Imputation Approaches for Animal Movement Modeling

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.     

Hierarchical Nonlinear Spatio-temporal Agent-Based Models for Collective Animal Movement

Modeling complex collective animal movement presents distinct challenges. In particular, modeling the interactions between animals and the nonlinear behaviors associated with these interactions, while accounting for uncertainty in data, model, and parameters, requires a flexible modeling framework. To address these challenges, we propose a general hierarchical framework for modeling collective movement behavior with multiple stages. Each of these stages can be thought of as processes that are flexible enough to model a variety of complex behaviors. For example, self-propelled particle (SPP) models (e.g., Vicsek et al. in Phys Rev Lett 75:1226–1229, 1995) represent collective behavior and are often applied in the physics and biology literature. To date, the study and application of these models has almost exclusively focused on simulation studies, with less attention given to rigorously quantifying the uncertainty. Here, we demonstrate our general framework with a hierarchical version of the SPP model applied to collective animal movement. This structure allows us to make inference on potential covariates (e.g., habitat) that describe the behavior of agents and rigorously quantify uncertainty. Further, this framework allows for the discrete time prediction of animal locations in the presence of missing observations. Due to the computational challenges associated with the proposed model, we develop an approximate Bayesian computation algorithm for estimation. We illustrate the hierarchical SPP methodology with a simulation study and by modeling the movement of guppies.Supplementary materials accompanying this paper appear online.     

Dynamic Models of Animal Movement with Spatial Point Process Interactions

When analyzing animal movement, it is important to account for interactions between individuals. However, statistical models for incorporating interaction behavior in movement models are limited. We propose an approach that models dependent movement by augmenting a dynamic marginal movement model with a spatial point process interaction function within a weighted distribution framework. The approach is flexible, as marginal movement behavior and interaction behavior can be modeled independently. Inference for model parameters is complicated by intractable normalizing constants. We develop a double Metropolis–Hastings algorithm to perform Bayesian inference. We illustrate our approach through the analysis of movement tracks of guppies (Poecilia reticulata).     

Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement

We discuss the notorious problem of order selection in hidden Markov models, that is of selecting an adequate number of states, highlighting typical pitfalls and practical challenges arising when analyzing real data. Extensive simulations are used to demonstrate the reasons that render order selection particularly challenging in practice despite the conceptual simplicity of the task. In particular, we demonstrate why well-established formal procedures for model selection, such as those based on standard information criteria, tend to favor models with numbers of states that are undesirably large in situations where states shall be meaningful entities. We also offer a pragmatic step-by-step approach together with comprehensive advice for how practitioners can implement order selection. Our proposed strategy is illustrated with a real-data case study on muskox movement.Supplementary materials accompanying this paper appear online.     

Multi-scale Modeling of Animal Movement and General Behavior Data Using Hidden Markov Models with Hierarchical Structures

Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of N possible states. The states are loosely connected to behavioral modes that manifest themselves at the temporal resolution at which observations are made. Due to advances in tag technology and tracking with digital video recordings, data can be collected at increasingly fine temporal resolutions. Yet, inferences at time scales cruder than those at which data are collected and, which correspond to larger-scale behavioral processes, are not yet answered via HMMs. We include additional hierarchical structures to the basic HMM framework, incorporating multiple Markov chains at various time scales. The hierarchically structured HMMs allow for behavioral inferences at multiple time scales and can also serve as a means to avoid coarsening data. Our proposed framework is one of the first that models animal behavior simultaneously at multiple time scales, opening new possibilities in the area of animal movement and behavior modeling. We illustrate the application of hierarchically structured HMMs in two real-data examples: (i) vertical movements of harbor porpoises observed in the field, and (ii) garter snake movement data collected as part of an experimental design. Supplementary materials accompanying this paper appear online.     

