Inference on Partially Observed Quasi-stationary Markov Chains With Applications to Multistate Population Models

If the full capture histories of captured individuals are available, inferences on multistate open population models may be conducted using the well known Arnason–Schwarz model. However, data of this detail is not always available. It is well known that inference on the transition probabilities of a Markov chain may be conducted using aggregate data and we extend this approach to aggregate data on multistate open population models. We show that for parameters to be identifiable we need to augment the aggregate data and we achieve this by batch marking a cohort of individuals according to their initial state, so that the batch marking augments the aggregate data. Model performance is examined by conducting several simulation studies and the model is applied to a real data set where full capture histories are available so it may be compared with the Arnason–Schwarz estimates. This article has supplementary material online.     

Dynamic multistate site occupancy models to evaluate hypotheses relevant to conservation of Golden Eagles in Denali National Park, Alaska

The recent development of multistate site occupancy models offers great opportunities to frame and solve decision problems for conservation that can be viewed in terms of site occupancy. These models have several characteristics (e.g., they account for detectability) that make them particularly well suited for addressing management and conservation problems. We applied multistate site occupancy models to evaluate hypotheses related to the conservation and management of Golden Eagles (Aquila chrysaetos) in Denali National Park, Alaska, and provided estimates of transition probabilities among three occupancy states for nesting areas (occupied with successful reproduction, occupied with unsuccessful reproduction, and unoccupied). Our estimation models included the effect of potential recreational activities (hikers) and environmental covariates such as a snowshoe hare (Lepus americanus) index on transition probabilities among the three occupancy states. Based on the most parsimonious model, support for the hypothesis of an effect of potential human disturbance on site occupancy dynamics was equivocal. There was some evidence that potential human disturbance negatively affected local colonization of territories, but there was no evidence of an effect on reproductive performance parameters. In addition, models that assume a positive relationship between the hare index and successful reproduction were well supported by the data. The statistical approach that we used is particularly useful to parameterize management models that can then be used to make optimal decisions related to the management of Golden Eagles in Denali. Although in our case we were particularly interested in managing recreational activities, we believe that such models should be useful to for a broad class of management and conservation problems.     

Integrating occupancy modeling and interview data for corridor identification: A case study for jaguars in Nicaragua

Corridors are critical elements in the long-term conservation of wide-ranging species like the jaguar (Panthera onca). Jaguar corridors across the range of the species were initially identified using a GIS-based least-cost corridor model. However, due to inherent errors in remotely sensed data and model uncertainties, these corridors warrant field verification before conservation efforts can begin. We developed a novel corridor assessment protocol based on interview data and site occupancy modeling. We divided our pilot study area, in southeastern Nicaragua, into 71, 6 × 6 km sampling units and conducted 160 structured interviews with local residents. Interviews were designed to collect data on jaguar and seven prey species so that detection/non-detection matrices could be constructed for each sampling unit. Jaguars were reportedly detected in 57% of the sampling units and had a detection probability of 28%. With the exception of white-lipped peccary, prey species were reportedly detected in 82–100% of the sampling units. Though the use of interview data may violate some assumptions of the occupancy modeling approach for determining ‘proportion of area occupied’, we countered these shortcomings through study design and interpreting the occupancy parameter, psi, as ‘probability of habitat used’. Probability of habitat use was modeled for each target species using single state or multistate models. A combination of the estimated probabilities of habitat use for jaguar and prey was selected to identify the final jaguar corridor. This protocol provides an efficient field methodology for identifying corridors for easily-identifiable species, across large study areas comprised of unprotected, private lands.     

