Calculation of population-level onset, median, and termination dates of flowering
For each population of each species described above, we calculated a distribution of individual-level peak flowering dates—assumed to be normally distributed (Clark and Thompson 2011)—based on the flowering attributes of the species and the temperature conditions corresponding to its site and year of observation. First, we calculated the median flowering DOY at the location and year from which each specimen was collected based on its pre-defined intercept and phenological responsiveness to mean annual temperature (i.e., 1, 4, and 8 days per °C, Fig. 1a). Then, we obtained the standard deviation of each local population (i.e., its degree of intrapopulation variation in flowering dates) based on the flowering attributes of the simulated species as outlined above. Next, we arbitrarily defined population-level flowering onset DOYs for each population and year as the 10thpercentile of a normally distributed population whose mean and standard deviation we obtained in the previous steps (i.e., the DOYs by which the first 10% of individuals in a local population at a givenlocation and year would have reached their median flowering dates). Similarly, the population-level flowering termination dates were calculated as the 90th percentile of a normally distributed population with the same characteristics as described above (i.e., the DOYs by which all but 10% of individuals in a local population at a given location and year would have reached their peak (or mean) flowering dates).
Through this process, we obtained a sample of 1000 annual population-level distributions of flowering dates for each of 1200 hypothetical species. For each of these populations, the quantiles of their flowering distribution—representing the nthindividual reaching peak flowering within a population)—were known a priori, representing a benchmark against which to compare estimates derived from simulated specimen data.