William J. Price

Nonlinear estimation of growth curve models for germination data analysis

Logistic, Gompertz, Richards and Weibull growth curves were evaluated for their suitability as mathematical and empirical models to represent cumulative germination. By avoiding the limitations associated with the method of moments and single-value germination indices, the fitted models provided superior description of the time course of germination. The four-parameter Weibull model gave the best fit across a relatively wide range of seed species and germination conditions, and the resulting parameter estimates reflected identifiable aspects of the germination process. The nonlinear estimation of the germination response included a parameter summary, together with their asymptotic standard errors and correlation matrix, along with an approximate band for the expectation function, pairwise plots of the parameter inference region, and profile t plots. Evaluation of the fitted models also included information on lack of fit and residual structure. Empirical results and hypothesis testing were demonstrated with reference to a replicated experiment designed to determine the effects of reduced water potential on germination of onion seeds. Kevwords: nonlinear regression, cumulative germination, growth curves, Weibull model.

ASSESSING VARIABILITY OF AGREEMENT MEASURES IN REMOTE SENSING USING A BAYESIAN APPROACH

Remote sensing imagery is a popular accessment tool in agriculture, forestry, and rangeland management. Spectral classification of imagery provides a means of estimating production and identifYing potential problems, such as weed, insect, and disease infestations. Accuracy of classification is traditionally based on ground truthing and summary statistics such as Cohens Kappa. Variability assessment and comparison of these quantities have been limited to asymptotic procedures relying on large sample sizes and gaussian distributions. However, asymptotic methods fail to take into account the underlying distribution of the classified data and may produce invalid inferential results. Bayesian methodology is introduced to develop probability distributions for Cohens Conditional Kappa that can subsequently be used for image assessment and comparison. Techniques are demonstrated on a set of images used in identifYing a species of weed, yellow starthistle, at various spatial resolutions and flying times.

MODELING SEASONAL WINE GRAPE DEVELOPMENT USING A MIXTURE TECHNIQUE

Biological growth data typically display an increasing sigmoidal pattern over time. Grape development is no exception and shows a similar general trend. A detailed examination of the growth process in grapes, however, reveals a few systematic deviations from this pattern. Specifically, grape development is often characterized by localized areas of growth plateaus leading to an overall growth pattern referred to as a double sigmoidal curve. Capturing and characterizing these local changes in growth is important as they represent important phases in grape development such as veraison. This paper utilizes a model adapted from the technique of mixture models to estimate the growth curve of grapes. The resulting model provides a more accurate description of the growth process and has parameter estimates directly related to the various phases of grape development. The model is demonstrated using data collected from an experimental trellis tension monitoring system in the Chardonnay grape varietie.

PREDICTION OF YELLOW STARTHISTLE SURVIVAL AND MOVEMENT OVER TIME AND SPACE

Yellow starthistle is a noxious weed that has become a serious plant pest with devastating impact on ranching operation and natural resources in western states. Early detection of yellow starthistle and predicting its spread has important managerial implications and greatly reduce the economic losses due to this weed. The dispersal of yellow starthistle consists of two main components, plant survival and seed movement. Resources and direct factors relating to these components are not typically available or are difficult to obtain. Alternatively, topographic factors, such as slope, aspect and elevation, are readily available and can be related to plant survival and seed movement. In this study, several GIS network models incorporating these topographic factors are considered for the prediction of yellow starthistle spread. The models differed in their assessment of the costs of movement derived from these factors. Models were evaluated based on their predictive ability and residual analysis. The optimal model gave an accurate estimate of the dispersal boundary for the study area. Further validation of the estimated model using an independent data set from a larger area also verified its predictive capability.

