Nonparametric spatial covariance functions: Estimation and testing

Spatial autocorrelation techniques are commonly used to describe genetic and ecological patterns. To improve statistical inference about spatial covariance, we propose a continuous nonparametric estimator of the covariance function in place of the spatial correlogram. The spline correlogram is an adaptation of a recent development in spatial statistics and is a generalization of the commonly used correlogram. We propose a bootstrap algorithm to erect a confidence envelope around the entire covariance function. The meaning of this envelope is discussed. Not all functions that can be drawn inside the envelope are candidate covariance functions, as they may not be positive semidefinite. However, covariance functions that do not fit, are not supported by the data. A direct estimate of the L₀ spatial correlation length with associated confidence interval is offered and its interpretation is discussed. The spline correlogram is found to have high precision when applied to synthetic data. For illustration, the method is applied to electrophoretic data of an alpine grass (Poa alpina).     

Estimating the spatio-temporal risk of disease epidemics using a bioclimatic niche model

There are presently few tools available for estimating epidemic risks from forest pathogens, and hence informing pro-active disease management. In this study we demonstrated that a bioclimatic niche model can be used to examine questions of epidemic risk in temperate eucalypt plantations. The bioclimatic niche model, CLIMEX, was used to identify regional variation in climate suitability for Mycosphaerella leaf disease (MLD), a major cause of foliage damage in temperate eucalypt plantations around the world. Using historical observations of MLD damage, we were able to convert the relative score of climatic suitability generated by CLIMEX into a severity ranking ranging from low to high, providing for the first time a direct link between risk and impact, and allowing us to explore disease severity in a way meaningful to forest managers. We determined that the ‘Compare Years’ function in CLIMEX could be used for site-specific risk assessment to identify severity, frequency and seasonality of MLD epidemics. We explored appropriate scales of risk assessment for forest managers. Applying the CLIMEX model of MLD using a 0.25° or coarser grid size to areas of sharp topographic relief frequently misrepresented the risk posed by MLD, because considerable variation occurred between individual forest sites encompassed within a single grid cell. This highlighted the need for site-specific risk assessment to address many questions pertinent to managing risk in plantations.     

Estimation of the spatial covariance in Universal Kriging: Application to forest inventory

This paper presents a simple least squares procedure for estimating the spatial covariance and compares it with the numerically more difficult restricted maximum likelihood procedure. Thereafter, it compares design-based and kriging techniques for the estimation of spatial averages in the context of double sampling, as used in forest inventory, where terrestrial sample plots are combined with auxiliary information based on aerial photographs. A case study illustrates the theory.     

Estimating prevalence using composites

We are interested in estimating the fraction of a population that possesses a certain trait, such as the presence of a chemical contaminant in a lake. A composite sample drawn from a population has the trait in question whenever one or more of the individual samples making up the composite has the trait. Let the true fraction of the population that is contaminated be p. Classical estimators of p, such as the MLE and the jackknife, have been shown to be biased. In this study, we introduce a new shrinking estimator which can be used when doing composite sampling. The properties of this estimator are investigated and compared with those of the MLE and the jackknife.     

A far-near sparse covariance model with application in climatology

Environmental and Ecological Statistics - Teleconnection, the strong dependence between two distant locations, provides interesting information for discovering the structures in spatial data. While...     

Characterizing the spatial structure of songbird cultures

Recent advances have shown that human-driven habitat transformations can affect the cultural attributes of animal populations in addition to their genetic integrity and dynamics. Here I propose using the song of oscine birds for identifying the cultural spatial structure of bird populations and highlighting critical thresholds associated with habitat fragmentation. I studied song variation over a wide geographical scale in a small and endangered passerine, the Dupont's Lark Chersophilus duponti, focusing on (1) cultural population structure, to determine a statistical representation of spatial variation in song and identify cultural units, and (2) the minimum patch size needed for an individual to develop a stable repertoire. I found that overall song diversity depends on variation among populations (beta-cultural diversity). Abrupt thresholds occurred in the relationships between individual song dissimilarity and geographic distance, and between individual song diversity and patch area. Spatial autocorrelation analysis showed that populations located as little as 5 km apart may have independently evolved their song traditions. Song diversity stabilized in patches as small as 100 ha supporting as few as 8-20 males. Song repertoires of smaller patches were significantly poorer. Almost one-quarter of the study populations inhabited patches <100 ha, and their cultural traditions appear to have eroded. The analysis of spatial patterns in birdsong may be a useful tool for detecting subpopulations prone to extinction.     

