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. Author manuscript; available in PMC: 2021 Aug 1.
Published in final edited form as: Ecol Lett. 2020 Apr 28;23(8):1212–1222. doi: 10.1111/ele.13521

Table 1. Variables, parameters, and their definitions in the SIS system of equations.

Parameter values are realistic for plant-pollinator networks. The only exception is Nk, which was adjusted to reproduce realistic values of R0, λ, and mean steady-state prevalence in the models. The value of Nk is much higher than the observed floral abundance in the wildflower plots, due to the fact that the SIS model assumes a closed system, whereas the bees observed did not forage exclusively inside the plot. Therefore, the correct Nk should be one where the plot area has been sufficiently extended to support the population of bees.

Variables and parameters Short description Central value, comments, and reference
yq and ck Fractions of infected/contaminated individuals of bee species q and flower species k
sq and uk Fractions of susceptible/uncontaminated individuals of bee species q and flower species k

Q and K Bee and flower species richness Mean from empirical data
q and k Labels for bee and flower species
Mq and Nk Abundance of bee species q and flower species k Bee abundance 50, order-of-magnitude estimate based on observations at the wildflower plots. Flower abundance 2000 (see caption).
1 / (γq + μq) Reciprocal of the sum of bee recovery and mortality rates 3 days. Central value between species that are non-host vectors (recovery time < 1 day) and species that can develop active infections (if chronic, life expectancy of ~1 month; however, not all exposed individuals become infected, so we chose an intermediate value of 10 days).
1 / ζk Flower decontamination time 3 hours (Figueroa et al. 2019)
αq,k Rate at which uncontaminated flowers of species k become contaminated when foraged on by an infected bee of species q Combination of other parameters αq,k=ηq,kfqrqϕq,k
βq,k Rate at which a susceptible bee of species q becomes infected when foraging on contaminated flowers of species k Combination of other parameters βq,k=ηq,kfqrqψq,k
ηq,k Fraction of foraging time a bee of species q spends on flowers of species k We require that k=1Kηq,k=1
fq Fraction of day bee species q spends foraging 2 hours / day (Otterstatter & Thomson 2008)
rq Foraging rate for a bee of species q 5 flowers / minute, order-of-magnitude estimate based on observations
q,k Bee-to-flower transmission: probability of an infected bee of species q contaminating a single flower of species k when foraging on it 0.01 (Otterstatter & Thomson 2008)
ψq,k Flower-to-bee transmission: probability of a bee of species q becoming infected when foraging on a contaminated flower of species k 0.01 (Truitt et al. 2019)