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A method for testing whether model predictions fall within a prescribed factor of true values, with an application to pesticide leaching

A quantitative method is described for testing whether model predictions fall within a specified factor of true values. The technique is based on classical theory for confidence regions on unknown population parameters and can be related to hypothesis testing in both univariate and multivariate situations. A capability index is defined that can be used as a measure of predictive capability of a model, and its properties are discussed. The testing approach and the capability index should facilitate model validation efforts and permit comparisons among competing models. An example is given for a pesticide leaching model that predicts chemical concentrations in the soil profile.

Ecological Modelling

A framework for integrating inferred movement behavior into disease risk models

Movement behavior is an important contributor to habitat selection and its incorporation in disease risk models has been somewhat neglected. The habitat preferences of host individuals affect their probability of exposure to pathogens. If preference behavior can be incorporated in ecological niche models (ENMs) when data on pathogen distributions are available, then variation in such behavior may dramatically impact exposure risk. Here we use data from the anthrax endemic system of Etosha National Park, Namibia, to demonstrate how integrating inferred movement behavior alters the construction of disease risk maps. We used a Maximum Entropy (MaxEnt) model that associated soil, bioclimatic, and vegetation variables with the best available pathogen presence data collected at anthrax carcass sites to map areas of most likely Bacillus anthracis (the causative bacterium of anthrax) persistence. We then used a hidden Markov model (HMM) to distinguish foraging and non-foraging behavioral states along the movement tracks of nine zebra ( Equus quagga ) during the 2009 and 2010 anthrax seasons. The resulting tracks, decomposed on the basis of the inferred behavioral state, formed the basis of step-selection functions (SSFs) that used the MaxEnt output as a potential predictor variable. Our analyses revealed different risks of exposure during different zebra behavioral states, which were obscured when the full movement tracks were analyzed without consideration of the underlying behavioral states of individuals. Pathogen (or vector) distribution models may be misleading with regard to the actual risk faced by host animal populations when specific behavioral states are not explicitly accounted for in selection analyses. To more accurately evaluate exposure risk, especially in the case of environmentally transmitted pathogens, selection functions could be built for each identified behavioral state and then used to assess the comparative exposure risk across relevant states. The scale of data collection and analysis, however, introduces complexities and limitations for consideration when interpreting results.

Etosha National Park

Selecting a distributional assumption for modelling relative densities of benthic macroinvertebrates

The selection of a distributional assumption suitable for modelling macroinvertebrate density data is typically challenging. Macroinvertebrate data often exhibit substantially larger variances than expected under a standard count assumption, that of the Poisson distribution. Such overdispersion may derive from multiple sources, including heterogeneity of habitat (historically and spatially), differing life histories for organisms collected within a single collection in space and time, and autocorrelation. Taken to extreme, heterogeneity of habitat may be argued to explain the frequent large proportions of zero observations in macroinvertebrate data. Sampling locations may consist of habitats defined qualitatively as either suitable or unsuitable. The former category may yield random or stochastic zeroes and the latter structural zeroes. Heterogeneity among counts may be accommodated by treating the count mean itself as a random variable, while extra zeroes may be accommodated using zero-modified count assumptions, including zero-inflated and two-stage (or hurdle) approaches. These and linear assumptions (following log- and square root-transformations) were evaluated using 9 years of mayfly density data from a 52 km, ninth-order reach of the Upper Mississippi River (n = 959). The data exhibited substantial overdispersion relative to that expected under a Poisson assumption (i.e. variance:mean ratio = 23 ??? 1), and 43% of the sampling locations yielded zero mayflies. Based on the Akaike Information Criterion (AIC), count models were improved most by treating the count mean as a random variable (via a Poisson-gamma distributional assumption) and secondarily by zero modification (i.e. improvements in AIC values = 9184 units and 47-48 units, respectively). Zeroes were underestimated by the Poisson, log-transform and square root-transform models, slightly by the standard negative binomial model but not by the zero-modified models (61%, 24%, 32%, 7%, and 0%, respectively). However, the zero-modified Poisson models underestimated small counts (1 ??? y ??? 4) and overestimated intermediate counts (7 ??? y ??? 23). Counts greater than zero were estimated well by zero-modified negative binomial models, while counts greater than one were also estimated well by the standard negative binomial model. Based on AIC and percent zero estimation criteria, the two-stage and zero-inflated models performed similarly. The above inferences were largely confirmed when the models were used to predict values from a separate, evaluation data set (n = 110). An exception was that, using the evaluation data set, the standard negative binomial model appeared superior to its zero-modified counterparts using the AIC (but not percent zero criteria). This and other evidence suggest that a negative binomial distributional assumption should be routinely considered when modelling benthic macroinvertebrate data from low flow environments. Whether negative binomial models should themselves be routinely examined for extra zeroes requires, from a statistical perspective, more investigation. However, this question may best be answered by ecological arguments that may be specific to the sampled species and locations. ?? 2004 Elsevier B.V. All rights reserved.

