Table 1.

Parameters for equations (2.1)–(2.5). (Our mechanistic susceptible–infected model (equations (2.1)–(2.4)) and corresponding expression for the basic reproduction number (R₀; equation (2.5)) contains 13 parameters, of which six are temperature-dependent arising from four thermal functions (figure 1). We incorporated the thermal dependency of the temperature-dependent parameters using the MTE relationships that were previously determined from experimental data on individual hosts in Kirk et al. [29,30].)

temperature-independent parameters
parameter	description	source	value
ϕS	input of susceptibles	methods used in this study	3.535 day−1
ϕI	input of infecteds	methods used in this study	0.465 day−1
K	adult density-dependent recruitment constraint	abundance measured in this study	170
ψ	maximum per capita recruitment	assumed (such that abundance remains constant near K)	1.33 day−1
h	harvesting	methods used in this study	0.0235 day−1
γ	environmental spore mortality	experimental medium removal rate used in this study	0.0286 day−1
θ	corpse degradation	average from degradation experiment	0.1 day−1
temperature-dependent parameters
parameter	description	source	function	unit
μ(T)	natural mortality rate	[29]	Sharpe–Schoolfielda,b	day−1
χ(T)	contact rate	[30]	Sharpe–Schoolfielda	day−1
σ(T)	probability of infection	[30]	Sharpe–Schoolfielda,b
λ(T)	parasite shedding rate	[29]	Sharpe–Schoolfielda,c	day−1
α(T)	parasite-induced mortality rate	[29]	Sharpe–Schoolfielda,c	day−1
ω(T)	parasite intensity at host death	[29]	Sharpe–Schoolfielda,c

^aSee figure 1 for functional forms.

^bNatural mortality rate and probability of infection were determined by underlying expressions which use Sharpe–Schoolfield functions (see the electronic supplementary material for more details).

^cThe model parameters shedding rate, parasite-induced mortality rate and parasite intensity at death were each modelled as proportional to within-host infection intensity, which is modelled using a Sharpe–Schoolfield function.