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).