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Interaction vs reproduction graphs.

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Populations have different characteristic structures determined by the type of interactions of one player with other members of the populations.

Structure:

mean-field/well-mixed populations:

Well mixed population without any structures, i.e. groups or pairwise encounters are formed randomly. This is often called the mean-field approximation.

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linear lattice:

The players are arranged on a straight line - that is actually on a ring in order to reduce finite size and boundary effects - and interact with equal numbers of neighbors to their left and right.

square lattice:

All players are arranged on a rectangular lattice with periodic boundary conditions. The neighborhood size may be four (von Neumann-) or eight (Moore neighborhood).

hexagonal lattice:

The players are arranged on a hexagonal or honeycomb lattice interacting with their six nearest neighbors.

triangular lattice:

The players are arranged on a triangular lattice interacting with their three nearest neighbors.

linear small world network:

Small world network with an underlying structure of a linear lattice (see above), i.e. first the population is initialized with a linear lattice geometry and then a certain fraction of bonds (see Frac new joints below) is randomly rewired. Note that the rewiring process leaves the connectivity of the players alone.

square small world network:

Small world network with an underlying structure of a rectangular lattice (see above).

hexagonal small world network:

Small world network with an underlying structure of a hexagonal or honeycomb lattice (see above).

triangular small world network:

Small world network with an underlying structure of a triangular lattice (see above).

random graphs:

Randomly drawn bonds/connections between players. The neighborhood size determines the average number of bonds (average connectivity) of one player, i.e. the players interact with different numbers of other individuals.

random regular graphs:

The structure of random regular graphs is similar to random graphs with the additional constraint that each player has an equal number of interaction partners.

Neighborhood size:

Determines the number of potential interaction partners. This corresponds to the connectivity of a player. In the case of random graphs, this specifies the average number of interaction partners.

Frac new joints:

Fraction of bonds that get randomly rewired to obtain a small world network out of some underlying regular lattice. Note that fractions close to one will require an enormous number of rewired bonds.