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Preface1. On Earth as it is in the Heavens2. Does Ecology Have Laws?3. Equilibrium and Accelerated Death4. The Maternal E_ect Hypothesis5. Predator-Prey Interactions and the Period of Cycling6. Inertial Growth7. Practical Consequences8. Shadows on the WallA Notes and Further ReadingB Essential Features of the Maternal Effect ModelC AppreciationsBibliographyIndex.

Uncertainty analyses typically recognize separate stochastic and subjective sources of uncertainty, but do not systematically combine the two, although a large amount of data used in analyses is partly stochastic and partly subjective. We have developed methodology for mathematically combining stochastic and subjective sources of data uncertainty, based on new "hybrid number" approaches. The methodology can be utilized in conjunction with various traditional techniques, such as PRA (probabilistic risk assessment) and risk analysis decision support. Hybrid numbers have been previously examined as a potential method to represent combinations of stochastic and subjective information, but mathematical processing has been impeded by the requirements inherent in the structure of the numbers, e.g., there was no known way to multiply hybrids. In this paper, we will demonstrate methods for calculating with hybrid numbers that avoid the difficulties. By formulating a hybrid number as a probability distribution that is only fuzzily known, or alternatively as a random distribution of fuzzy numbers, methods are demonstrated for the full suite of arithmetic operations, permitting complex mathematical calculations. It will be shown how information about relative subjectivity (the ratio of subjective to stochastic knowledge about a particular datum) can be incorporated. Techniques are also developed for conveying uncertainty information visually, so that the stochastic and subjective components of the uncertainty, as well as the ratio of knowledge about the two, are readily apparent. The techniques demonstrated have the capability to process uncertainty information for independent, uncorrelated data, and for some types of dependent and correlated data. Example applications are suggested, illustrative problems are shown, and graphical results are given.

Toxic chemicals can exert effects on all levels of the biological hierarchy, from cells to organs to organisms to populations to entire ecosystems. However, most risk assessment models express their results in terms of effects on individual organisms, without corresponding information on how populations, groups of species, or whole ecosystems may respond to chemical stressors. Ecological Modeling in Risk Assessment: Chemical Effects on Populations, Ecosystems, and Landscapes takes a new approach by compiling and evaluating models that can be used in assessing risk at the population, ecosystem

A probabilistic language based on stochastic models of population growth is proposed for a standard language to be used in environmental assessment. Environmental impact on a population is measured by the probability of quasiextinction. Density‐dependent and independent models are discussed. A review of one‐dimensional stochastic population growth models, the implications of environmental autocorrelation, finite versus "infinite" time results, age‐structured models, and Monte Carlo simulations are included. The finite time probability of quasiextinction is presented for the logistic model. The sensitivity of the result with respect to the mean growth rate and the amplitude of environmental fluctuations are examined. Stochastic models of population growth form a basis for formulating reasonable criteria for environmental impact estimates.