Quantitative approaches to evolutionary biology traditionally consider evolutionary change in isolation from an important pressure in natural selection: the demography of coevolving populations. In Analysis of Evolutionary Processes, Fabio Dercole and Sergio Rinaldi have written the first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones. The book shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics.
After introducing the basics of evolutionary processes and classifying available modeling approaches, Dercole and Rinaldi give a detailed presentation of the derivation of the AD canonical equation, an ordinary differential equation that focuses on evolutionary processes driven by rare and small innovations. The authors then look at important features of evolutionary dynamics as viewed through the lens of AD. They present their discovery of the first chaotic evolutionary attractor, which calls into question the common view that coevolution produces exquisitely harmonious adaptations between species. And, opening up potential new lines of research by providing the first application of AD to economics, they show how AD can explain the emergence of technological variety.
Analysis of Evolutionary Processes will interest anyone looking for a self-contained treatment of AD for self-study or teaching, including graduate students and researchers in mathematical and theoretical biology, applied mathematics, and theoretical economics.
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Fabio Dercole & Sergio Rinaldi
"The first comprehensive textbook on the methods and applications of adaptive dynamics,Analysis of Evolutionary Processes is very timely indeed. It will be of great interest not only to researchers already using AD but also to those who want to apply it but are not yet familiar with the methods. Dercole and Rinaldi's book is well written, self-contained, and suitable for self-study and teaching in applied mathematics and mathematical biology on the graduate and advanced undergraduate levels."--Stefan A. H. Geritz, University of Helsinki
"This is a major achievement--a self-contained presentation of the adaptive dynamics approach, of its role within evolutionary theory, and of the kind of evolutionary dynamics that can be predicted. I believe it will become a standard text for researchers and students in evolutionary dynamics. To my knowledge there is no other book that presents the theory of AD, places it in a proper biological context, and develops it with an approach that is mathematically sound but not overwhelming."--Andrea Pugliese, University of Trento, Italy
"The first comprehensive textbook on the methods and applications of adaptive dynamics,Analysis of Evolutionary Processes is very timely indeed. It will be of great interest not only to researchers already using AD but also to those who want to apply it but are not yet familiar with the methods. Dercole and Rinaldi's book is well written, self-contained, and suitable for self-study and teaching in applied mathematics and mathematical biology on the graduate and advanced undergraduate levels."--Stefan A. H. Geritz, University of Helsinki
"This is a major achievement--a self-contained presentation of the adaptive dynamics approach, of its role within evolutionary theory, and of the kind of evolutionary dynamics that can be predicted. I believe it will become a standard text for researchers and students in evolutionary dynamics. To my knowledge there is no other book that presents the theory of AD, places it in a proper biological context, and develops it with an approach that is mathematically sound but not overwhelming."--Andrea Pugliese, University of Trento, Italy
In this chapter we introduce the basic elements and the empirical evidence of evolutionary processes. Since the groundbreaking work The Origin of Species by Charles Darwin (1859), a great deal of effort has been dedicated to the subject (see, e.g., Fisher, 1930; Haldane, 1932; Dobzanski, 1937; Mayr, 1942, 1963, 1982; Wright, 1969; Dawkins, 1976, 1982, 1986; Cavalli-Sforza and Feldman, 1981; Maynard Smith, 1989, 1993; Maynard Smith and Szathmary, 1995, just to mention a few masterpieces). Our discussion on the origin of evolutionary theory is mainly taken from the introduction by Ernst Mayr (2001) to the seventeenth printing of Darwin's famous book, and from Dieckmann (1994, Chapter 1), Schrage (1995), Rizzoli-Larousse (2003), and the web pages of the University of California Museum of Paleontology. Throughout the exposition we emphasize that, even though the major scientists who developed evolutionary theory were stimulated by the study of nature, their ideas not only apply to the biological realm, but also capture many phenomena of self-organization encountered in social sciences, economics, and engineering.
