Degree Type


Date of Award


Degree Name

Doctor of Philosophy



First Advisor

David C. Glenn-Lewin


A general statistical framework is proposed for unifying definitions of pattern and process in ecology and Statistics and Probability; This statistical framework allows several pattern techniques used in ecology, namely nested ANOVA, two term local variance, and paired quadrat variance, to be compared the variogram as a function of aggregation. There are two unbiased estimators of the variogram under aggregation, and they are compared in a simulation study. Which is better depends on the process autocorrelation;Another ecological quantity of interest is average patch size in a transect of data. The effects of three factors: (1) the signal-to-noise ratio, (2) the expected sizes of the patches relative to the plot size, and 3) the distribution of patch sizes, are determined for three estimators of average patch size: (1) two term local variance, (2) a moving two-sample t-test, and (3) a Bayesian approach using simulated annealing, in a 3 x 2 x 3 factorial simulation experiment. All three factors are important to the performance of the methods, and the Bayesian approach is the method which is recommended. An example from grassland vegetation is included;Besides estimation, spatial prediction is important in ecology. For spatial prediction, it has been usual to predict one variable at a time (e.g. kriging or cokriging). It is often desirable to predict the joint spatial abundance of ecological variables. Simultaneous spatial prediction of several variables is developed using covariances and variograms and cross-variograms. It is shown that the multivariable spatial predictor is the same as cokriging one variable at a time. However, multivariable spatial prediction yields the mean-squared-prediction-error matrix, and so allows construction of joint multivariable prediction regions.



Digital Repository @ Iowa State University,

Copyright Owner

Jay Michael Ver Hoef



Proquest ID


File Format


File Size

151 pages