Fig. 1

Reaction norm models for disease resilience. a–c A model of realized performance in infectious conditions (\({\mathrm{P}}_{\mathrm{PLE}}\)) as it depends on environmental pathogen load (\({\mathrm{PL}}_{\mathrm{E}}\)), host performance potential (\({\mathrm{P}}_{0}\)), host resistance (\(\mathrm{R}\)) and host tolerance (\(\mathrm{T}=-1/\upbeta\); with the slope of the regression of performance versus \(\mathrm{PL}\), \(\upbeta \le 0\)) for two host animals with different levels of \({\mathrm{P}}_{0}\), R and T, exposed to different \({\mathrm{PL}}_{\mathrm{E}}\) levels. \(\mathrm{T}\) and \(\mathrm{R}\) are favourably correlated in (a) and unfavourably in (b) and (c); \({\mathrm{PL}}_{\mathrm{E}}\) is lower in (c) than in (a) and (b). Resistance reduces \({\mathrm{PL}}_{\mathrm{E}}\) to within-host pathogen load (\({\mathrm{PL}}_{\mathrm{W}}\)) with performance recapture along the reaction norm to the \({\mathrm{P}}_{\mathrm{PLE}}\) level. In (a) \({\mathrm{P}}_{\mathrm{0,2}}>{\mathrm{P}}_{\mathrm{0,1}}\), but \({\mathrm{P}}_{\mathrm{PLE},2}<{\mathrm{P}}_{\mathrm{PLE},1}\) because individual 2 is less resistant to infection (lower reduction from \({\mathrm{PL}}_{\mathrm{E}}\) to \({\mathrm{PL}}_{\mathrm{W}}\): \({\mathrm{R}}_{2}<{\mathrm{R}}_{1}\)) and also less tolerant to it (steeper slope: \({\upbeta }_{2}\) is more strongly negative than \({\upbeta }_{1}\)). In (b), the \(\mathrm{T}\) levels are the same as in (a), but \({\mathrm{R}}_{2}>{\mathrm{R}}_{1}\); this causes a stronger reduction from \({\mathrm{PL}}_{\mathrm{E}}\) to \({\mathrm{PL}}_{\mathrm{W}}\) in individual 2, climbing a longer stretch of the reaction norm, and this reduces the \({\mathrm{P}}_{\mathrm{PLE}}\) difference. In (c), \(\mathrm{T}\) and \(\mathrm{R}\) are the same as in (b), but \({\mathrm{PL}}_{\mathrm{E}}\) is lower; hence individual 2′s stronger \(\mathrm{R}\) can now reduce \({\mathrm{PL}}_{\mathrm{E}}\) to a more favourable \({\mathrm{PL}}_{\mathrm{W}}\) level, neutralizing its lower \(\mathrm{T}\); with that its \({\mathrm{P}}_{\mathrm{PLE}}\) becomes higher. (d) A model of improving resilience through increases in \(\mathrm{R}\) and \(\mathrm{T}\) while keeping \({\mathrm{P}}_{0}\) unchanged, see the "Economic values: theory" section below. The starting position (black dot) is based on initial resistance and tolerance levels \(\mathrm{R}\) and \(\mathrm{T}\), with pathogen load \({\mathrm{PL}}_{\mathrm{W}1}\) and performance \({\mathrm{P}}_{\mathrm{PLW}1}\). From there, resistance is increased by \(\mathrm{\Delta R}\) and tolerance from \(\mathrm{T}\) by \(\mathrm{\Delta T}\) to \(\text{T}^{\prime}\) (a move to a shallower reaction norm), leading to a new position following the green arrow, with performance \({\mathrm{P}}_{\mathrm{PLW}2}\) (white dot)