grid cells was modelled as a function of landscape attributes known to influence fisher distribution. We found a close relationship between grid cell estimates of fisher state variables from the models using detection–non-detection data and those from the SCR model, likely due to informative spatial covariates across a large landscape extent and a grid cell resolution that worked well with the movement ecology of the species. Fisher occupancy and density were both positively associated with the proportion of coniferous-mixed forest and negatively associated with road density. As a result, spatially explicit management recommendations for fisher were similar across models, though relative variation was dampened for the detection–non-detection data. Synthesis and applications . Our work provides empirical evidence that models using detection–non-detection data can make similar inferences regarding relative spatial variation of the focal population to models using more expensive individual encounters when the selected spatial grain approximates or is marginally smaller than home range size. When occupancy alone is chosen as a cost-effective state variable for monitoring, simulation and sensitivity analyses should be used to understand how inferences from detection–non-detection data will be affected by aspects of study design and species ecology.
Journal of Applied Ecology↗
Representing plant diversity in land models: An evolutionary approach to make ‘Functional Types’ more functional
Plants are critical mediators of terrestrial mass and energy fluxes, and their structural and functional traits have profound impacts on local and global climate, biogeochemistry, biodiversity, and hydrology. Yet Earth System Models (ESMs), our most powerful tools for predicting the effects of humans on the coupled biosphere-atmosphere system, simplify the incredible diversity of land plants into a handful of coarse categories of ‘Plant Functional Types’ (PFTs) that often fail to capture ecological dynamics such as biome distributions. The inclusion of more realistic functional diversity is a recognized goal for ESMs, yet there is currently no consistent, widely accepted way to add diversity to models, i.e. to determine what new PFTs to add and with what data to constrain their parameters. We review approaches to representing plant diversity in ESMs and draw on recent ecological and evolutionary findings to present an evolution-based functional type approach for further disaggregating functional diversity. Specifically, the prevalence of niche conservatism, or the tendency of closely related taxa to retain similar ecological and functional attributes through evolutionary time, reveals that evolutionary relatedness is a powerful framework for summarizing functional similarities and differences among plant types. We advocate that Plant Functional Types based on dominant evolutionary lineages (‘Lineage Functional Types’) will provide an ecologically defensible, tractable, and scalable framework for representing plant diversity in next-generation ESMs, with the potential to improve parameterization, process representation, and model benchmarking. We highlight how the importance of evolutionary history for plant function can unify the work of disparate fields to improve predictive modeling of the Earth system.
Global Change Biology↗
The Everglades Depth Estimation Network (EDEN) for Support of Ecological and Biological Assessments
The Everglades Depth Estimation Network (EDEN) is an integrated network of real-time water-level monitoring, ground-elevation modeling, and water-surface modeling that provides scientists and managers with current (1999-present), online water-depth information for the entire freshwater portion of the Greater Everglades. Presented on a 400-square-meter grid spacing, EDEN offers a consistent and documented dataset that can be used by scientists and managers to (1) guide large-scale field operations, (2) integrate hydrologic and ecological responses, and (3) support biological and ecological assessments that measure ecosystem responses to the implementation of the Comprehensive Everglades Restoration Plan.
Fact Sheet↗
The scaling of geographic ranges: implications for species distribution models
Context The geographic ranges of many species are responding to ongoing environmental change. Processes operating at different levels of biological organization, with corresponding spatial extents and grains and temporal rates, interact with the evolving configuration of environmental conditions to determine range dynamics. Objectives To synthesize understanding of scales and scaling, including relevant biological levels of organization, focusing on the processes that mediate species-environment relationships and the models used to make inferences about species distributions. Methods We review concepts related to the scaling of geographic ranges and implications for the most commonly used analytic methods, using simple simulations to illustrate important issues. Results Many processes lead to species distributions being dependent on environmental conditions within sites and within a neighborhood. Studies with large extents and fine grains can cut across several levels of biological organization (individual, within-population, and metapopulation processes) complicating interpretation. Many geographic ranges are not in dynamic equilibrium, but common models used for inference assume equilibrium. Interspecific interactions shape species distributions at multiple scales, and arguments for ignoring species interactions also assume equilibrium. Conclusions There is a need for timely science to inform policy and management decisions; however, we must also strive to provide predictions that best reflect our understanding of ecological systems. Species distributions evolve through time and reflect responses to environmental conditions that are mediated through individual and population processes. Species distribution models that reflect this understanding, and explicitly model dynamics, are likely to give more accurate predictions.