Ecological Modelling

The ODD protocol: A review and first update

The ‘ODD’ (Overview, Design concepts, and Details) protocol was published in 2006 to standardize the published descriptions of individual-based and agent-based models (ABMs). The primary objectives of ODD are to make model descriptions more understandable and complete, thereby making ABMs less subject to criticism for being irreproducible. We have systematically evaluated existing uses of the ODD protocol and identified, as expected, parts of ODD needing improvement and clarification. Accordingly, we revise the definition of ODD to clarify aspects of the original version and thereby facilitate future standardization of ABM descriptions. We discuss frequently raised critiques in ODD but also two emerging, and unanticipated, benefits: ODD improves the rigorous formulation of models and helps make the theoretical foundations of large models more visible. Although the protocol was designed for ABMs, it can help with documenting any large, complex model, alleviating some general objections against such models.

Ecological Modelling

Using spatiotemporal statistical models to estimate animal abundance and infer ecological dynamics from survey counts

Ecologists often fit models to survey data to estimate and explain variation in animal abundance. Such models typically require that animal density remains constant across the landscape where sampling is being conducted, a potentially problematic assumption for animals inhabiting dynamic landscapes or otherwise exhibiting considerable spatiotemporal variation in density. We review several concepts from the burgeoning literature on spatiotemporal statistical models, including the nature of the temporal structure (i.e., descriptive or dynamical) and strategies for dimension reduction to promote computational tractability. We also review several features as they specifically relate to abundance estimation, including boundary conditions, population closure, choice of link function, and extrapolation of predicted relationships to unsampled areas. We then compare a suite of novel and existing spatiotemporal hierarchical models for animal count data that permit animal density to vary over space and time, including formulations motivated by resource selection and allowing for closed populations. We gauge the relative performance (bias, precision, computational demands) of alternative spatiotemporal models when confronted with simulated and real data sets from dynamic animal populations. For the latter, we analyze spotted seal ( Phoca largha ) counts from an aerial survey of the Bering Sea where the quantity and quality of suitable habitat (sea ice) changed dramatically while surveys were being conducted. Simulation analyses suggested that multiple types of spatiotemporal models provide reasonable inference (low positive bias, high precision) about animal abundance, but have potential for overestimating precision. Analysis of spotted seal data indicated that several model formulations, including those based on a log-Gaussian Cox process, had a tendency to overestimate abundance. By contrast, a model that included a population closure assumption and a scale prior on total abundance produced estimates that largely conformed to our a priori expectation. Although care must be taken to tailor models to match the study population and survey data available, we argue that hierarchical spatiotemporal statistical models represent a powerful way forward for estimating abundance and explaining variation in the distribution of dynamical populations.