Inference and model comparison for species accumulation functions using approximating pure birth processes

Soberon and Llorente proposed using the mean S(t; ϕ) of a pure birth process as a model for species accumulation functions and obtained ordinary least squares point estimates for the vector of parameters ϕ. They provided useful biological interpretations for S(t; ϕ) as well as for the birth rates of the process; they also expressed the strong need for an objective tool to compare different models for a given species accumulation data set. We show that the functions S(t; ϕ) proposed by Soberon and Llorente are generally not means of pure birth processes but that they can be well approximated by the mean of a suitable nonhomogeneous pure birth process B(t). We suggest using S(t; ϕ) and an upper bound for the (unknown) variance of the approximating pure birth process to make statistical inferences about ϕ. A nonlinear regression model with mean S(t; ϕ) and normal errors, possibly correlated, is proposed using a likelihood approach. This model can be compared with other relevant models under consideration by means of their corresponding likelihood ratio, providing a useful, objective, and quantitative tool for comparing different models in the light of the observed data. The suggested approach is exemplified with two species accumulation data sets.     

Estimating the three-dimensional structure of canopy foliage based on the light measurements in a Betula ermanii stand

In order to more accurately evaluate the functional activity of forest stands by canopy production and evapotranspiration, we improved the methods for field measurements and statistical modeling to estimate foliage configuration (spatial distribution of leaves) while simultaneously reconstructing the three-dimensional photosynthetically active photon flux density (PPFD) distribution (PPFD pattern) in a forest canopy. By using a sensor (photodiode) array, a PPFD pattern was observed in summer 2002 under the canopy in an even-aged, pure stand of Japanese mountain birch Betula ermanii Cham. (17-years old) in Hokkaido, northern Japan. A Markov chain Monte Carlo (MCMC) sampling technique is developed such that a set of foliage configurations generated by the model referred to as the Gibbs foliage canopy (GFC) approximates the field-measured PPFD pattern. The posterior distribution of the foliage configurations is generated by the parallel tempering MCMC of eight independent series of foliage configurations. The GFC model generated the posterior distribution of the LAI estimates (mean 4.56) that appeared to be appropriate in comparison to other LAI estimates of the B. ermanii stand based on the indirect and nondestructive methods by LAI-2000 (LAI = 3.43) and litterfall traps (LAI = 5.56) because they could be under- and overestimated, respectively. Our evaluations of the canopy production and evapotranspiration rates suggest that the relationship between LAI and canopy functions was not very simple because it depended on the nonlinear functional forms of the leaf responses of photosynthesis and transpiration to PPFD. The current study demonstrates an application of MCMC techniques that can generate a set of possible structures of unobserved/unobservable objects based on the high-resolution dataset obtained by some indirect (or remote-sensing) methods.     

How geostatistics can help you

Abstract. Geostatistics is basically a technology for estimating the local values of properties that vary in space from sample data. Research and development in the last 15 years has shown it to be eminently suited for soil and ripe for application in soil survey and land management. The basic technique, ordinary kriging, provides unbiased estimates with minimum and known variance. Data for related variables can be incorporated to improve estimates using cokriging. By more elaborate analysis using disjunctive kriging the probabilities of deficiency and excess can be estimated to aid decision.
The variogram is crucial in all geostatistics; it must be estimated reliably from sufficient data at a sensible scale and modelled properly. Once obtained it can be used not only in the estimation itself but also to choose additional sampling sites, improve a monitoring network or design an optimal sampling scheme for a survey. It may also be used to control a multivariate classification so that the resulting classes are not too fragmented spatially to manage.     

Changes in the waterbird community of the Lake Sevan-Lake Gilli area, Republic of Armenia: a case for restoration

