I can find no agreed definition of the term "natural selection" in the literature.
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What is Natural Selection?
The following definitions and descriptions can be found in the literature.
1. A metaphorical expression (Darwin).
2. A false term (Darwin).
3. Differential reproduction (Simpson).
4. Differential mortality (Simpson).
5. A tautology: the fittest individuals in a population (defined as those which leave the most offspring) will leave the most offspring (Waddington).
6. Anything tending to promote systematic, heritable change in a population from one generation to the next (Simpson).
7. What selection actually, directly favors is effectiveness of reproduction. That is almost a tautology, because we define natural selection as differential reproduction (Simpson).
8. Both differential mortality and sexual selection do, or at least can, lead to differential reproduction and hence they are special cases of the present broader concept of natural selection (Simpson).
The question has been considered in great detail in many publications and in several books, e.g.:
John Endler (1986) Natural Selection in the Wild (Princeton University Press)
Elliott Sober (1983, 1994) The Nature of Selection (University of Chicago Press)
Endler (p.4) gives a definition that depends on the meanings of the terms trait (=attribute) but he does not define trait. He told me that trait can refer to cytoplasmic, genotypic, or phenotypic characteristics, or to any combination of these (private communication)..
To me, the meaning of the term natural selection is most simply illustrated by an example. About one in 400 black people worldwide have sickle-cell anemia which is caused by inheriting two copies of a recessive gene that makes those with one copy of it (about 1 in 12 black people worldwide) resistant to malaria (Encyclopaedia Britannica 2001). According to Endler (p.126), in the seventeenth century, Dutch slave traders introduced people from a single area of West Africa at random into two regions: Curacao (which had no malaria) and Surinam (which had malaria). Today, the descendants in Surinam have a significantly higher sickle-cell frequency than do those in Curacao.
Here, again, during the period of observation, no new chracters have appeared and so no evolution has been observed.