Mathematics Of Genetic Diversity

This book draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.

Applied Mathematics and Omics to Assess Crop Genetic Resources for Climate Change Adaptive Traits focuses on practical means and approaches to further the use of genetic resources for mitigating the effects of climate change and improving crop production. Genetic diversity in crop plants is being further explored to increase yield, disease resistance, and nutritional value by employing recent advances in mathematics and omics technologies to promote the adaptation of crops to changing climatic conditions. This book presents a broad view of biodiversity and genetic resources in agriculture and provides answers to some current problems. It also highlights ways to provide much-needed information to practitioners and innovators engaged in addressing the effects of global climate change on agriculture. The book is divided into sections that cover: The implications of climate change for drylands and farming communities The potential of genetic resources and biodiversity to adapt to and mitigate climate change effects Applications of mathematics and omics technologies Genomics and gene identification We are in the midst of significant changes in global climates, and its effects are already being felt throughout the world. The increasing frequency of droughts and heat waves has had negative impacts on agricultural production, especially in the drylands of the world. This book shares the collective knowledge of leading scientists and practitioners, giving readers a broader appreciation and heightened awareness of the stakes involved in improving and sustaining agricultural production systems in the face of climate change.

Population genetics is the mathematical investigation of the changes in the genetic structure of populations brought about by selection, mutation, inbreeding, migration, and other phenomena, together with those random changes deriving from chance events. These changes are the basic components of evolutionary progress, and an understanding of their effect is therefore necessary for an informed discussion of the reasons for and nature of evolution. It would, however, be wrong to pretend that a mathematical theory, depending as it must on a large number of simplifying assump tions, should be accepted unreservedly and that its conclusions should be accepted uncritically. No-one would pretend that in the event of disagreement between observation and mathematical prediction, the discrepancy is due to anything other than the inadequacy of the mathematical treatment. The biological world is, of course, far too complex for the study of population genetics to be simply a branch of applied mathematics, so that while we are concerned here with the mathematical theory, I have tried to indicate which of our results should continue to apply in a context wider than that in which they are formally derived. The difficulties involved in the joint discussions of mathematical and genetical problems are obvious enough. I have tried to aim this book rather more at the mathematician than at the geneticist, and for this reason a brief glossary of common genetical terms is included.

"It is close to being a masterpiece...could well be the classic presentation of the area." Warren J. Ewens, University of Pennsylvania, USA Population genetics is concerned with the study of the genetic, ecological, and evolutionary factors that influence and change the genetic composition of populations. The emphasis here is on models that have a direct bearing on evolutionary quantitative genetics. Applications concerning the maintenance of genetic variation in quantitative traits and their dynamics under selection are treated in detail. * Provides a unified, self-contained and in-depth study of the theory of multilocus systems * Introduces the basic population-genetic models * Explores the dynamical and equilibrium properties of the distribution of quantitative traits under selection * Summarizes important results from more demanding sections in a comprehensible way * Employs a clear and logical presentation style Following an introduction to elementary population genetics and discussion of the general theory of selection at two or more loci, the author considers a number of mutation-selection models, and derives the dynamical equations for polygenic traits under general selective regimes. The final chapters are concerned with the maintenance of quantitative-genetic variation, the response to directional selection, the evolutionary role of deleterious mutations, and other topics. Graduate students and researchers in population genetics, evolutionary theory, and biomathematics will benefit from the in-depth coverage. This text will make an excellent reference volume for the fields of quantitative genetics, population and theoretical biology.

An inspiring introduction to a vital scientific field. The reader is taken through ten mathematical derivations that lead to important results, explaining in a hands-on manner the key concepts and methods of theoretical population genetics. The derivations are carefully worked out and easy to follow. Particular attention is given to the underlying assumptions and the mathematics used. The results are discussed and broadened out with relevant current implications. All topics feature questions with helpful answers. The book is intended for the reader who already knows some population genetics but requires a more comprehensive understanding. It is particularly suited to those who analyse genetic data and wish to better grasp what their results actually mean. It will also be helpful for those who wish to understand how population genetics contributes to the explanation of evolution. Or as the writers claim: If one wants to understand life – in all its improbable and amazing richness – one must start by understanding population genetics.

A definitive account of the origins of modern mathematical population genetics, first published in 2000.