Ecological Archives E088-155-A1

Jason Matthiopoulos, Kate Graham, Sophie Smout, Christian Asseburg, Stephen Redpath, Simon Thirgood, Peter Hudson, and John Harwood. 2007. Sensitivity to assumptions in models of generalist predation on a cyclic prey. Ecology 88:2576–2586.

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
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


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