Disease and thermal acclimation in a more variable and unpredictable climate

Supplementary Methods Modeling methods: We used a mathematical model to describe how the timescale and predictability of temperature variation should interact to influence the geometric population growth rate (G) of a microparasite within a host, assuming the same level of parasite exposure for all hosts. In this model, we explored the consequences of differential rates of parasite and host acclimation for parasite population growth, assuming that both parasite infectivity and host resistance increase with time following a temperature shift. In the context of this model, parasite infectivity (I) refers to the geometric population growth rate of a microparasite in the absence of host resistance, and host resistance (R) refers to the effectiveness of the host immune system and/or behavioral avoidance mechanisms at reducing parasitic growth. R is bound between 0 (completely ineffective at reducing parasitic growth) and 1 (completely resistant to infection). I is constrained to be greater than 0, and I > 1 indicates positive population growth of a microparasite when R = 0. Parasite population growth is then modeled as a function of parasite infectivity and host resistance such that: GG = II I (II × RR) (1) Rather than model temperature effects explicitly, we made the simplifying assumption that parasite infectivity or host resistance each starts at some low “unacclimated” level following any unpredictable temperature shift, and then gradually increases to a higher “acclimated” level given sufficient time at the new temperature (Supplementary Fig. 1a). We modeled the increase in infectivity and resistance through time (I = i{t} and R = r{t}) as logistic functions starting at low initial values (i0 and r0) and approaching higher levels as acclimation time grows large (i{t∞} or r{t∞}). Each logistic curve has two parameters, the half-saturation point M (the time at which infectivity or resistance is half-way to being fully acclimated) and rate constant λ, which controls the degree of curvature. We used λ = 6 in all simulations.