Geographical Genetics has a unique focus on the mathematical relationships of spatial statistical measures of patterns to stochastic processes. It also develops the probability and distribution theory of various spatial statistics for analysis of population genetic data, detailing exact methods for using various spatial features to make precise inferences about migration, natural selection, and other dynamic forces. The book also reviews the experimental literature on the types of spatial patterns of genetic variation found within and among populations. And it makes an unprecedented strong connection between observed measures of spatial patterns and those predicted theoretically. Along the way, it introduces readers to the mathematics of spatial statistics, applications to specific population genetic systems, and the relationship between the mathematics of space-time processes and the formal theory of geographical genetics.
Written by a leading authority, this is the first comprehensive treatment of geographical genetics. It is a much-needed guide to the theory, techniques, and applications of a field that will play an increasingly important role in population biology and ecology.
New edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions
Two new chapters on neural networks and simulation have also been added
Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science
Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering
A hands-on approach is used with Maple as a pedagogical tool throughout; Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author's website with additional applications and further links of interest at Maplesoft's Application Center
Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies.
Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a "toolbox" provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided.
The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.
Fitness Landscapes and the Origin of Species presents both an overview of the forty years of previous theoretical research and the author's new results. Sergey Gavrilets uses a unified framework based on the notion of fitness landscapes introduced by Sewall Wright in 1932, generalizing this notion to explore the consequences of the huge dimensionality of fitness landscapes that correspond to biological systems.
In contrast to previous theoretical work, which was based largely on numerical simulations, Gavrilets develops simple mathematical models that allow for analytical investigation and clear interpretation in biological terms. Covering controversial topics, including sympatric speciation and the effects of sexual conflict on speciation, this book builds for the first time a general, quantitative theory for the origin of species.
Introducing an innovative model that uses fractal geometry to describe the complex physical structure of nature, Mark Ritchie shows how species traits, particularly body size, lead to spatial patterns of resource use that allow species to coexist. He explains how this criterion for coexistence can be converted into a "rule" for how many species can be "packed" into an environment given the supply of resources and their spatial variability. He then demonstrates how this rule can be used to predict a range of patterns in ecological communities, such as body-size distributions, species-abundance distributions, and species-area relations. Ritchie illustrates how the predictions closely match data from many real communities, including those of mammalian herbivores, grasshoppers, dung beetles, and birds.
This book offers a compelling alternative to "neutral" theory in community ecology, one that helps us better understand patterns of biodiversity across the Earth.
West clarifies fundamental misconceptions in the application of theory to empirical data. He examines the field's successes and failures, and describes the research areas where much important work is yet to be done. West reveals how a shared underlying theoretical framework unites findings of sex-ratio variation across a huge range of life forms, from malarial parasites and hermaphroditic worms to sex-changing fish and mammals. He shows how research on sex allocation has been central to many critical questions and controversies in evolutionary and behavioral biology, and he argues that sex-allocation research serves as a key testing ground for different theoretical approaches and can help resolve debates about social evolution, parent-offspring conflict, genomic conflict, and levels of selection.
Certain to become the defining book on the subject for the next generation of researchers, Sex Allocation explains why the study of sex allocation provides an ideal model system for advancing our understanding of the constraints on adaptation among all living things in the natural world.