Addressing onsite sampling in recreation site choice models

Independent experts and politicians have criticized statistical analyses of recreation behavior, which rely upon onsite samples due to their potential for biased inference. The use of onsite sampling usually reflects data or budgetary constraints, but can lead to two primary forms of bias in site choice models. First, the strategy entails sampling site choices rather than sampling individuals—a form of bias called endogenous stratification. Under these conditions, sample choices may not reflect the site choices of the true population. Second, exogenous attributes of the individuals sampled onsite may differ from the attributes of individuals in the population—the most common form in recreation demand is avidity bias. We propose addressing these biases by combining two the existing methods: Weighted Exogenous Stratification Maximum Likelihood estimation and propensity score estimation. We use the National Marine Fisheries Service's Marine Recreational Fishing Statistics Survey to illustrate methods of bias reduction, employing both simulated and empirical applications. We find that propensity score based weights can significantly reduce bias in estimation. Our results indicate that failure to account for these biases can overstate anglers' willingness to pay for improvements in fishing catch, but weighted models exhibit higher variance of parameter estimates and willingness to pay.     

Using data augmentation via the Gibbs Sampler to incorporate missing covariate structure in linear models for ecological assessments

Missing covariate values in linear regression models can be an important problem facing environmental researchers. Existing missing value treatment methods such as Multiple Imputation (MI), the EM algorithm and Data Augmentation (DA) have the assumption that both observed and unobserved data come from the same distribution, most commonly a multivariate normal or a conditionally multivariate normal family. These methods do try to incorporate the missing data mechanism and rely on the assumption of Missing At Random (MAR). We present a DA method which does not rely on the MAR assumption and can model missing data mechanisms and covariate structure. This method utilizes the Gibbs Sampler as a tool for incorporating these structures and mechanisms. We apply this method to an ecological data set that relates fish condition to environmental variables. Notice that the presented DA method detects relationships that are not detected when other missing data methods are employed.

Using multilevel spatial models to understand salamander site occupancy patterns after wildfire

Studies of the distribution of elusive forest wildlife have suffered from the confounding of true presence with the uncertainty of detection. Occupancy modeling, which incorporates probabilities of species detection conditional on presence, is an emerging approach for reducing observation bias. However, the current likelihood modeling framework is restrictive for handling unexplained sources of variation in the response that may occur when there are dependence structures such as smaller sampling units that are nested within larger sampling units. We used multilevel Bayesian occupancy modeling to handle dependence structures and to partition sources of variation in occupancy of sites by terrestrial salamanders (family Plethodontidae) within and surrounding an earlier wildfire in western Oregon, USA. Comparison of model fit favored a spatial N-mixture model that accounted for variation in salamander abundance over models that were based on binary detection/non-detection data. Though catch per unit effort was higher in burned areas than unburned, there was strong support that this pattern was due to a higher probability of capture for individuals in burned plots. Within the burn, the odds of capturing an individual given it was present were 2.06 times the odds outside the burn, reflecting reduced complexity of ground cover in the burn. Ther was weak support that true occupancy was lower within the burned area. While the odds of occupancy in the burn were 0.49 times the odds outside the burn among the five species, the magnitude of variation attributed to the burn was small in comparison to variation attributed to other landscape variables and to unexplained, spatially autocorrelated random variation. While ordinary occupancy models may separate the biological pattern of interest from variation in detection probability when all sources of variation are known, the addition of random effects structures for unexplained sources of variation in occupancy and detection probability may often more appropriately represent levels of uncertainty.     

Estimating variation in surface emissivities of intertidal macroalgae using an infrared thermometer and the effects on temperature measurements