Agent-Based Inference for Animal Movement and Selection

Contemporary ecologists often find themselves with an overwhelming amount of data to analyze. For example, it is now possible to collect nearly continuous spatiotemporal data on animal locations via global positioning systems and other satellite telemetry technology. In addition, there is a wealth of readily available environmental data via geographic information systems and remote sensing. We present a modeling framework that utilizes these forms of data and builds on previous research pertaining to the quantitative analysis of animal movement. This approach provides additional insight into the environmental drivers of residence and movement as well as resource selection while accommodating path uncertainty. The methods are demonstrated in an application involving mule deer movement in the La Sal Range, Utah, USA. Supplemental materials for this article are available online.     

Phosphate and Nitrate Movement Through Simulated Golf Greens

Phosphorus and nitrogen can leach from porous golf greens potentially causing degradation of ground water quality. Agreenhouse experiment was carried out with 52 cm columns (15 cm diam.) made to USGA green specifications and sodded to `Tifdwarf' bermudagrass to determine the effects of fertilizer sources at various rates on P and N leaching. Fertilizers were balanced soluble and controlled-release (polyand sulfur coated) sources at N rates of 0, 12, 24, and 49 kg N ha^-1 and at P rates of 0, 5, 11, and 21 kg ha^-1 every other week for a total of 6 applications. Controlled-release N was from NH₄ and urea and the soluble source N was from KNO₃, urea, and (NH₄)PO₄. Irrigation rate was 0.63 cm per day initially and increased to 1.25 cm per day at week 7. Weeklyleachate collections for 23 weeks were analyzed for P andNO₃-N. Concentrations of N and P were lower in the leachatefor the controlled-release source than for the soluble source. Leaching of P continued for the entire 23 weeks of theexperiment, whereas N was essentially exhausted by week 15indicating that P leaches at a slower rate than N. For the low Prate (5 kg ha^-1) for the controlled-release source there was no increase in P concentration in the leachate compared to control. Thus, low P rates will not result in degradation of water quality due to increased P. For the controlled-release source at the low rate <10% of the P added leached, whereasthe values for N were in the range of 20 to 45% for all ratesand sources. Control treatments resulted in N concentrations in the leachate as high as 26 mg L^-1. Results show thatP leaching is a potential problem only at high rates of solublesources and high irrigation, whereas N is more readily leached.     

Interactions of Protein and Starch Studied Through Amyloglucosidase Action

The access of amyloglucosidase to the carbohydrate molecule was taken as a measure of interactions occurring among starch, amylose, amylopectin, β-dextrin and purified gluten, gliadins, high molecular weight glutenin subunits, or bovine serum albumin when they were mixed together and gelatinized before digestion. The most relevant decrease in liberated glucose, denoting coverage of some reaction sites for amyloglucosidase, occurred when gliadins were mixed with the carbohydrates. Other proteins were not as effective as gliadins. Amylopectin was not affected by any protein. Comparison of results allows some hypothesis to be formulated about the influence of structure on molecular interactions.     

Reflected Stochastic Differential Equation Models for Constrained Animal Movement

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modeling unconstrained animal movement. We present methods for simulation and inference based on augmenting the constrained movement path with a latent unconstrained path and illustrate this augmentation with a simulation example and an analysis of telemetry data from a Steller sea lion (Eumatopias jubatus) in southeast Alaska.     

Modeling of Nitrogen Losses Through Ammonia Volatilization in Second-season Corn

ABSTRACT

Knowledge on the behavior of cumulative N-NH₃ volatilization is important for defining the strategies to reduce the N losses, as well as increasing the efficiency of nitrogen fertilization in different environments. The present study, which uses nonlinear models, aims at assessing the cumulative N-NH₃ losses through volatilization by applying different rates of urea over time to two soils cultivated with second-season corn. Two experiments were carried out; one in a clayey Oxisol, and another in a sandy-clay loam Ultisol in a randomized block experimental design. N-NH₃ volatilization was quantified by using semi-open static chambers and spectrophotometry (salicylate blue). The cumulative N-NH₃ losses were similar at both rates of urea and in both soils assessed, ranging from 34.04% to 43.15% of the N applied. The highest N-NH₃ volatilization occurred from 1.03 to 6.48 days after applying the fertilizer, and the highest volatilization rates ranged from 0.90 to 2.91 kg ha^-1 d^-1. The shortest time to reach the highest volatilization rate, associated with the highest daily rate of N-NH₃ volatilization, was seen in the Ultisol. Although the volatilizations accumulated in both soils were similar, this result was only seen due to the climatic conditions after applying the fertilizer, which contributed to minimize the N-NH₃ losses. The use of nonlinear models has shown an appropriate data adjustment, providing parameters that help to understand the behavior of N-NH₃ volatilization accumulated over time in second-season corn.     