ESTIMATING THE LIKELIHOOD OF YELLOW STARTHISTLE OCCURRENCE USING AN EMPIRICALLY DERIVED NONLINEAR REGRESSION MODEL

Yellow starthistle is a noxious weed common in the semiarid climate of Central Idaho and other western states. Early detection of yellow starthistle and predicting its infestation potential have important scientific and managerial implications. Weed detection and delineation are often carried out by visual observation or survey techniques. However, such methods may be ineffective in detecting sparse infestations. The distribution of yellow starthistle over a large region may be affected by various exogenous variables such as elevation, slope and aspect. These landscape variables can be used to develop prediction models to estimate the potential invasion of yellow starthistle into new areas. A nonlinear prediction model has been developed based on a polar coordinate transformation to investigate the ability of landscape characteristics to predict the likelihood of yellow starthistle occurrence in North Central Idaho. The study region included the lower Snake river and parts of the Salmon and Clearwater basins encompassing various land use categories. The model provided accurate estimates of incidence of yellow starthistle within each specified land use category and performed well in subsequent statistical validations. INTRODUCTION Yellow starthistle (Centaurea solstitialis L.) is an introduced noxious weed currently infesting millions of acres of rangeland in the United States. It is considered poor forage for all classes oflivestock and may cause a fatal neurological disorder in horses (Sheley et al.1999). It can also cause serious economic loss due to its potential forage yield reduction and ecosystem degradation of grasslands. Yellow starthistle is common in the semiarid climate of northern Idaho and many other western states. It thrives best on warm, deep, well drained soils with 30-75 cm of annual Conference on Applied Statistics in Agriculture Kansas State University New Prairie Press https://newprairiepress.org/agstatconference/1999/proceedings/3 Applied Statistics in Agriculture 15 precipitation. However, this winter annual can survive and dominate annual plant communities in unproductive soils (e.g. rocky and shallow sites) when annual precipitation is below 25 cm. Major invasion has occurred on rangeland and non-crop land, however, cultivated lands such as dryland grain, grass, legume, seed crop and pasture are also susceptible to invasion by yellow starthistle (Lass et al., 1999). Yellow starthistle is native to the east central region of Europe, and it seeds are believed to have been brought in alfalfa seeds shipped to North America in the early 1800s (Sheley et aI., 1999). It is estimated that nearly two million ha ofland are currently infested with yellow starthistle in the Western States (Lass et aI., 1999). Infestations have been established in Idaho, Oregon, California, Washington, and Utah, and most recently in Arizona, Colorado, Montana, Nevada, New Mexico, and North Dakota. In 1955, the infestation in Idaho was less than 10 ha, but has increased to approximately 200,000 ha in less than 45 years. Early detection of yellow starthistle and predicting its infestation potential is an important consideration as the plant expands into new areas. While identification of weed infestations is carried out using visual observations, such methods are often ineffective in detecting sparse infestations in remote areas. Prediction models will allow land managers to focus on sites with a high likelihood of infestation based on demographic characteristics (e.g. elevation, slope, land use) of currently infested sites. Landscape variables such as slope, aspect, and elevation have been used previously to determine the likelihood of occurrence for a specified weed (e.g. Prather and Shafii, 1994; Dewey et al., 1991) or vegetation species (e.g. Myster et aI., 1997). The objective of this research was to develop an empirically derived prediction model based on landscape characteristics to assess the likelihood of yellow starthistle occurrence in North Central Idaho.

Probability Distributions for the Mean and Variance Using Maximum Entropy and Bayesian Analysis

Estimation of moments such as the mean and variance of populations is generally carried out through sample estimates. Given normality of the parent population, the distribution of sample mean and sample variance is straightforward. However, when normality cannot be assumed, inference is usually based on approximations through the use of the Central Limit theorem. Furthermore, the data generated from many real populations may be naturally bounded; i.e., weights, heights, etc. Thus, a normal population, with its infinite bounds, may not be appropriate, and the distribution of sample mean and variance is not obvious. Using Bayesian analysis and maximum entropy, procedures are developed which produce distributions for the sample mean and combined mean and standard deviation. These methods require no assumptions on the form of the parent distribution or the size of the sample and inherently make use of existing bounds.

