According to simple models of selection the genetic variance in a population should be reduced by selection. (Fisher's fundamental theorem states that the rate at which a population can evolve is limited by its variance). If we select the next generation from one population we will only ever capture as much, and probably only a subset of, the variation that exists in a the first generation.
Did Darwin ever discuss this loss of variation? What did he conclude?
(For now lets ignore the potential roles of sexual antagonism, pleiotropy and such)
A little clarification on my question:
Darwin saw variation in phenotypes, and variation in fitness dependent on phenotype - an effect he called selection. He also saw that this variation was heritable (but did not know how). This is the basic concept of evolution, and is mathematically speaking, the breeders equation:
$r = h^2 s$
He also would have realized that life must therefore have started out as a simple unit, and new variance in traits (and whole new traits) must have arisen over time, i.e. that some kind of changes (mutations) were going on in the heritable information (genes). However, what I'm asking is, did he realize that selection would act to reduce the variation in a population? This would reduce the rate at which evolution can occur over time (Fisher's fundamental theorem - assuming no influx of variance or potential for pleiotropy to maintain variation). Or was it Fisher that first formally discussed the concept of lost phenotypic/genetic variance?
Answer
After reading your question, I had a vague memory that this subject was indirectly touched upon in "On the Origin of Species", so I did some text searches (in this pdf version I found online). From what I can see, Darwin never used the technical term 'variance' (I don't know how old this use of the word is), but 'variability' is often used, both with regard to accumulated variation but also meaning variation between individuals within a population.
All-in-all, I could not find clear support for the idea that selection will decrease the amount of variation. However, there are number of passages where the subject of variation vs selection comes up (often indirectly), but, to me, these just as often (most often?) indicate that Darwin saw no risk that selection would reduce variation as the opposite. Here are the most interesting passages I could find (searching for combinations of 'variab*', 'selection', 'decrease' etc), with page references referring to the pdf version and a short comment below each quote:
A large number of individuals, by giving a better chance for the appearance within any given period of profitable variations, will compensate for a lesser amount of variability in each individual, and is, I believe, an extremely important element of success. (p. 44)
This is clearly discussing amounts of variation within species, where large numbers can compensate for a smaller amounts of standing variability, by increasing the chance of advantageous mutations.
Nothing can be effected, unless favourable variations occur, and variation itself is apparently always a very slow process. The process will often be greatly retarded by free intercrossing. Many will exclaim that these several causes are amply sufficient wholly to stop the action of natural selection. I do not believe so. On the other hand, I do believe that natural selection will always act very slowly, often only at long intervals of time, and generally on only a very few of the inhabitants of the same region at the same time. (p. 103)
Not directly related to selection vs variation, but deals with the rate of evolution vs amount of variation.
But what here more especially concerns us is, that in our domestic animals those points, which at the present time are undergoing rapid change by continued selection, are also eminently liable to variation. Look at the breeds of the pigeon; see what a prodigious amount of difference there is in the beak of the different tumblers, in the beak and wattle of the different carriers, in the carriage and tail of our fantails, &c., these being the points now mainly attended to by English fanciers. Even in the sub-breeds, as in the short-faced tumbler, it is notoriously difficult to breed them nearly to perfection, and frequently individuals are born which depart widely from the standard. There may be truly said to be a constant struggle going on between, on the one hand, the tendency to reversion to a less modified state, as well as an innate tendency to further variability of all kinds, and, on the other hand, the power of steady selection to keep the breed true. In the long run selection gains the day, and we do not expect to fail so far as to breed a bird as coarse as a common tumbler from a good short-faced strain. But as long as selection is rapidly going on, there may always be expected to be much variability in the structure undergoing modification. (p. 141)
This is maybe the most interesting passage, which to me indicates that he saw little risk that selection could/would limit variability (see especially beginning and end).
For forms existing in larger numbers will always have a better chance, within any given period, of presenting further favourable variations for natural selection to seize on, than will the rarer forms which exist in lesser numbers. Hence, the more common forms, in the race for life, will tend to beat and supplant the less common forms, for these will be more slowly modified and improved. (P. 162)
Also on limitations for variation that selection can act on, and the value of large populations.
... firstly, because new varieties are very slowly formed, for variation is a very slow process, and natural selection can do nothing until favourable variations chance to occur, and until a place in the natural polity of the country can be better filled by some modification of some one or more of its inhabitants. And such new places will depend on slow changes of climate, or on the occasional immigration of new inhabitants, and, probably, in a still more important degree, on some of the old inhabitants becoming slowly modified, with the new forms thus produced and the old ones acting and reacting on each other. (p. 163)
On the limiting nature of variation, but does not connect selection to decreased variation.
It cannot be asserted that organic beings in a state of nature are subject to no variation; it cannot be proved that the amount of variation in the course of long ages is a limited quantity; no clear distinction has been, or can be, drawn between spe- cies and well-marked varieties. (p. 425)
On variation over the long run.
These are the most interesting sections I found on the subject from my (quick and limited) searches. I hope you find them useful. However, this is only based on the first edition of "On the Origin of Species", and it is possible that it is is modified in later editions or that he touches upon this in his other writings. However, when looking at these particular passages in the sixth edition, I cannot see a major change in his thinking.
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