Female cones typically expand from buds in the spring, remaining small and closed for the first year. Pollination occurs the second year, after which cones expand rapidly and then brown as they mature. Cones can begin to open in fall of this second year, but seeds may release throughout winter. Cones begin to fall from trees soon after, but, depending on species, may remain on the tree for years. For example, P. echinata trees hold cones for many years. The serotinous cones of P. contorta, P. banksiana, and P. serotina remain on trees, with seeds intact until heated by fire.
Our cone counts record an estimate of the number of cones seen through binoculars together with the fraction of the crop that the count represents. This is the basis for a conditional binomial likelihood in model fitting, binom(yc|n, p), with known y (cone count), c (seeds per cone), and p (crop fraction) and unknown n. We count both the number of green, unopened cones that will open this year and the brown cones that opened last year. The count of cones opened last year is a minimum count, because some cones may have already fallen.
The crop fraction p is an estimate of how much of the crop has been observed and thus has uncertainty. When the entire crop is visible, p = 1, and uncertainty in p is zero. However, when a value is assigned of, say, p = 0.5, then the observer additionally assigns a standard deviation representing her uncertainty in p. If p is believed to fall within an interval (0.4, 0.6] then the standard deviation in p could be 0.1.
The likelihood is then a betaBinom(yc | n, a, b), where parameters a and b come from the estimate of p and its standard deviation (through moment matching), and the beta-Binomial marginalizes this uncertainty in p.
Cones have two seeds per bract. To obtain seeds per cone, cones are sampled from multiple individuals and locations and counted.
Serotinous species like P. contorta can produce both serotinous cones, which remain closed and attached to the stem until opened by heat during fire, and non-serotinous cones, the latter opening in autumn and releasing seeds like most other species. The proportions of serotinous and non-serotinous cones varies by individual tree. For these species, we record each individual as serotinous, non-serotinous, or mixed.
Seed predation begins in the canopy, where squirrels dismember cones and song birds can extract seeds after cones open and before seeds are dispersed. Uncertainty in the model has to allow for variation in seeds per cone, in addition to cone production and seed dispersal. Due to canopy predation, seed trap counts are conservative.