I should have mentioned I heard about George Price on the Radiolab episode An Equation for Good. They interview the author of his biography, so his story is available there in short form. In a sense, George’s life played out as a metaphor of his own equation.

]]>Interesting! I don’t know anything about George Price except his paper on Fisher’s fundamental theorem, which is really fun to read—first taking apart Fisher’s three papers on this subject and then trying to figure out what Fisher must have meant.

]]>Although i read as much of the literature on GS as i could –probably mostly in late 80’s-90’s–2000’s —Price equation was never mentioned until fairly recently. I view Price equation as a generalization of Fisher’s FTNS (its sort of like the difference between the continuous logisitic equation and its discrete version—both are correct as are Fisher and Price—but one has a stable equilbirium distirbution and the other is chaotic. (I learned this in a paper by E Montroll.)

Price deals with ‘extended or inclusive fitness’ –Fisher deals with a more limited form (in fact i would say Fisher’s theorem deals with ‘haploids’ or ‘clones’. The most fit clones survive. (One can look at some influential papers in theoretical population genetics and they make this assumption for ‘mathematical conveniance’ –ie they are studying th genetics of some mating (diploid, sexually reproducing ) species but for ‘conveniance ‘ they assume its haploid (clones). This way they only have to follow one gene’s trajectory. (In many cases it actually works—this approach is called Fisher’s ‘beanbag genetics’).

( Fisher dids deal with diploids (eg sex, epistasis, dominance)—under special cases (but Fisher just linearizes out all interactions.

i view this as conceptually similar to trying to model phase transitions in condensed matter physics by ‘linearizing out the interactions’ –eg they say ‘as a first approximation a crystal, or computer, is essentially an ideal gas’. It actually works in many cases.)

tThere is a famous paper by astrophysicist Chandresekhar called ‘stochastic problems in physics and astronomy’ in Rev Modern Physics in 1943–i just read the physics part. its last section has an error in it ( on diffsuion in a potential) which confused me for a long time–until i read some article on WW saying it was an error. )

https://arxiv.org/abs/1304.1844 is one more paper—i think I agree with this paper although i think the authors also make the same ‘mistake’ Fisher made –at least elsewhere —they linearize out interactions and end up with ‘beanbag genetics’. In a sense one could interpret this as aiming to legitimize GWAS (and discount Landes LP-model –Landes of MIT sort of was one of creators of GWAS but he revised it the way Price revised Fisher–‘optimizers dont optimize everythijng’ though Fisher’s theorem still hold–‘surivivors survive’.I think this is analgous to Schrodinger’s view in his book ‘what is life’—explains wave function collapse by saying most of the ‘other states’ ‘dissapear’ via Born’s rule. ) .

Those quotes from Price are amusing (since i’m not sure ive ever seen his original paper ). Alex Rosenburg (philosophy of science at Duke ) has a 2005 paper/exchange i Philo and Biology called ‘Mathen’s and Ariew’s Obituary for Fitness :reports of its death has been greatly exaggerated’. (This is a sort of debate over whether Fiher’s theorem is the same as 2nd la of thermodynamics or whether its a version of newton’s law –a principlal of least action. Confusion seems to be a trait that is selected for (maybe one could ave a ne law similar to MEP (max entropy proudction) like MCPP Max confusion production pcp (tho the acronym and similar ones are in use including this area—refers to a kind of ‘boat’– a a large asian country).

Some apparent ‘creationists’ have adopted price’s theorem to make their point (i’m not intelligent enough to understand what the or their grand design is) see the book geneticentropy(dot)org –their view seems to be that while Fisher possibly had some similar views, if Price’s revised argument prevalied over Fisher then they will use Price. This is analogous to some free market economists said if adam smith and arrow-hahn’s profoof that the ‘free market’ needs some revisions due to chaos and computability theory, then they will use chaos and computability thoery to prove that free markets are still optimal or possible—ie ‘this is the best of all possible worlds’.

Price gave up theoretical biology, becamer a christian, and i hear worked serving the poor and died as pauper (didnt get no royalties)..

]]>Ironically (given this content of your post), the writing felt a bit confounding at times. But Price’s life story is an amazing one, and I found the ideas woven into the book deep. It changed my understanding of evolutionary effects.

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