Estimating wildfire growth from noisy and incomplete incident data using a state space model

Wildfire behaviors are complex and are of interest to fire managers and scientists for a variety of reasons. Many of these important behaviors are directly measured from the cumulative burn area time series of individual wildfires; however, estimating cumulative burn area time series is challenging due to the magnitude of measurement errors and missing entries. To resolve this, we introduce two state space models for reconstructing wildfire burn area using repeated observations from multiple data sources that include different levels of measurement error and temporal gaps. The constant growth parameter model uses a few parameters and assumes a burn area time series that follows a logistic growth curve. The non-constant growth parameter model uses a time-varying logistic growth curve to produce detailed estimates of the burn area time series that permit sudden pauses and pulses of growth. We apply both reconstruction models to burn area data from 13 large wildfire incidents to compare the quality of the burn area time series reconstructions and computational requirements. The constant growth parameter model reconstructs burn area time series with minimal computational requirements, but inadequately fits observed data in most cases. The non-constant growth parameter model better describes burn area time series, but can also be highly computationally demanding. Sensitivity analyses suggest that in a typical application, the reconstructed cumulative burn area time series is fairly robust to minor changes in the prior distributions.     

Estimating metabolic rate for butadiene at steady state using a Bayesian physiologically-based pharmacokinetic model

In a study of 133 volunteer subjects, demographic, physiologic and pharmacokinetic data through exposure to 1,3-Butadiene (BD) were collected in order to estimate the percentage of BD concentration metabolized at steady state, and to determine whether this percentage varies across gender, racial, and age groups. During the 20 min of continuous exposure to 2 parts per million (ppm) of BD, five measurements of exhaled concentration were made on each subject. In the following 40 min washout period, another five measurements were collected. A Bayesian hierarchical compartmental physiologically-based pharmacokinetic model (PKPB) was used. Using prior information on the model parameters, Markov Chain Monte Carlo (MCMC) simulation was conducted to obtain posterior distributions. The overall estimate of the mean percent of BD metabolized at steady state was 12.7% (95% credible interval: 7.7–17.8%). There was no significant difference in gender with males having a mean of 13.5%, and females 12.3%. Among the racial groups, Hispanic (13.9%), White (13.0%), Asian (12.1%), and Black (10.9%), the significant difference came from the difference between Black and Hispanic with a 95% credible interval from −5.63 to −0.30%. Those older than 30 years had a mean of 12.2% versus 12.9% for the younger group; although this was not a statistically significant difference. Given a constant inhalation input of 2 ppm, at steady state, the overall mean exhaled concentration was estimated to be 1.75ppm (95% credible interval: 1.64–1.84). An equivalent parameter, first-order metabolic rate constant, was also estimated and found to be consistent with the percent of BD metabolized at steady state across gender, race, and age strata.     

A multivariate prediction of spatial process with non-stationary covariance for Kuwait non-methane hydrocarbons levels

Predicting unmeasured realizations of multivariate spatial process responses is a fundamental problem in environmetrics. The study of levels of air pollutants is important for understanding and improving air quality in major urban areas. This research aims to handle the prediction in a Bayesian framework for non-methane hydrocarbons NMHC pollutant for the State of Kuwait where records of six monitor stations located in different sites are observed at successive time points. Our objective is to study the distribution level of NMHC with respect to time and metreological parameters and space and use this distribution to predict the concentration of NMHC in other sites of Kuwait using the minimum amount of data (reducing the cost). We will implement a hierarchical Bayesian approach assuming Gaussian random field technique that allows us to pool the data from different sites in predicting the exposure of the non-methane hydrocarbons in different regions of Kuwait.     

Estimating travel time of recharge water through a deep vadose zone using a transfer function model

We estimate the travel time of percolating water through a deep vadose zone at the regional scale using a transfer function model and a physical based conceptual flow model (Hydrus-1D), thereby exploiting the time series of precipitation, actual evapotranspiration and groundwater piezometry and generic vadose zone data. With the transfer function model we observe a high variability of estimated travel time varying from 0.9 to 3.1 years, corresponding to estimated vertical water flux velocities varying from 6.6 to 28.0 m/year. These results were compared with the travel time estimated from the physical based conceptual model. With the flow model, estimated travel time varies between 4.7 and 15.5 years, corresponding to water flux velocities varying between 1.7 and 4.1 m/year. The estimated travel time calculated with the flow model were therefore about five times larger than those estimated with the transfer function model. This could be explained by the fact that the transfer function model considers heterogeneous recharge from the vadose zone as well as from the vicinity of the piezometer through the so called “pushing effect”. In addition, the flow model requires various hydrogeological and hydrodynamic parameters which were estimated using generic parametrisation approaches, that are largely affected by uncertainty and may not reflect the local conditions. In contrast, the transfer function model only exploits available measurable time series and has the advantage of being site-specific.     

