Joel E. Cohen

I write this foreword for two reasons: first, to acknowledge the gratitude of our court system to scientists willing to lend their talents to forensic tasks, and of myself, in particular, for the pathbreaking work of Eric Stallard, Kenneth G. Manton, and Joel E. Cohen in the Manville Asbestos Case; and second, because their work suggests both great strength and utility in their statisti­ cally based design and its limitations in predicting events strongly affected by political and social choices that are difficult to foretell as well as by de­ mographic and epidemiologic factors that can be prophesied with somewhat more confidence - at least in the short term. It is by now almost axiomatic that almost every important litigation in the United States requires experts to help judges and juries arrive at an under­ standing of the case sufficient to permit a sensible resolution within the flexible scope of our rules of law. The Supreme Court has laid down useful rough cri­ teria for the courts in assessing the capability of proffered experts beginning 1 with the Daubert line of cases. It has also allowed the courts to appoint ex­ 2 perts to supplement those designated by the parties. Dr. Joel E. Cohen and Professor Margaret E. Berger were appointed by me in the Manville asbestos cases pursuant to Rule 706 of the Federal Rules of Evidence to help project future claims. Discovery provisions have improved utilization of experts by 3 requiring advance reports and depositions.

I write this foreword for two reasons: first, to acknowledge the gratitude of our court system to scientists willing to lend their talents to forensic tasks, and of myself, in particular, for the pathbreaking work of Eric Stallard, Kenneth G. Manton, and Joel E. Cohen in the Manville Asbestos Case; and second, because their work suggests both great strength and utility in their statisti­ cally based design and its limitations in predicting events strongly affected by political and social choices that are difficult to foretell as well as by de­ mographic and epidemiologic factors that can be prophesied with somewhat more confidence - at least in the short term. It is by now almost axiomatic that almost every important litigation in the United States requires experts to help judges and juries arrive at an under­ standing of the case sufficient to permit a sensible resolution within the flexible scope of our rules of law. The Supreme Court has laid down useful rough cri­ teria for the courts in assessing the capability of proffered experts beginning 1 with the Daubert line of cases. It has also allowed the courts to appoint ex­ 2 perts to supplement those designated by the parties. Dr. Joel E. Cohen and Professor Margaret E. Berger were appointed by me in the Manville asbestos cases pursuant to Rule 706 of the Federal Rules of Evidence to help project future claims. Discovery provisions have improved utilization of experts by 3 requiring advance reports and depositions.

Food webs hold a central place in ecology. They describe which organisms feed on which others in natural habitats. This book describes recently discovered empirical regularities in real food webs: it proposes a novel theory unifying many of these regularities, as well as extensive empirical data. After a general introduction, reviewing the empirical and theoretical discoveries about food webs, the second portion of the book shows that community food webs obey several striking phenomenological regularities. Some of these unify, regardless of habitat. Others differentiate, showing that habitat significantly influences structure. The third portion of the book presents a theoretical analysis of some of the unifying empirical regularities. The fourth portion of the book presents 113 community food webs. Collected from scattered sources and carefully edited, they are the empirical basis for the results in the volume. The largest available set of data on community food webs provides a valuable foundation for future studies of community food webs. The book is intended for graduate students, teachers and researchers primarily in ecology. The theoretical portions of the book provide materials useful to teachers of applied combinatorics, in particular, random graphs. Researchers in random graphs will find here unsolved mathematical problems.

The focus of this monograph is on generalizing the notion of variation in a set of numbers to variation in a set of probability distributions. The authors collect some known ways of comparing stochastic matrices in the context of information theory, statistics, economics, and population sciences. They then generalize these comparisons, introduce new comparisons, and establish the relations of implication or equivalence among sixteen of these comparisons. Some of the possible implications among these comparisons remain open questions. The results in this book establish a new field of investigation for both mathematicians and scientific users interested in the variations among multiple probability distributions. The work is divided into two parts. The first deals with finite stochastic matrices, which may be interpreted as collections of discrete probability distributions. The first part is presented in a fairly elementary mathematical setting. The introduction provides sketches of applications of concepts and methods to discrete memory-less channels in information theory, to the design and comparison of experiments in statistics, to the measurement of inequality in economics, and to various analytical problems in population genetics, ecology, and demography. Part two is more general and entails more difficult analysis involving Markov kernels. Here, many results of the first part are placed in a more general setting, as required in more sophisticated applications. A great strength of this text is the resulting connections among ideas from diverse fields: mathematics, statistics, economics, and population biology. In providing this array of new tools and concepts, the work will appeal to the practitioner. At the same time, it will serve as an excellent resource for self-study of for a graduate seminar course, as well as a stimulus to further research.

Examines the problem of the unprecedented rise in the world's population, showing how overpopulation will force future generations to make difficult choices among the competing values of economic development, environmental quality, and procreative freedom

What is the minimum dimension of a niche space necessary to represent the overlaps among observed niches? This book presents a new technique for obtaining a partial answer to this elementary question about niche space. The author bases his technique on a relation between the combinatorial structure of food webs and the mathematical theory of interval graphs. Professor Cohen collects more than thirty food webs from the ecological literature and analyzes their statistical and combinatorial properties in detail. As a result, he is able to generalize: within habitats of a certain limited physical and temporal heterogeneity, the overlaps among niches, along their trophic (feeding) dimensions, can be represented in a one-dimensional niche space far more often than would be expected by chance alone and perhaps always. This compatibility has not previously been noticed. It indicates that real food webs fall in a small subset of the mathematically possible food webs. Professor Cohen discusses other apparently new features of real food webs, including the constant ratio of the number of kinds of prey to the number of kinds of predators in food webs that describe a community. In conclusion he discusses possible extensions and limitations of his results and suggests directions for future research.