Appendix B. Choosing size variables and classes of Chamaecrista keyensis.
Plant size variable selection
Based on survival We used logistic regressions to evaluate which of the three size variables (total stem length, longest stem length, and the number of stems) best predicted annual mortality. In addition, since fires alter mortality, separate logistic analyses were carried out for plants that were subjected to a fire and those that were not (e.g., plants in the control sites and individual plants remaining unburned at burn sites, based on post-burn visual assessments). Before carrying out the logistic regressions, size variables were transformed to make the regressions fit better. In general, cubic root and natural log were the best transformations for longest stem length and total stem length, respectively, for all four years. For the number of stems, which could not be transformed to normality, we used three or four categories in a categorical independent variable. Survival was usually best predicted by total stem length (Table B1).
Estimation of the total stem length of 2001 plants Since only number of stems and longest stem lengths were collected in 2001, we generated a linear regression to predict total length for 2001. We used data from 2000, when all three size variables were collected at the same time of the year as 2001. The 1999 census was conducted two months earlier due to burn events in 1999. The regression included plants with more than one stem only because plants with only one stem have total length equal to the longest stem length. In addition, if an estimated total stem length is longer than the maximum possible total stem length (longest stem length * number of stems), we replace the estimate with the maximum possible value. The equation is as follows (r2 = 0.907):
Ln(total length) = 0.348 + 1.037*ln(longest stem length) + 0.09311*nst.
Although we are aware of the potential bias of our back transformation method, we decided to keep it because the back transformation function recommended by Baskerville (1972) requires estimates of population variance and it was impossible for us to separate measurement variation from true population variation. In addition, our regression function only overestimated mean total stem length by 0.5% when applied to plants of 2000.
Based on fecundity We determined relationships between size variables and fecundity for both qualitative (producing fruit or not) and quantitative (the number of fruits) fruit production variables. For the qualitative fruit production variable, we predicted fruiting from the number of stems, ln total stem length and cubic root longest stem in logistic regression. Separate analyses were carried out for plants burned vs. not burned in the previous year since the influence of burning on reproduction is mostly reflected in the following year. Total length and longest stem length were equally significant predictors of the onset of fruit production (6 out of 7 analyses; Table B2). For quantitative fruit production, we used ANOVA on reproductive plants only. Ln transformed total fruit production was the dependent variable, while number of stems was the fixed factor, and ln total stem length and cubic root longest stem were covariates. Total length was the best and sole predictor of the number of fruit in most years (Table B3).
Size class selection
Application of Moloney algorithm We chose total stem length as the best overall predictor of demographic parameters (Tables B1–B3). We then applied the Moloney algorithm (1986) to define plant size (total stem length) class, using a Pascal program developed by P. F. Quintana-Ascencio. The Moloney algorithm is an optimization algorithm to define size cut-off points that minimize sampling and distribution errors simultaneously for each size class. Since the maximum file size handled by the program was limited, we divided the data into two populations with each containing all 4 censuses (N1 = 966 from Orchid and Poisonwood blocks, N2 = 946 from Iris and Dogwood blocks) and analyzed them separately. Alternatively, we analyzed each of three census periods (census 98-99, 99-00, 00-01) separately. We started by finding the smallest size class. The resultant size cutoff for the first size class was then used as the minimum size for the next size class search. This process was repeated until the remaining number of plants became too small to divide (<20). Scatterplots of cutoff point and the sum of distribution and sampling error were generated for all five files (two of which were divided based on populations and three divided based on census period) to help determine the best size cut-off (e.g., Fig. B1). We generated three cut-off points: 15, 37, and 79 cm, and from these four possible size (total stem length) classes: 1-15, 16 37, 38-79, >79 cm based on the overall information (Table B4).
Table B1. Results of logistic regressions for selection of the best size variable(s) to predict plant survival.
Year
Plant type
No. plots
No. plants
Selected variable(s)
98-99
burned
4
504
Longest stem
unburned
2
265
Longest stem
99-00
burned
2
404
Total length
unburned
10
1214
Total length
00-01
burned
1
93
Total length
unburned
11
1754
Total length, number of stems
Table B2. Results of logistic regressions for selection of the best size variable(s) to predict fruiting (binary, non- seedlings only).
Year
Plant type
No. plots
No. plants
Selected variable(s)
1998
Unburned†
6
588
Total length and longest length
1999
Burned in 98
4
228
Total length and longest length
Unburned in 98
8
1073
Total length, longest length, number of stems
2000
Burned in 99
2
169
Total length
Unburned in 99
10
1225
Total length, longest length
2001
Burned in 00
1
66
Longest length
Unburned in 00
11
1682
Total length, longest length
Note: The selected variables are listed in descending order of significance.
†1998 burns occurred after plant reproduction.
Table B2. Results of logistic regressions for selection of the best size variable(s) to predict fruiting (binary, non-seedlings only).
Year
Plant type
No. plots
No. plants
Selected variable(s)
1998
Unburned†
6
588
Total length and longest length
1999
Burned in 98
4
228
Total length and longest length
Unburned in 98
8
1073
Total length, longest length, number of stems
2000
Burned in 99
2
169
Total length
Unburned in 99
10
1225
Total length, longest length
2001
Burned in 00
1
66
Longest length
Unburned in 00
11
1682
Total length, longest length
†1998 burns occurred after plant reproduction.
Table B3. Results of ANCOVA for selection of the best size variable(s) to predict quantitative fruit production (for reproductive individuals only).
Year
Plant type
No. plots
No. plants
Selected variable(s)
1998
Unburned†
6
62
None
1999
Burned in 98
4
110
Total length
Unburned in 98
8
350
Total length
2000
Burned in 99
2
77
Total length, number of stems
Unburned in 99
10
445
Total length
2001
Burned in 00
1
10
None
Unburned in 00
11
323
Total length
†1998 burns occurred after plant reproduction.
Table B4. Size cut-off points and corresponding sums of errors from the Moloney algorithm with the following parameters: the size of decreasing steps = 1, the number of replicates for calculation = 50, the lower class value = 1, the minimum number of individuals by class = 20.
Output
Population1
Population2
Census1
Census2
Census3
Adopted size cut
Total no. plants
966
946
468
1199
1617
-
Max length (cm)
1243
4160
537
1441
4160
-
1st size cut (cm)
15
2
8
17
5
15
1st cut sum of error
(adopted error)
0.14 (0.14)
0.02 (0.11)
0.04 (0.04)
0.14 (0.15)
0.07 (0.08)
-
2nd size cut(cm)
43
37
38
37
41
37
2nd cut sum of error
(adopted error)
0.07 (0.09)
0.07 (0.07)
0.05 (0.06)
0.14 (0.14)
0.06 (0.07)
-
3rd size cut (cm)
68
79
95
89
69
79
3rd cut sum of error
(adopted error)
0.13 (0.14)
0.09 (0.09)
0.10 (0.11)
0.13 (0.15)
0.09 (0.10)
-
Note: The cutoff that has the local minimum sum of error is given, along with the adopted cutoff and its corresponding sum of error (italics).
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| FIG. B1. Scatterplot of sum of distribution and sampling errors and the smallest size class cutoff of Chamaecrista keyensis based on total stem length (cm) for Orchid and Poisonwood populations. Arrow points to the cut-off with lowest sum of error. |
Baskerville, G. L. 1972. Use of logarithmic regression in estimation of plant biomass. Canadian Journal Forest Research 2:49–53.
Moloney, K. A. 1986. A generalized algorithm for determining category size. Oecologia 69:176–180.