Peter Scott has braught me a copy of Sean H. Rice: "Evolutionary Theory:Mathematical and Conceptual Foundations" which is not available in our library. It seems excellent, though, with my weak background in biology, it may take several moths to get some grip on the topics. At the end of Chapter 6, he says:
"In deriving equation 6.4, Price started with only a basic description of the kind of quantities involved in evolution; phenotypes of parents, phenotypes of their offsprings, and numbers of offspring. He then asked mhat mathematical relations must hold between these basic pieices, without imposing any further restrictions.
The resulting equation initially seems so simple that it is hard to seehow it relates to actual evolutionary questions. When we look closely at this result, though, we see that it shows an underlying unity that was obscured by our special case models. It also provides a foundation on which to build new models, a fact that we will use in the following chapters of the book.
Not all fields of science have the kind of foundational analytical results that we have used in this chapter. In many subjects, building special case models is the only approach to theory. It is hardly surprising, though, that evolutionary biology has such foundations. Since the initial work of Darwin and Wallace, it has seemed to many people that at its core evolution has simple and universal principles. What we have seen in this chapter is that phrasing these universal principles mathematically need not narrow them, but rather allows us to see their full significance."
"In deriving equation 6.4, Price started with only a basic description of the kind of quantities involved in evolution; phenotypes of parents, phenotypes of their offsprings, and numbers of offspring. He then asked mhat mathematical relations must hold between these basic pieices, without imposing any further restrictions.
The resulting equation initially seems so simple that it is hard to seehow it relates to actual evolutionary questions. When we look closely at this result, though, we see that it shows an underlying unity that was obscured by our special case models. It also provides a foundation on which to build new models, a fact that we will use in the following chapters of the book.
Not all fields of science have the kind of foundational analytical results that we have used in this chapter. In many subjects, building special case models is the only approach to theory. It is hardly surprising, though, that evolutionary biology has such foundations. Since the initial work of Darwin and Wallace, it has seemed to many people that at its core evolution has simple and universal principles. What we have seen in this chapter is that phrasing these universal principles mathematically need not narrow them, but rather allows us to see their full significance."
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