How did the Rabbits in Australia upset the Balance of Nature?

In Australia in the 1950s, the rabbit population was so large that they ate the land bare and erosion set in, making the land infertile. The government attempted to reduce the rabbit population by introducing foxes, wire fences and poisons, but nothing worked. Finally, they intentionally infected rabbits in the most populated areas. The virus was transmitted from rabbit to rabbit by insects. Over the next three years rabbits died by the millions, agriculture rebounded and everybody was happy.

Then, unfortunately, there was a sudden upset in the balance of nature. The Explorit Science Center reports that the virus had been successfully introduced into European rabbits too and, "with a scarcity of rabbits, foxes began eating poultry, rats and mice. The resulting reduction in the numbers of mice caused a decline in the numbers of owls whose normal diet (mice) became less abundant" - and this disruption continued down the food chain (explorit.org).