Ecological Monographs

Use of landscape simulation modeling to quantify resilience for ecological applications

Goals of fostering ecological resilience are increasingly used to guide U.S. public land management in the context of anthropogenic climate change and increasing landscape disturbances. There are, however, few operational means of assessing the resilience of a landscape or ecosystem. We present a method to evaluate resilience using simulation modeling. In this method, we use historical conditions (e.g., in North America, prior to European settlement), quantified using simulation modeling, to provide a comparative reference for contemporary conditions, where substantial departures indicate loss of resilience. Contemporary ecological conditions are compared statistically to the historical time series to create a resilience index, which can be used to prioritize landscapes for treatment and inform possible treatments. However, managing for resilience based on historical conditions is tenuous in the Anthropocene, which is characterized by rapid climate change, extensive human land use, altered disturbance regimes, and exotic species introductions. To account for the future variability of ecosystems resulting from climate and disturbance regime shifts, we augment historical simulations with simulations of ecosystem dynamics under projected climate and land use changes to assess the degree of departure from benchmark historical conditions. We use a mechanistic landscape model (FireBGCv2) applied to a large landscape in western Montana, USA, to illustrate the methods presented in this paper. Spatially explicit ecosystem modeling provides the vehicle to generate the historical and future time series needed to quantify potential resilience conditions associated with past and potential future conditions. Our methods show that given selection of a useful set of metrics, managers could use simulations like ours to evaluate potential future management directions.

Ecosphere

A multi-model framework for simulating wildlife population response to land-use and climate change

Reliable assessments of how human activities will affect wildlife populations are essential for making scientifically defensible resource management decisions. A principle challenge of predicting effects of proposed management, development, or conservation actions is the need to incorporate multiple biotic and abiotic factors, including land-use and climate change, that interact to affect wildlife habitat and populations through time. Here we demonstrate how models of land-use, climate change, and other dynamic factors can be integrated into a coherent framework for predicting wildlife population trends. Our framework starts with land-use and climate change models developed for a region of interest. Vegetation changes through time under alternative future scenarios are predicted using an individual-based plant community model. These predictions are combined with spatially explicit animal habitat models to map changes in the distribution and quality of wildlife habitat expected under the various scenarios. Animal population responses to habitat changes and other factors are then projected using a flexible, individual-based animal population model. As an example application, we simulated animal population trends under three future land-use scenarios and four climate change scenarios in the Cascade Range of western Oregon. We chose two birds with contrasting habitat preferences for our simulations: winter wrens (Troglodytes troglodytes), which are most abundant in mature conifer forests, and song sparrows (Melospiza melodia), which prefer more open, shrubby habitats. We used climate and land-use predictions from previously published studies, as well as previously published predictions of vegetation responses using FORCLIM, an individual-based forest dynamics simulator. Vegetation predictions were integrated with other factors in PATCH, a spatially explicit, individual-based animal population simulator. Through incorporating effects of landscape history and limited dispersal, our framework predicted population changes that typically exceeded those expected based on changes in mean habitat suitability alone. Although land-use had greater impacts on habitat quality than did climate change in our simulations, we found that small changes in vital rates resulting from climate change or other stressors can have large consequences for population trajectories. The ability to integrate bottom-up demographic processes like these with top-down constraints imposed by climate and land-use in a dynamic modeling environment is a key advantage of our approach. The resulting framework should allow researchers to synthesize existing empirical evidence, and to explore complex interactions that are difficult or impossible to capture through piecemeal modeling approaches. ?? 2008 Elsevier B.V.

Ecological Modelling

Ecology, distribution, and predictive occurrence modeling of Palmers chipmunk ( Tamias palmeri ): a high-elevation small mammal endemic to the Spring Mountains in southern Nevada, USA

Although montane sky islands surrounded by desert scrub and shrub steppe comprise a large part of the biological diversity of the Basin and Range Province of southwestern North America, comprehensive ecological and population demographic studies for high-elevation small mammals within these areas are rare. Here, we examine the ecology and population parameters of the Palmer’s chipmunk ( Tamias palmeri ) in the Spring Mountains of southern Nevada, and present a predictive GIS-based distribution and probability of occurrence model at both home range and geographic spatial scales. Logistic regression analyses and Akaike Information Criterion model selection found variables of forest type, slope, and distance to water sources as predictive of chipmunk occurrence at the geographic scale. At the home range scale, increasing population density, decreasing overstory canopy cover, and decreasing understory canopy cover contributed to increased survival rates.