Accurate measurements of surface temperatures with an infrared (IR) thermometer require input of the emissivities of the surfaces being measured; however, few determinations of the emissivities of intertidal organisms’ surfaces have been made. Emissivities of intertidal macroalgae were measured to determine whether algal species, measurement angle, hydration, and layering affected them. Emissivities were similar and averaged 0.94 among 11 of 13 species. The species with lower and more variable emissivities (Chondracanthus exasperatus and Desmarestia viridis) differed in morphology from the other species, which were relatively flat thin blades with little surface texture. Measurement angle caused emissivities to decrease significantly in Mazzaella splendens but not in three other species. Hydration and layering of Ulva lactuca also had no effect. At 22 °C, measured temperatures were within 1 °C of actual temperatures when thermometer emissivity settings ranged from 0.75 to 1.00. When emissivities were set lower than actual values, measured temperatures were lower than actual temperatures at 15 °C and higher than actual temperatures at 60 °C. When the IR thermometer was used to measure surface temperatures of nine species of intertidal algae immediately before they were inundated by the incoming tide, temperatures were higher in mid intertidal than low intertidal individuals and higher on a sunnier day than an overcast day. Temperatures of U. lactuca increased with increasing height on the shore, but temperatures of Ulvaria obscura did not. Temperatures were also higher in Fucus distichus blades than receptacles, and lower in U. lactuca and M. splendens occurring in the lower layers of stacks of algae.     

Intergenerational effects of climate generate cohort variation in lizard reproductive performance

An evaluation of the link between climate and population dynamics requires understanding of climate effects both within and across generations. In ectothermic vertebrates, demographic responses to climate changes should crucially depend on balancing needs for heat and water. Here, we studied how temperature and rainfall regimes experienced before and during adulthood influenced reproductive performances (litter size, offspring size, and survival) in a natural population of the live-bearing common lizard, Lacerta vivipara, monitored continuously from 1989 to 2004. Rainfall regime, but not temperature, had both immediate and delayed effects on these reproductive performances. Rainfall during the first month of life was positively correlated with juvenile survival. Females experiencing more rainfall during gestation produced smaller neonates that showed greater survival when controlling for the positive effect of body size on survival. Furthermore, females that experienced heavier rainfall when in utero produced fewer but longer neonates during adulthood. These demographic effects of rainfall on adult reproductive traits may come from maternal effects of climate conditions and/or from delayed effects of rainfall on the environment experienced early in life. Irrespective of the precise mechanism, however, this study provides evidence of intergenerational climate effects in natural populations of an ectothermic vertebrate.     

Scaling-up spatially-explicit ecological models using graphics processors

How the properties of ecosystems relate to spatial scale is a prominent topic in current ecosystem research. Despite this, spatially explicit models typically include only a limited range of spatial scales, mostly because of computing limitations. Here, we describe the use of graphics processors to efficiently solve spatially explicit ecological models at large spatial scale using the CUDA language extension. We explain this technique by implementing three classical models of spatial self-organization in ecology: a spiral-wave forming predator-prey model, a model of pattern formation in arid vegetation, and a model of disturbance in mussel beds on rocky shores. Using these models, we show that the solutions of models on large spatial grids can be obtained on graphics processors with up to two orders of magnitude reduction in simulation time relative to normal pc processors. This allows for efficient simulation of very large spatial grids, which is crucial for, for instance, the study of the effect of spatial heterogeneity on the formation of self-organized spatial patterns, thereby facilitating the comparison between theoretical results and empirical data. Finally, we show that large-scale spatial simulations are preferable over repetitions at smaller spatial scales in identifying the presence of scaling relations in spatially self-organized ecosystems. Hence, the study of scaling laws in ecology may benefit significantly from implementation of ecological models on graphics processors.     

Improvements in anisotropic models of single tree effects in Cartesian coordinates

For anisotropic density functions of e.g. fruit or leaf dispersal, most mathematical research is only done in polar coordinates. However, in software solutions aiming to derive inverse models for real world dispersal data, Cartesian coordinates may be preferred for several reasons. Thus, we introduce an anisotropic model in Cartesian coordinates following the approach in Wälder et al. (2009) with the von Mises approach. By introducing a correction factor, we thereby consider the fundamental attribute, that the integral over a density function with respect to the Cartesian coordinates has to be equal 1. It may have been overlooked so far that guaranteeing for this attribute needs different approaches whether working in polar or Cartesian coordinates. One result is that our approach can be used also for other anisotropic models rather than models from the von Mises approach.     