Estimating California ecosystem carbon change using process model and land cover disturbance data: 1951-2000

Land use change, natural disturbance, and climate change directly alter ecosystem productivity and carbon stock level. The estimation of ecosystem carbon dynamics depends on the quality of land cover change data and the effectiveness of the ecosystem models that represent the vegetation growth processes and disturbance effects. We used the Integrated Biosphere Simulator (IBIS) and a set of 30- to 60-m resolution fire and land cover change data to examine the carbon changes of California's forests, shrublands, and grasslands. Simulation results indicate that during 1951-2000, the net primary productivity (NPP) increased by 7%, from 72.2 to 77.1 Tg C yr⁻¹ (1 teragram = 10¹² g), mainly due to CO₂ fertilization, since the climate hardly changed during this period. Similarly, heterotrophic respiration increased by 5%, from 69.4 to 73.1 Tg C yr⁻¹, mainly due to increased forest soil carbon and temperature. Net ecosystem production (NEP) was highly variable in the 50-year period but on average equalled 3.0 Tg C yr⁻¹ (total of 149 Tg C). As with NEP, the net biome production (NBP) was also highly variable but averaged −0.55 Tg C yr⁻¹ (total of -27.3 Tg C) because NBP in the 1980s was very low (-5.34 Tg C yr⁻¹). During the study period, a total of 126 Tg carbon were removed by logging and land use change, and 50 Tg carbon were directly removed by wildland fires. For carbon pools, the estimated total living upper canopy (tree) biomass decreased from 928 to 834 Tg C, and the understory (including shrub and grass) biomass increased from 59 to 63 Tg C. Soil carbon and dead biomass carbon increased from 1136 to 1197 Tg C.Our analyses suggest that both natural and human processes have significant influence on the carbon change in California. During 1951-2000, climate interannual variability was the key driving force for the large interannual changes of ecosystem carbon source and sink at the state level, while logging and fire were the dominant driving forces for carbon balances in several specific ecoregions. From a long-term perspective, CO₂ fertilization plays a key role in maintaining higher NPP. However, our study shows that the increase in C sequestration by CO₂ fertilization is largely offset by logging/land use change and wildland fires.     

A spatial model of phytoplankton patchiness

The one-dimensional theory of critical-length scales of phytoplankton patchiness is developed to include phytoplankton growth and herbivore grazing as functions of time and space. The critical-length scale L _c for the pathch is then determined by the initial spatial distribution and concentration of the limiting nutrient and herbivores in addition to the daily averaged values of the growth and loss processes. The response of an initial phytoplankton patch to the stresses of turbulent diffusion, nutrient depletion, light periodicity, and nocturnal or continuous herbivore grazing is investigated numerically for several oceanic conditions. Nocturnal grazing, while less stressful on primary production than continous grazing, results in lower phytoplankton standing stocks. Increase in biomass of vertically migrating zooplankton results in a net loss of nutrient which might otherwise be egested, recycled, and utilized in the euphotic zone under continuous grazing conditions. The Ivlev constant is shown via sensitivity analysis to be a significant parameter ultimately influencing phytoplankton production. It is demonstrated numerically that diffusion of phytoplankton cells from areas of high concentration to low concentration prevents the local extinction of the standing stock, thereby rendering a positive herbivore grazing-threshold unnecessary for ecosystem stability.     

A hierarchical model for spatial capture-recapture data

Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture-recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.     

Kin-related spatial structure in brown bears Ursus arctos

Kin-related social structure may influence reproductive success and survival and, hence, the dynamics of populations. It has been documented in many gregarious animal populations, but few solitary species. Using molecular methods and field data we tested: (1) whether kin-related spatial structure exists in the brown bear (Ursus arctos), which is a solitary carnivore, (2) whether home ranges of adult female kin overlap more than those of nonkin, and (3) whether multigenerational matrilinear assemblages, i.e., aggregated related females, are formed. Pairwise genetic relatedness between adult (5 years and older) female dyads declined significantly with geographic distance, whereas this was not the case for male–male dyads or opposite sex dyads. The amount of overlap of multiannual home ranges was positively associated with relatedness among adult females. This structure within matrilines is probably due to kin recognition. Plotting of multiannual home-range centers of adult females revealed formation of two types of matrilines, matrilinear assemblages exclusively using an area and dispersed matrilines spread over larger geographic areas. The variation in matrilinear structure might be due to differences in competitive abilities among females and habitat limitations. The influence of kin-related spatial structure on inclusive fitness needs to be clarified in solitary mammals.     

