Posted by: Jeremy Fox | December 20, 2011

Neutral drift: this means War!

When teaching new concepts to undergraduates, it often helps to make an analogy to something from everyday life with which they’re already familiar. Just the other day I was teaching neutral drift to ecology students, as part of a lecture on niches. I wanted to give them a reasonably precise sense of what neutral drift is and what sort of dynamics it generates, but without using any math, relying heavily on lots of computer simulations, or referring to evolutionary biology (since many of them hadn’t had an evolution class covering drift). And I wanted them to really understand it, not just memorize a definition or a bunch of facts they could regurgitate on an exam. I needed a good analogy, and I think I came up with one. I’m sufficiently pleased with it that I thought I’d share it in case others find it useful.

Neutral drift is pretty much exactly like the card game War. All of my students had, like me, played this game as kids and remembered it well. But if you didn’t, here’s how it works (from Wikipedia):

The deck is divided evenly among the two players, giving each a down stack. In unison, each player reveals the top card on his deck (a “battle”), and the player with the higher card takes both the cards played and moves them to the bottom of his stack. If the two cards played are of equal value, each player lays down three face-down cards and picks one of the cards out of the three (a “war”), and the higher-valued card wins all of the cards on the table, which are then added to the bottom of the player’s stack. In the case of another tie, the war process is repeated until there is no tie. The face value of each cards is as follows: Ace=14 King=13 Queen=12 Jack=11 2 through 10=Same as number on card (10=10, etc.) A player wins by collecting all the cards.

A two-player game of War is like the neutral drift of two alleles at a locus, or two identical competing species. The size of each player’s stack is analogous to the relative abundance of one of the two alleles or species, and battles are analogous to random events (births and deaths) that increase the relative abundance of one allele or species at the expense of the other. If you’ve ever played War, you already understand the following features of neutral drift:

  • Neutrality. Everybody is equally good at War (barring cheating!) Your chance of winning each battle is 50%, and that doesn’t change no matter how many or few cards you have, or how much practice you’ve had at War, or etc.
  • Randomness. The winner of any given battle is just a matter of luck, while the winner of the entire game is just a matter of whoever cumulatively gets luckiest over the course of many battles.
  • Slow dynamics. Playing a full game of War takes a looooonnnnggg time, so long that kids usually get bored with it and stop before the end. Analogously, neutral drift leads to slow changes in relative abundance.
  • Probability of fixation or exclusion depends on current abundances. The more cards you currently have (and thus the fewer your opponent has), the better your odds of winning the game.
  • Drift is a diversity-destroying process. One player or the other is going to win in the long run.*

You can even extend this analogy in various ways to help students understand other aspects of neutral and non-neutral dynamics. For instance, to help students understand the effects of low rates of migration from some external source, ask them to imagine what would happen if, before every battle, there was some very small chance that each player would have one random card added to his pile. To help them understand the effects of (directional) selection, ask them to imagine that one of the players somehow has a >50% chance of winning each battle (maybe he wins the battle if his card has value higher, equal, or one less than that of his opponent’s) And to test the students’ understanding, ask them to think of what sort of experiments one might conduct to distinguish a neutral from a non-neutral world. For instance, what sort of experiments might you conduct to test if one War player is somehow better than another, without knowing the rules of the game?

Now if only there were an ecological concept that could be explained by analogy with this game, which was a favorite of mine growing up.

*Actually, depending on the initial order of the cards, it’s possible for a game of War to comprise an infinite loop. No analogy is perfect.

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Responses

  1. Based on the Wikipedia description of the game B.S., which I also spent long hours playing as a kid, the strategy implications are the exact reverse of the “tragedy of the commons”. When someone calls “B.S.”, all non-cheaters potentially share the advantage, but only the cheater potentially suffers a cost. I think there’s an analogy about cheater males in there somewhere, too…

  2. I take it you didn’t try to teach them what neutral theory says about where all those different suits, numbers and faces came from before the game started? It wouldn’t have taken long 🙂

    • The different suits and numbers are just an analogy for instances of good luck and bad luck. But no, I didn’t teach them neutral theory’s implausible explanation* for why multiple players exist, so that War gets played at all. 😉

      *Well, the explanation in the context of ecology–neutral speciation–is implausible…

  3. I will use this analogy next time that I teach neutral dynamics. I would change maybe 2 things in your explanation:
    – to ensure that it is truly random, each player will get 2 suits that are randomly shuffled. This will result in a 50% of winning for each player. If you shuffle the full deck and randomly distribute, the strength of each player’s hand will be different, and thus will result in predictable win/loss (see this website http://www.rajgiri.net/index.php?page=6, figure “P1 win percentage vs initial strength
    – with all the students in a class room, you can even make this the classical Hubbell or Bell metacommunity version by letting players randomly exchange 2 or 3 cards with all their neighbouring players.

    • Thanks Karl!

      Re: asymmetry in the initial deal, yes, you have a point, although for pedagogical purposes I don’t know that you’d need to get into this. Based on their performance on the exam, my undergrads pretty much all understood the analogy as I described it, and none were confused by–or even thought of–the issue you raise. Then again, the issue you raise is a pretty easy one to explain and I don’t think you’d risk confusing the students or overcomplicating the analogy by introducing it.

      On the other hand, one could argue that since the initial deal is random (each player is equally likely to be dealt any card initially), the traditional version is still random. Similarly, if an organism is endowed at birth (through some ‘accident’ of development) with some “random” increment or decrement to it’s future survival probability and reproductive success, that will create the same neutral drift as if that random increment or decrement arose because of chance events later in the organism’s life. This gets into philosophical questions about what “randomness” is, which I posted on a while back.

  4. here is another example to explain Markov Chains with board games: http://freakonometrics.blog.free.fr/index.php?post/2011/12/20/Basic-on-Markov-Chain-(for-parents)

  5. I prefer to teach my students that random genetic drift is a ubiquitous mechanism of evolution that can affect all sorts of alleles. Slightly deleterious alleles can be fixed by random genetic drift. Beneficial alleles can be lost by random genetic drift. And neutral alleles can be lost or fixed by random genetic drift.

    I point out that Neutral Theory and random genetic drift are not synonyms so the concept of “neutral drift” is not very meaningful unless you are only talking about what happens to neutral alleles and not nearly neutral alleles.

    • Absolutely. I suggest this analogy not because random drift only happens when there is no selection, but because I think this analogy is one way to make clear to students what random drift means. Once the students are clear on that, one could even extend the analogy to incorporate weak or even strong selection (e.g., by changing the rules of the game so that player 1 wins the battle if the value of his card is equal to or one less than the value of player 2’s card).

      Elsewhere I complain that ecologists often talk as if “neutral” and “drift” are one and the same, although looking back my terminology in that post is slightly sloppy (I refer at one point to “neutral drift” in evolution).

  6. […] monthly compendium of evolutionary writing is here. Includes my discussion of how to use a children’s card game to teach the concept of random drift (which I refer to, somewhat imprecisely, as “neutral drift”, but I have another post […]


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