Landscape Ecology↗
Modeling functional flows in California rivers
Environmental flows are critical to the recovery and conservation of freshwater ecosystems worldwide. However, estimating desired ranges of environmental flows across large, diverse landscapes is challenging. To advance protections of environmental flows for streams in California, USA, we developed a statewide modeling approach focused on functional components of the natural flow regime. Functional flow components in California streams—fall pulse flows, wet season peak flows and base flows, the spring flow recession, and dry season baseflows—support essential physical and ecological processes in riverine ecosystems. These functional flow components can be represented by functional flow metrics (FFMs) and quantified by their magnitude, timing, frequency, duration, and rate-of-change from daily streamflow records. After quantifying FFMs at reference-quality streamflow gages in California, we used machine-learning methods to estimate their natural range of values for all stream reaches in the state based on physical watershed characteristics and climatic factors. We found that the models performed well in predicting FFMs in streams across a diversity of landscape and climate contexts, according to several model performance criteria. Using the predicted FFM values, we established initial estimates of ecological flows that are expected to support critical functions and are broadly protective of ecosystem health. Modeling functional flows statewide offers a pathway for increasing the pace and scale of environmental flow protections in California and beyond.
California↗
Coral restoration can drive rapid increases in reef accretion potential
Coral-reef degradation is disrupting the balance between reef accretion and erosion and threatening the persistence of essential coral-reef habitats. In south Florida, most reefs are already net eroding, and without intervention, valuable ecosystem services may be lost. Coral restoration holds the potential to reverse those trends; however, typical restoration monitoring does not adequately capture key geo-ecological functions. We addressed this knowledge gap using carbonate budgets and Structure-from-Motion models to evaluate the impact of coral restoration on reef-accretion potential and structural complexity at eight offshore and three inshore coral reefs in the Lower Florida Keys. Within 2–6 years following outplanting, restoration of rapidly growing A. cervicornis populations increased reef-accretion potential to 2.8 mm y − 1 and drove significant increases in structural complexity. There was no measurable impact of restoring slower-growing, massive corals on reef-accretion potential inshore; however, whereas the severe 2023 coral-bleaching event immediately following our study caused near-complete mortality of A. cervicornis , 59% of massive corals survived, highlighting potential trade-offs between coral growth and survival on future restoration efficacy. We conclude that although restoration can produce rapid, small-scale increases in reef-accretion potential, there remain important uncertainties about how and whether ecosystem-scale benefits of restoration on important geo-ecological reef functions can persist long term.
south Florida↗
Statistical aspects of point count sampling
The dominant feature of point counts is that they do not census birds, but instead provide incomplete counts of individuals present within a survey plot. Considering a simple model for point count sampling, we demon-strate that use of these incomplete counts can bias estimators and testing procedures, leading to inappropriate conclusions. A large portion of the variability in point counts is caused by the incomplete counting, and this within-count variation can be confounded with ecologically meaningful varia-tion. We recommend caution in the analysis of estimates obtained from point counts. Using; our model, we also consider optimal allocation of sampling effort. The critical step in the optimization process is in determining the goals of the study and methods that will be used to meet these goals. By explicitly defining the constraints on sampling and by estimating the relationship between precision and bias of estimators and time spent counting, we can predict the optimal time at a point for each of several monitoring goals. In general, time spent at a point will differ depending on the goals of the study.
Book chapter↗
Spatially-structured statistical network models for landscape genetics
A basic understanding of how the landscape impedes, or creates resistance to, the dispersal of organisms and hence gene flow is paramount for successful conservation science and management. Spatially structured ecological networks are often used to represent spatial landscape‐genetic relationships, where nodes represent individuals or populations and resistance to movement is represented using non‐binary edge weights. Weights are typically assigned or estimated by the user, rather than observed, and validating such weights is challenging. We provide a synthesis of current methods used to estimate edge weights and an overview of common model types, stressing the advantages and disadvantages of each approach and their ability to model landscape‐genetic data. We further explore a set of spatial‐statistical methods that provide ecologists with alternative approaches for modeling spatially explicit processes that may affect genetic structure. This includes an overview of spatial autoregressive models, with a particular focus on how correlation and partial correlation are used to represent neighborhood structure with the inverse of the covariance matrix (i.e., precision matrix). We then demonstrate how to model resistance by specifying an appropriate statistical model on the nodes, conditioned on the edge weights, through the precision matrix. This integration of network ecology and spatial statistics provides a practical analytical framework for landscape‐genetic studies. The results can be used to make statistical inferences about the relative importance of individual landscape characteristics, such as the vegetative cover, hillslope, or the presence of roads or rivers, on gene flow. In addition, the R code we include allows readers to explore landscape‐genetic structure in their own datasets, which will potentially provide new insights into the evolutionary processes that generated ecological networks, as well as valuable information about the optimal characteristics of conservation corridors.
