ESM 1a Sensitivity analysis for the change in accuracy of the rule of thumb with multiplicative percent changes in the transmission rate (). The change in 95th percentile discovery-prevalence for the approximation rule of thumb (closed circles) and HLB simulation model (open circles), and their quotient, for a sample size N of 10 and sampling interval Δ of 25 days (A and B), 50 days (C and D), 75 days (E and F) and 100 days (G and H). HLB age class 6-10 is used to provide the default parameter values from which the percentage change is referenced. Page 2.

ESM1b Sensitivity analysis for the change in accuracy of the rule of thumb with multiplicative percent changes in the dispersal scale (1/). The change in 95th percentile discovery-prevalence for the approximation rule of thumb (closed circles) and HLB simulation model (open circles), and their quotient, for a sample size N of 10 and sampling interval Δ of 25 days (A and B), 50 days (C and D), 75 days (E and F) and 100 days (G and H). HLB age class 6-10 is used to provide the default parameter values from which the percentage change is referenced.Page 1.

ESM 1cThe change in the sampling interval Δ (days) required to achieve a discovery-prevalence of 0.001 (0.1%) (left-hand panel) and 0.005 (0.5%) (right-hand panel) for changing total population size and for the different age classes. The sample size N is fixed at 10% and thus changes with total population size accordingly. Page 3.

ESM 1d Additional discussion of results in the context of the assumption of exponential increase made by the rule of thumb approximation.

ESM 1eProbability distributions for discovery-prevalence for the different HLB planting age classes. The mean (equation 6) and 95th percentile discovery-prevalences are shown for the rule of thumb (solid and open circles respectively) and the HLB simulation model (dashed and dotted lines respectively). The sample size N is 50 trees and sample interval Δ 50 days. The different planting age classes are: age 0-2 years (A), 3-5 years (B), 6-10 years (C) and >10 years (D). Discovery-prevalence q* is the fraction of the population infected.Page 5.

ESM 2a The citrus canker Miami study sites. The upper left panel shows the general location of the sites in Florida. The right hand panel shows the location of residential citrus trees (green dots) in each site are citrus trees in residential properties. Black dots denote the location of all infected trees at the end of the observation period. The background is a satellite image of the area. The four study sites are the 4 discrete areas of green host trees from north to south and are named as Miami 1, Miami 2, Miami 3 and Miami 4 respectively. Miami 4 is enlarged on the lower left hand panel to illustrate the finer scale spatial pattern of the citrus trees and terminal distribution of the epidemic. Page 1.

ESM 2bThe change with time in epidemic prevalence for each of the Miami Study sites. The red line denotes the observed epidemic progress curves (change in proportion of infected trees with time) and the black line denotes the logistic fit to the curves as reported in the main manuscript. Page 2.

ESM2cProbability distributions for discovery-prevalence for the different Miami study sites. The mean and 95th percentile discovery-prevalences are shown for the rule of thumb (solid and open circles respectively) and the citrus canker Miami dataset (dashed and dotted lines respectively). The sample size is 50 trees and sample interval 50 days. The study sites are Miami 1 (A), Miami 2 (B), Miami 3 (C) and Miami 4 (D). Discovery-prevalenceq* is the fraction of the population infected. Page 3.

ESM2dThe change in discovery-prevalence with sample size, N. Shown is the rule-of-thumb (mean discovery-prevalence) (equation 6) from the approximation equation (grey triangle) and its 90% confidence interval (5th and 95th percentiles), and the mean discovery-prevalence calculated from the citrus canker Miami data using simple random sampling (red dots) and stratified-random sampling (blue dots). Shown are results for the study sites Miami 1 (A,B), Miami 2 (C,D), Miami 3 (E,F) and Miami 4 (G-H) and for a sampling interval Δ of 25 days (A, C, E, G) and 50 days (B, D, F, H). Note that the difference in y-scale in plots A, C, E, G and B, D, F, H. Discovery-prevalenceq* is the fraction of the population infected.Page 4.

ESM 2eThe change in the sampling interval Δ (days) required to achieve a discovery-prevalence of 0.001 (0.1%) (left-hand panel) and 0.005 (0.5%) (right-hand panel) for changing total population size for each of the Miami sites. The sample size N is fixed at 10% and thus changes with total population size accordingly. Page 5.

ESM3 A single realisation of the HLB epidemic simulation model for Age class 6-10. Left hand panel show citrus planting with healthy trees (green) and infected trees (increasing severity as white to red intensity). The corresponding upper and lower right-hand panels show the corresponding change in incidence and severity respectively with time.