Fitting animal survival models with temporal random effects

Estimating temporal variance in animal demographic parameters is of particular importance in population biology. We implement the Schall’s algorithm for incorporating temporal random effects in survival models using recovery data. Our frequentist approach is based on a formulation of band-recovery models with random effects as generalized linear mixed models and a linearization of the link function conditional on the random effects. A simulation study shows that our procedure provides unbiased and precise estimates. The method is then implemented on two case studies using recovery data on fish and birds.     

Different modes of resource variation provide a critical test of ideal free distribution models

Ideal free distribution (IFD) models are perhaps the group of mathematical models of behavior that have been the most widely and successfully applied by empiricists. These models can be applied to nearly any situation in which consumers compete—by any mechanism—for resources that are patchily distributed in their environment. Although IFD models have come to be broadly accepted, experiments that simultaneously test more than a single prediction are rare. Instead, investigators normally either test (1) for a relationship between the distribution of consumers and the distribution of resources or (2) whether average fitnesses are equal across resource patches. We conducted experiments with pea aphids (Acyrthosiphon pisum Harris) feeding on two patches of fava beans (Vicia faba L.) to fully independently parameterize an IFD model with interference competition and then test quantitative predictions about aphid spatial distributions and the payoffs of patch choice. We found a precise fit between aphids’ predicted and observed reproductive successes. Furthermore, by varying patch “quality” in two ways, we were able to show that aphid distributions vary with the mode of resource variation in the predicted manner: aphids (1) matched resources when patches varied in size but not quality and (2) overmatched the good patch when patches varied in quality but not size (predicted as a consequence of weak interference). The close correspondence between quantitative predictions of the model with observed behaviors suggests that IFD theory is a framework with more explanatory power than is generally appreciated.     

Assessment of canopy stomatal conductance models using flux measurements

Stomatal conductance (g) is a key parameter in controlling energy and water exchanges between canopy and the atmosphere. Stomatal conductance models proposed by Ball, Woodrow and Berry (BWB) and Leuning have been increasingly used in land surface schemes. In a recent study, a new diagnostic index was developed by Wang et al. to examine the response of g to humidity and new models were proposed to resolve problems identified in the BWB and Leuning models. This approach is theoretically sound, but relies on canopy latent heat and CO₂ fluxes and environmental variables at the leaf surface which are not available at most eddy correlation (EC) observation sites. In this study, we tested the diagnostic index by empirically correcting EC measurements to canopy-level fluxes and by replacing leaf surface variables by their corresponding ambient air variables, and re-examined the stomatal conductance models of BWB, Leuning, and Wang et al. We found that the impact of the above modifications on the evaluation of g–humidity relationships is very small. This study provides a practical approach to investigate the stomatal response to humidity using routine EC measurements.     

Updating coarse-scale species distribution models using small fine-scale samples

Large, fine-grained samples are ideal for predictive species distribution models used for management purposes, but such datasets are not available for most species and conducting such surveys is costly. We attempted to overcome this obstacle by updating previously available coarse-grained logistic regression models with small fine-grained samples using a recalibration approach. Recalibration involves re-estimation of the intercept or slope of the linear predictor and may improve calibration (level of agreement between predicted and actual probabilities). If reliable estimates of occurrence likelihood are required (e.g., for species selection in ecological restoration) calibration should be preferred to other model performance measures. This updating approach is not expected to improve discrimination (the ability of the model to rank sites according to species suitability), because the rank order of predictions is not altered. We tested different updating methods and sample sizes with tree distribution data from Spain. Updated models were compared to models fitted using only fine-grained data (refitted models). Updated models performed reasonably well at fine scales and outperformed refitted models with small samples (10-100 occurrences). If a coarse-grained model is available (or could be easily developed) and fine-grained predictions are to be generated from a limited sample size, updating previous models may be a more accurate option than fitting a new model. Our results encourage further studies on model updating in other situations where species distribution models are used under different conditions from their training (e.g., different time periods, different regions).     

Cluster detection using Bayes factors from overparameterized cluster models

In this paper, we consider the use of a partition model to estimate regional disease rates and to detect spatial clusters. Formal inference regarding the number of partitions (or clusters) can be obtained with a reversible jump Markov chain Monte Carlo algorithm. As an alternative, we consider the ability of models with a fixed, but overly large, number of partitions to estimate regional disease rates and to provide informal inferences about the number and locations of clusters using local Bayes factors. We illustrate and compare these two approaches using data on leukemia incidence in upstate New York and data on breast cancer incidence in Wisconsin.     