Ecological Monographs↗
Assessing hypotheses about nesting site occupancy dynamics
Hypotheses about habitat selection developed in the evolutionary ecology framework assume that individuals, under some conditions, select breeding habitat based on expected fitness in different habitat. The relationship between habitat quality and fitness may be reflected by breeding success of individuals, which may in turn be used to assess habitat quality. Habitat quality may also be assessed via local density: if high‐quality sites are preferentially used, high density may reflect high‐quality habitat. Here we assessed whether site occupancy dynamics vary with site surrogates for habitat quality. We modeled nest site use probability in a seabird subcolony (the Black‐legged Kittiwake, Rissa tridactyla ) over a 20‐year period. We estimated site persistence (an occupied site remains occupied from time t to t + 1) and colonization through two subprocesses: first colonization (site creation at the timescale of the study) and recolonization (a site is colonized again after being deserted). Our model explicitly incorporated site‐specific and neighboring breeding success and conspecific density in the neighborhood. Our results provided evidence that reproductively “successful” sites have a higher persistence probability than “unsuccessful” ones. Analyses of site fidelity in marked birds and of survival probability showed that high site persistence predominantly reflects site fidelity, not immediate colonization by new owners after emigration or death of previous owners. There is a negative quadratic relationship between local density and persistence probability. First colonization probability decreases with density, whereas recolonization probability is constant. This highlights the importance of distinguishing initial colonization and recolonization to understand site occupancy. All dynamics varied positively with neighboring breeding success. We found evidence of a positive interaction between site‐specific and neighboring breeding success. We addressed local population dynamics using a site occupancy approach integrating hypotheses developed in behavioral ecology to account for individual decisions. This allows development of models of population and metapopulation dynamics that explicitly incorporate ecological and evolutionary processes.
Brittany↗
Carrying capacity of spatially distributed metapopulations
Carrying capacity is a key concept in ecology. A body of theory, based on the logistic equation, has extended predictions of carrying capacity to spatially distributed, dispersing populations. However, this theory has only recently been tested empirically. The experimental results disagree with some theoretical predictions of when they are extended to a population dispersing randomly in a two-patch system. However, they are consistent with a mechanistic model of consumption on an exploitable resource (consumer–resource model). We argue that carrying capacity, defined as the total equilibrium population, is not a fundamental property of ecological systems, at least in the context of spatial heterogeneity. Instead, it is an emergent property that depends on the population’s intrinsic growth and dispersal rates.
Trends in Ecology and Evolution↗
Ecogeomorphologic response of a tidally restricted salt marsh to tidal restoration and sea-level rise
Diked marshes with decades of restricted tidal flow exhibit fundamentally altered hydrologic and ecologic dynamics that result in limited vertical accretion, land subsidence, and underdeveloped tidal channels. These changes complicate marsh restoration efforts and constrain the marsh's ability to build elevation in response to future sea levels. In this study, we developed an integrated hydrodynamic and marsh accretion model to conduct the first assessment of the restoration potential of a diked marsh in response to reintroduction of tidal flow and sea-level rise (SLR). We applied our model to evaluate changes in biomass production in the Herring River estuary, Cape Cod, MA, USA—which has experienced significant ecological shifts due to more than a century of tidal restriction—in response to a range of SLR scenarios, tidal flow conditions, management interventions, and biomass production rates through 2100. We found that with restoration of tidal flow, the simulated marsh extent expanded in areas with efficient drainage, increasing biomass production by up to 4.4 times. However, when SLR was imposed, parts of the marsh gradually transitioned to open water, leading to a decline in marsh coverage from 19% to as low as 12%. Management interventions aimed at enhancing marsh elevation and improving the drainage capacity of tidal channels slowed marsh loss, supporting marsh area through 2100. Our findings provide insight into the key drivers of marsh resilience and loss, and our approach can be applied across tidally restricted and restored systems to develop targeted, adaptive restoration strategies that achieve desired ecological outcomes.
