Mark Wilden
Written February 27, 2003
Last edited
September 21, 2003
Richard Dawkins explains how selection at the individual level can result in apparent selection at a group level. His example uses teams of rowers. Selecting individual rowers solely on the basis of individual fitness (number of victories) leads to a team with group fitness, even if the definition of group fitness is not considered when selecting those rowers.
It is possible to imagine a compatible combination of genes as being selected together as a unit... Suppose it is important in a really successful crew that the rowers should coordinate their activities by means of speech... Because of the importance of communication, a mixed crew will tend to win fewer races than either a pure English crew or a pure German crew. The coach does not realize this. All he does is shuffle his men around, giving credit points to individuals in winning boats, marking down individuals in losing boats [Dawkins discusses minorities and majorities, which don't figure here]. What will emerge as the overall best crew will be one of the two stable states--pure English or pure German, but not mixed. Superficially, it looks as though the coach is selecting whole language groups as units. This is not what he is doing. He is selecting individual oarsmen for their apparent ability to win races... Selection at the low level of the single gene can give the impression of selection at some higher level. The Selfish Gene, Oxford, 1989, p. 84-5.
It seemed logical to me that teams could (appear to) be selected on the basis of homogeneity. If speaking the same language makes a team more fit, then the Top 8 rowers with the best win-loss records will tend all to speak the same language.
I decided to test this with a Visual Basic program (downloadable here).
A pool of a few thousand rowers is created--half righties and half lefties. At the beginning of a Meet, each team captain picks rowers from the pool, in order of fitness (i.e., based on how many victories the rower has). Then all teams "race" in a round-robin tournament. I defined a quantity called Homogeneity that looks at a team of rowers and determines how close they are to being all the same (instead of English and German speakers, I started with left and right-handers, per Dawkins's later example)
Property Get Homogeneity() As Double
For Each r In p_rowers
Sum = Sum + r.Handed
Next
Homogeneity = Abs(Sum - NumRowersPerTeam / 2#) / (NumRowersPerTeam / 2#)
End Property
A team of all right-handers has a Homogeneity of 1.0. Half righties and half lefties has a Homogeneity of 0.5. This function evaluates how close each team is to the "best" Homogeneity and picks the winner on that basis:
Function PickWinner(t1 As Team, t2 As Team) As Team
Const bestHomogeneity As Double = 1
If Abs(bestHomogeneity - t1.Homogeneity) < Abs(bestHomogeneity - t2.Homogeneity) Then
Set PickWinner = t1
Else
Set PickWinner = t2
End If
End Function
After a meet, the teams are dissolved. The rowers retain their win-loss records, are shuffled, and then are selected for teams for the next meet. After a number of meets, I looked at the Top 8 rowers (the "best" team--even if they never rowed together). It didn't take long to see that the simulation produced Dawkins's results. Sure enough, the best team after a few meets was either all righties or all lefties.
Dawkins goes on to assert that group heterogeneity can also be selected for. Again, simply by combining rowers randomly into teams, racing them against each, and recording the win-loss record of each rower, he says that the Top 8 rowers will end up being composed of half lefties and half righties. It will look as if the best team was selected as a whole.
I was skeptical about whether this could indeed produce stable top team composition. It seemed to me it could be possible that since both types of rowers could be on any given winning team, all types of rowers would have an equal chance of being on the very best team. That would mean the very best team at any point would indeed be a mixture, but you'd expect to see at least a few freak occurrences of all-left or all-right teams. I felt there was too much opportunity for movement into the Top 8. But Dawkins was right again. After a few meets, the Top 8 were always Homogeneity 0.5.
But there could be another explanation. If every handedness has the same chance to get into the Top 8 at any time, then one would indeed expect half of one kind and half of another.
So I tried one last attempt--setting the "best" Homogeneity to 0.5. In an 8-rower team, this means that the very best team has either 2 lefties and 6 righties or 2 righties and 6 lefties. Could individual rower selection lead to an asymmetrical group selection? My hypothesis (and the whole purpose of this project) was that it would not (otherwise I wouldn't have bothered).
I should have had more faith in Dawkins. Yes, even an asymmetrical "best team" is produce by selection among individuals without knowing the composition of the "best team." Seeing this result in front of my eyes was somewhat breathtaking.
A somewhat similar program is described at The Selfish Gene Algorithm: a New Evolutionary Optimization Strategy.