Waterbird species richness (Gaviiformes, Podicipediformes, Pelecaniformes, Ciconiiformes, Phoenicopteriformes, Falconiformes, Anseriformes, Gruiformes, Charadriiformes, Passeriformes) has been significantly affected by a 19.5 m lowering of the water level in Lake Sevan (1933-2000), and the complete draining of nearby Lake Gilli (1960-2000) in the Republic of Armenia. Twenty-three former breeders are currently nonbreeders in the area. Four former breeders (black stork Ciconia nigra, glossy ibis Plegadis falcinellus, white-winged scoter Melanitta fusca, little crake Porzana parva) have been extirpated from the area. Four former nonbreeders (cattle egret Bubulcus ibis, red-breasted goose Branta ruficollis, sociable lapwing Chettusia gregaria, lesser black-backed gull Larus fuscus) have been absent from the area for at least 20 years. The red-breasted merganser Mergus serrator is the only former nonbreeder discovered breeding in the Lake Sevan basin. We recommend that management plans of the 1960s and 1970s be used to further develop and enact new efforts to increase the water level of Lake Sevan by at least 6 m, and that Lake Gilli and its surrounding wetlands be restored as a means of increasing waterbird species richness overall, and protecting regional populations of globally threatened or near-threatened species (Dalmatian pelican Pelecanus crispus, red-breasted goose Branta ruficollis, ferruginous pochard Aythya nyroca, white-headed duck Oxyura leucocephala, corn crake Crex crex, great snipe Gallinago media, black-winged pratincole Glareola nordmanni, white-tailed eagle Haliaeetus albicilla).     

Age and growth in wild Kemp''s ridley seaturtles Lepidochelys kempii from skeletochronological data

Skeletochronological analysis provides age estimates, not actual ages, for seaturtles. Unlike age and growth data from captive and headstart turtles, these estimates predict the actual patterns of age and growth in free-living turtles. A moderate-sized sample of 69 Lepidochelys kempii, salvaged from the Atlantic and Gulf coasts of the USA, had straight-line carapace lengths (SCL) of 188–720 mm and age-estimates of 2–15 years. The von Bertalanffy growth model provides the best fit for the age-estimate and size data and predicts maturity between 11 and 16 years, depending upon the body size selected to represent sexual maturity. The logistic growth model suggests later maturity of 13–19 years. Comparison of the Atlantic and Gulf components of the sample suggests a faster growth rate for ridleys in the Gulf of Mexico, although the sizes of the subsamples are too small for this interpretation to be reliable without additional data. Our age and growth estimates indicate that some members of the early cohorts of headstart ridleys are mature and may have nested already.     

Sharp bounds under contaminated or corrupted sampling with verification,with an application to environmental pollutant data

Let F denote a distribution of interest and G a possibly spurious distribution. This article derives and nonparametrically estimates sharp bounds on characteristics of F when the data are a mixture of F and G, and a fraction of the data is verified to be from F. Contaminated and corrupted mixtures, with and without monotonicity restrictions, are analyzed. The methods are particularly useful in analyzing environmental pollutant measurements obtained using gas chromatography-mass spectroscopy. Results are applied to measurements of organic pollutant concentrations from the Love Canal. We argue that a corruption with monotonic verification model may be the most appropriate model for this type of data.     

A review of applications of model–data fusion to studies of terrestrial carbon fluxes at different scales

Model–data fusion is defined as matching model prediction and observations by varying model parameters or states using statistical estimation. In this paper, we review the history of applications of various model–data fusion techniques in studies of terrestrial carbon fluxes in two approaches: top-down approaches that use measurements of global CO₂ concentration and sometimes other atmospheric constituents to infer carbon fluxes from the land surface, and bottom-up approaches that estimate carbon fluxes using process-based models. We consider applications of model–data fusion in flux estimation, parameter estimation, model error analysis, experimental design and forecasting. Significant progress has been made by systematically studying the discrepancies between the predictions by different models and observations. As a result, some major controversies in global carbon cycle studies have been resolved, robust estimates of continental and global carbon fluxes over the last two decades have been obtained, and major deficiencies in the atmospheric models for tracer transport have been identified. In the bottom-up approaches, various optimization techniques have been used for a range of process-based models. Model–data fusion techniques have been successfully used to improve model predictions, and quantify the information content of carbon flux measurements and identify what other measurements are needed to further constrain model predictions. However, we found that very few studies in both top-down and bottom-up approaches have quantified the errors in the observations, model parameters and model structure systematically and consistently. We therefore suggest that future research will focus on developing an integrated Bayesian framework to study both model and measurement errors systematically.     

