Publisher's Synopsis
This book combines ecological model building and the application of advanced statistical methods for parameter estimation. Written for model builders and statisticians in the field of ecology, it provides the statistical and numerical tools needed to estimate parameters from experimental data. These tools range from standard methods to highly advanced ones for parameter identification using ordinary differential equations. Detailed examples based on real data illustrate their use. It provides the necessary link between data and models, between simulation and statistics.;The book starts with an introductory chapter which outlines the scope of problems to be treated in later chapters. Chapter 2 provides the statistical means. The first part of this chapter is mainly addressed to readers unfamiliar with statistical theory. The second part of this chapter contains some advanced techniques of parameter estimation in ordinary differential equations which might be of interest even to the experienced statistician.;Chapter 3 is concerned with parameter estimation in models formulated as probability distribution functions. Since the most basic problem in many ecological studies is the estimation of species abundance, the first part of this chapter is concerned with spatial patterns and density estimation. The second part of this chapter is devoted to survival distributions. As a special feature, the influence of time dependent covariates such as temperature on the survival function is treated in the frame of the accelerated life model, which is widely used in medical statistics.;In chapter 4 population models for age structured populations and for populations exhibiting both age structure and development stages are developed starting from the classical Leslie theory. In addition the book demonstrates how one reduces the number of parameters to be estimated by deriving the elements of the population projection matrix from parametric survival distributions.;Chapter 5 treats models in the form of ordinary differential equations. The methods demonstrated here are advanced from the numerical point of view. As typical applications, parameter estimation for a plant growth model and a competition model is performed by use of a recently developed boundary value method.
