Sunday, May 27, 2012

The Evolution of Cooperation

Saw Martin Nowak yesterday - he's giving a public lecture in Cambridge on Monday on "The Evolution of Cooperation" which I would urge people to attend (I can't make it).

Dawkins implies that that Steven Pinker and Robert Trivers signed one of the objecting letters to Nature but this is false. And although there are 1 or 2 pretty good biologists in the rest of the list that Dawkins cites, none is really of the 1st rank*. With approximately 4M biologists in the world the fact that 154 signed some letters to Nature objecting to a paper that turns a dogma into a rule of thumb is not such a big deal.

It also turns out that the paper by West that tried to (re-)formulate kin selection on a more rigorous basis does do by re-defining B, C and R and making B and C a function of R. And that in this re-formulation, R is not necessarily 1 for clones nor 1/2 for siblings. Epicycles!

Jerry Coyne has commented on the Dawkins Prospect article. He draws attention to a paper in Science showing that monogamy seems to have been a precursor to the evolution of eusociality. I remember that “monogamy” paper and it’s neat. {PS but I realised this morning (29th) what the problem is with it. They infer whether a precursor species was monogamous by whether its extant descendants are monogamous. Hence if eusocial species are predominantly monogamous then by definition it will be inferred that their precursor species are as well. All a bit circular, and doesn't say anything about whether eusociality leads to monogamy or vice versa. Pity they don't use trained statisticians to review biology papers in Science}

I think his comments highlight the difference in outlook between typical biologists and typical mathematicians, but that on substance you don’t differ much (here at least) from Nowak et. al.
Everyone agrees that Hamilton’s Rule is a useful rule of thumb that has helped bring various phenomena “within the ambit of scientific understanding” and that relatedness is very important in biology. But Nowak & al’s main point seems to me to be that when you look at the maths carefully in detail you find that Hamilton’s Rule is often an approximation and sometimes plain wrong, and that (as you agree) it never provides a (correct) explanation that differs from standard Natural Selection.

Most biologists (at least 20th C ones) tend to react to this with “well OK, the mathematicians may not like this model but it’s pretty useful in our field, we all know that models are imperfect that that biological systems are very complex” whereas most mathematicians will think “OK, refuted, next…”

PS: an interesting illustration of this is given in the exchange of brief correspondences in Nature. Abbot et al provide a table of "Areas in which inclusive fitness theory has made successful predictions about behaviour in eusocial insects" but as NTW point out "Fitting data to generalized versions of Hamilton’s rule is not a test of inclusive fitness theory".  Again this is an illustration of the differences in rigour and outlook between typical 20th C biologists and mathematicians.

Jerry also needs to engage with some of the biology in NTW. For example “among the 70,000 or so known parasitoid and other apocritan Hymenoptera, all of which are haplodiploid, no eusocial species has been found. Nor has a single example come to light from among the 4,000 known hymenopteran sawflies and horntails, …. It has further turned out that selection forces exist in groups that diminish the advantage of close collateral kinship…Most of these countervailing forces act through group selection or, for eusocial insects in particular, through between-colony selection.”

* The other people Dawkins lists are David Queller, Jerry Coyne, Richard Michod, Eric Charnov, Nick Barton, Alex Kacelnik, Leda Cosmides, John Tooby, Geoffrey Parker, Paul Sherman, Tim Clutton-Brock, Paul Harvey, Mary Jane West-Eberhard, Stephen Emlen, Malte Andersson, Stuart West, Richard Wrangham and Bernard Crespi. I've linked to all the extant Wikipedia articles on them. Only a few are FRS/NAS members: Nowak probably has more papers in Nature, Science and PNAS than all of them put together and he's much younger than most of them.

Saturday, May 26, 2012

More on NTW and Kin/Group Selection

Discussion continues about the Dawkins review of EO Wilson's book and the Nowak-Tarnita-Wilson paper.