Estimating behavioral parameters in animal movement models using a state-augmented particle filter

Data on fine-scale animal movement are being collected worldwide, with the number of species being tagged and the resolution of data rapidly increasing. In this study, a general methodology is proposed to understand the patterns in these high-resolution movement time series that relate to marine animal behavior. The approach is illustrated with dive data from a northern fur seal (Callorhinus ursinus) tagged on the Pribilof Islands, Alaska, USA. We apply a state-space model composed of a movement model and corresponding high-resolution vertical movement data. The central goal is to estimate parameters of this movement model, particularly their variation on appropriate time scales, thereby providing a direct link to behavior. A particle filter with state augmentation is used to jointly estimate the movement parameters and the state. A multiple iterated filter using overlapping data segments is implemented to match the parameter time scale with the behavioral inference. The time variation in the auto-covariance function facilitates identification of a movement model, allows separation of observation and process noise, and provides for validation of results. The analysis yields fitted parameters that show distinct time-evolving changes in fur seal behavior over time, matching well what is observed in the original data set.     

Male choice and competition in Tetraopes tetraophthalmus: effects of local sex ratio variation

Summary Male milkweed beetles (Tetraopes tetraophthalmus) are shown to exhibit choice between potential mates. Males, however, also exhibit direct competition for access to potential mates. These differences in male behavior are dependent on the local sex ratio, with males becoming increasingly choosy when the sex ratio is female-biased, and more competitive when the sex ratio is malebiased. Females show neither choice nor competition. In both the laboratory and in the field, body size is important in determining patterns of competition and choice. Larger males win most aggressive encounters, and males generally prefer large females as mates. The combination in a single sex, of competition for mates and mate choice is not predicted by classical sexual selection theory. Male choice and competition may have evolved in T. tetraophthalmus due to the combination of (1) the mating system (2) the pattern of variation in female fecundity, and (3) the spatially and temporally variable operational sex ratios. This explanation is not dependent on high heritability of body size.     

Addressing the environmental risk of persistent organic pollutants in China

The Stockholm Convention on persistent organic pollutants (POPs) was adopted in 2001. This year is the 10th anniversary of the adoption of the Convention. Until now, 22 chemicals or chemical categories have been listed as POPs in the Stockholm Convention. The POPs Research Center was established in Tsinghua University in the same year when the Convention was adopted. In the last ten years, much work has been done by Chinese researchers to understand the environmental risk of POPs in China. This article aims to review the recent research progress of our POPs Research Center and some other Chinese researchers?? studies in addressing the environmental risk of POPs, including the priority screening and inventory study of POPs, monitoring and modeling of POPs pollution and exposure, and environmental risk assessment and modeling of POPs. Although great advances in addressing the environmental risk of POPs have been made in recent years, we are still facing quite a few problems, such as data scarcity and uncertainty in environmental risk assessment of POPs. The study on the effect of POPs mixtures is in its infancy and currently POPs are usually assessed from legal perspective by risk assessment of single chemicals. These problems should be well addressed by further efforts. Further studies should also be taken in future to study environment risk of POPs by considering aspects of coupled dynamics between climate processes and POPs. Such sound scientific, riskbased information can support decision-making aiming to effectively minimize the risk level of POPs.     

Population viability analysis for several populations using multivariate state-space models

The International Union for the Conservation of Nature and Natural Resources (IUCN), the world's largest and most important global conservation network, has listed approximately 16,000 species worldwide as threatened. The most important tool for recognizing and listing species as threatened is population viability analysis (PVA), which estimates the probability of extinction of a population or species over a specified time horizon. The most common PVA approach is to apply it to single time series of population abundance. This approach to population viability analysis ignores covariability of local populations. Covariability can be important because high synchrony of local populations reduces the effective number of local populations and leads to greater extinction risk. Needed is a way of extending PVA to model correlation structure among multiple local populations. Multivariate state-space modeling is applied to this problem and alternative estimation methods are compared. The multivariate state-space technique is applied to endangered populations of pacific salmon, USA. Simulations demonstrated that the correlation structure can strongly influence population viability and is best estimated using restricted maximum likelihood instead of maximum likelihood.     

