Glossary

Glossary

UNDER CONSTRUCTION

Time

For infinite populations time is deterministically modeled. When using numerical integration of ordinary differential equations (ODE), the time increment is automatically chosen by the integrator (Fifth-order Runge-Kutta method with adaptive step size). When using numerical integration of partial differential equations (PDE), the time increment is an adjustable parameter.

For finite populations time is simulated in units of Monte-Carlo steps (MC steps). If the population size is $N$, then an MC step consists of $N$ individual actions.

synchronous time

All $N$ players act simultaneously, in parallel, each time step.  This models situations where external influences such as diurnal rhythms or seasonal changes lead to a synchronization of the breeding season or where competitive interactions are synchronized under harsh environmental conditions such as occur in the arctic or in a desert.

asynchronous time

Under favorable climatic conditions animals may breed and reproduce throughout the year. To model this, during each time step a sequence of $N$ players are chosen at random (with replacement) to act in turn. In a given time step, some players may not be chosen at all, and others may be chosen multiple times.

An action may change the traits of a vertex's player. When a player at a vertex has changed, that player's game payoffs are calculated by playing a round of games with their interaction group.

lingering asynchronous time: The payoffs of the neighbors who play with the changed player are averaged in with their past interactions. The change builds on whatever fitness they had, modeling biology where the effects of all past interactions impact fitness.

memoryless asynchronous time: The payoffs of the players who play with the changed player are recalculated from scratch, modeling biology where earlier interactions have no residual effect on fitness.

When a player is chosen to act, they may imitate a player in their reproduction neighborhood, they may reproduce (prompting a neighboring player to die to make room for the offspring), they may die (prompting a neighboring player to reproduce to replace them), all of which may change someone's traits and thence game strategies. Which of these actions occur, and in what order, is governed primarily by the population update settings.

....Similarly, the time between subsequent reports of the state of the population can be customized....

--Fairfield 22:05, 13 March 2010 (UTC)