A Simulation Model of the Population Dynamics and Evolution of Myxomatosis

Abstract

Myxoma virus was released into Australia to control the introduced European rabbit, Oryctolagus cuniculus. Within a few years after introduction, the virulence of the virus had declined to an intermediate level, while the resistance of field rabbits and increased sharply. In the nearly 40 yr since the disease was introduced, host resistance has continued to increase, while viral virulence has only recently begun to show signs of counter—increases in some areas. The two questions of interest are thus: Is this system in a coevolutionary arms race (Dawkins and Krebs 1979); that is, will both host and pathogen continue to evolve antagonistically? Will the virus continue to control the rabbit in the future? We present a simulation model based loosely on previous host–pathogen models (Anderson and May 1979), but with detailed accounting of the virus titer in infected hosts, and using realistic estimates of the demographic parameters of the rabbit, including age structure and seasonally varying reproduction. For a single virulence grade, by varying the non—disease (or "natural") mortality of the rabbit, the age at first reproduction of the rabbit, and the virulence grade of the virus, we explored the parameter range for which the rabbit population is controlled. For the most prevalent grades of the virus, grades IIIB and IV, the virus can control the rabbit for most realistic values of natural mortality and age at first reproduction. However, control is dependent on both natural mortality and virus virulence. Since natural mortality varies both geographically and seasonally, the usefulness of the virus may vary geographically and seasonally, and management policies must be sensitive to this variation. When competing against several virus strains that together encompass the complete range of virulence seen in the field, a strain of grade IV virulence competitively excludes strains of all other grades. This competitively dominant grade is close to the most prevalent virulence grades seen in the field. We discuss possible mechanisms of coexistence, including local competitive exclusion with global persistence, variability in host resistance, high mutation rates, and trade—offs between within—host and between—host competitive ability. By examining the effects of flea transmission efficiency, we are able to show that, contrary to commonly held belief, whatever effect fleas have upon the outcome of selection on virulence cannot be due to differences in transmission efficiency between fleas and mosquitoes. Finally, by including host resistance, we improve our prediction of the most prevalent grade of virulence. We conclude that control of the rabbit by the virus is likely for the near future, but that until we understand the genetics of resistance in the rabbit and the relationship between resistance and virulence for different grades of virulence, for different grades of virulence, we cannot make a useful prediction of the long—term state of this system.