Sunday, November 20, 2011

QED (Richard Feynman) and The Price of Altruism (Oren Harman) - JDC: #7 and #8)

Richard Feynman describes strangeness better than anyone

If you can't explain it to a six year old, you don't really understand it. 

Before QED, "Surely your joking Mr. Feynman" and "What do you care what other people think?", his autobiographical works, were all I had read. 

However, I was excited to read a slightly more technical work because no one puts complicated physical phenomena so simply. His wonderful humility, sparkling sense of humor and highest standards of explication are unmatched among the science writers I have read. 

It was a joy to learn how the probabilistic nature of photons lead to our everyday experience with light: it moves in straight lines, it bends (or slows down) in different media such as water, white light can be decomposed into its various colors when passed through a prism or diffraction grating, plus many more.

Some unanswered questions remain. I don't understand the origin of the complex component of the amplitude vector that Feynman gives to each photon in his vector diagrams. Although this was not a focus of his teaching in the book, it was something I would like to investigate further. This, combined with my excitement to learn more from whatever has been published of his masterful teaching, lead me to purchase the complete "Feynman Lectures on Physics." I doubt they will fall under the purview of the current Junot Diaz Challenge postings, but perhaps I will write some thoughts as I have them, here.

Altruism <= game theory + (multi-level) selection

Oren Harman's book about George Price is a very engaging, in-depth, discussion of the history of the science of evolution after Darwin. Two central questions of the book, and indeed, evolutionary biologists in the 20th century were: what is it that nature selects (genes, organisms, groups, populations)? What explains that a self-interested evolving unit (gene, organism, group) acts, at times, altruistically (accepting a cost to itself to benefit another)? Examples discussed in the book that shed light on these questions include: The sex-ratio in organisms (selection at the level of the individual should result in 1:1 and often does), virulence of viruses (natural processes of attenuation imply group selection may be at work), and the life-cycle of slime mold. Starving slime molds consist of single-celled amoeba which die for others (creating a stalk of dead cells) to allow other amoeba to climb and create a fruiting body (cells of amoeba higher up) which will be transported by animals or the wind to live another day (check out a nice movie of the process below).

(Fascinatingly, it was found that in the wild, these stalks are typically formed from a single clone. That is, the amoeba that group together are identical. They share the same genome and are therefore not anymore altruistic than a cell in my arm, which sacrifices itself after absorbing a toxin from the environment to protect a cell in my liver, or brain or any other integral organ to improve my survival chances and thus the chances that I will pass-on my genes - the very same genes that include instructions for reproducing that sacrificial skin cell.)

My history-myth about multilevel selection

George Price, among many others described in this book, were entranced by questions of how best to apply the ideas of evolution to solve evolutionary riddles. In particular, could altruism among units of evolution (genes and/or individuals and/or groups) be understood best by analyzing the problem at the level of the gene or higher up or both. 

Richard Dawkin's own wonderful book, The Selfish Gene, argues that the gene is the only necessary unit to consider when trying to understand a given phenomena. He envisions each individual as a vehicle or husk, for its genes. The gene is in a fight against all other genes to reproduce itself most effectively. The gene will only form alliances if that means that it will improve its reproductive success (as in the case of multicellular organisms).

This gene's-eye view of evolution is a powerful way to understand the evolutionary solutions to biological problems, and it, combined with William Hamilton's cost benefit equation*, can explain a wide-range of phenomena. Among these are wonderful game theoretic problems (introduced as a mathematical discipline by John von Neumann^ and popularized by many others including John Nash) such as the prisoner's dilemma that cast multi-agent problems in a mathematical frame (finding evolutionary stable strategies in a population).

However, it was found that the gene's-eye view is not mutually-incompatible with the view that group selection can also occur. Just as the laws of physics must always be obeyed when one employs a biological or chemical law to solve a biological problem (since the equivalent physical statement of the problem may be intractable or represent an inefficient solution path), so too rules of genetic selection must be obeyed (including the laws of chemistry and physics!) when one uses individual or group selection ideas to solve a problem. Harman summarizes David Sloan Wilson's work** on group selection as follows: began to become clear that the unit of selection [gene, individual or group] and the level of selection [gene, individual or group] depended entirely on different criteria. Of course genes were replicators, and clear units of permanence. But whether a certain level of life could be viewed by selection depended not on permanence but on where fitness differences resided in the biological hierarchy. Here is why: If a population is viewed as a nested hierarchy of units, with genes existing within populations and so on, fitness differences can exist at any or all levels of the hierarchy because heritable variation can exist at all these levels... Despite all the history and hype, the gene's-eye view and group selection are not, an never should have been, antithetical.

Price's mathematical treatment of trait change in evolution

George Price's work is a wonderful addition to this discussion because he provides the mathematical relationship that allows us to account for the average trait change in evolution due to selection and transmission. 

Here, Harman has used z and z(overlined) to mean a character (e.g. a phenotype) and its respective average value; w is the fitness of the character; and the covariance, Cov, and expected value, E, functions are as they are typically defined mathematically. However, if one wants to consider the resultant trait change due to transmission one level down (e.g. from organism to gene), we can consider the nested version:

where the right hand side is inputed iteratively as many times as needed (for each level). With enough data, we can imagine determining which of the terms in the sum is most important and attribute the relative importance of group or individual or gene selection. I have to admit that I have not seen this done, but would love to see an example of this to more fully appreciate its value. 

Overall, Harman's treatment of the history of evolutionary biology and his biography of George Price's life (of which I have not commented here) is excellent. I really enjoyed considering some of these wonderful problems and hope you will too if you have the inclination and the time. Thank you Scott and Veena for this thoughtful present.*^

* Hamilton's cost benefit equation states that an organism is willing to incur a cost, C if the aggregate benefits, B, to its kin, defined by r, are greater (rB > C). Ideal relatedness can be calculated: a parent or sibling shares 1/2 of genes (r = 0.5), each grandparent or uncle shares 1/4 (r = 0.25), each first cousin shares 1/8 (r = 0.125). Note these assume that there is no incest. The calculation is simple in that for every line drawn as a consequence of sexual reproduction, one simply needs to multiply the previous relatedness by 1/2. If there are multiple ways to reach a family member, the two paths are added (e.g. for a sister, 1/2 * 1/2 + 1/2 * 1/2 = 1/2 since I can think of the connection from me between mom and sister or dad and sister). Note that for half siblings, r = 0.25. Thus J.B.S. Haldane famously quipped:
I would lay down my life for two brothers or eight cousins.
Note that Hamilton's cost-benefit equation is being applied by J.B.S. Haldane at the level of the individual instead of the gene. Dawkins does this often in his book as well.

^ Incidentally, John von Neumann also provided the mathematical basis of quantum theory and is therefore the godfather of both of these books.

** For a nice review article on multilevel selection by David Sloane Wilson and E. O. Wilson check out this pdf.

*^Scott Johnson and Veena Reddy, now members of my family, gave this book as a gift to me a few years ago (this shows you how many books I still need to read) after I told them about my proposal to work with two microorganisms (distinct single-knockout mutants) in the lab to see if they could evolve to cooperate over time. With this platform technology (i.e. knock-outs which via natural evolutionary process maximize fitness through cooperation), one could engineer "multicellular" cooperative microbe populations that solve important problems (e.g. photosynthesize light and create biofuels [cooperation between algae and engineered yeast]).

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