Studies included in MASTIF
Previously published studies were incorporated provided that they offer one or both data types having a direct connection to individual tree-year production. The most common reason for excluding a study was the absence of raw data. Observations that connect with whole-tree-yr fecundity are essential; we cannot extract tree-year production from averages per tree, averages per trap or stand, or coefficients of variation. There are many studies in the literature based on tree-year observations for which we could not obtain the original data. Some MASTIF collaborations began with discussions on data availability from published studies.
Some studies have observations at the tree-year scale that do not connect to tree-year production. Some fine studies based on tree counts obtained in ways that do not directly connect to whole tree production had to be excluded. For example, counts per observation time provide a valuable relative estimate for changing production by an individual tree, but they cannot be connected to total crop production by the tree.
Seed trap studies that lack location information either for traps or trees do not allow for estimates of fecundity.
Two classes of observations
The MASTIF analysis uses two main data classes, termed seed-trap data and crop-count data. These data types are treated as conditionally independent given estimated maturation statuses and fecundities of mast-producing trees. Seed-trap data are counts from seed traps within mapped stands. The data model links seed-trap counts to an intensity function for expected seeds per area of ground surface per year. This intensity is linked, in turn, to tree fecundity through a transport model, or dispersal kernel, again, requiring known locations of trees and seed traps.
Crop-count data are counts associated not with surface area of forest floor, but rather with individual trees and years. There are three elements to the data model, the crop count of seeds, fruits, or cones observed, the crop fraction, an estimate of the entire crop represented by the count, and the crop-fraction standard error to allow for uncertainty in the crop fraction.
Crop counts in the MASTIF network are obtained in one of at least three different ways. For many conifers canopies are sufficiently open and cones sufficiently large that they can be counted with binoculars. Examples include the Franklin network, the USFS longleaf network, Duke Forest (DUKE), and all of the NEON sites sampled by us. The crop fraction is the estimate of the entire crop that is represented by the crop count. The crop-fraction standard error assigned to an observation necessarily declines as the crown fraction approaches one. Conversely, the crop fraction standard error is expected to increase as the fraction of the crop declines to zero.
A second crop-count method has been used where conspecific crowns are isolated and wind dispersal is limited. Here the crop fraction is based on the ratio of seed-trap area for traps placed beneath the canopy to the projected crown area. Examples include HNHR (Knops and Koenig 2012) and Katie Greenberg’s acorn mast network that includes BCEF (Rose et al. 2011). The crop-fraction standard error estimate depends on uncertainty in the canopy projection area.
A third crop-count method is based on evidence for past cone production that is preserved on trees. This has been used for Abies balsamea at western Quebec sites (Messaoud et al. 2007) and for Pinus edulis at southwest sites (Redmond et al. 2012). The crop-fraction standard error estimate here can accommodate deteriorating cone evidence with time before counts were obtained.
The crop-count data model
For data sets where both seed traps and counts are available MASTIF integrates them making use of conditional independence (Clark et al. 2019); latent states represented by maturation state and fecundity absorb the marginal dependence between seed-trap and crop-count data.
Crop counts of seeds, fruits, or cones are combined 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 (fruit or cone count), c (seeds per fruit or cone), p (crop fraction), and unknown number of seeds n, the quantity of interest. 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 can additionally assign 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 might be in the range of, say, (0.05 – 0.2).
Where there is no estimated standard deviation, we assigned it. For example, the Franklin network does not include estimates of canopy fraction, reporting instead all cones that could be seen. From our extensive crop counts in this region we synthesized crop fraction estimates and uncertainty for the same species.
In cases where crop counts are taken from traps beneath a tree crown the crop fraction is
p = A_s/A_c.
for total seed-trap collection area A_s and canopy projection area A_c.
The conditional binomial likelihood binom(cy | n, p) is combined with a distribution for crop fraction beta(p | a, b), where parameters (a, b) come from the estimate of p and its standard deviation (through moment matching). Marginalizing the uncertainty in the estimate of the crop fraction p gives betaBinom(y | n, a, b) (Clark et al. 2019).
Specifically about cones
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 have two seeds per bract. To obtain seeds per cone, cones are sampled from multiple individuals and locations and counted.
Cones begin to fall from trees soon after, but, depending on species, may remain on the tree for years. For example, the serotinous cones of P. contorta, P. banksiana, and P. serotina remain on trees, with seeds intact until heated by fire. P. contorta can produce both serotinous cones 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.
Clark, J.S., C. Nunes, and B. Tomasek. 2019. Foodwebs based on unreliable foundations: spatio-temporal masting merged with consumer movement, storage, and diet. Ecological Monographs, in press. Appendix.
Knops, J. M. H., and W. D. Koenig. 2012. Sex allocation in California oaks: trade-offs or resource tracking? PLoS One 7(8): e43492. doi:10.1371/journal.pone.0043492.
Messaoud, Y., Y. Bergeron, and H. Asselin. 2007. Reproductive potential of balsam fir (Abies balsamea), white spruce (Picea glauca), and black spruce (P. mariana) at the ecotone between mixed wood and coniferous forests in the boreal zone of western Quebec. American Journal of Botany 94: 746–754.
Redmond, M. D., F. Forcella, and N. N. Barger. 2012. Declines in pinyon pine cone production associated with regional warming. Ecosphere 3(12):120. http://dx.doi.org/10.1890/ES12-00306.1
Rose, Anita K.; Greenberg, Cathryn H.; Fearer, Todd M. 2011. Acorn Production Prediction Models for Five Common Oak Species of the Eastern United States.