Ed Thorpe is the mathematician who wrote “Beat the Dealer.” In that book, he detailed his invention of card counting. He  proved for the first time that it was possible to beat the Las Vegas casinos in blackjack, something that was believed to be impossible. He also invented the Black-Scholes equation several years before Black and Scholes (and in fact Black and Scholes directed credited Thorpe’s writing for inspiring them), which resulted in a Nobel Prize. Except he didn’t share in the Prize because he used the equation to make millions of dollars on Wall Street rather than publishing it. But that’s another story.

Thorpe writes about the time he was asked to dinner with Warren Buffett. Ralph Gerard, the dean of UC Irvine, where Ed was a professor of mathematics, was thinking about moving his money from Buffett to Ed. Warren was secretly assessing Ed’s bona fides.

Ed passed muster when he correctly answered Warren’s question about the oddly numbered dice. This is a curious phenomenon. Let’s say you have three dice. The first die A is numbered 3,3,3,3,3,3. The second die is numbered 6,5,2,2,2,2. The third die C is numbered 4,4,4,4,1,1.

If you roll the dice, then most of the time, die A will beat B, B will beat C, and… C will beat A.This is called a violation of the transitive rule. Normally, in most things in human urban life, if A is better than B and B is better than C, then A is better than C. But not always. And certainly not always in biology.

Here is another example. When my son was in kindergarten, they were taught about the example of the poisonous frog, snake, and the leopard. They were taught non was better than the other because the frog can kill the leopard, the leopard can kill the snake, and the snake can kill the frog.

Perhaps the best everyday example of nontransitive property is in the game of rock-paper-scissors, or in Korean, guy-by-bo.

The problem is that most evolutionary biologists think in transitive terms. Evolution is commonly thought of as a linear process where each organism evolves to become the best adapted to a particular ecological niche. I don’t think this is the best approach toward thinking about evolution. As I’ve detailed in previous posts, the most important affect on evolution is probably from parasites and pathogens, and the second most important is probably from competing organisms, both of which change over time.

If I might coin a term, I believe most evolution is spiral evolution. Evolution goes around and around, repeating the same motifs, with slow change in the overall trajectory of the spiral. (Let’s ignore Gould’s theory of jerky evolution for the moment, although I think his arguments are valid.)

I like to think of evolution in terms of multi-generational, highly flexible repertoire of genes, where any particular combination of genes may be superior to other combination of genes in a particular moment in time, but not at other moments in time. See my post on the Red King Theory for details.

This is like the concept of meta is the game Magic the Gathering. In that game, depending on what cards most of the other players are playing, your deck of cards may or may not have a high chance of winning. Each set of cards can beat another type of a deck, but in turn are vulnerable to specific types of decks. What you want to do is select cards that can beat the most common decks that are in fashion at the moment.

Frequency Dependent Selection

Biologists call this frequency-dependent selection. You see a few examples of this in everyday life. For example, left handedness is probably an example of this. If the proportion of right handed people is 90% (and it is), then there are some advantages in being left handed. If you’re playing baseball against a leftie, or you’re in a sword fight against a leftie, then it can be more difficult than confronting a rightie, when the ratio of letie to rightie is 10:90. As the proportion of left handed people increases, that advantage diminishes for the leftie. Conversely, the disadvantages of being left handed, such as tools and practices ill-adapted to left handed people remain, and probably diminish at a different rate. There is a frequency at which the advantage and the disadvantage equal each other and it turns out that 10% is the optimal frequency for that trait, at least among humans.

Biologists think of frequency-dependent selection as an exception rather than the rule, but from my observations, it may be a lot more common than usually believed.

Meta Changes Over Time

So this leads to several observations, First, in evolution, what you need is a portfolio of strategies, like different deck in Magic or special teams. And you need the versatility  and diversity. You need backup strategies. This is because with every generation, the competing organisms and pathogens change. The strategy that was highly successful a shot time ago may be the most unsuccessful strategy. In fact, it is highly likely to be the most unsuccessful strategy because the competing organisms likely has adopted a meta strategy that is the most effective against your previous strategy. In other words, the meta changes over time.

So what is the best strategy in reproduction? One option is to rapidly alternate your phenotype each generation to stay ahead of the competition, as is outlined in my Red King Theory post. The second option is to distribute the frequency of the phenotypes, not just to produce diversity to give natural selection something to work with but also because the diversity increases the fitness of each variant. That is to say, what you want to do is to produce progeny that have diversity (for example 10% that are left handed) because just on the basis of the frequency of that variant, the fitness can change. Right handed offspring have maximal fitness if 10% of their siblings are left handed, and left handed offspring have maximal fitness if 90% of their siblings are right handed.

The counter-example is found in modern agriculture, where a single crop with very similar or identical genetic background is cultivated over a wide area, Such crops are very brittle to pathogens and widespread failures have happened and continue to happen.

Nature, Nurture, Neither

This lead to a concept I call in-utero shuffling. In addition to nature and nurture, there is a third determinant. There are certain traits, such as disease resistance and as personality, whose fitness is highly dependent on the frequency of the phenotype in the population. Such traits can be shuffled genetically, or can be randomly shuffled like a card deck in utero in insure a diversity of phenotypes. As an example, in most human populations, the ratio among the Myers-Briggs personality types are fairly constant. And identical twins raised in the same family often have very different personality types, with the difference being noticeable from infancy. That is probably because each group of humans need a certain percentage of each personality type–a certain portion of strategic thinkers, certain portion of excellent crafts people, certain portion of creative artists, etc. Imagine a family or a tribe where everyone is focused on strategy and no one on execution. That would be a disaster.

Group Selection Across Time and Space

If this sounds a bit like group selection, it is.

As I said before, genes don’t evolve in isolation. They evolve in the context of the genetic background within the individual, the genetic background of the cooperative organisms around them (those of the same species, for example in their tribe or flock, those of symbiotic species, those of competitive species, and most importantly those of pathogenic species–no gene has a fitness that is objective and independent of the genes around them, the fitness is only relative to other genes), and of the genetic background of organisms in the past (and in a theoretical and probabilistic sense, the likely genes they are likely to encounter in the future). In other words, genes are selected by evolution as a unit across not just space but also across time. What this means is that you need cooperative genes. Genes that take turns getting expressed, sort of like the cyclists who take turns leading the peloton, because their overall fitness over multiple generations is maximized that way. This is a rather unorthodox view, but I think the one that best fits with the data we have.