We present an individual-based model describing the distribution and resource gain of territorial individuals in situations where the rank order of territory quality changes over time. The model integrates both competitive (territory-holding ability) asymmetries and a memory function. A balance of effects resulted in a peak in movement rates, but not resource gain, for individuals of intermediate ability. Furthermore, when the system was reduced to a linear array of territories (as commonly used in empirical studies) the model generated quite different predictions because of the severe limitation in movement that the linear array imposes. We suggest that the model can be used to generate testable predictions for territorial species such as salmonids, and that future empirical work should take into account the consequences of reductions in movement imposed by a linear array of territories. Copyright 1999 The Association for the Study of Animal Behaviour.