Darwinians Excel at Games
Martin Nowak (Harvard) sure got good press for his evolutionary game theories last week. In Nature,1 he retold the glorious story of how he and Karl Sigmund met in an Austrian mountain cottage and applied the “prisoner’s dilemma” game to a new theory for social evolution. The same week, in Science,2 as part of a special section on mathematics in biology, the two of them published a detailed accounting of the many insights game theory has provided to Darwinists.
Thousands of papers have been written on game theory since Nowak and Sigmund dreamed up this new approach for characterizing biological interactions (for example, see 10/17/2002). Martin especially liked game theory because it didn’t require hard lab work: “At university, I found labs disappointing,” he says. “ – experiments failed for no good reason. But theory was beautiful. You could do theory while walking through the forest or lying in the grass. Theory was not grey, but a golden tree of life.”
His Science piece claims some progress, but lists some substantial challenges ahead. He does not specify how many hours of lying in the grass these puzzles will require:
Many challenges lie ahead. Evolutionary game theory is formulated in terms of phenotypes, thereby ignoring the complexity of the genotype-phenotype mapping. More work is needed on the interaction of strategies encoded in genomic sequences. Most evolutionary game dynamics have been studied in the context of infinitely large populations. We expect that finite population size effects will lead to surprising outcomes and might question the importance of traditional evolutionary stability. Cultural interpretations of replicator dynamics often assume that successful strategies spread by imitation or learning, but the learning of complicated strategies from behavioral observations is a nontrivial task that needs specific investigation. Similarly, studying human language requires a connection between the mathematics of game theory, learning theory, and computational linguistics.
Despite these challenges, Nowak is confident that game theory provides a conceptual framework that is just shy of a panacea. It can be applied to everything in biology, he claims, from interactions between proteins in a cell to social interactions between people:
The applications of evolutionary game theory pervade by now all areas of biology. Interactions among genes, viruses, cells, and humans are often instances of evolutionary games that are amenable to empirical and theoretical investigation. Game theory is the appropriate tool whenever the success of an individual depends on others.
With all the popularity his approach has garnered, Nowak is like a kid in a candy store: “I am no longer embarrassed to work on games. They are the generic description of evolutionary interactions among genes, cells and people. Children love games. Scientific creativity is to never stop playing.”
Children love games. Children also love fairy tales. Children are suckers for logical fallacies. Grow up, Martin.
These guys should read the piece by Robert M. May in the same issue of Science3 on “Uses and Abuses of Mathematics in Biology.” Though not targeting game theory or evolution specifically, May shows how mathematics can confuse, not clarify, issues, and lead to false conclusions if the assumptions or inputs are wrong or imprecise. He does mention how Darwin might have avoided the now-discredited view of blending inheritance had he known a little math (Charlie said, “I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense.”) If Darwin had grasped the significance of Mendel’s results, Robert May claims, he might have made better progress against critics. (Or perhaps more accurately, would have gasped and moaned.)
May points out differences between mathematical uses in physics and biology. Tycho collected planetary data, Kepler described patterns that made the observations coherent, and Newton provided fundamental laws to explain the patterns. Mathematical biology is partly in each stage, but “every stage in this caricature is usually vastly more complex than in the early days of physics,” May warns. He provides examples of abuses, and some good uses, such as in immunology. But he ends on a word of caution that Darwinian game theorists should read and heed:
Mathematics, however, does not have the long-standing relation to the life sciences that it does to the physical sciences and engineering. It is therefore not surprising to find occasional abuses. … Perhaps most common among abuses, and not always easy to recognize, are situations where mathematical models are constructed with an excruciating abundance of detail in some aspects, whilst other important facets of the problem are misty or a vital parameter is uncertain to within, at best, an order of magnitude. It makes no sense to convey a beguiling sense of “reality” with irrelevant detail, when other equally important factors can only be guessed at. Above all, remember Einstein’s dictum: “models should be as simple as possible, but not more so.”
Exercise: Re-read this quote, and then read Nowak’s quote above about the challenges facing game theory. How likely are evolutionary game theorists to be duped by a beguiling sense of reality? (A phrase which, being interpreted, means, fantasy.)
Extra credit: Apply the same analysis to Antonelli’s claim (see 01/12/2004) and to computerized models of evolution (see 08/20/2003 and 12/19/2002s).
1Martin A. Nowak, “Prisoners of the dilemma,” Nature 427, 491 (05 February 2004); doi:10.1038/427491a.
2Martin A. Nowak and Karl Sigmund, “Evolutionary Dynamics of Biological Games,” Science Volume 303, Number 5659, Issue of 6 Feb 2004, pp. 793-799, 10.1126/science.1093411.
3Robert M. May, “Uses and Abuses of Mathematics in Biology,” Science Volume 303, Number 5659, Issue of 6 Feb 2004, pp. 790-793, 10.1126/science.1094442.