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.