MULTIVARIATE STATISTICAL ANALYSIS OF COLEOPTERA SPECTRAL REFLECTANCE

The insect order Coleoptera, commonly known as beetles, comprises 40% of all insects which in turn account for half of all identified animal species alive today. Coleopterans frequently have large elytra (the hardened front wings) that can have a wide range of colors. Spectral reflectance readings from these elytra may be used to uniquely identify coleopteran taxonomic groups. Multiple samples of eleven species of wood boring beetles were selected from the University of Idaho William Barr Entomology Museum. Spectrometer readings for each specimen were then fit to normal distribution mixture models to identify multiple peak reflectance wavelengths. Eighteen prominent peaks were identified across all taxonomic groups and genders creating a multivariate response structure. Multivariate statistical procedures including principal component and discriminant analyses were employed to assess the differentiation of taxonomic groups and genders based on spectral reflectance. The first three axes of the principal component analysis 20 26th Annual Conference on Applied Statistics in Agriculture New Prairie Press http://newprairiepress.org/agstatconference/2014/ 1 Annual Conference on Applied Statistics in Agriculture Kansas State University New Prairie Press http://newprairiepress.org/agstatconference/2014/proceedings/1 accounted for 96% of the variation and provided a clear clustering of genus and gender for a subset of taxonomic groups. The linear discriminant analysis under an assumption of multivariate normality provided a distinct classification of taxonomic groups resulting in an overall 4% misclassification rate; while the nearest neighbor discriminant analysis with a proportional prior gave an overall error rate of 5.2%. Internal bootstrap validation of the latter discriminant model yielded an average error rate of 3.5%. An external cross validation of the same model, conducted on independent samples of the same species with new individuals resulted in an average misclassification error rate of only 6.5%. Given the low error rates of misclassification, such multivariate statistical approaches are recommended for analysis of spectral reflectance in Coleoptera and other similar insect groups.

USING LANDSCAPE CHARACTERISTICS AS PRIOR INFORMATION FOR BAYESIAN CLASSIFICATION OF REMOTELY SENSED IMAGERY

Yellow starthistle is a dominant weed of north-central Idaho canyon grasslands. The distribution of yellow starthistle can be affected by general landscape characteristics, such as land use, as well as specific terrain related features such as elevation, slope, and aspect. Slope and aspect can be considered as indicators of plant community composition and distribution. Hence, these variables may be incorporated into prediction models to estimate the likelihood of yellow starthistle occurrence. An empirically derived nonlinear model based on landscape characteristics was developed to predict the likelihood of yellow starthistle occurrence in north central Idaho (Shafii, et al. 1999). While the model was employed to predict the invasion potential of yellow starthistle into new areas, it could also be used as auxiliary data for classifying this weed species in remotely sensed imagery. To accomplish this, the predicted values of the model are regarded as prior information on the presence of yellow starthistle. A Bayesian image classification algorithm using this prior information is then applied to a corresponding set of remotely sensed data. The end result is a map indicating the posterior probabilities of yellow starthistle occurrence given the landscape characteristics. This technique is demonstrated considering the presence and absence of prior information and is shown to result in lower omissional and commissional error rates when the landscape characteristics are utilized.

COMPARING BINOMIAL BOOTSTRAP AND BAYESIAN ESTIMATION METHODS IN ASSESSING THE AGREEMENT BETWEEN CLASSIFIED IMAGES AND GROUND TRUTH DATA.

The degree of agreement between classification and ground truth in remotely sensed data is often quantified with an error matrix and summarized using agreement measures such as Cohens kappa. In the case of ground truth however, the kappa statistic can be shown to be a transformation of the marginal proportions commonly referred to as omissional and commissional error rates. A more meaningful statistical interpretation of remote sensing results and less ambiguous conclusions can be obtained via direct utilization of these measures. Several estimation techniques have been suggested for these marginal proportions. In this study, we will develop the exact binomial, bootstrap and Bayesian estimation methods for omissional and commissional errors. Emphasis will be placed on comparing the various estimation methods and their corresponding empirical distributions. Results are demonstrated with reference to a study designed to evaluate the detectability of yellow hawkweed and oxeye daisy using multispectral digital imagery in Northern Idaho.

SPATIAL ANALYSIS OF GRASSHOPPER DENSITY AS INFLUENCED BY ANTHROPOGENIC HABITAT CHANGES

The rangeland environment in southern Idaho has been heavily impacted by human activities. Invasion by exotic plant species, frequent fires, grazing pressure, and other ecological disturbances have greatly affected the structure and dynamics of grasshopper populations. Quantification of spatial patterns of grasshopper density and species composition is important in order to determine their influence on grassland ecosystems, as well as evaluating managerial decisions concerning vegetation manipulations, grazing practices, and spraying programs. A spatial statistical approach to modeling the heterogeneity of grasshopper populations is presented, and the impact of vegetation and grazing treatments on grasshopper density is investigated. Empirical applications are demonstrated with reference to repeated field surveys conducted over several years in south central Idaho.