Nevada

Emergence of ratio-dependent and predator-dependent functional responses for pollination mutualism and seed parasitism

Prey ( N ) dependence [ g ( N )], predator ( P ) dependence [ g ( P ) or g ( N , P )], and ratio dependence [ f ( P / N )] are often seen as contrasting forms of the predator's functional response describing predator consumption rates on prey resources in predator–prey and parasitoid–host interactions. Analogously, prey-, predator-, and ratio-dependent functional responses are apparently alternative functional responses for other types of consumer–resource interactions. These include, for example, the fraction of flowers pollinated or seeds parasitized in pollination (pre-dispersal) seed-parasitism mutualisms, such as those between fig wasps and fig trees or yucca moths and yucca plants. Here we examine the appropriate functional responses for how the fraction of flowers pollinated and seeds parasitized vary with the density of pollinators (predator dependence) or the ratio of pollinator and flower densities (ratio dependence). We show that both types of functional responses can emerge from minor, but biologically important variations on a single model. An individual-based model was first used to describe plant–pollinator interactions. Conditional upon on whether the number of flowers visited by the pollinator was limited by factors other than search time (e.g., by the number of eggs it had to lay, if it was also a seed parasite), and on whether the pollinator could directly find flowers on a plant, or had to search, the simulation results lead to either a predator-dependent or a ratio-dependent functional response. An analytic model was then used to show mathematically how these two cases can arise.

Ecological Modelling

Modeling pesticide fate in a small tidal estuary

The exposure analysis modeling system (EXAMS), a pesticide fate model developed by the U.S. Environmental Protection Agency, was modified to model the fate of the herbicides atrazine and metolachlor in a small tidally dominated estuary (Bath Creek) in North Carolina, USA where freshwater inflow accounts for only 3% of the total flow. The modifications simulated the changes that occur during the tidal cycle in the estuary, scenarios that are not possible with the original EXAMS model. Two models were created within EXAMS, a steady-state model and a time-variant tidally driven model. The steady-state model accounted for tidal flushing by simply altering freshwater input to yield an estuary residence time equal to that measured in Bath Creek. The tidal EXAMS model explicitly incorporated tidal flushing by modifying the EXAMS code to allow for temporal changes in estuary physical attributes (e.g., volume). The models were validated with empirical measurements of atrazine and metolachlor concentrations in the estuary shortly after herbicide application in nearby fields and immediately following a rain event. Both models provided excellent agreement with measured concentrations. The steady-state EXAMS model accurately predicted atrazine concentrations in the middle of the estuary over the first 3 days and under-predicted metolachlor by a factor of 2-3. The time-variant, tidally driven EXAMS model accurately predicted the rise and plateau of both herbicides over the 6-day measurement period. We have demonstrated the ability of these modified EXAMS models to be useful in predicting pesticide fate and exposure in small tidal estuaries. This is a significant improvement and expansion of the application of EXAMS, and given the wide use of EXAMS for surface water quality modeling by both researchers and regulators and the ability of EXAMS to interface with terrestrial models (e.g., pesticide root zone model) and bioaccumulation models, we now have an easily-accessible and widely accepted means of modeling chemical fate in estuaries. ?? 2006 Elsevier B.V. All rights reserved.

Ecological Modelling

A model of the productivity of the mallard duck

This paper describes a stochastic computer model that simulates recruitment of the mallard ( Anas platyrhynchos ) under different habitat conditions and management scenarios. The model incorporates several environmental phenomena and biological relations that affect mallard recruitment. Major events include arrival of mallards in the spring, daily survival of hens, initiation of nests, selection of nest sites, survival of nests until hatching, and survival of broods until fledging. The model was originally developed as a tool for synthesizing the results of research. Subsequently, we applied the model to a variety of management situations. We also describe the sources of estimates used in the model, evaluate its sensitivity to input parameters, and review some practical applications.