Modeling Contaminant Transport Through Capped Dredged Sediment Using a Centrifuge

The presence of contaminated sediment poses a barrier to essential waterway maintenance and construction in many ports and harbors, which support 95% of U.S. foreign trade. Cost effective solutions to remediate contaminated sediments in waterways need to be applied. Capping is the least expensive remediation alternative available for marine sediments that is unsuitable for open water disposal. Dredged material capping and in situ capping alternatives, however, are not widely used because regulatory agencies are concerned about the potential for contaminant migration through the caps. Numerous studies have been conducted on the effects of diffusion through caps, however, there is a lack of experimental data documenting the effects of consolidation induced transport of contaminants through caps. This study examines consolidation induced advective contaminant transport in capped sediment utilizing a research centrifuge. Centrifuge modeling simulates the increase in the gravitational acceleration (g) of a prototype, which is N times larger than the model, where N is gravitational acceleration factor. For contaminant migration, the time of transport in the model is inversely proportional to the square of the acceleration factor in the prototype. In this study, consolidation induced advective transport was modeled for 22.5 hours at 100-g, which modeled a contaminant migration time of 25 years for a prototype that was 100 times larger than the centrifuge model. Thus, advection and dispersion dominated the migration of contaminants. The centrifuge modeling results were compared to an analytical solution for advection and dispersion.     

Phosphate-Enhanced Movement of Arsenic Out of Lead Arsenate-Contaminated Topsoil and Through Uncontaminated Subsoil

Past use of lead arsenate insecticides has resulted in elevated concentrations of lead (Pb) andarsenic (As) in topsoils of many existing and former deciduous tree fruit orchard sites throughoutthe world. Application of phosphate (PO4)-containing fertilizers to these soils can increase soil Assolubility, phytoavailability and downward mobility. A laboratory soil column experiment wasconducted to determine if As released by phosphate additions to a topsoil artificially contaminatedwith lead arsenate (1.65 mmol total Pb/kg; 1.10 mmol total As/kg) would be appreciably resorbedby the underlying uncontaminated subsoil. Treatments were a factorial combination of topsoilamendment with monoammonium phosphate (MAP, 0 or 16.67 mmol PO4/kg), and amount ofleaching (1, 5 and 10 pore volume displacements (PVD) with distilled water under saturated flowconditions). Soil As decreased in the topsoil with increasing amount of leaching and increased inthe subsoil. Addition of MAP substantially increased loss of topsoil. As, promoted As transportinto and through the subsoil, and increased dissolved As concentrations in the column leachates.After 10 PVDs, 95% of the initial soil As remained in the -MAP columns, while 56% of the initialsoil As remained the +MAP columns. Dissolved Pb concentrations were <0.05 µmol/Lin all column leachates. The data are consistent with a mechanism of PO4-enhanced release of Asin the topsoil and subsequent promotion of As movement through the subsoil by continuingcompetition of dissolved As and PO4 for ion adsorption sites. The experimental results indicatethat use of PO4-containing fertilizers on lead arsenate-contaminated soils has the potential togreatly enhance downward movement of soil As.     

