The Edge has a post with many evolutionary biologists remembering George C. Williams. In it Robert Trivers described a incident at an earlier memorial session commemorating William D. Hamilton suggesting a disagreement between Williams and Hamilton about the maintenance of sexual reproduction:
We [Williams and Trivers] last saw each other at the William Hamilton memorial session at Amherst in 2000 during the meetings of the Human Behavior and Evolution Society, at which both of us spoke. He was sitting behind me while others preceded us and I could hear Doris saying, "Now, George, don't do what you are thinking of. Just tell the stories you have about Bill, don't do it." So I was full of anticipation when George got up because I knew he was surely going to do exactly what his wife thought was a bad idea. George gets up and says "I wish Bill were here today, because I have a bone to pick with him".Curious to find out what exactly that bone was, I fortunately found the proceedings of the Meeting for the Year 2000 [scroll down to the 12th conference, click on the "Program" link and a pdf should open] of the Human Behaviour and Evolution Society. Williams's contribution starts at page 128, but the crucial passage is on page 130:
And then he went and picked that bone for the entire talk. It had to do with the evolution of sex and patterns of evidence that George had pointed out years ago that contradicted (so George said) aspects of Bill's parasite approach. I thought it was wonderful. There were those that said it was inappropriate and why didn't he tell stories, but I thought it was perfect for the occasion, both vintage George Williams — no wasted motion with that organism! — and a tribute to the enduring importance of Bill's ideas.
No real scientists ever agree on everything, and Bill and I had a brief conflict last year at the Stony Brook conference. I am not convinced that adaptation by local pathogens to parental genotypes need be the major problem solved by sexuality. I think that the general unpredictability of offspring environments is what provides the main advantage. This issue is most appropriately settled not by modeling or data gathering but by consulting authorities. For a reliable insight on the significance of sexuality there are many appropriate authorities, but one that is especially clear is the strawberry plant (Fragaria). Offspring that develop immediately in the parents’ environment, with pathogens adapted to those parents’ genotypes, will not be sexually produced; whereas those that develop at variable times in the future, over a large range of habitats will be. The allocation of resources to sexual and asexual reproduction must be that which balances the two-fold cost of meiosis by the advantage of genetic diversity among widely dispersed seeds.[Update, 8.6.2013: The above quoted piece has also been re-published as Williams (2000) "Some thoughts on William D. Hamilton." Trends in Ecology and Evolution 15(7): 302.]
The above, of course, relates back to Williams's book of 1975 (Sex and Evolution, Princeton University Press), in which the third chapter is devoted to organisms with a life-history that contradicts the Red Queen hypothesis. While the chapter is titled "The Strawberry-Coral Model," it is not about a mathematical or computer model, but about a purely conceptual (verbal) model. It could also be called a life-history pattern or scenario.
Strawberries, corals and other organisms corresponding to that life history pattern produce runners, polyps or the like asexually. This clonal progeny necessarily lives close to their parents and their supposedly co-adapted parasites , whereas the dispersal stages are produced sexually. This is the exact opposite of what the parasite Red Queen hypothesis predicts. The progeny staying close to the parents should be produced sexually, if recombination was a protection against co-adapting parasites.
Thinking about strawberry-coral type organisms, the potato, Solanum tuberosum, should be even worse for the Red Queen hypothesis than the strawberry or corals. Its sexually produced fruits are not only dispersed by fruit eating Vertebrates, but they are also rich in fungicidal and pesticidal Solanine. The asexually produced tubers, however, are not rich in Solanine as long as they stay underground and do not get green.
P.S.: Unfortunately, Hamilton was already dead when Williams picked this bone, and by now Williams is dead too. It would have been nice and worthwhile to see them duke this out.