The historical background to morphometric studies; The mathematical framework of morphometric analyses; The biological background to multivariate analysis; Some simple forerunners of multivariate morphometrics; Some practical considerations; The use of angles between vectors; Formal background of discriminant functions analysis; Canonical variates; Canonical correlations; Variation in the apparently homogeneous sample; Du praw's non-linnean taxonomy; Principal components and principal coordinates analyses; Factor analysis; The measurement of environmental variation; Multivariate studies in ecology; Phytosociological studies; The quantitative comparison of faunal elements; Genetical aspects of morphometrics; Coordinated applications of multivariate analysis; Some applications of discriminatory topology; The relationships between morphometric analyses and numerical taxonomy...

This book offers a thorough and up-to-date treatment of the use of morphometric procedures in a wide variety of contexts. As one of the most dynamic and popular fields on the contemporary biological scene, morphometrics is gaining notice among researchers and students as a necessary complement to molecular studies in the understanding and maintenance of biodiversity. This is the first reference to meet that growing need.

''An important addition to your library.'' ---American Scientist

This volume is based on the NATO Advanced Study Institute, "Advances in Mor phometries" held in 11 Ciocco, Tuscany, Italy from July 18-30, 1993, and directed by Leslie F. Marcus. The "Advances in Morphometries" ASI was advertised in Nature and a number of professional journals. Announcements were sent to relevant institutions and departments throughout the world. Because NATO required that the majority of attendees be from NATO countries, the 71 persons attending represented nine NATO countries, four eastern European countries, now recognized as equal partners for AS Is, and a few participants from non-NATO countries. Participants were all active scholars in different disciplines within biology, as well as computer science, statistics, geology and paleontology. Their experience ranged from that of graduate students to senior faculty, as well as one emeritus scholar. A complete list of the those attending and their addresses, phone and FAX numbers and, where available, e-mail addresses is given in the participants list. All the local arrangements were made by Marco Corti and Anna Loy of the University of Rome "Ia Sapienza. " They made the initial contact with the II Ciocco conference center and then arranged for computer and Xerox rentals, design of logos, organization of posters, and publication of poster abstracts.

The first edition of Geometric Morphometrics for Biologists has been the primary resource for teaching modern geometric methods of shape analysis to biologists who have a stronger background in biology than in multivariate statistics and matrix algebra. These geometric methods are appealing to biologists who approach the study of shape from a variety of perspectives, from clinical to evolutionary, because they incorporate the geometry of organisms throughout the data analysis. The second edition of this book retains the emphasis on accessible explanations, and the copious illustrations and examples of the first, updating the treatment of both theory and practice. The second edition represents the current state-of-the-art and adds new examples and summarizes recent literature, as well as provides an overview of new software and step-by-step guidance through details of carrying out the analyses. - Contains updated coverage of methods, especially for sampling complex curves and 3D forms and a new chapter on applications of geometric morphometrics to forensics - Offers a reorganization of chapters to streamline learning basic concepts - Presents detailed instructions for conducting analyses with freely available, easy to use software - Provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results

This book aims to explain how to use R to perform morphometrics. Morpho- tric analysis is the study of shape and size variations and covariations and their covariations with other variables. Morphometrics is thus deeply rooted within stat- tical sciences. While most applications concern biology, morphometrics is becoming common tools used in archeological, palaeontological, geographical, or medicine disciplines. Since the recent formalizations of some of the ideas of predecessors, such as D’arcy Thompson, and thanks to the development of computer techno- gies and new ways for appraising shape changes and variation, morphometrics have undergone, and are still undergoing, a revolution. Most techniques dealing with s- tistical shape analysis have been developed in the last three decades, and the number of publications using morphometrics is increasing rapidly. However, the majority of these methods cannot be implemented in available software and therefore prosp- tive students often need to acquire detailed knowledge in informatics and statistics before applying them to their data. With acceleration in the accumulation of me- ods accompanying the emerging science of statistical shape analysis, it is becoming important to use tools that allow some autonomy. R easily helps ful?ll this need. Risalanguage andenvironment forstatisticalcomputingandgraphics. Although there is an increasing number of computer applications that perform morphometrics, using R has several advantages that confer to users considerable power and possible new horizons in a world that requires rapid adaptability.

The idea of form is one of the most fundamental concepts underlying all of the sciences. Our visual system is so well developed that we are able to effortlessly classify and compare visual images. What is not so well developed has been our ability to measure this visual information. This book examines a number of recent approaches currently in use to numerically characterize the biological form. It presents a unique overview of these methods, starting with a review of measurement set in a historical framework. The book will be of interest to graduate students in addition to a wide range of researchers, including those in the specialized fields of human biology, growth and development, orthodontics, botany, biology, ecology, zoology, as well as dentistry and medicine.

It is human nature to measure things, and this holds true for science as well as everyday life. The five papers in this book demonstrate the usefulness of a morphometric approach to a variety of subjects in natural history, including systematics, phenotypic plasticity in response to environmental variation, and ontogenetic adaptation. As our understanding of genetic control mechanisms and epigenetics has matured over the last several decades, it has become clear that morphometric assessment continues to be important to our overall understanding of natural variability in growth and form. The tremendous growth of our knowledge base during the last century has necessitated that we find new ways to measure and track greater detail as well as greater numbers of parameters among populations and individuals.

This introduction to morphometrics does not rely on complex mathematics and statistics. It includes application case studies in fields ranging from paleontology to evolutionary ecology, and it discusses software for analyzing and comparing shape.