Incorporating Telemetry Error into Hidden Markov Models of Animal Movement Using Multiple Imputation

When data streams are observed without error and at regular time intervals, discrete-time hidden Markov models (HMMs) have become immensely popular for the analysis of animal location and auxiliary biotelemetry data. However, measurement error and temporally irregular data are often pervasive in telemetry studies, particularly in marine systems. While relatively small amounts of missing data that are missing-completely-at-random are not typically problematic in HMMs, temporal irregularity can result in few (if any) observations aligning with the regular time steps required by HMMs. Fitting HMMs that explicitly account for uncertainty attributable to location measurement error, temporally irregular observations, or other forms of missing data typically requires computationally demanding techniques, such as Markov chain Monte Carlo (MCMC). Using simulation and a real-world bearded seal (Erignathus barbatus) example, I investigate a practical alternative to incorporating measurement error and temporally irregular observations into HMMs based on multiple imputation of the position process drawn from a single-state continuous-time movement model. This two-stage approach is relatively simple, performed with existing software using efficient maximum likelihood methods, and completely parallelizable. I generally found the approach to perform well across a broad range of simulated measurement error and irregular sampling rates, with latent states and locations reliably recovered in nearly all simulated scenarios. However, high measurement error coupled with low sampling rates often induced bias in both the estimated probability distributions of data streams derived from the imputed position process and the estimated effects of spatial covariates on state transition probabilities. Results from the two-stage analysis of the bearded seal data were similar to a more computationally intensive single-stage MCMC analysis, but the two-stage analysis required much less computation time and no custom model-fitting algorithms. I thus found the two-stage multiple-imputation approach to be promising in terms of its ease of implementation, computation time, and performance. Code for implementing the approach using the R package “momentuHMM” is provided.Supplementary materials accompanying this paper appear online.     

Understanding Consumer Preference for Functional Barley Tortillas Through Sensory,Demographic, and Behavioral Data

Consumption of whole grains as part of a health‐promoting diet is encouraged among Americans due to beneficial nutrients and phytochemicals. The main objectives of this study were to investigate the effect of whole barley flour particle size on consumer acceptance of whole grain and soluble fiber‐enriched tortillas; to examine the effect of demographic and behavioral data on consumer acceptance; and to establish relationships between consumer acceptance and survey results to identify market opportunities among particular groups of consumers. Four experimental tortillas and two representative commercial brands were tested by 95 untrained panelists using a 9‐point hedonic scale for appearance, color, flavor, texture, and overall acceptability. Demographic and behavioral data on age, gender, ethnicity, frequency of tortilla consumption, daily effort to include fiber in the diet, consumption of tortillas containing ≥1 g of dietary fiber/serving, consumption of low‐fat tortillas, and tortilla brands and type used were collected. Potential market segments for these tortillas include older consumers (41+), women, Hispanics, and Asians, and frequent tortilla consumers. A response surface relating flavor and texture to overall acceptability produced almost equivalent results to the multivariate PLS results in terms of predicting overall acceptability, which facilitates analysis and interpretation.     

Valorization of Organic Wastes to Reduce the Movement of Priority Substances Through a Semiarid Soil

In this work, we examined the effect of two different organic wastes, composted sheep manure and coir, on the sorption, persistence, and mobility of three pesticides (alachlor, chlorfenvinphos, and chlorpyrifos) included as priority substances in European Directive 2013/39/EU. With this aim, leaching studies were conducted using disturbed soil columns filled with a typical agricultural soil (hipercalcic calcisol) from a semiarid area (southeastern Spain) to determine their potential for groundwater pollution. The three compounds were found in leachates of unamended soil although in different proportions: 53% (alachlor), 9% (chlorfenvinphos), and 6% (chlorpiryfos). The addition of organic wastes significantly increased the sorption of the studied pesticides. As a consequence, the half-lives of the studied pesticides were higher in amended than in unamended soils. A marked reduction of the amount recovered in leachates was observed in the amended soils, except for chlorpiryfos, whose recoveries barely changed. According to their potential groundwater pollution calculated as the groundwater ubiquity score (GUS) index, alachlor and chlorfenvinphos show medium leachability while chlorpiryfos is unlikely to leach.     

