Summary: The burrow system of the fossorial form of the water vole
(Arvicola terrestris scherman Shaw.) (Mammalia, Rodentia) :
an approach using graph theoretical methods and simulation models
by J.-P. AIROLDI ' et D. DE WERRA2
'Centre deformation du Brevet dfEnseignementSecondairelBiologie,
Universite' de Berne, Gertrud Wokerstrasse 5, CH - 3012 Berne, Suisse.
Dkpartement de mathirnatiques, Ecole polytechnique fe'de'rale,
MA - Ecublens, CH - 1015 Lausanne, Suisse.
Summary. - 41 burrow systems of the fossorial form of the water vole (Arvicola terrestris
L.), a small rodent inhabiting meadows, pastures and orchards in central Europe, have been ana-
lysed using methods of graph theory. Four main types exist : a) linear structures (trees), b) trees
with a few cycles, c) mixture of linear and cyclic structures, d) essentially cyclic structures. The
intersections with 3 branches clearly predominate (97%). The lengths of the edges (segments joi-
ning a dead-end and an intersection or two intersections) follow an exponential distribution with
a mean and a standard deviation being usually very close. The nest is generally closer to a cen-
tral point than would be expected by chance. The connections between any two intersections or
an intersection and a dead-end can be summarised in the form of an adjacency matrix ; a method
of reducing its size by eliminating the trees connected to the cyclic part was used when compu-
ting the shortest paths, in order to save computing time and space.
Two simulation models are briefly described. The first one is rather simple and produces