Appendix B. Equations and development of the temporal estimation of seed banks.
Canopy seed bank estimates
The mean number of full seeds per cone was 19.4 for the live, 21.3 for the 3y-MPB, and 19.5 for the 6y-MPB stands, so for simplicity we used the overall mean (20.1 full seeds per cone) in all estimations. The total number of canopy seeds in a given stand (Sstand canopy (seeds ha-1)) was calculated as:
Sstand canopy = Ctree × D × 20.1
where, Ctree is cones tree-1 and D is stand density (trees ha-1) and Canopy cone openness (%) from Table 1. Annual seed release from the canopy cone fall due to breakage (SRbreakage (seeds ha-1 yr-1)) was calculated as:
SRbreakage = Cbreakage × 20.1
where, Cbreakage is the number of fallen cones through breakage (cones ha-1 yr-1) (Fig. 2). For simplicity, we used constant Cbreakage rates for years 0 to 2, 3 to 4, and 5 to 6, using the rates measured in the different stand types (Figs 2). Annual seed release as a result of canopy cone opening (SRcanopy cone opening (seeds ha-1 yr-1)) was calculated as:
SRcanopy cone opening =  × Sstand canopy
where, Change in canopy cone opennessMBP (% yr-1) is the rate of opening of canopy cones during the 3y-MPB period (Fig. 2). RM lodgepole pine normally increases its canopy cone openness through natural aging of cones in living trees over time (Lamont 1991). We estimated that this natural rate of canopy cone opening is 0.25 % yr-1 based upon the increase in cone openness with age detected in the raw-data scores of cone openness of different cone ages presented in Crossley (1956). This normal increase in canopy cone openness was incorporated into the estimations and applied each year for all three stand types. Percent increase in canopy cone openness level (% canopy cone openness of control live trees in 3y-MPB stands minus % canopy cone openness of 3y-MPB stands, see Fig. 2) resulted from tree death caused by the MPB-outbreak. There appeared to be no incremental increase in canopy cone openness as stands moved from the 3y-MPB to the 6y-MPB status, so this term was not included in the SRcanopy cone opening for the 6y-MPB stand type up to six years.
Pre-dispersal predation is defined as loss of seed (eaten in place) and cones from the canopy by twig cutting by squirrels; these cones are eventually hoarded to a cache. Seeds that are consumed in place in the canopy tree of immature and mature cones were assumed to be negligible since we did not observe residual cone rachi (cone cores) on the forest floor (Steele et al. 2002) after squirrel feeding. Based on the findings of Wheatley et al. (2002) and our field observations (where we usually observed one squirrel along our 100 m long transects) we assumed that all stands had a density of 1 squirrel ha-1. Post-dispersal of cones was defined as predation by squirrels of ground cones from breakage. We avoided using pre-and post-dispersal rates from other studies (for reasons given above, see Discussion). Instead we set our total squirrel predation rate (pre- and post-dispersal) to 50 000 cones year-1 or 1 050 000 seeds year-1 (based on 20.1 full seeds cone-1) in all stand types based on the annual nutritional requirements of a pine squirrel (Lotan 1970) and data from Smith (1968). Annual seed release due to pre-dispersal predation from squirrels (SRpre-predation (seeds ha-1 yr-1)) was calculated as:
SRpre-predation = 1 050 000 – SRpost-predation
where, SRpost-predation (seeds ha-1 yr-1) is seed loss from marked cones that were from breakage (Table 2). We assumed that all cones (i.e., seeds) removed by squirrels would eventually be eaten or rot in the cache. For simplicity, we used constant SRpost-predation rates for years 0 to 2, 3 to 4, and 5 to 6, using the rates measured in the different stand types (Table 2).
Because there were some differences in total numbers of cones on trees in the three stages, we started with a canopy seed bank of 13 406 400 seeds ha-1 (Fig. 3B, Table 4) from year six in the 6y-MPB stage and back-calculated the seed that was lost per year in the 3y-MPB and live stand types on an annual basis. To calculate the canopy seed bank Scanopy (seeds ha-1) at any given year (summing backwards in time to year 0) the following equation was used:
Scanopy at yr = Scanopy at yr+1 + (SRbreakage at yr +1 + SRcanopy cone opening at yr +1 + SRpre-predation at yr+1)
Forest floor-seed bank estimates
The annual of addition to the forest floor seed bank from seed falling directly from the canopy (SFcanopy cone opening) (i.e., widely dispersed seeds) was determined:
SFcanopy cone opening = SRcanopy cone opening × (1- 0.895)
Seed released directly on to the forest floor, canopy coneopening, and cones opening on the forest floor is heavily preyed upon by ground-foraging vertebrates (e.g., mice, voles); we used a predation rate of 89.5 % (seeds yr-1) for the seed released each year base upon values from Pinus contorta forests (Vander Wall 1994, 2008). This predation byground-foraging vertebrates typically occurs within the first few weeks after release (Despain 2001; Vander Wall 2008); this seed was therefore not considered to be part of the seed bank. We generously assumed that 10.5 % of the fallen seeds would be in an annual seed bank. While we recognize that imbibed seeds in the middle of the growing season will either germinate or rot, some of the seeds that is released later in the growing season could be carried-over to the next growing season. However, based on our preliminary findings (Teste et al., unpublished data) the actual amount of seeds carried over is very low; therefore all of this seed added to the forest floor seed bank that was not eaten, remained likely viable for only one year.
The annual addition to the seed bank due to seed release fromopening of ground cones on the forest floor (SFground cone opening (seeds ha-1 yr-1)) (i.e., locally dispersed seed) was calculated as:
SFground cone opening = [SRbreakage × ()] × (1 - 0.895)
where, Δ Ground-cone openness (% yr-1) is based upon the initial ground-cone openness value in June minus the final value for each stand type in late September (values shown in Fig. 2) but are assumed to represent a yearly rate as this is the time of maximum surface heating. All of this added-seed remained viable for only one year.
Embedded and buried seed found each year (in closed and partially open cones) (SFBuried (seeds ha-1)) was derived from the density of embedded and buried cones (CBuried) (embedded and below the moss) and their openness values (CBuried openness) determined for the different stand types (Table 3) and was calculated as follows:
SFBuried = CBuried × [1 – ()] × 20.1
We assumed that some seeds within these embedded and buried cones are viable; we found viable seeds from embedded and buried cones extracted from the forest floor (Teste et al. unpublished). To calculate the total forest floor seed bank SFTotal (seeds ha-1) at any given year the following equation was used:
SFTotal = SFcanopy cone opening + SFground cone opening + SFBuried
British Columbia Ministry of Forests. 1995. Bark Beetle Management Guidebook. [WWW document]. URL http://www.for.gov.bc.ca/tasb/legsregs/fpc/fpcguide/beetle/betletoc.htm
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