Effect of Lime Application on the Movement of Atrazine and Nitrate-Nitrogen Through Undisturbed-Saturated Soil Columns

Adsorption studies of Cr(III) on biogas residual slurry (BRS) were caried out under varying conditions of shaking time (5–180 min), metal ion concentration (10–40 mg L^-1), adsorbent concentration (1.0 to 8.0 g L^-1) and initial pH (1.5–5.0). Adsorption follows Langmuir isotherm, being endothermic in nature. For a Cr(III) concentration of 10 mg L^-1, a maximum removal of 85% by 4 g L^-1 of adsorbent was obtained at an initial pH ≥ 3.0. Desorption of Cr(III) from the spent adsorbent has also been investigated. Removal of Cr(III) from tannery wastewater by BRS was testified.     

Modeling Herbicide Movement to Ground Water in Irrigated Sandy Soils of the San Joaquin Valley, California

A semi-empirical probabilistic transport model was developed to simulate simazine and diuron well water concentrations in an agriculturally intensive coarse soil region of Fresno County, California. Model inputs included five random variables: the organic carbon normalized soil adsorption coefficient, root zone degradation, application rate, depth to ground water, and ground water recharge age. Transport was simulated in two phases: initial transport through the root zone using the mechanistic model LEACHM, and a second empirically-based phase that simulated transport from the bottom of the root zone to the water table, and ultimately to domestic water wells. Best-fit calibration estimates for combined deep vadose/shallow ground water degradation half-lives were 330 d and 455 d for simazine and diuron, respectively. Simulations based on these fitted half-lives yielded coefficients of determination and root mean square errors of 0.973 and 0.993, and 0.367 and 0.364 for observed vs predicted simazine and diuron concentration percentiles, respectively. The calibrated model output also described the observed relationships of decreasing detection frequency and decreasing concentration with increasing depth to ground water. A novel contribution is the calculation of regional mass budgets for the herbicides. In modeling results, 9–54% and 2–16% (10th–90th percentiles) of applied simazine and diuron, respectively, leached out of the 1.5 m root zone, while the upper 10th percentile of well water concentrations corresponded to approximately 1–2% of application for both pesticides.     

微孔管渗灌时土壤水分运动的有限元模拟及其应用

为了深入了解新型微孔渗灌管的灌水性能，提供推广应用渗灌的科学理论和技术依据，建立了含有第3类边界条件的二维微孔管渗灌土壤水分运动的数学模型，采用有限单元法进行了模拟。检验结果表明模型具有较高的精度。模型的仿真应用结果表明：供水水压力、土壤初始含水率、渗管的渗水速率等对渗灌效果都有明显影响。供水压力增大渗灌后土壤湿润范围内的平均含水率增大。初始含水率越高，湿润锋越不明显，总渗水量越小。随着渗管渗水速率的增大，渗管周围将出现饱和区，并存在渗水速率临界值，该值与土壤初始含水率有关。增加渗管的渗水速率可以提高渗灌的灌水效果。     

Modeling the Interfacial Interactions between CrtS and CrtR from Xanthophyllomyces dendrorhous , a P450 System Involved in Astaxanthin Production

Xanthophyllomyces dendrorhous is a natural source of astaxanthin, a carotenoid widely used in the food industry. In this yeast, astaxanthin is synthesized from β-carotene by a cytochrome P450, CrtS, which depends on CrtR, the four-domain cytochrome P450 reductase (CPR). Although Saccharomyces cerevisiae has an endogenous CPR (ScCPR), expression of CrtS does not result in astaxanthin production unless it is coexpressed with CrtR. Assuming that CrtS could interact with the FMN-binding domain of either CrtR or ScCPR (XdFMNbd and ScFMNbd, respectively), the aim of this work was to identify possible interaction differences between these alternative complexes by protein modeling and short molecular dynamics simulations. Considering the recently proposed membrane orientation of a mammalian P450, our CrtS-CrtR model predicts that both N-terminal ends stand adjacent to the membrane plane, allowing their anchoring. Compared with the possible interface between CrtS and both FMNbd, the Xanthophyllomyces system appears to be stabilized by more saline bridges.