Regulation and Stability of a Free-Living Host-Parasite System: Trichostrongylus tenuis in Red Grouse. II. Population Models

1. The population dynamics of red grouse, Lagopus lagopus scoticus and the parasitic nematode, Trichostrongylus tenuis were explored to determine whether interactions between the parasite and host were sufficient to generate cycles in grouse abundance. Two alternative models were used that explicitly consider the dynamics of either the free-living, or arrested larval stages of the parasite. 2. Providing that the life expectancy of the free-living larvae is more than 2-4 weeks, the parasite can readily establish in grouse populations. Larval arrestment tends to reduce the intrinsic growth rate of the parasite and thus increases the size of the host population required for the parasite to establish. 3. Grouse numbers will tend to cycle when the parasites exhibit low degrees of aggregation and parasite-induced reductions in host fecundity are greater than parasite-induced increases in host mortality. The population cycles produced in the model have the slow increase followed by a rapid decline characteristic of the grouse population studied at Gunnerside. 4. The period of the cycles is determined by the intrinsic growth rate of the grouse population and either larval life expectancy (Model I), or the duration of larval arrestment (Model II). Cycle periods decrease as host population growth rate increases, and lengthen with increases in either free-living larval life expectancy, or the duration of larval arrestment. If the duration of larval arrestment is sufficiently long (>6 months), the cycles die out and the dynamics of the grouse-nematode system are very stable. 5. Estimates of all of the model's parameters may be made from long-term records of grouse populations. Numerical analysis of the model's behaviour suggest that a model with limited arrested larval stages more closely corresponds to the grouse populations in the North of England. The 4-5 year cycles exhibited by these populations will be more sporadic, or absent on estates where the parasite is unable to establish. 6. The analysis shows that the empirical data collected on T. tenuis are consistent with it being the cause of the cycles observed in grouse populations in the North of England.