The spatial structure of interzonal copepod populations in the Southern Ocean

The vertical distributions of Calanoides acutus, Calanus propinquus and Rhinicalanus gigas have been studied during Cruises I and II of the R.V. Ob in the Indian sector of the Southern Ocean. During the spawning period, all 3 species reveal the highest concentrations, and occupy the highest positions in the water column. During the period of feeding and growth, they begin slowly to disperse and to descend to greater depths. In spring, the populations ascend again to the water surface. In both seasons, later stages migrate first. Pronounced temperature gradients may prevent the ascent, and result in the breeding and subsequent growth of the new generation occurring in subsurface waters. Details of the vertical distributions of populations depend on their seasonal state and the local hydrology.     

Estimating population abundance using counts from an auxiliary population

Environmental and Ecological Statistics - We develop a new method for estimating population abundance for notoriously difficult to count populations. This is made possible using an easy to count...     

Estimating the biogenic enhancement factor of weathering using an inverse viability method

To determine the influence of the biosphere on weathering we use a dynamic model of the global carbon cycle. It takes into account the most important processes for the long-term evolution of the Earth. The model is solved under a slowly changing environment of increasing solar luminosity and volcanic activity and continental area. By comparing the model results for the global average temperature with data derived from δ¹⁸O values from cherts it is possible to quantify the biogenic enhancement factor of weathering. For this purpose a newly developed inverse viability method is applied, which allows for calculating the range of possible biogenic enhancement factors consistent with the data. We find that in the Precambrian the weathering was 5.4 times lower than in the Phanerozoic era. This supports the hypothesis that the Cambrian explosion was caused by a positive feedback between the spread of biosphere, increased silicate weathering, and a consequent cooling of the climate.     

Dissecting the tragedy: A spatial model of behavior in the commons

Much of the discussion of the tragedy of the commons focuses on aggregate impacts, often in data-poor developing country settings. Few non-experimental empirical studies shed light on contextual circumstances driving the extent of rent dissipation and overexploitation. We utilize a high-resolution data set to estimate a behavioral model of fishermen's spatial choices. A unique policy setting allows us to measure the degree to which individual fishermen's choices appear aimed at mitigating the tragedy of the commons in a small numbers setting. We find evidence of partial mitigation in excess of what we would expect under pure self-interest but short of what would occur under group-maximizing behavior. We also examine how contextual factors in the fishery shape the degree of cooperation within the fishing season and find evidence that competition for the common pool resource distorts fishermen's implicit cost of distance—creating a form of “common property inertia”.     

A zero-inflated Bayesian spatial model with near-locating measurements

Zero-inflated data arise in many contexts. In this paper, we develop a zero-inflated Bayesian hierarchical model which deals with spatial effects, correlation among near-locating measurements as well as excess zeros simultaneously. Inference, including the sampling from the posterior distributions, predictions at new locations, and model selection, is carried out by using computationally efficient Markov chain Monte Carlo techniques. The posterior distributions are simulated using a Gibbs sampler with the embedded ratio-of-uniform method and the slice sampling algorithm. The approach is illustrated via an application to herbaceous data collected in the Missouri Ozark Forest Ecosystem Project. The results from the proposed model are compared with those generated from a non-zero inflated model. The proposed model fully incorporates the information from data collection and provides more reliable inference. A predictive $p$ value is computed for model checking and it indicates that the proposed model fits the data well.     

Interaction between flow, transport and vegetation spatial structure

This paper summarizes recent advances in vegetation hydrodynamics and uses the new concepts to explore not only how vegetation impacts flow and transport, but also how flow feedbacks can influence vegetation spatial structure. Sparse and dense submerged canopies are defined based on the relative contribution of turbulent stress and canopy drag to the momentum balance. In sparse canopies turbulent stress remains elevated within the canopy and suspended sediment concentration is comparable to that in unvegetated regions. In dense canopies turbulent stress is reduced by canopy drag and suspended sediment concentration is also reduced. Further, for dense canopies, the length-scale of turbulence penetration into the canopy, δ _e , is shown to predict both the roughness height and the displacement height of the overflow profile. In a second case study, the relation between flow speed and spatial structure of a seagrass meadow gives insight into the stability of different spatial structures, defined by the area fraction covered by vegetation. In the last case study, a momentum balance suggests that in natural channels the total resistance is set predominantly by the area fraction occupied by vegetation, called the blockage factor, with little direct dependence on the specific canopy morphology.