Ecological Archives M081-019-A3

Nathan L. Stephenson, Phillip J. van Mantgem, Andrew G. Bunn, Howard Bruner, Mark E. Harmon, Kari B. O’Connell, Dean L. Urban, and Jerry F. Franklin. 2011. Causes and implications of the correlation between forest productivity and tree mortality rates. Ecological Monographs 81:527–555.

Appendix C. Case study methods.

Minimum dbh for our analyses of both data sets was 5 cm, determined by the minimum dbh measured in Oregon and Washington (though minimum dbhs of the complete BCI and California data sets were 1 and 0 cm, respectively). Based on available literature (e.g., Clark and Clark 1999), we judged that calculated tree diameter growth rates (described below) of <-2 or >40 mm/yr resulted from unacceptably large measurement errors; we therefore removed such trees from all analyses (1.8% and 1.3%, respectively, of BCI and Pacific States trees). Both the BCI and Pacific States data sets included only free-standing tree species, not lianas. For BCI, our final data set (after removal of species for which shade tolerance data were not available; see below) included two species of palms, comprising 1% of measured stems. A majority of these palms showed positive diameter growth, so all were retained in the data set.

We wished to have (1) a size class corresponding to overstory trees (≥50 cm dbh), (2) a size class corresponding to small understory trees (those most likely to be suppressed; <15 cm dbh), (3) a diameter growth-rate class corresponding to trees growing slowly enough to have notably enhanced mortality rates (<2 mm/yr), and (4) when possible, >100 living trees within each GS group for a forest, allowing mortality rates within GS groups to be calculated with reasonable confidence. Given these constraints, we defined three tree diameter growth-rate classes (-2 to <2, 2 to <6, and 6 to 40 mm/yr) and three size classes (5 to <15, 15 to <50, and ≥50 cm dbh), for a total of nine GS groups. We also explored using more classes, or somewhat changed boundaries between classes, and got qualitatively similar results.

For all plots, we used the three most recent censuses for which data were available at the time of our analyses (referred to as censuses 1, 2, and 3); census years are given in Appendix B. Only trees alive and with dbh ≥5 cm at census 2 were analyzed across the three censuses.

The first census interval (censuses 1 to 2, the “growth interval”) was used to calculate growth rates by subtracting each tree’s dbh at census 1 from its dbh at census 2, then dividing by years elapsed. The growth interval was 5.3 yr at BCI, and averaged 5.5 yr in the Pacific States plots (range, 4 to 10 yr). At BCI, 147 trees with dbh ≥5 cm at census 2 were of unknown dbh at census 1, having not yet reached the minimum 1 cm dbh for inclusion in the broader BCI data set. To grow from <1 to ≥5 cm dbh over the 5.3-year growth interval, these trees had diameter growth rates >7 mm/yr; all were therefore assigned to the 6 to 40 mm/yr class. This was not an issue in California, where all trees with dbh ≥5 cm at census 2 had already reached breast height (the minimum size for inclusion in the broader California data set) at census 1. Finally, in Oregon and Washington 1228 trees with dbh ≥5 cm at census 2 were of unknown dbh at census 1, having not yet reached the minimum 5 cm dbh for inclusion in the Oregon and Washington data. For calculating proportions of trees within the various GS groups, we assigned these trees to growth rate classes in the same proportions as the equivalent trees in the California data set (i.e., those California trees with dbh <5 cm at census 1, dbh ≥5 cm at census 2).

The second census interval (censuses 2 to 3, the “mortality interval”) was used to calculate mortality rates for the entire forest and for individual LH and GS groups. The mortality interval was 4.8 yr at BCI, and averaged 5.4 yr in the Pacific States plots (range, 4 to 7 yr). Mortality rates, m, were calculated as 1 - (s / n)1/t where n is the number of living trees at census 2, s is the number of those trees surviving to census 3, and t is the length of the mortality interval in years. Because our interests ultimately lay with forest structure and biomass dynamics rather than the fates of genetic individuals (i.e., ramets rather than genets), we counted as dead all trees whose main stems died during the mortality interval, whether or not resprouts or living branches were present below breast height. Because the mortality intervals for plots in the Pacific States varied from four to seven years, we calculated combined mortality rates among plots, weighted according to the number of trees in each plot, as follows. First, m was calculated separately for an individual plot based on the length of its particular mortality interval, then was multiplied by n for that plot. This annualized the absolute number of trees that died in the plot. This annualized number was then summed across all Pacific States plots and divided by n summed across all plots, yielding m for all Pacific States plots combined.

When calculating mortality rates for Pacific States GS groups, we excluded the 1228 Oregon and Washington trees with dbh <5 cm at census 1, as we could not determine growth-rate classes for these trees individually. However, exclusion of these trees almost certainly had no major effect on results. First, the excluded trees comprised <5% of Pacific States trees. Second, two-tailed randomization tests of living and dead California trees (with replacement, 10,000 iterations), all of which could be assigned individually to growth-rate classes, indicated no differences in calculated mortality rate within any given GS group whether trees <5 cm dbh at census 1 were included or excluded (P = 0.78 to 1.00).

The 4340 BCI trees belonging to species that were not classified according to shade tolerance all belonged to uncommon species – those with too few individuals to determine shade tolerance (Welden et al. 1991). To help judge whether the absence of these unclassified trees might affect our analyses and conclusions, for the classified and unclassified trees we compared proportions of trees belonging to canopy and subcanopy species, and mortality rates. Proportions differed little: 34 and 38% of trees belonged to canopy species (66 and 62% to subcanopy species), respectively, for trees that were unclassified and classified according to shade tolerance. Unclassified trees had a somewhat lower mortality rate than classified trees: 2.03 and 2.22% yr-1, respectively. Given that differences in proportions and mortality rates were small, and that unclassified trees comprised only 9% of BCI trees otherwise available for analysis, we judged that absence of the unclassified trees was unlikely to significantly affect our conclusions.


Clark, D. A., and D. B. Clark. 1999. Assessing the growth of tropical rain forest trees: issues for forest modeling and management. Ecological Applications 9:981–997.

Welden, C. W., S. W. Hewett, S. P. Hubbell, and R. B. Foster. 1991. Sapling survival, growth, and recruitment: relationship to canopy height in a neotropical forest. Ecology 72:35–50.

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