One discussant asks for an example of how Group Selection might work that cannot be explained more parsimoniously at a gene level. Perhaps the simplest example would be cultural advantages enable one group to out-compete another which is otherwise genetically identical. eg Christians vs Pagans in 2nd-5thC Europe. SKorea v NKorea.

Another way of seeing where some of the problems with Hamilton's rule and kin selection lie can be taken from the Supplementary Information to NTW.  On p19 they show the basic point with Fig 3
Fig 3b from NTW SI*

"Relatedness does not measure the ability of a population to support evolution of cooperation. (a) A large well-mixed population has very low relatedness, R = 0, while a population that occupies a one dimensional spatial grid has maximum relatedness, R = 1. Nevertheless for birth-death (BD) updating both population structures are equally unable to support evolution of cooperation. (b) Now we compare two populations that are both arranged on a one dimensional spatial grid, and hence both populations have maximum relatedness, R = 1. But the first one uses birth-death (BD) updating and does not support evolution of cooperation, while the second one used death-birth (DB) updating and does support evolution of cooperation provided b/c > 2. BD updating means that individuals reproduce proportional to payoff and the offspring replace randomly chosen neighbors. DB updating means that individuals die at random and then the neighbors compete for the empty site proportional to payoff. Relatedness is R = (q − Q)/(1 − Q), where q is the average relatedness of two individuals who interact and Q is the average relatedness in the population. These mathematical examples are chosen to be as simple as possible, but they make the more general point that relatedness data in the absence of a precise understanding of population dynamics are not very useful." (NTW SI p 19)*
I agree that something like evolution is probably necessary to get life going. And it may well be that my friends at Lifeboat are wrong about the singularity etc.. But it is certainly not the case that silicon life is logically impossible. And the idea of "mutable, heritable, digital particles of information" does not in general make sense.

* reproduced by kind permission of Prof Nowak. I've changed the notation to q and Q from Q and Q-bar since I don't know how to make a Q-bar in HTML.

Friday, May 25, 2012

The difference between a great scientist and a 5th rater

On Weds attended an excellent talk by Bill Newsome on neuroscience and free will, at Kings College London, organised by the Faraday Institute.  What I found especially impressive was that, although I think he had been somewhat bamboozled by Pat Churchland into the view that "randomness is not free will" missing the distinction between randomness and controlled stochasticity, during the Q and A he modified his position between the first Q (when this point was put to him) and subsequent answers, and he actually drew the attention of the audience to the fact that he was arguing himself more to the first Q's position.  Only a person of great intellectual integrity would do this - a mark of a truly first-rate scientist.

By contrast I find that Dawkins has a review in Prospect of the great EO Wilson's The Social Conquest of Earth which Dawkins ex-cathedra rejects ("This is not a book that should be tossed lightly aside. It should be thrown with great force." ) and tries, rather pathetically since he doesn't have the mathematical skill to so do, to re-fight the battle over Nowak, Tarnita and Wilson. He is reduced to arguing that "one can make a good case that the 2010 paper would never have been published in Nature had it been submitted anonymously and subjected to ordinary peer-review, bereft of the massively authoritative name of Edward O Wilson."  Can one indeed? He hasn't and AFAIK nor has anyone else, for the simple reason that it isn't true.  I know Nowak and Tarnita and I know that the paper was peer reviewed with the utmost rigour.   It's true that many famous evolutionary biologists objected to the paper, but no-one has found a flaw in the mathematics.
From N-T-W Fig 3c. "For calculating inclusive fitness one has to keep track of all competitive interactions that occur in the population. Here A acts on B changing its payoff and fitness. If A or B compete with other individuals, then their fitness values are also affected by A’s action, although no action is directed towards them. Inclusive fitness theory is not a simplification over the standard approach"* 
The fact is that Hamilton's rule is a rule of thumb which is often pretty helpful for biologists trying to figure out what is going on.  But it's almost impossible to give good definitions of C, B and R which work correctly in most real circumstances, and sometimes it breaks down altogether.

