2 POPULATION GENETICS
was enormous and they set the standards for mathematical modeling and for rigor of
theoretical investigations for the subsequent decades.
Prior to 1900, the year when Mendel’s work was rediscovered and then rapidly ac-
cepted, the hereditary mechanisms were unknown. Darwin believed in blending inher-
itance, according to which the hereditary material itself blended. However, as already
noted by Darwin, blending inheritance produces uniformity and destroys variation
that is so ubiquitous. In modern terms, heritable variance would be halved in each
generation of random mating with blending inheritance (Fisher 1930). Therefore, one
half of the heritable variance maintained in a population would have to arise anew
in each generation. There were controversial lines of thought about the nature of this
huge amount of new variation and its consequences for evolution. The ‘gradualists’,
to which Darwin and the biometricians adhered, considered the changes across gener-
ations as gradual and incremental, whereas the ‘saltationists’ (e.g., T.H. Huxley and
Galton) held that evolutionary changes occurred in ‘jumps’ of considerable magnitude.
Much of the scientific dispute about Darwin’s theory of evolution originated from the
ignorance of the true hereditary mechanisms.
Despite the early work of Yule (1902), Hardy (1908), and Weinberg (1908), who
showed that under the particulate mode of inheritance proposed by Mendel (1866),
genetic variability is preserved under random mating, it was not before 1918 that the
synthesis between genetics and the theory of evolution through natural selection began
to take shape through Fisher’s (1918) work (see Provine (1971) for a detailed account
of the history of population genetics).
Today, the hereditary mechanisms have b een firmly established and our knowledge
about the molecular biology of the genes is rapidly increasing. Mutations are known
to be the ultimate source of genetic variability, and many different processes at the
chromosomal and molecular level have been identified that generate mutations. On
the phenotypic level, the role of selection in shaping evolutionary change has been
amply documented, whereas on the molecular level, a significant amount of neutral
evolution appears to take place, its extent still being disputed. Nevertheless, there
remain many open problems, some of which are qualitative in nature and some quan-
titative. Questions concerning the processes involved in speciation events or in the
evolution of sex belong to the first class, whereas questions concerning the prediction
of the expected evolutionary change of a population subject to selection belong to the
second class. Such predictions are highly nontrivial, unless confined to one or a few
generations, because there exist many different forms of selection and the response
to selection depends on the pattern and amount of genetic variability in the p opula-
tion. This variation, however, is a function of many genetic details (such as number of
genes determining a trait, mutational properties, degree of linkage), of the demogra-
phy (population size, mating structure), and of the selective forces acting. Therefore,
the genetic variability may change from one generation to the next.
One of the main purposes of this book is to provide the mathematical theory for
predicting the evolutionary change under the combined action of selection, mutation,
and recombination, and to present applications to several topics of evolutionary in-
terest, in particular, related to the evolution of quantitative traits. The first chapter,
which is rather elementary, introduces fundamental concepts of population genetics
and studies several evolutionary mechanisms in isolation, whereas later chapters are
concerned with their interactions. Let us now summarize some of the very basic genetic