## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## March 22, 2007

### Lizard Game

The rocky Coast Range of California is the setting for an unusual game played by the brightly colored side-blotched lizard (Uta stansburiana). Each male of the species has one of three throat colors, and each color of lizard has a different mating behavior.

The lizards' antics are like the game of rock-paper-scissors. In the playground version, each of the two players holds a hand behind his or her back. A fist means rock, spread fingers mean paper, or two fingers in a "V" mean scissors. On the count of three, the players reveal their hands. The following rules determine the winner: Scissors cut papter, paper wraps rock, and rock breaks scissors. If both players make the same gesture, the game is a tie.

The lizards play a similar game. Each type of lizard has its own strategy for mating with females. As in rock-paper-scissors, sometimes one strategy wins, sometimes another.

Strategy #1: Have a Lot of Territory

The Orange-Throated Lizard: These males establish large territories, with several females. The more females the more often they can mate.

The Blue-Throated Lizard: These males defend small territories holding just a few females. Because the territories are so small, they can guard their mates carefully.

Strategy #3: Be Sneaky

The Yellow-Striped-Throated Lizard: These males are sneaky and can mimic the markings and behavior of females.

So, orange-throated males are able to grab territory and females from blue-throated lizards when orange-throated lizards are rare.

But, blue-throated males can take over a population of yellow-striped-throated males when blue-throated lizards are rare.

Completing the cycle, yellow-striped-throated lizards can sneak into the orange-throated territories when yellow-striped-throated lizards are rare.

Biologists Barry Sinervo of the University of California at Santa Cruz and Curt M. Lively of Indiana University have studied how the populations of the three different types of lizards change from year to year. They found a six-year cycle, with each color sometimes dominating. When a population hits a low, that type of lizard has the most babies the next year, helping to keep the cycle going.

Stuck in an endless cycle, side-blotched lizards keep on playing their never-ending mathematical game of survival.

Muse, April 1999, p. 26-27.