Because Dawkins is (at best) a 5th rate scientist he seems to be incapable of modifying his scientific views in the light of new evidence, and clings on to his dogmatic mantras from the 1960s.

PS Interesting comment threads on the Prospect article. I've explained that part of the problem is that almost none of the "140 biologists" who signed letters to Nature denouncing Nowak-Tarnita-Wilson really understood the maths.  Someone suggested that Stuart West and Alan Grafen do.  But with the best will in the world neither West nor Grafen are Mathematicians (degrees in Zoology, Experimental Psychology, and Economics).

West tries to state a rigorous version of kin selection post N-T-W in this paper and I haven’t had time to go through it all, except to say that basing your entire work on linear regressions shows that you are an economist/zoologist and not a mathematician! The world is usually much more complex than this. No-one denies that Hamilton’s Rule is a good rule of thumb, but that’s not what Dawkins believes.

* reproduced by kind permission of Prof Nowak

Wednesday, May 23, 2012

Science is not a Priesthood

A (very) distinguished scientist emails me about his comments on a Nature article.

Many of these people seem to think that Science is some kind of Priesthood with Commandments On Tablets Of Stone. If they rule out the possibility of anything major unexpected then they have no chance of making major discoveries. Of course unusual, iconoclastic ideas may be wrong - they almost always are - but the ones that are not wrong are the source of all major progress.  As my correspondent knows much better than most!

Saturday, May 19, 2012

Beethoven, human conflict and a single atom

Another highly eventful but mostly unbloggable week.  Music lesson with Kathron on Sun, the LSE seminar went well on Mon, and last night Ruth Palmer came round and we worked on Beethoven's wonderful 6th violin sonata.

Interesting article in Science called "Religious and Sacred Imperatives in Human Conflict" by Scott Atran and Jeremy Ginges.  Though to say "Moralizing gods emerged over the last few millennia" (as they do in the abstract) is slightly odd - most theists would deny that God evolves at all and most atheists AFAIK would deny that god(s) exist.

Although it's going back a while, it's hard not to be impressed by this stunning image from Science of the forces exerted at various angles from a single atom of Tungsten and a single molecule of Carbon Monoxide.
Overlayed scanning tunneling and atomic force microscopy images of a single atom

Sunday, May 13, 2012

Nice letter from the President of the IMA

Busy though largely unbloggable week. On Friday celebrated Grandson's 13th birthday - quite a milestone!

Honoured and delighted to receive a letter from the President of the IMA saying that I'm invited by the Council to become a Fellow “in recognition of your personal contribution to the advancement of mathematics as a discipline and a profession.” He says "We're particularly keen to expand on the sector outside universities and you are an ideal example." My father was a Vice-President so I’m doubly pleased.

Went sailing today near Horton, and on the way back visited my grandparents' grave in Horton churchyard.

On Monday I give a seminar at the LSE about some of my secular work. All are welcome though it will be somewhat technical.

Monday, May 07, 2012

BegatWorld 1.0

Long and interesting discussion on free will with a distinguished physicist. He started from a position that Creation and free will are incompatible but I think I've got him to agree that they are not.  He asks for a "toy model" of a universe in which there is free will and I've come up with what I call BegatWorld 1.0.

In this there exists a finite set of persons P1..n which varies over time t0...infinity and at any time t any person who exists at time t may Beget another new person who then exists at time t+1.

God begins by creating some persons and then allows them to get on with it (God has of course created the entire system and sustains it, so God remains the Creator of all the persons).

BegatWorld 1.0 has an infinite number of possible histories* and if you were interested in genealogy or persons it could be fascinating to watch. And if your purpose was to create lots of loving persons (and you assume that if A begat B then A tends to love B and B tends to love A and that love tends to grow transitively over time) this would not be a bad way of doing it.

Of course it’s wildly over-simplified but it might be helpful as a starting-point for discussion.

* At time t there can be (2^t)*N[0] persons where N[0] is the number at t=0, and there are 2^N[t] possible begettings at time t. So the number of of possible histories to time t is really spectacular!