Data analyses
We used hierarchical mixed-effect models to test for differences in i)p CA quantity between Pinus pollen produced in 2013 and 2014 and between Pinus species (inter-annual and inter-specific variability study), ii) p CA quantity between shaded and fully sun-exposed pollen of Pinus sylvestris (ambient solar radiation exclusion experiment). In both experiments tree was set to random effect, and differences in p CA abundance were tested in samples from trees between (i) different years and (ii) shaded and unshaded treatments (both set as fixed effects). Parameters of the model were estimated using Bayesian inference. In both cases, our model essentially replicates a t-test with the trees set as a random effect to account for potential individual-level effects related to, for example, local adaptation (Bell et al., 2018). Bayesian inference was used to characterise uncertainty at different parts of the analytical process, and was based on three main components characterising variance in the pollen picking procedure, the GC-MS instrument, and the variance in the sample (see Fig. S1 in Supporting Information).
A Bayesian framework was used because of the challenges related to the precise quantification of pollen grains using the py-GC-MS technique, for which replication is realistically achievable to a relative standard deviation of ~ 5% (Seddon et al., 2017). Our hierarchical modelling approach enables us to incorporate an additional sub-model to account for this uncertainty, and provides the first quantitative solution to a component-based proxy system model outlined in Seddon et al. (2019). Differences between years or treatment were based on Bayesian 95% credible intervals (CRIs), which contain 95% of the values from the posterior distribution of parameter estimates, and are analogous to frequentist 95% confidence intervals (Ellison, 2004). CRIs were calculated based on the posterior. For further details about the statistical model developed, see Supporting Information. All statistical analyses were performed in RStudio (RStudio Team, 2015) using the R statistical software package version 3.3.1 (R Core Team, 2017).