Evolution of strategies in the Artificial Life model: An Attempt of historical interpretation


Mikhail S. Burtsev



Keldysh Institute of Applied Mathematics of Russian Academy of Sciences


Kinship is one of the major determinants of the social dynamics. Altruistic behavior toward relatives is an evolutionary stable strategy, but how can it change the overall dynamics of the social system? Computer simulations with the proposed model demonstrate that if conditions of local interactions and constrained resource capacity are held then kin-selection could dramatically change territoriality and level of internal warfare. In the social sciences the causes of destruction of kinship organization are conventionally considered as rooted in the fields of politics, economics, and religion. The results of the simulations indicate that a kinship organization can destruct itself without taking into consideration any of the aforementioned additional factors.


Cooperation with relatives is usually found across communities and historical epochs. In many cases kin relations constitute the basis of a social organization. Investigations of this phenomenon in the framework of the game theory provide us with the understanding that kin cooperation is an evolutionary stable strategy (ESS) for different type of games. The question here, however, is why in the majority of historical cases kinship organization ceased to exist and was transformed to other forms of social organization? It is widely accepted among the social science scholars to seek for the causes of transformation of kinship organization in the domains of technology development, economics and politics [1]. An alternative approach ties the decline in kinship organization with the spread of religions of non-violence such as Christianity or Buddhism [2]. In order to distinguish clearly endogenous factors of evolution of society with kin relations from above mentioned exogenous factors one has to study "pure" models prior to considering aspects external to kinship organization. Game theory models sometimes could be solved analytically but require a lot of assumptions about features of society dynamics. The evolutionary agent based modeling gives a chance to handle more important details of the real social systems.

A clear-cut artificial life model was used to simulate the evolution of a kinship organization in the presented study. The model consists of the world divided into cells and evolving population of agents. Every agent in the population was interpreted as an extended family or a descent group [1]. The world contains two kinds of objects: agents and randomly appearing patches of resource. Each agent observes part of the local environment and performs certain actions. An agent can move in space and interact with other agents. Each agent has a limited capacity to store the resource internally. When an agent performs an action, its internal resource decreases. If the agent "consumes" the patch of the resource in the knot, the internal resource of the agent increases. When the agent produces offspring, the parent gives half of its resource to the newborn. The offspring inherits behavior of the parent modified by mutations. The agent can differentiate kin and non-kin neighbors. If the internal energy resource goes to zero, the agent dies. Detailed description of the model could be found in [3].

Typical dynamics of evolution in simulations was as follows. The figure 1 illustrates that at the fist stage the population is trapped in the state with high level of territoriality. In this state every knot of the world is usually occupied by only one agent who fights with non-kin and escape from kin. At a certain point of time (7 106 on the fig.1.) the evolving system switches to another state with higher population size, declined kinship and without fighting among agents. This state is stable if evolution is "conservative" which corresponds with the societies with strong influence of tradition or religion. For the simulations corresponding to the case with weak influence of tradition and religion (not shown on the figure) constant oscillations between war and peace are observed.

Fig. 1. The dynamics of population size, number of aggressive and kin selective agents in the model in the presence of stabilizing factor.

The results of simulations lead to the following conclusions:

1. Cooperation of relatives could drive evolving population to decline of territoriality and internal warfare.

2. Additional mechanisms are required to make peaceful equilibrium stable. Possible candidates to be a factor of stabilization are traditions, religion and state.

3. Weakening of stabilizing factors leads to dynamical regime where aggressive and peaceful strategies of behavior oscillate.


This work was supported by Russian Fund for Basic Research project #04-01-00510.



1. Pasternak B., Ember C.R. and Ember E. Sex, Gender, and Kinship: A Cross-Cultural Perspective. Upper Saddle River, NJ: Prentice Hall, 1997. P. 285-290.

2. Коротаев А.В. Социальная эволюция: факторы, закономерности, тенденции. М.: Вост. лит., 2003. C. 163-189.

3. Burtsev M.S. Tracking the Trajectories of evolution // Artificial Life, 2004. Vol. 10, Iss. 4.