Modelling the kin-selection hypothesis for red grouse population cycles
The periodic fluctuations in numbers of red grouse (Lagopus lagopus scoticus (Lath.)) populations in Scotland and northern England remain a puzzle to population ecologists despite sustained research. Other workers have suggested that territoriality, philopatry and kin selection, as expressed in the differential behaviour between kin and non-kin, can, through their effects on the efficiency of space use, combine to cause cyclic dynamics. However, since the first preliminary formulation of the hypothesis in 1990, little modelling work has been done on the subject. In this thesis, I present a series of models which explore the plausibility of the kin-selection hypothesis for red grouse populations under different assumption regimes. I first develop, analyse and validate a simple, deterministic model using functions of age structure as indexes of the social and, due to philopatry, spatial attributes of the population. A control version of the model is incapable of cyclic dynamics, while a modification, containing the assumed effects of kin selection, produces cycles of realistic period and amplitude. Parameterisation of the model with field data from two studies in north-east Scotland yields output which resembles the observed dynamics. A more detailed study of the possible effects of kin selection and philopatry on individual requirements for space yields a parameterised response function which is then used to study the dynamics of individual family clusters. A model of the relatively short-term process of family cluster formation demonstrates that continuous changes in crowding may have a discontinuous effect on the ability of clusters to form. A socially and spatially explicit simulation model is finally developed to examine the relative importance of these factors in the long-term dynamics. Based on its results, I conclude that spatial heterogeneity in the activity of animals, caused by clustering, is sufficient to produce cycles and that variations in territorial requirements due to differential behaviour between kin and non-kin can have a secondary, amplifying role in the process.