I now work in the Malacology Department in the Senckenberg Museum für Naturkunde Görlitz.

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Privat, Dr J.M.C. Hutchinson, Senckenberg Museum für Naturkunde Görlitz, Am Museum 1, 02826 Görlitz, GERMANY

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In case (i) minimisation of mortality per unit increase of state is optimal under certain baseline conditions. In case (ii) behaviour is constant over time under baseline conditions (the ‘Risk-spreading Theorem’). We analyse how these patterns are modified by complicating factors, e.g. time penalties, premature termination of the food supply, stochasticity in food supply or in metabolic expenditure, and state-dependence in the ability to obtain food, in metabolic expenditure and in predation risk. From this analysis we obtain a variety of possible explanations for why an animal should reduce its intake rate over time (i.e. show satiation). We show how earlier work can be viewed as special cases of our results.

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2. Analytic approaches depend on using the root-mean-square step length, not the mean. However, a more flexible approach to making and testing predictions is Monte-Carlo simulation. With a random walk long-term displacements have a large variance, so a single observation is unlikely to disprove this null hypothesis.

3. Restricting movement to a square lattice is a reasonable approximation even when rectangular boundaries are incorporated. Describing the boundary configuration accurately is more important.

4. The observed non-uniformity in turning angles should have been incorporated as it has a large effect on predicted net displacements, unless the arena is tightly constricted. Randomness of movement within a day can be distinguished from that between days. For Waser’s population it makes sense to predict long-term displacements using only long-distance daily displacements.

5. In conclusion, there are better approaches to establish whether boundaries exist and whether movements follow a random walk.

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Selecting a parking space is a sequential-search problem. Intriguingly, where others have parked determines the pattern of spaces available. Earlier optimality models of parking ignored this game-theoretic aspect, unrealistically assuming random occurrences. This chapter instead simulates populations of cars: agents (drivers) may accept any unoccupied space as they proceed down a dead-end street towards the destination; otherwise they take the first as they drive back out. Several simple decision heuristics are considered, inspired by those from other sequential-search domains. Parameter values generating Nash equilibria are sensitive to conditions and performance criteria. An evolutionary algorithm allows the different heuristics to compete. The winner exploits the emergent environment structure: since adjacent sites often fill sequentially, they empty at similar times, so recently encountered spaces predict more spaces ahead. But high car densities may arise far from the destination, so additionally the winner rejects spaces until within a fixed distance of the destination.

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