A set of nonlinear regression models for animal movement in response to a single landscape feature

The study of individual animal movement in relation to objects in a landscape is important in many areas of ecology and conservation biology. Yet, many of the models used by ecologists do not account for landscape features and thus may not be conducive to analysis of animal movement data. This article develops a set of nonlinear regression models for both move angles and move distances in relation to a single object in the landscape. Our models incorporate the concept of perceptual range from theories of animal movement behavior. We describe numerical methods for obtaining the maximum likelihood estimates of the model parameters. For illustration, we show results from both computer simulated data and real movement data collected for a red diamond rattlesnake (Crotalus ruber) via radio telemetry field techniques.     

Soil salinity characteristics using moderate resolution imaging spectroradiometer (MODIS) images and statistical analysis

Remote sensing is currently a tremendous asset in controlling and monitoring soil salinity. Moderate resolution imaging spectroradiometer (MODIS) images can be obtained daily, are free, offer more opportunities to acquire cloud-free images and may be preferred over high-resolution spatial data. The main objective of this study was to evaluate the capability of MODIS imagery to assess soil properties when coupled with field soil sampling. The study area was ～95,000 ha, located in the south-east of Fars Province, Iran. In total, 240 soil samples were selected from 60 georeferenced soil pits, following a stratified random sampling approach. Sixteen spectral indices were calculated from a nadir-viewed MODIS scene to establish statistical correlation models between measured soil properties and MODIS band values. A precise map of the soil properties was produced using geostatistical techniques. A paired-sample t-test indicates that there are no significant differences between values estimated using MODIS data statistical modeling and laboratory-measured soil properties of samples collected through fieldwork. The results also indicate that image transformation (salinity index (SI) to radiance) reduces estimation errors and increases both model efficiency and the R ² of the models. The results also indicate that MODIS imagery provides useful information on soil properties.     

Selecting the ideotype of improved rice cultivars using multiple regression and multivariate models

ABSTRACT

Plant breeders require a classification of the limitations and the capabilities that exist in plants by appropriate statistical methods; this issue leads to the concept of the ideotype. Therefore, the aim of this research was to determine the ideotype of improved rice cultivars. The experiment was carried out based on a randomized complete blocks design with three replications and 13 improved rice cultivars in northern Iran in 2016 and 2017, the required data for determining ideotype was collected. The results demonstrated that the optimal values of six important traits which selected by the multiple regression model explained 64% of the paddy yield (PY). The determined ideotype would increase PY from 6,623 kg ha^?1 to 8764–9685 kg ha^?1. Selection of desirable phenological traits revealed the highest correlation with the first canonical variable, can cause of selection of superior cultivars with the best agronomic traits. The most genetic distance was observed between cv. ‘Kados’, ‘Shiroodi’ and ‘Dasht’ using mahalanobis method. It was concluded that the methods used in this study, owing to its concern with the genetic variations between cultivars, can be used in determining plant ideotypes in conjunction with other methods and it can guide plant breeders to move through ideotype crops.     

Estimating critical state soil mechanics parameters from constant cell volume triaxial tests

Compaction, tillage, stresses around growing roots and other soil deformation events may be predicted by the critical state model of soil mechanics, but estimating the parameters is time consuming and expensive. We develop a back analysis of the constant cell volume triaxial test, in which the critical state parameters are derived from the results of a single test. This both saves much labour and provides more information than traditional analyses, which require several triaxial compression tests and an isotropic compression test to yield the same information. The method finds, using a minimization algorithm and a quasi-analytical solution to the stress–strain equations, the simulated soil deformation (and hence the properties used in that simulation) that best fits the test data. The minimization is a form of regression analysis. For normally consolidated samples the method provides stable estimates of the slope of the critical state line (M), the slope of the virgin compression line (λ) and elastic modulus (E). The standard errors of the estimates are small in relation to the means of these parameters. The estimates appear to be more reliable than those of more commonly used estimation procedures. The slope of the rebound line (κ) is estimated, but a measure of the accuracy of the estimate cannot be calculated.     

