Dynamics of alliance formation and the egalitarian revolution

Arguably the most influential force in human history is the formation of social coalitions and alliances (i.e., long-lasting coalitions) and their impact on individual power. In most great ape species, coalitions occur at individual and group levels and among both kin and non-kin. Nonetheless, ape societies remain essentially hierarchical, and coalitions rarely weaken social inequality. In contrast, human hunter-gatherers show a remarkable tendency to egalitarianism, and human coalitions and alliances occur not only among individuals and groups, but also among groups of groups. Here, we develop a stochastic model describing the emergence of networks of allies resulting from within-group competition for status or mates between individuals utilizing dyadic information. The model shows that alliances often emerge in a phase transition-like fashion if the group size, awareness, aggressiveness, and persuasiveness of individuals are large and the decay rate of individual affinities is small. With cultural inheritance of social networks, a single leveling alliance including all group members can emerge in several generations. Our results suggest that a rapid transition from a hierarchical society of great apes to an egalitarian society of hunter-gatherers (often referred to as "egalitarian revolution") could indeed follow an increase in human cognitive abilities. The establishment of stable group-wide egalitarian alliances creates conditions promoting the origin of cultural norms favoring the group interests over those of individuals.Comment: 37 pages, 15 figure

Finiteness of the Fixed Point Set for the Simple Genetic Algorithm

The infinite population simple genetic algorithm is a discrete dynamical system model of a genetic algorithm. It is conjectured that trajectories in the model always converge to fixed points. This paper shows that an arbitrarily small perturbation of the fitness will result in a model with a finite number of fixed points. Moreover, every sufficiently small perturbation of fimess preserves the finiteness of the fixed point set. These results allow proofs and constructions that require finiteness of the fixed point set. For example, applying the stable manifold theorem to a fixed point requires the hyperbolicity of the differential of the transition map of the genetic algorithm, which requires (among other things) that the fixed point be isolated

Reinterpreting No Free Lunch

Since it’s inception, the “No Free Lunch theorem” has concerned the application of symmetry results rather than the symmetries themselves. In our view, the conflation of result and application obscures the simplicity, generality, and power of the symmetries involved. This paper separates result from application, focusing on and clarifying the nature of underlying symmetries. The result is a general set-theoretic version of NFL which speaks to symmetries when arbitrary domains and co-domains are involved. Although our framework is deterministic, we note situations where our deterministic set-theoretic results speak nevertheless to stochastic algorithms

Group Properties of Crossover and Mutation

It is supposed that the finite search space Ω has certain symmetries that can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries, then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of Ω are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on Ω to induce a group structure on Ω itself

Representation Invariant Genetic Operators

A genetic algorithm is invariant with respect to a set of representations if it runs the same no matter which of the representations is used. We formalize this concept mathematically, showing that the representations generate a group that acts upon the search space. Invariant genetic operators are those that commute with this group action. We then consider the problem of characterizing crossover and mutation operators that have such invariance properties. In the case where the corresponding group action acts transitively on the search space, we provide a complete characterization, including high-level representation-independent algorithms implementing these operators

State Aggregation and Population Dynamics in Linear Systems

We consider complex systems that are composed of many interacting elements, evolving under some dynamics. We are interested in characterizing the ways in which these elements may be grouped into higher-level, macroscopic states in a way that is compatible with those dynamics. Such groupings may then be thought of as naturally emergent properties of the system. We formalize this idea and, in the case that the dynamics are linear, prove necessary and sufficient conditions for this to happen. In cases where there is an underlying symmetry among the components of the system, group theory may be used to provide a strong sufficient condition. These observations are illustrated with some artificial life examples

04081 Abstracts Collection -- Theory of Evolutionary Algorithms

From 15.02.04 to 20.02.04, the Dagstuhl Seminar 04081 ``Theory of Evolutionary Algorithms\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available