Table 1.

Parameters for the theoretical model

Parameter/variable	Description
S, I j, I MP,  N	Number of hosts that are: susceptible, infected by species j, infected by both species, alive (total)
a	Maximum per‐capita host birth rate
$\mathit{}\stackrel{\sim }{\mathbf{b}},\mathit{b}(\mathit{x})$	Host natural mortality rate: baseline, trade‐off for hosts with strategy x
${\mathit{c}}_{\mathit{j}}^1$	Strength of trade‐off for species j
${\mathit{c}}_{\mathit{j}}^2$	Shape of trade‐off for species j
f j, f MP	Relative fecundity for hosts infected by: species j, both species
q	Density‐dependence coefficient
${\mathit{\alpha }}_{\mathit{j}},\mathit{}{\mathit{\alpha }}_{\mathit{M}\mathbf{P}}$	Additional mortality rate for hosts infected by: species j, both species
${\mathit{}\stackrel{\sim }{\mathbf{\beta }}}_{\mathit{j}}$	Baseline transmission rate for species j
β M(x, y)	Transmission rate for defensive mutualists with strategy y when hosts have strategy x
β P(y)	Transmission rate for parasites when hosts are infected by defensive mutualists with strategy y
γ j	Recovery rate for hosts infected by species j
λ M(x, y)	Force of infection for the defensive mutualist when hosts and defensive mutualists have strategies x and y, respectively
${\mathit{\lambda }}_{\mathit{P},\mathit{S}},{\mathit{\lambda }}_{\mathit{P}}(\mathit{y})$	Force of infection for the parasite when hosts are: susceptible, already infected by defensive mutualists with strategy y
ν	Host birth rate: $\nu =(a-qN)(S+f_M{I}_M+f_P{I}_P+f_{\mathit{MP}}{I}_{\mathit{MP}})$
x	Host susceptibility strategy to protective parasite/defensive mutualist
y	Strength of protection conferred to the host