Barley yellow dwarf is a widespread disease that affects small
grains and many grass species, as well as wheat, barley and oat. The disease is
caused by an aphid transmitted virus. Rochow conducted a study near Ithaca, New
York, which showed that a shift in the dominant strain occurred between 1957
and 1976. Motivated by this phenomenon, we develop a model for the competition
between different strains of the barley yellow dwarf virus. Our main goal is to
understand the phase diagram of the model, that is, to identify parameter
values where one strain competitively excludes the other strain and where both
strains coexist. Our analysis applies to a number of other systems as well, for
example to a model of competition of water flea species studied by Hanski and
Ranta and Bengtsson.