The potential aboveground carbon storage of north American forests

To assess the possibility of using C offset as a method of sequestering CO₂ produced by the burning of fossil fuels, it is necessary to have accurate estimates of C reservoirs and fluxes. Recent studies have shown that estimates of C commonly used in the past are too large, and this may lead to confusion about the global C budget. Field data used in recent estimates of present C storage for the North American boreal and eastern deciduous forest biomes were reanalyzed to estimate their maximum potential C storage. The original data were collected using a stratified two-stage cluster survey sampling design. The reanalysis suggests that the boreal forest and eastern deciduous forest could sequester possibly as little as 13.4% (3.0 Pg) and 18.5% (1.5 Pg), respectively, more C than they presently store. These estimates represent the potential increase in C storage under present conditions, if the study areas were allowed to revert back into forests.     

Using the truncated auto-Poisson model for spatially correlated counts of vegetation

With vegetation data there are often physical reasons for believing that the response of neighbors has a direct influence on the response at a particular location. In terms of modeling such scenarios the family of auto-models or Markov random fields is a useful choice. If the observed responses are counts, the auto-Poisson model can be used. There are different ways to formulate the auto-Poisson model, depending on the biological context. A drawback of this model is that for positive autocorrelation the likelihood of the auto-Poisson model is not available in closed form. We investigate how this restriction can be avoided by right truncating the distribution. We review different parameter estimation techniques which apply to auto-models in general and compare them in a simulation study. Results suggest that the method which is most easily implemented via standard statistics software, maximum pseudo-likelihood, gives unbiased point estimates, but its variance estimates are biased. An alternative method, Monte Carlo maximum likelihood, works well but is computer-intensive and not available in standard software. We illustrate the methodology and techniques for model checking with clover leaf counts and seed count data from an agricultural experiment.     

Accounting for changes in soil carbon under the Kyoto Protocol: need for improved long-term data sets to reduce uncertainty in model projections

Abstract. Soils can be used as a biospheric sink for carbon under Article 3.4 of the Kyoto Protocol and parties are able to use agricultural soil carbon sinks to contribute towards carbon emission reduction targets. This should be done 'taking into account uncertainties, transparency in reporting, and verifiability'. Models are often tested against data sets of long-term changes in soil organic carbon (SOC), but most data sets have only mean SOC values available at each sample date, with no estimates of error about the mean. We show that when using data sets that do not include estimates of error about the mean, it is not possible to reduce the error (root mean squared error) between modelled and measured values below 6.8–8.5%, even with site-specific model calibration. Equivalent errors for model runs using regional default input values are 12–34%. Using error as an indicator of the certainty that can be attached to model projections, we show that a significant reduction in uncertainty is needed for Kyoto accounting. Uncertainties for modelling during the first Kyoto Commitment Period could be reduced by better replication of soil measurements at benchmark sites. This would allow model error to be separated from measurement error, which would allow more comprehensive model testing and, ultimately, more certainty to be attached to model predictions.     

Dating chicks: Calibration and discrimination in a nonlinear multivariate hierarchical growth model

The motivation for this work was to investigate the possibility of accurately determining the age of a tern chick using easily obtained body measurements. We describe the construction of a nonlinear multivariate hierarchical model for chick growth and show how it can be estimated using Markov chain Monte Carlo techniques. A simple extension of the analysis allows for estimation of the ages of unknown chicks. Posterior distributions of the unknown ages are derived, so that the accuracy of age determination can be examined. We further extend our model and analysis to include the possibility that chicks fall into distinct groups with different growth characteristics. The technique is illustrated using data on the weight and wing length of black-fronted terns from the Ohau River, New Zealand. It is found that dating to within one day is possible, but only in some areas of the data space. The concept of “braiding” of multivariate growth curves is introduced to explain the varying accuracy of age determination.