Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models.* Rapidly expanding area of research for biologists and applied mathematicians* Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models* Provides the reader with the tools needed to construct and interpret models* Offers specific applications of both the models and the methods* Authors have played a dominant role in the field for yearsEssential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology. * Provides the background mathematics required to understand why certain algorithms work* Guides the reader through probability theory, entropy and combinatorial optimization* In-depth coverage of molecular biology and protein structure prediction* Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction* Includes class tested exercises useful for self-study* Source code of programs available on a Web site Primarily aimed at advanced undergraduate and graduate students from bioinformatics, computer science, statistics, mathematics and the biological sciences, this text will also interest researchers from these fields.

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology. * Provides the background mathematics required to understand why certain algorithms work* Guides the reader through probability theory, entropy and combinatorial optimization* In-depth coverage of molecular biology and protein structure prediction* Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction* Includes class tested exercises useful for self-study* Source code of programs available on a Web site Primarily aimed at advanced undergraduate and graduate students from bioinformatics, computer science, statistics, mathematics and the biological sciences, this text will also interest researchers from these fields.

Population Genetics of Multiple Loci F. B. Christiansen University of Aarhus, Denmark "This is a very beautiful and powerful study of an area that Christiansen has dominated for many years." - Marcus Feldman, Stanford University, USA Population genetics thrives on the constant interaction between theoretical and empirical knowledge. In the first instance, population genetics was developed using one-locus, two-allele models for genetic variation. The simplicity of these models opened up theoretical developments in population and evolutionary genetics to biologists without specialist training in mathematics. Population genetics of multi-allelic loci is more complex and requires more mathematical insight, and its study is predominantly undertaken by mathematical biologists. Traditional formulations of multi-locus theory do not simplify by assuming two alleles per locus. In this elegant presentation the author provides a formulation of multi-locus population genetics that retains the simplicity of two-allele models.* Provides an accessible and natural extension of classical population genetics to multiple loci* Exposes the population genetic aspects of sexual reproduction* Describes the complexity of evolutionary interactions among genes* Provides the background for insight into the functioning of genetic algorithms applied in computer science* Written by a world leader in the fieldThe book is divided into two main sections. Part I - Recombination and Segregation - includes coverage of random mating, inbreeding, migration and mixing. Part II - Selection - covers numerous phenomena involving natural selection including viability, fertility, mutation and migration. The author has successfully presented the theory in a way that is intelligible to anyone with a reasonably good background in basic mathematics and is devoted to learning multiple loci population genetics. The text is primarily aimed at advanced undergraduate and postgraduate students and researchers interested in genetics and population biology. It is also essential reading for those working or researching in biomathematics and adaptive computing.

Spatio-temporal pattern formation is a major area of research within the subject of mathematical biology. The topic involves the use of mathematical modelling to analyse how patterns in biology are created and develop. For example, the growth, over time, of the intricate and beautiful patterns on certain sea-shells or the striped markings on a tiger can be modelled and their development predicted in terms of nonlinear mathematical processes. The current volume captures the breadth of recent research into various aspects of spatio-temporal pattern and form, such as development biology, reaction-diffusion systems and morphometrics. Brings the ideas of the classic On Growth and Form by D'Arcy Thompson, the founding classic of mathematical biology, fully up to date and looks to future developments in the subject.* Foreword provided by Professor John Tyler Bonner, Princeton University.* World class collection of internationally renowned contributors from both experimental and theoretical backgrounds Taking its inspiration from D'Arcy Thompson's classic and still influential volume On Growth and Form, this new volume presents a collection of 21 articles from the Plenary Speakers of the recent D'Arcy Thompson Conference, held at the University of Dundee, 20-24 September 1998. The topics covered include pattern formation in development biology, reaction-diffusion systems, intercellular systems and morphometrics, offering the reader a stimulating blend of theory and experiment. This book will be of particular interest to bio-mathematicians and development biologists. Paediatric clinicians, evolutionary biologists, orthodontists, anatomists, physiologists and many other members of the biology community will also benefit greatly from it.

Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models.* Rapidly expanding area of research for biologists and applied mathematicians* Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models* Provides the reader with the tools needed to construct and interpret models* Offers specific applications of both the models and the methods* Authors have played a dominant role in the field for yearsEssential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology. * Provides the background mathematics required to understand why certain algorithms work* Guides the reader through probability theory, entropy and combinatorial optimization* In-depth coverage of molecular biology and protein structure prediction* Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction* Includes class tested exercises useful for self-study* Source code of programs available on a Web site Primarily aimed at advanced undergraduate and graduate students from bioinformatics, computer science, statistics, mathematics and the biological sciences, this text will also interest researchers from these fields.

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology. * Provides the background mathematics required to understand why certain algorithms work* Guides the reader through probability theory, entropy and combinatorial optimization* In-depth coverage of molecular biology and protein structure prediction* Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction* Includes class tested exercises useful for self-study* Source code of programs available on a Web site Primarily aimed at advanced undergraduate and graduate students from bioinformatics, computer science, statistics, mathematics and the biological sciences, this text will also interest researchers from these fields.

Population Genetics of Multiple Loci F. B. Christiansen University of Aarhus, Denmark "This is a very beautiful and powerful study of an area that Christiansen has dominated for many years." - Marcus Feldman, Stanford University, USA Population genetics thrives on the constant interaction between theoretical and empirical knowledge. In the first instance, population genetics was developed using one-locus, two-allele models for genetic variation. The simplicity of these models opened up theoretical developments in population and evolutionary genetics to biologists without specialist training in mathematics. Population genetics of multi-allelic loci is more complex and requires more mathematical insight, and its study is predominantly undertaken by mathematical biologists. Traditional formulations of multi-locus theory do not simplify by assuming two alleles per locus. In this elegant presentation the author provides a formulation of multi-locus population genetics that retains the simplicity of two-allele models.* Provides an accessible and natural extension of classical population genetics to multiple loci* Exposes the population genetic aspects of sexual reproduction* Describes the complexity of evolutionary interactions among genes* Provides the background for insight into the functioning of genetic algorithms applied in computer science* Written by a world leader in the fieldThe book is divided into two main sections. Part I - Recombination and Segregation - includes coverage of random mating, inbreeding, migration and mixing. Part II - Selection - covers numerous phenomena involving natural selection including viability, fertility, mutation and migration. The author has successfully presented the theory in a way that is intelligible to anyone with a reasonably good background in basic mathematics and is devoted to learning multiple loci population genetics. The text is primarily aimed at advanced undergraduate and postgraduate students and researchers interested in genetics and population biology. It is also essential reading for those working or researching in biomathematics and adaptive computing.

Spatio-temporal pattern formation is a major area of research within the subject of mathematical biology. The topic involves the use of mathematical modelling to analyse how patterns in biology are created and develop. For example, the growth, over time, of the intricate and beautiful patterns on certain sea-shells or the striped markings on a tiger can be modelled and their development predicted in terms of nonlinear mathematical processes. The current volume captures the breadth of recent research into various aspects of spatio-temporal pattern and form, such as development biology, reaction-diffusion systems and morphometrics. Brings the ideas of the classic On Growth and Form by D'Arcy Thompson, the founding classic of mathematical biology, fully up to date and looks to future developments in the subject.* Foreword provided by Professor John Tyler Bonner, Princeton University.* World class collection of internationally renowned contributors from both experimental and theoretical backgrounds Taking its inspiration from D'Arcy Thompson's classic and still influential volume On Growth and Form, this new volume presents a collection of 21 articles from the Plenary Speakers of the recent D'Arcy Thompson Conference, held at the University of Dundee, 20-24 September 1998. The topics covered include pattern formation in development biology, reaction-diffusion systems, intercellular systems and morphometrics, offering the reader a stimulating blend of theory and experiment. This book will be of particular interest to bio-mathematicians and development biologists. Paediatric clinicians, evolutionary biologists, orthodontists, anatomists, physiologists and many other members of the biology community will also benefit greatly from it.