Glossary

UNDER CONSTRUCTION

THE BIG PICTURE (population, player, graph, vertex)

A player is an individual member of the population being modeled.  A player has one or more traits.  If finite, the size of the population is [math]\displaystyle{ N }[/math].  If the population is structured, that is, modeled with one or more graphs, each player occupies a vertex (a position, a node) in each graph, and each vertex is occupied by a player.  This being so, we sometimes say "player" to refer to their "vertex" and vice versa.

Traits

A player's traits determine their inherent fitness.  If they reproduce, their offspring gets a (perhaps mutated) copy of their traits.  If an interaction game is being played, their traits also determine their strategy which will impact their behavior which will impact how much the game pays off for them, which then also impacts their fitness.

Graphs

A graph models a relation between players.  It is a list, for each player p, of the players that p considers to be its neighbors in the relation modeled by the graph. Often the graph is undirected (bidirected), i.e. whenever p is among v's neighbors, v is among p's neighbors.  If the graph contains even one exception to that rule, it is called a directed graph.  Unrequited neighborliness. There are three logically distinct relations that are represented by graphs in Evoludo (though often they are identical, which simplifies things for all concerned), called replacement, interaction and reference:

Replacement

In the replacement graph your neighbors are the vertices where your offspring could be put, or containing players that might imitate you. If the graph is undirected, one could think of the graph vertices as territories in a territorial species.  The replacement graph would then model which territories adjoin, under the assumption that territories are static and deaths are replaced by births from adjacent territories, to keep all territories occupied by exactly one player. Your replacement group is your replacement neighbors randomly subselected or augmented, see random neighbors.

Interaction

In the interaction graph your neighbors are the players with whom you could play a game. The interaction graph is usually undirected, and is often equal to the replacement graph. Your interaction group is your interaction neighbors randomly subselected or augmented, see random neighbors.

Reference

In the reference graph your neighbors are the players whom you look at to calculate whether to change your game strategy. It is usually set equal either to the inverse of the replacement graph (if v is a neighbor of p, then in the inverse graph, p is a neighbor of v, which only makes a difference for directed graphs), or to the interaction graph.

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 [math]\displaystyle{ N }[/math], then a single MC step consists of [math]\displaystyle{ N }[/math] individual actions.

synchronous time

All [math]\displaystyle{ N }[/math] 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 [math]\displaystyle{ N }[/math] 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 some 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.

Action

A player that is chosen to act 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 strategy. 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)