Appendix A. Notation and parameter values used in the paper (state variables in upper case).

Symbol | Definition | Value |

Harrier multispecies functional response (MSFR) |
||

_{} |
Per capita harrier, hourly rates of consumption of grouse, voles and pipits. | |

_{} |
Density of grouse chicks, voles and pipits | |

_{} |
Attack rates for grouse chicks, voles and pipits | 7×10^{-4}, 3.8, 1.8 |

_{} |
Handling time for grouse chicks, voles and pipits | 2.7, 2.2, 1.7 |

_{} |
Shape parameters for three prey species | 2.5, 1.1, 2.0 |

Harrier single-species functional response
(SSFR) |
||

_{} |
Prey density at which consumption is half its maximum value | 51 |

_{} |
Maximum consumption of grouse | 0.2 |

_{} |
Shape parameter for functional response | 5.1 |

Parasite model for grouse dynamics |
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N |
Grouse density | |

D |
Free-living parasite larvae | |

T |
Adult parasites | |

b |
Grouse fecundity | 1.8 |

d |
Grouse mortality | 1.03 |

v |
Density-dependent reduction in grouse breeding success | 2×10^{-3} |

_{} |
Parasite pathogenecity | 2×10^{-4} |

_{} |
Parasite reduction in host fecundity | 5×10^{-4} |

_{} |
Parasite fecundity | 8.5 |

_{} |
Transmission constant | 90 |

_{} |
Adult worm mortality | 1.24 |

_{} |
Arrested larvae mortality | 0.6 |

_{} |
Rate at which arrested larvae develop into worms | 25 |

_{} |
Aggregation of parasites in hosts | 0.5 |

Aggressiveness model for grouse dynamics |
||

N |
Grouse density (territorial males only) | |

A |
Aggressiveness of male grouse | |

b |
Grouse rearing success (male offspring only) | 1.5 |

s |
Survival of territorial males | 0.5 |

_{} |
Maximum and minimum annual increases in aggressiveness | 1.73, 0.97 |

_{} |
Equilibrium male density | 25 |

C |
Shape parameter for interaction between density and aggressiveness | 15 |

_{} |
Strength of density dependence | 0.1 |

_{} |
Shape parameter for generalized Beverton-Holt density dependence | 1 |

_{} |
Timing parameter for delayed density dependence | 0.3 |

Phenomenological model for grouse dynamics |
||

N |
Grouse density | |

b |
Brood size per grouse parent | 2.61 |

s |
Grouse survival | 0.5 |

r |
Saturation parameter for density dependence | 3.5×10^{-3} |

n |
Exponent parameter for density dependence | 6 |

Other notation |
||

H |
Harrier density | |

q |
No. hours spent by a harrier foraging for grouse chicks each year | 900 |