Ecological Archives E088-070-A1

Steven I. Higgins, William J. Bond, Edmund C. February, Anfries Bronn, Douglas I. W. Euston-Brown, Beukes Enslin, Navashni Govender, Louise Rademan, Sean O'Regan, Andre L. F. Potgieter, Simon Scheiter, Richard Sowry, Lynn Trollope, and Winston S. W. Trollope. 2007. Effects of four decades of fire manipulation on woody vegetation structure in savanna. Ecology 88:1119–1125.

Appendix A. Estimating tree height.

Size class, but no height data was collected in the time 1 surveys. The size classes are summarized in Table A1 of this appendix. For multi-stemmed individuals canopy diameter classes were used, while for single stemmed individuals stem diameter classes were used. To simplify the analysis of these data we transform the size classes into height by using the relationship between height and size class which is defined by the time 2 survey (the second survey recorded both size class and height). We prefer to do this transformation in a non-parametric way because this makes no assumptions about how the data are distributed. The only assumption made is that the relationship between size class and height has not changed over the course of the experiment.

Pseudo-code for the non-parametric method of estimating height from size class is:

For landscape p=1:4
For plot j=1:12
For size class i=1:8
Sample n heights from hi=(h1,h2,h3,...hN)
end i
to generate ĥj,p=(ĥ1,ĥ2,ĥ3,...ĥZ)
end j
end p

where i is one of the size classes defined in Table 1, n is the number of individuals in size class i in plot j at time 1; hi=(h1,h2,h3,...hN) is the empirical distribution of heights in size class i in landscape p observed at time 2, N is the total number of stems in size class i in landscape p at time 2, ĥj,p=(ĥ1,ĥ2,ĥ3,...ĥZ) is the estimated empirical distribution of heights at time 1 in plot j of landscape p, and Z is the number of stems in plot j at time 1.

We tested this algorithm by using it to estimate time 2 height distributions from time 2 size class information. We then compared the estimated distributions to the observed distributions. In all cases there was a strong correlation (>0.99) between the estimated and observed empirical probability distribution of heights. Moreover, there was no evidence of bias (under or over-predicting the proportion of large or small trees).

TABLE A1. Description of the size classes used in the vegetation surveys. Classes 1–3 are canopy diameter classes, whereas classed 4–8 are stem diameter classes.

Size Class

Diameter (cm)

Single-stemmed

1

0.00 – 30.48

No

2

30.48 – 91.44

No

3

> 91.44

No

4

0.00 – 2.54

Yes

5

2.54 – 7.62

Yes

6

7.62 – 12.7

Yes

7

12.7 – 17.78

Yes

8

> 17.78

Yes


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