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Doubts and Adjustments to the Model

Although he collected a great amount of data and observations during his first trip to Brazil, Hamilton admitted that he should perform those again more systematically: “There are several other experiments that I would like to make to amplify and confirm the results I obtained last time. I would like to make more careful series of transferance experiments with adequate controls to find out if wasps from distant localities are less likely to be accepted on a nest than wasps from nearby nests. I also want to make some homing experiments to find out the flight range.” (Z1X83/1/10, Hamilton to West-Eberhard, October 5, 1967). Hamilton was planning on doing so in his second trip to Brazil in 1968-1968, but also the results of this second trip did not turn out to provide conclusive answers with respect to the wasp puzzle.

Still in the late 1960s and early 1970s, Hamilton was not totally satisfied about how his theory could match the complexity of the biological world. In a letter again to M.J. West-Eberhard Hamilton confessed his frustration: “I am still quiet unhappy about that theory in general, feeling that although it seems to be on the right lines it needs considerable elaboration before it begins to match the complexity of biological situations” (Z1X83/1/10, Hamilton to West-Eberhard, October 5, 1967). In a slightly different tone, in a letter from 1966 to W.E. Kerr, he wrote: “I am still cautios about the value of my theory in the case of the social Hymenoptera more cautios, I think, than Prof. E.O. Wilson who so generously supported it at a recent meeting of the Royal Entomological Society” (ZIX89/1/1, Hamilton to Kerr, May 6, 1966).

In the same letter to West-Eberhard, Hamilton expressed his ideas about inbreeding and its relation to viscosity: “I am now inclined to place relatively more weight on inbreeding as a factor raising the coefficient of relationship and so facilitating social evolution and less on the special features of male haploid relatedness than I was when I wrote those papers” (Z1X83/1/10, Hamilton to West-Eberhard, October 5, 1967). In the late 1960s, after his second trip to Brazil, Hamilton was asked to work on a paper where he could explain and revise his 1964 arguments and ideas about “how relatedness affects the evolution of social insects” (Hamilton 1996, 255). Beside other modifications, in the 1972 paper Altruism and Related Phenomena, mainly in Social Insects, Hamilton included inbreeding into his formulation of the mathematical model of inclusive fitness and newly discussed the situation of Polygynous wasp colonies (Hamilton, 1972).

Hamilton was able to incorporate inbreeding into the model thanks to the rederivation of his formula developed during his collaboration with George Price (Hamilton 1996, 256). Although the model was improved, that did not actually mean that it was able to address the puzzle posed, mostly by Polygyny, to the hap- lodiploidy hypothesis. Inbreeding might be a good way to explain the puzzle as it raises the degree of relatedness in the colony. Hamilton argued: “Unless there is a very high degree of inbreeding, why does not intracolony selection for queen-like behavior break down the system? Why do workers work so willingly and by what device are the fierce struggles for dominance that occur, for example, in queenless Apis and Vespa colonies prevented?” But Hamilton admitted as well that: “If inbreeding is the answer, would we not expect more genetic diversity between colonies, relative to uniformity within colonies, than we actually observe?” and added “But these questions cannot be answered yet.” (Hamilton 1972, 216).

So, adding inbreeding to the model, did not actually help to provide a solution of the puzzle. In fact, Hamilton in the 1972 review would still claim that: “In my opinion, the polygyny in Polybiini, [...] provides the most testing difficulty for the interpretation of the social insect pattern which is offered in this review” (Hamilton 1972, 216). Already in the letter to Kerr mentioned above, Hamilton admitted that looking into haplodiploidy was likely not enough to explain the evolution of biological altruism: “I feel that the male-haploidy cannot be more than half the story, and that the other half must involve the classical concepts of the fabricating, provisioning, long-lived Hymenoptera.” (ZIX89/1/1, Hamilton to Kerr, May 6, 1966). This means that Hamilton was thinking about including other factors and processes in the explanation of how altruistic behaviors might have emerged in evolutionary history. Still, such factors would have had to contribute, according to Hamilton, to raise the relatedness in the colony (Hamilton 1972).

 
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