Validation of ecological state space models using the Laplace approximation

Many statistical models in ecology follow the state space paradigm. For such models, the important step of model validation rarely receives as much attention as estimation or hypothesis testing, perhaps due to lack of available algorithms and software. Model validation is often based on a naive adaptation of Pearson residuals, i.e. the difference between observations and posterior means, even if this approach is flawed. Here, we consider validation of state space models through one-step prediction errors, and discuss principles and practicalities arising when the model has been fitted with a tool for estimation in general mixed effects models. Implementing one-step predictions in the R package Template Model Builder, we demonstrate that it is possible to perform model validation with little effort, even if the ecological model is multivariate, has non-linear dynamics, and whether observations are continuous or discrete. With both simulated data, and a real data set related to geolocation of seals, we demonstrate both the potential and the limitations of the techniques. Our results fill a need for convenient methods for validating a state space model, or alternatively, rejecting it while indicating useful directions in which the model could be improved.     

The community effects of phenotypic and genetic variation within a predator population

Natural populations are heterogeneous mixtures of individuals differing in physiology, morphology, and behavior. Despite the ubiquity of phenotypic variation within natural populations, its effects on the dynamics of ecological communities are not well understood. Here, we use a quantitative genetics framework to examine how phenotypic variation in a predator affects the outcome of apparent competition between its two prey species. Classical apparent competition theory predicts that prey have reciprocally negative effects on each other. The addition of phenotypic trait variation in predation can marginalize these negative effects, mediate coexistence, or generate positive indirect effects between the prey species. Long-term coexistence or facilitation, however, can be preceded by long transients of extinction risk whenever the heritability of phenotypic variation is low. Greater heritability can circumvent these ecological transients but also can generate oscillatory and chaotic dynamics. These dramatic changes in ecological outcomes, in the sign of indirect effects, and in stability suggest that studies which ignore intraspecific trait variation may reach fundamentally incorrect conclusions regarding ecological dynamics.     

Environmental variation mediates the deleterious effects of Coleosporium ipomoeae on Ipomoea purpurea

Variation in the environment is common within and between natural populations and may influence selection on plant resistance by altering the level of damage or the fitness consequences of damage from plant enemies. While much is known about how environmental variation influences the amount of damage a plant experiences, few studies have attempted to determine how variation in the environment may alter the fitness consequences of damage, particularly in plant-pathogen interactions. In this work we manipulated a rust pathogen, Coleosporium ipomoeae, in field experiments and showed that this pathogen reduced several components of fitness in its natural host plant, Ipomoea purpurea. Furthermore, we showed that the deleterious effects of C. ipomoeae were variable. We identified variation in the quality of a plant's microenvironment, the abundance of secondary enemy damage, and the length of a growing season as variable components of the environment that may influence the magnitude of damage and tolerance, causing the interaction between C. ipomoeae and I. purpurea to vary from parasitism to commensalism. Considering how environmental variation impacts the magnitude and negative fitness effects of pathogen damage is important to understanding spatially variable selection and coevolution in this and other plant-pathogen interactions.     

Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations

Many biological populations are subject to periodically changing environments such as years with or without fire, or rotation of crop types. The dynamics and management options for such populations are frequently investigated using periodic matrix models. However the analysis is usually limited to long-term results (asymptotic population growth rate and its sensitivity to perturbations of vital rates). In non-periodic matrix models it has been shown that long-term results may be misleading as populations are rarely in their stable structure. We therefore develop methods to analyze transient dynamics of periodic matrix models. In particular, we show how to calculate the effects of perturbations on population size within and at the end of environmental cycles. Using a model of a weed population subject to a crop rotation, we show that different cyclic permutations produce different patterns of sensitivity of population size and different population sizes. By examining how the starting environment interacts with the initial conditions, we explain how different patterns arise. Such understanding is critical to developing effective management and monitoring strategies for populations subject to periodically recurring environments.