When studying the dynamics of living systems, insight can often be gained by developing a mathematical model that can predict future behaviour of the system
or help classify system characteristics. However, in living cells, organisms, and
especially groups of interacting individuals, a large number of different factors
influence the time development of the system. This often makes it challenging to
construct a mathematical model from which to draw conclusions.

One traditional way of capturing the dynamics in a mathematical model is to
formulate a set of coupled differential equations for the essential variables of the
system. However, this approach disregards any spatial structure of the system,
which may potentially change the behaviour drastically. An alternative approach
is to construct a cellular automaton with nearest neighbour interactions, or even
to model the system as a complex network with interactions defined by network
topology.

In this thesis I first describe three different biological models of ageing and
cancer, in which spatial structure is important for the system dynamics. I then turn
to describe characteristics of ecosystems consisting of three cyclically interacting
species. Such systems are known to be stabilized by spatial structure. Finally, I
analyse data from a large mobile phone network and show that people who are
topologically close in the network have similar communication patterns.

This main part of the thesis is based on six different articles, which I have
co-authored during my three year PhD at the Center for Models of Life. Apart
from these, I have co-authored another six articles, which also relate to spatial
models of living systems. These are included as appendixes, but not described in
detail in the thesis.