The Price of Altruism (61 page)

12.
Bill Hamilton letter to George Price, March 26, 1968, BL:KPX1_4.5.5.

13.
Hamilton describes his own perception of George’s depressing revelation in
Narrow Roads
, 320.

14.
Draft of an unsent letter from George Price to Bill Hamilton, March 26, 1968, BL:KPX1_4.5. 8.

15.
The letter is addressed to “W.D. Hamilton, ? ?, Brazil.”

16.
George Price letter to Kathleen, April 11, 1968, GPP.

17.
Charles Darwin,
The Descent of Man
, chapter 17. Antlers are effective shields against other branching antlers, Darwin wrote, but would not protect against unbranched antlers projecting forward.

18.
G. Stonehouse, “Thermoregulatory Function of Growing Antlers,”
Nature
218 (1968), 870–72.

19.
Draft of George Price, “Antlers, Intraspecific Combat, and Altruism,” 1–32, BLGPC.

20.
Ibid., 16.

21.
The precise description was this: “Basically,
get even
behaviour requires that animal A in conflict with B should hold in memory a measure, SB, of the seriousness of recent Category II (all-out combat) acts by B, and a measure, SA, of its own recent category II acts against B. Then the tendency, RAB, for A to retaliate against B is given by R
_AB
= S
_B
– S
_A
. The strategy for A against a roughly equal opponent, B, can be stated as: ‘Fight as hard as possible at Category I level (deescalated). If SB > SA, retaliate at level II. If S
_B
S
_A
, fight at level I; except that when combat has been at level I for a long time, try a probe’” Ibid., 17.

22.
Ibid., 19.

23.
George did not consider that punishing exacts a price, and that free riders who fail to punish would therefore hold an advantage over those who did. This kind of free-riding game-theoretic thinking would occupy modelers in later years.

24.
George Price letter to Bill Hamilton, August 3, 1968, GPP.

25.
George Price letter to Thomas Meyer, October 14, 1968, GPP; John Orr declaration on Flat 3, 1a, Little Titchfield, July 30, 1968, GPP.

26.
Bill Hamilton letter to George Price, August 29, 1968, GPP.

27.
The condition was that there should be statistical association between the
genotypes
of donor and receiver; this is what is meant by “altruists finding one another”: organisms that share those genes that contribute to their behaving altruistically coming together in groups.

28.
Strictly speaking, George had not shown how the covariance equation could translate into Hamilton’s kin-selection equation, replacing relatedness with association, but he understood immediately that this was now possible. For a formal derivation that does this, see Appendix 1: Covariance and Kin Selection.

29.
George Price letter to Alice Avery Price, September 21, 1968, GPP.

30.
George Price letter to Alice Avery Price, September 24, 1968, GPP.

31.
George Price letter to Annamarie Price, October 2, 1968, GPP; George Price letter to Howard Klevens, October 9, 1968, GPP.

32.
Kohn,
A Reason for Everything
, 221.

33.
Steve Jones, “View from the Lab: A Mastermind for a Number of Reasons,”
UK Telegraph
, January 23, 2002.

34.
Ibid.; Newton E. Morton, “Professor Cedric B. Smith, pioneer in statistical genetics: Died January 10, 2002, at the age of 84,”
Genetic Epidemiology
22, no. 4 (2002), 283–84.

35.
George Price letter to Annamarie Price, October 2, 1968; interview with Annamarie Price, April 13, 2008.

36.
George Price, “Supplementary Details of Intended Research,” draft proposal to the Science Research Council, BLGPC, KPX_5.4.

37.
A corollary of this system would be for males to take advantage of any mating opportunity outside of marriage, but not to provide for any children born. Thus, two distinct categories of female sexual partners would become recognized, with dichotomous treatment of each.

38.
George Price letter to Ludwig Luft, January 29, 1969, GPP. George asked Luft, a German-born Jewish émigré to America, for the lyrics from Schumann’s
Dichterliebe
for a paper he was preparing on the evolution of love.

39.
George Price letter to Edison Price, February 3, 1969, GPP; Edison Price letters to George, February 22 and March 2, 1969, GPP; George Price letter to Kathleen Price, March 5, 1969, GPP.

40.
George Price letter to Kathleen Price, May 1, 1969, GPP.

41.
Interview with Kathleen Price, April 13, 2008; George Price letter to Ludwig Luft, July 22, 1969, GPP.

42.
George Price letter to Tatiana, May 11, 1969, GPP; George Price letter to Kathleen Price, March 5, 1969, GPP. In truth Edison had paid for George’s airfare from London and expenses in New York, but George was sour over an unpaid loan and little help with the apartment.