1.1 ORIGINS OF EVOLUTIONARY THEORY
The idea that living organisms have been diversifying themselves through time, starting from a common origin, goes back to the Greek naturalistic philosophy. Among the precursors of evolutionary theory, as we define it today, we can mention Anaximander of Miletus (610-546 BC), Empedocles of Acragas (495-435 BC), and later some clergymen, such as Saint Augustine (354-430). The evolutionary conceptions of Greek philosophy were known during the Renaissance. However, no further contribution arose until the eighteenth century, when European scholars still believed that the universe was created in essentially its present and final state. During the eighteenth century, the work of intellectuals known as "encyclopedists" spread the Illuminism doctrine and, in particular, the results of pioneering research in systematic biology, aimed at hierarchically classifying organisms into groups that successively share more and more visible structural characteristics. Their work brought a better understanding of the concept of species and highlighted fundamental similarities between widely disparate organisms. Such similarities were in contrast with the hypothesis of creation in final state and prepared the ground for evolutionary theory. A considerable contribution came from Georges-Louis Leclerc Buffon (1707-1788), author of a compendium of biological history, and from Erasmus Darwin (1731-1802), Charles' grandfather, who first discussed the conjecture that life could have evolved from a common ancestor and posed the question of how a species could evolve into another. The first explicit evolutionary theory was formulated by Jean Baptiste Lamarck (1744-1829), disciple of Buffon, who introduced the notion of inheritance. The "Lamarckian" hypothesis, that simple life forms continually come into existence from dead matter and continually become more complex, was strongly criticized by most naturalists of the time. In particular, one of the most active antievolutionists, Georges Cuvier (1769-1832), paradoxically provided evidence to the evolutionary hypothesis with his research in systematic biology, comparative anatomy, and paleontology.
At this point Charles Darwin (1809-1882) and Alfred Russel Wallace (1823-1913) formulated the evolutionary theory that we still accept today. In their papers published in the same issue of the Journal of the Proceedings of the Linnean Society (Darwin, 1858; Wallace, 1858, often cited as a single paper with the title "On the Tendency of Species to form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection") they presented their theory of evolution by natural selection, arguing that
there is individual variation in innumerable characteristics of populations, some of which may affect the individual ability to survive and reproduce;
there is likely to be a hereditary component to much of this variation, but evolutionary change ultimately relies on the appearance of new variant forms of organisms, called mutants;
generation by generation there is a natural selection of the characteristics associated with greater survival and reproductive success, whose frequencies in the populations increase over time;
the cumulative effects of mutations and natural selection, over a long period of time, alter the characteristics of species from those of their ancestors;
all living organisms have descended with modifications from a common ancestor, thus developing hierarchical patterns of similarities.
Darwin and Wallace combined empirical observations with theoretical insights gained from Malthus' (1798) work on competition and population growth. They had a precise idea of natural selection and realized the need of mutations. However, they were not aware of the laws of heredity, discovered seven years later by Gregor Mendel (1822-1884), who realized the discrete nature of heredity determinants, which we now call genes (Mendel, 1865). Darwin actually introduced the concept of natural selection and deserves, more than anyone else, the credit for having started, and firmly supported, the scientific and philosophical revolution from the dogma of creation and constancy of species to evolutionary theory.
The decisive event in Darwin's life was the five-year period spent as a naturalist on the vessel Her Majesty's Ship Beagle (from December 1831 to October 1836), in which he surveyed the coast of South America and the off-lying islands, collecting invaluable observations on the tropical forests of Brazil, on fossils in the Pampas of Argentina, on the geology of the Andes, and on the animal life of the Galapagos Islands (Darwin, 1839). After the return of the Beagle, Darwin spent most of his time in the analysis and interpretation of his findings and became later more acknowledged than Wallace, thanks to his famous book The Origin of Species (1859).
A third important scientist in the development of evolutionary theory, though by far less acknowledged than Darwin and Wallace, is Patrick Matthew (1790-1874). In a letter to Charles Lyell (April 10, 1860) Darwin says: "In last Saturday Gardeners' Chronicle, a Mr. Patrick Matthew publishes long extract from his work on Naval Timber & Arboriculture published in 1831, in which he briefly but completely anticipates the theory of Natural Selection. - I have ordered the book, as some few passages are rather obscure but it is, certainly, I think, a complete but not developed anticipation." Matthew's evolutionary insights lie buried in an appendix of a book he wrote on raising trees of optimal quality for the Royal Navy (Matthew, 1831). In that appendix Matthew expressed his theory based on how tree species might vary in form and how artificial selection might improve cultivated trees.
Let us now listen directly to Darwin, Wallace, and Matthew. "The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. The green and budding twigs may represent existing species; and those produced during each former year may...
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