Population Fluctuations in Red Grouse: Analysis of Bag Records and a Simulation Model

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Abstract
A time-series analysis of numbers of red grouse (L. lagopus) shot per annum was carried out for 52 moors in northern England [UK] where data were available for at least 20 consecutive years during the period 1870-1977. Correlograms were constructed and auto-correlation coefficients were tested for statistical significance. In the most representative sub-sample of moors, 83% of the series had significant negative coefficients at T + 2 or T + 3 years or both. A mathematical model was fitted to the fluctuations to describe their quasi-cyclic nature and the average cycle-length was 4.84 .+-. 0.086 yr. Field observations and data from trials with captive grouse were combined to construct a simulation model of a red grouse population; its main features were: an inverse logistic curve relating mean numbers of the parasitic nematode Trichostrongylus tenuis in adult red grouse to their breeding success; T. tenuis accumulation by young red grouse to steady state levels (the numbers of worms accumulated per bird varied according to a combined effect of the density of grouse prior to the breeding season and the worm burden of these grouse); a logisitic curve relating the proportion of grouse shot with the density of grouse available; and an annual survival rate of the non-shot population inversely proportional to the density of old grouse. The simulation model successfully captured mean levels and other population parameters, but it fit well to observed fluctuation patterns only when stochastic elements were introduced to represent known effects of weather. The model showed that red grouse cycles could be caused by effects of T. tenuis working together with stochastic elements and a time delay arising from the uptake of worms.