43.
George Price letter to Ludwig Luft, July 22, 1969, GPP; George Price letter to Tatiana, May 11, 1969, GPP.

44.
Garrett Hardin, “The Tragedy of the Commons,”
Science
162 (1968), 1243–48.

45.
The amateur mathematician was William Forster Lloyd (1794–1852) and the source, W. F. Lloyd,
Two Lectures on the Checks to Population
(Oxford: Oxford University Press, 1833), reprinted (in part) in
Population, Evolution, and Birth Control
, ed. Garret Hardin (San Francisco: Freeman, 1964), 37.

46.
Hardin, “The Tragedy of the Commons,” 1244.

47.
Sewall Wright letter to George Price, May 22, 1968, GPP.

48.
George Price, “Supplementary Details of Intended Research,” draft proposal to the Science Research Council, BLGPC, KPX_5. 4. These observations would later be challenged in the ethological literature.

49.
SRC grant proposal, written by Cedric Smith, March 31, 1969, and signed by the head of the department, Harry Harris, BLGPC, KPX1_10.1.

50.
George Price letter to Tatiana, May 11, 1969, GPP.

51.
John S. Price, “The Ritualization of Agonistic Behaviour as a Determinant of Variation along the Neuroticism/Stability Dimension of Personality,”
Proceedings of the Royal Society of Medicine
62 (1969), 37–40.

52.
Ibid., 39.

53.
See S. A. Frank and M. Slatkin, “The Distribution of Allelic Effects under Mutation and Selection,”
Genetics Research
55 (1990), 111–17.

54.
See Appendix 2: The Full Price Equation and Levels of Selection for a derivation of the full Price equation and an explanation of how it can be partitioned and expanded.

55.
Hamilton,
Narrow Roads
, 173.

56.
W. D. Hamilton, “Selection of Selfish and Altruistic Behaviour in Some Extreme Models,” in
Man and Beast: Comparative Social Behavior
, ed. J. F. Eisenberg and W. S. Dillon (Washington, DC: Smithsonian Press, 1971), 57–91.

57.
For Hamilton’s entertaining description of the conference see
Narrow Roads
, 185–97; quotes on 187, 189. Hamilton’s reply, following his hero Fisher before him, was eugenics. In the long run the best humans would have to be consciously selected.

58.
Ibid., 173.

59.
George Price letter to Bill Hamilton, July 28, 1969, BLGPC, BL:KPX1_4. 4. The precise correction George alluded to was that in his 1964 paper Hamilton had failed to state that his kin-selection model only held for an indefinitely large population where the average relatedness between individuals was zero, whereas in realistic finite populations that wasn’t quite the case, and it was there that spite could arise.

60.
Hamilton,
Narrow Roads
, 172–73. Hamilton wrote to a friend at the time that he hadn’t yet thought deeply about Price’s covariance equation, “apart from seeing how it provides just the key I was looking for in about 1962 when trying to get the ideas of social selection into mathematical form as simply as possible.” But Hamilton sensed nonetheless that the covariance equation “may be something like the introduction of Fisher’s idea of analysis of variance into statistics.” Hamilton letter to Colin Hudson, July 26, 1970, GPP.

61.
W. D. Hamilton, “Geometry for the Selfish Herd,”
Journal of Theoretical Biology
31 (1971), 295–311; George Price letter to Al Somit, July 20, 1969, GPP; George Price letter to Aunt Ethel, July 30, 1969, GPP; George Price letter to Ludwig Luft, July 22, 1969, GPP.

62.
George Price letter to Annamarie Price, November 11, 1969, GPP.

63.
John Maddox letter to George Price, February 11, 1970, BLWHC, Z1X102.1.1.2.3; George Price letter to Edison, April 19, 1970, GPP.

64.
George Price letter to Ludwig Luft, June 8, 1970, BLGPC, KPX1_1.6; The paper was revised and sent to
Science
as “The Nature of Selection” in December 1970 and rejected again. It was published posthumously, through the efforts of Steven Frank, in the
Journal of Theoretical Biology
175 (1995), 389–96; George even wrote to Shannon on October 16, 1969 (GPP), to ask whether he thought the covariance equation could be interpreted “in terms of information channel capacity.”

65.
George Price correspondence with Al Somit, March 5, 1969–May 20, 1970, GPP; interview with Al Somit, April 16, 2008.

CHAPTER 10: “COINCIDENCE” CONVERSION

1.
Bill Hamilton letters to George Price, December 5, 1969, January 11, 1970, BLGPC, BL:KPX1_4.5, and BL:KPX1_4.13.