Ecological Modelling

Simulation of cotton rat population dynamics and response to rodenticide applications in Florida sugarcane

Alternative deterministic simulation models were compared to test the management consequences of present uncertainty about the degree of density dependence involved in cotton rat population cycles in southern Florida sugarcane fields. Efficacy of rodenticide applied in different months was explored under six different scenarios of density dependence and independence in two population parameters: fecundity and juvenile survival. Output from the six models differed considerably in the number of rats produced, but was remarkably consistent in the most effective months to apply rodenticide. Since models without density-dependent fecundity were inherently unstable and an inverse relationship between fecundity and population size is apparent in field data, such a population-growth mechanism seems possible in Florida sugarcane fields. The model in which fecundity was density-dependent at all times produced rat densities closest to field data. Output from this model was most sensitive to changes in the amount litter size declines as population size increases. Field tests are necessary to validate the general agreement among the models about the most effective months to apply rodenticide.

Florida

Do bioclimate variables improve performance of climate envelope models?

Climate envelope models are widely used to forecast potential effects of climate change on species distributions. A key issue in climate envelope modeling is the selection of predictor variables that most directly influence species. To determine whether model performance and spatial predictions were related to the selection of predictor variables, we compared models using bioclimate variables with models constructed from monthly climate data for twelve terrestrial vertebrate species in the southeastern USA using two different algorithms (random forests or generalized linear models), and two model selection techniques (using uncorrelated predictors or a subset of user-defined biologically relevant predictor variables). There were no differences in performance between models created with bioclimate or monthly variables, but one metric of model performance was significantly greater using the random forest algorithm compared with generalized linear models. Spatial predictions between maps using bioclimate and monthly variables were very consistent using the random forest algorithm with uncorrelated predictors, whereas we observed greater variability in predictions using generalized linear models.

Ecological Modelling

Tidal marsh susceptibility to sea-level rise: importance of local-scale models

Increasing concern over sea-level rise impacts to coastal tidal marsh ecosystems has led to modeling efforts to anticipate outcomes for resource management decision making. Few studies on the Pacific coast of North America have modeled sea-level rise marsh susceptibility at a scale relevant to local wildlife populations and plant communities. Here, we use a novel approach in developing an empirical sea-level rise ecological response model that can be applied to key management questions. Calculated elevation change over 13 y for a 324-ha portion of San Pablo Bay National Wildlife Refuge, California, USA, was used to represent local accretion and subsidence processes. Next, we coupled detailed plant community and elevation surveys with measured rates of inundation frequency to model marsh state changes to 2100. By grouping plant communities into low, mid, and high marsh habitats, we were able to assess wildlife species vulnerability and to better understand outcomes for habitat resiliency. Starting study-site conditions were comprised of 78% (253-ha) high marsh, 7% (30-ha) mid marsh, and 4% (18-ha) low marsh habitats, dominated by pickleweed Sarcocornia pacifica and cordgrass Spartina spp. Only under the low sea-level rise scenario (44 cm by 2100) did our models show persistence of some marsh habitats to 2100, with the area dominated by low marsh habitats. Under mid (93 cm by 2100) and high sea-level rise scenarios (166 cm by 2100), most mid and high marsh habitat was lost by 2070, with only 15% (65 ha) remaining, and a complete loss of these habitats by 2080. Low marsh habitat increased temporarily under all three sea-level rise scenarios, with the peak (286 ha) in 2070, adding habitat for the endemic endangered California Ridgway’s rail Rallus obsoletus obsoletus . Under mid and high sea-level rise scenarios, an almost complete conversion to mudflat occurred, with most of the area below mean sea level. Our modeling assumed no marsh migration upslope due to human levee and infrastructure preventing these types of processes. Other modeling efforts done for this area have projected marsh persistence to 2100, but our modeling effort with site-specific datasets allowed us to model at a finer resolution with much higher local confidence, resulting in different results for management. Our results suggest that projected sea-level rise will have significant impacts on marsh plant communities and obligate wildlife, including those already under federal and state protection. Comprehensive modeling as done here improves the potential to implement adaptive management strategies and prevent marsh habitat and wildlife loss in the future.

