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Complex Dynamics in Adaptive Networks

woensdag, 21 april, 2010 - 16:30
Campus: Brussels Humanities, Sciences & Engineering campus
Faculteit: Science and Bio-engineering Sciences
Sven Van Segbroeck

The origin of life on earth and its evolution to modern human life required several
fundamental transitions: genes had to form a genome, uni-cellular organisms
had to become multi-cellular organisms and humans had to organize in societies.
None of these transitions would have been possible without the emergence of
cooperation among the original entities of selection, allowing the formation of
new, more complex, and independently reproducing, entities.

Interactions that involve cooperation are often formalized in terms games,
such as the famous prisoner’s dilemma. Players either cooperate or defect upon
interaction. Cooperators pay a cost (c) to provide a benefit (b > c) to their
partners. Defectors refuse to cooperate, and therefore incur no costs while
still ripping the benefits provided by others. The accumulation of received
benefits and expended costs defines the reproductive success of an individual.
Reproduction is either genetic or cultural, the latter meaning that the behavior of
successful individuals tends to be imitated more often and therefore spreads in the
population. When all individuals are equally likely to interact, the mathematics
of cooperation (evolutionary game theory) predicts that defection will prevail.

Cooperative behavior is evolutionary disadvantageous, unless additional
mechanisms foster its emergence. Recent theoretical studies suggest that the
structure of our social network may act as such a mechanism. One of the
assumptions of these studies is that individuals adjust their behavior by imitating
successful social acquaintances. Recent experimental work does, however, indicate
that humans often deviate from this learning paradigm: we do not always
follow the example of our peers, but also try to innovate by individually
exploring alternatives. In the first part of this dissertation, we propose to
model exploration behavior in terms of an individual-based learning rule. We
assume that individuals adjust their behavior based purely on such an individualbased
learning scheme and investigate how and to which extent the structure
of the social network affects the final game behavior. We show by means of
computer simulations that in that case the network structure no longer plays
such a prominent role.

Our results also suggest how the learning dynamics will change when taking
into account that realistic social networks are dynamical entities: we regularly
establish new contacts while existing contacts may fade away. The lifetime of
an interaction often depends on the behavior of the individuals involved, leading
to a complex interplay between individual behavior and network structure. This
type of networks are known as adaptive networks: a dynamical process that takes
place on the network, in this case the learning dynamics associated with each
individual, influences the network structure and vice versa. Recent theoretical
work indicates that adaptive networks provide an environment that may promote
cooperative behavior. This is for instance the case when individuals are given the
chance to break unwanted interactions, while keeping the good ones.

The evolutionary mechanism determining individuals’ willingness to change
partner remains unclear, and forms the second part of this dissertation. To
address this question, we assign each individual a topological strategy, which
determines how he handles unfavorable interactions. Depending on his topological
strategy, an individual will either break contact quickly in case he is dissatisfied
about an interaction, or behave in a more loyal way towards his social partners.
In this context, we study the co-evolution of the game strategy, the topological
strategy and the network structure.

We show, by means of computer simulations and analytical methods, that
the selection pressure on the topological strategy of cooperators will not be as
strong as on the topological strategy of defectors. Cooperators are only forced to
become less loyal when competition is fierce between cooperators and defectors.
As a consequence, defectors will exhibit a limited set of topological strategies,
whereas cooperators portray diversity in their topological strategy. Here, we
show that cooperation evolves more easily when individuals have the choice from
a broad spectrum of topological strategies.

The last part of this dissertation addresses adaptive networks in a completely
different context. The network now represents the paths along which a disease
may spread in a population. Infected individuals may transmit the disease
to their neighbors in the network. Most models of disease spreading classify
individuals in different health classes. The simplest model only distinguishes
between healthy and infected individuals. Depending on the disease at hand, and
the sophistication of the model, additional health classes are included, accounting
for instance for immunity, latency periods, etc. Additional realism can also be
added by taking geographical characteristics, heterogeneity, mobility, etc. into

In this dissertation we emphasize an aspect that has been neglected in most
studies: human behavior. Most often, individuals are assumed to behave in the
same way, irrespective of their health status or the number of infected in the
population. This is obviously not true in reality. Sick individuals are expected
to travel less than healthy individuals, and will for instance refrain from going
to work. Conversely, healthy individuals may try to escape from infection by
avoiding contact with infected. As such, we have another example of an adaptive
network. Indeed, the structure of the network is dynamic and coupled to the
dynamics that takes place on the network: epidemic spreading. Here, we propose
a model for epidemic spreading in an adaptive network, which allows for an
analytical treatment in the limit where the network adjusts faster than the disease
spreads. We use computer simulations to show that the analytical predictions also
hold for a much wider range of scenarios. Furthermore, we demonstrate that in
an adaptive network, the infectiousness of a disease depends on the fraction of
infected and the capacity of healthy individuals to avoid contact with infected.