Glossary: Difference between revisions

;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|traits]].  If finite, the size of the population is <math>N</math>.  If the population is structured, that is, modeled with one or more [[#Graphs|graphs]], each player occupies a vertex (a position, a node) in each [[#Graphs|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|fitness]].  If they [[#Reproduction|reproduce]], their offspring gets a (perhaps [[#Mutation|mutated]]) copy of their traits.  If an interaction [[#Game|game]] is being played, their traits also determine their [[#Strategy|strategy]] which will impact their [[#Behavior|behavior]] which will impact how much the game [[#Payoff|pays off]] for them, which then also impacts their [[#Fitness|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 [[#Reproduction|offspring]] could be put, or containing players that might [[#Imitation|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|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|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 [[Parameters/PDE#Time increment|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>N</math>, then a single MC step consists of <math>N</math> individual [[#Action|actions]].

:;synchronous time: All <math>N</math> players [[#Action|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>N</math> players are chosen at random (with replacement) to [[#action|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|action]] may change the [[#traits|traits]] of some vertex's player.  When a player at a vertex has changed, that player's game [[#payoff|payoffs]] are calculated by playing a [[#round|round]] of games with their [[#Interaction|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|fitness]].