California

Application of information theory methods to food web reconstruction

In this paper we use information theory techniques on time series of abundances to determine the topology of a food web. At the outset, the food web participants (two consumers, two resources) are known; in addition we know that each consumer prefers one of the resources over the other. However, we do not know which consumer prefers which resource, and if this preference is absolute (i.e., whether or not the consumer will consume the non-preferred resource). Although the consumers and resources are identified at the beginning of the experiment, we also provide evidence that the consumers are not resources for each other, and the resources do not consume each other. We do show that there is significant mutual information between resources; the model is seasonally forced and some shared information between resources is expected. Similarly, because the model is seasonally forced, we expect shared information between consumers as they respond to the forcing of the resources. The model that we consider does include noise, and in an effort to demonstrate that these methods may be of some use in other than model data, we show the efficacy of our methods with decreasing time series size; in this particular case we obtain reasonably clear results with a time series length of 400 points. This approaches ecological time series lengths from real systems.

Ecological Modelling

Test of a foraging-bioenergetics model to evaluate growth dynamics of endangered pallid sturgeon ( Scaphirhynchus albus )

Factors affecting feeding and growth of early life stages of the federally endangered pallid sturgeon ( Scaphirhynchus albus ) are not fully understood, owing to their scarcity in the wild. In this study was we evaluated the performance of a combined foraging-bioenergetics model as a tool for assessing growth of age-0 pallid sturgeon in the Missouri River. In the laboratory, three size classes of sturgeon larvae (18–44 mm; 0.027–0.329 g) were grown for 7 to 14 days under differing temperature (14–24 °C) and prey density (0–9 Chironomidae larvae/d) regimes. After accounting for effects of water temperature and prey density on fish activity, we compared observed final weight, final length, and number of prey consumed to values generated from the foraging-bioenergetics model. When confronted with an independent dataset, the combined model provided reliable estimates (within 13% of observations) of fish growth and prey consumption, underscoring the usefulness of the modeling approach for evaluating growth dynamics of larval fish when empirical data are lacking.

Ecological Modelling

The need for accuracy in modelling: An example

The need for accurate information in modelling depends on the objectives of the effort. but trustworthy data are essential for a model intended for use in the management of natural resources. This point is illustrated by referring to a recently published model of canvasback ducks. We demonstrate that several key assumptions are not supported by biological evidence, and that inferences drawn from the model could be dangerously misleading if they were used to guide the management of canvasback ducks.

Ecological Modelling

Comparison of climate envelope models developed using expert-selected variables versus statistical selection

Climate envelope models are widely used to describe potential future distribution of species under different climate change scenarios. It is broadly recognized that there are both strengths and limitations to using climate envelope models and that outcomes are sensitive to initial assumptions, inputs, and modeling methods Selection of predictor variables, a central step in modeling, is one of the areas where different techniques can yield varying results. Selection of climate variables to use as predictors is often done using statistical approaches that develop correlations between occurrences and climate data. These approaches have received criticism in that they rely on the statistical properties of the data rather than directly incorporating biological information about species responses to temperature and precipitation. We evaluated and compared models and prediction maps for 15 threatened or endangered species in Florida based on two variable selection techniques: expert opinion and a statistical method. We compared model performance between these two approaches for contemporary predictions, and the spatial correlation, spatial overlap and area predicted for contemporary and future climate predictions. In general, experts identified more variables as being important than the statistical method and there was low overlap in the variable sets (<40%) between the two methods Despite these differences in variable sets (expert versus statistical), models had high performance metrics (>0.9 for area under the curve (AUC) and >0.7 for true skill statistic (TSS). Spatial overlap, which compares the spatial configuration between maps constructed using the different variable selection techniques, was only moderate overall (about 60%), with a great deal of variability across species. Difference in spatial overlap was even greater under future climate projections, indicating additional divergence of model outputs from different variable selection techniques. Our work is in agreement with other studies which have found that for broad-scale species distribution modeling, using statistical methods of variable selection is a useful first step, especially when there is a need to model a large number of species or expert knowledge of the species is limited. Expert input can then be used to refine models that seem unrealistic or for species that experts believe are particularly sensitive to change. It also emphasizes the importance of using multiple models to reduce uncertainty and improve map outputs for conservation planning. Where outputs overlap or show the same direction of change there is greater certainty in the predictions. Areas of disagreement can be used for learning by asking why the models do not agree, and may highlight areas where additional on-the-ground data collection could improve the models.

Ecological Modelling