Massachusetts↗
Ground-Water Flow Model for the Spokane Valley-Rathdrum Prairie Aquifer, Spokane County, Washington, and Bonner and Kootenai Counties, Idaho
This report presents a computer model of ground-water flow in the Spokane Valley-Rathdrum Prairie (SVRP) aquifer in Spokane County, Washington, and Bonner and Kootenai Counties, Idaho. The aquifer is the sole source of drinking water for more than 500,000 residents in the area. In response to the concerns about the impacts of increased ground-water withdrawals resulting from recent and projected urban growth, a comprehensive study was initiated by the Idaho Department of Water Resources, the Washington Department of Ecology, and the U.S. Geological Survey to improve the understanding of ground-water flow in the aquifer and of the interaction between ground water and surface water. The ground-water flow model presented in this report is one component of this comprehensive study. The primary purpose of the model is to serve as a tool for analyzing aquifer inflows and outflows, simulating the effects of future changes in ground-water withdrawals from the aquifer, and evaluating aquifer management strategies. The scale of the model and the level of detail are intended for analysis of aquifer-wide water-supply issues. The SVRP aquifer model was developed by the Modeling Team formed within the comprehensive study. The Modeling Team consisted of staff and personnel working under contract with the Idaho Department of Water Resources, personnel working under contract with the Washington Department of Ecology, and staff of the U.S. Geological Survey. To arrive at a final model that has the endorsement of all team members, decisions on modeling approach, methodology, assumptions, and interpretations were reached by consensus. The ground-water flow model MODFLOW-2000 was used to simulate ground-water flow in the SVPR aquifer. The finite-difference model grid consists of 172 rows, 256 columns, and 3 layers. Ground-water flow was simulated from September 1990 through September 2005 using 181 stress periods of 1 month each. The areal extent of the model encompasses an area of approximately 326 square miles. For the most part, the model extent coincides with the 2005 revised extent of the Spokane Valley-Rathdrum Prairie aquifer as defined in a previous report. However, the model excludes Spirit and Hoodoo Valleys because of uncertainties about the ground-water flow directions in those valleys and the degree of hydraulic connection between the valleys and northern Rathdrum Prairie. The SVRP aquifer is considered to be a single hydrogeologic unit except in Hillyard Trough and the Little Spokane River Arm. In those areas, a continuous clay layer divides the aquifer into an upper, unconfined unit and a lower, confined unit. The model includes all known components of inflows to and outflows from the aquifer. Inflows to the SVRP aquifer include (1) recharge from precipitation, (2) inflows from tributary basins and adjacent uplands, (3) subsurface seepage and surface overflows from lakes that border the aquifer, (4) flow from losing segments of the Spokane River to the aquifer, (5) return percolation from irrigation, and (6) effluent from septic systems. Outflows from the SVRP aquifer include (1) ground-water withdrawals from wells, (2) flow from the aquifer to gaining segments of the Spokane River, (3) aquifer discharge to the Little Spokane River, and (4) subsurface outflow from the lower unit at the western limit of the model area near Long Lake. These inflow and outflow components are represented in the model by using MODFLOW-2000 packages. The parameter-estimation program PEST was used to calibrate the SVRP aquifer model. PEST implements a nonlinear least-squares regression method to estimate model parameters so that the differences between measured and simulated quantities are minimized with respect to an optimal criterion. Calibration data include 1,573 measurements of water levels and 313 measurements of streamflow gains and losses along segments of the Spokane and Little Spokane Rivers. Model parameters estimated during calib
Scientific Investigations Report↗
Temporal segmentation of animal trajectories informed by habitat use
Most animals live in seasonal environments and experience very different conditions throughout the year. Behavioral strategies like migration, hibernation, and a life cycle adapted to the local seasonality help to cope with fluctuations in environmental conditions. Thus, how an individual utilizes the environment depends both on the current availability of habitat and the behavioral prerequisites of the individual at that time. While the increasing availability and richness of animal movement data has facilitated the development of algorithms that classify behavior by movement geometry, changes in the environmental correlates of animal movement have so far not been exploited for a behavioral annotation. Here, we suggest a method that uses these changes in individual–environment associations to divide animal location data into segments of higher ecological coherence, which we term niche segmentation. We use time series of random forest models to evaluate the transferability of habitat use over time to cluster observational data accordingly. We show that our method is able to identify relevant changes in habitat use corresponding to both changes in the availability of habitat and how it was used using simulated data, and apply our method to a tracking data set of common teal (Anas crecca). The niche segmentation proved to be robust, and segmented habitat suitability outperformed models neglecting the temporal dynamics of habitat use. Overall, we show that it is possible to classify animal trajectories based on changes of habitat use similar to geometric segmentation algorithms. We conclude that such an environmentally informed classification of animal trajectories can provide new insights into an individuals' behavior and enables us to make sensible predictions of how suitable areas might be connected by movement in space and time.
Ecosphere↗