6 were maintained individually (with pooled data for stages with n <
6). Matrices with 2 or fewer of 5 stages with n
6 were pooled as shown.Appendix C. A summary of matrices for specific populations and years for Eryngium cuneifolium.
Part 1. A list of matrices with sample sizes (number of columns with n > 6), population identification number (year of last fire), years of data, model phase and time since fire.
|
Matrix |
Stages n > 6† |
Populations (fire year) |
Years‡ |
Phase |
Time since fire |
|
1 |
NA |
Plant and seed survival |
NA |
0 |
0 |
|
2 |
NA |
Seed bank expts |
NA |
1 |
1 |
|
3 |
1 |
57 (93) |
94-95 |
2 |
2 |
|
4 |
Pooled |
57 (93) |
95-97 |
3 |
3-4 |
|
5 |
4 |
72 86) |
90-91 |
4 |
5 |
|
6 |
4 |
85 (86) |
90-91 |
4 |
5 |
|
7 |
4 |
91 (86) |
90-91 |
4 |
5 |
|
8 |
3 |
72 (86) |
91-92 |
5 |
6 |
|
9 |
4 |
85 (86) |
91-92 |
5 |
6 |
|
10 |
4 |
91 (86) |
91-92 |
5 |
6 |
|
11 |
4 |
57 (93) |
98-99 |
5 |
6 |
|
12 |
5 |
16 (84) |
90-91 |
6 |
7 |
|
13 |
4 |
45 (84) |
90-91 |
6 |
7 |
|
14 |
5 |
72 (86) |
92-93 |
6 |
7 |
|
15 |
5 |
85 (86) |
92-93 |
6 |
7 |
|
16 |
5 |
91 (86) |
92-93 |
6 |
7 |
|
17 |
4 |
16 (84) |
91-92 |
7 |
8 |
|
18 |
5 |
45 (84) |
91-92 |
7 |
8 |
|
19 |
4 |
72 (86) |
93-94 |
7 |
8 |
|
20 |
4 |
85 (86) |
93-94 |
7 |
8 |
|
21 |
4 |
91 (86) |
93-94 |
7 |
8 |
|
22 |
3 |
16 (84) |
92-93 |
8 |
9 |
|
23 |
4 |
45 (84) |
92-93 |
8 |
9 |
|
24 |
5 |
72 (86) |
94-95 |
8 |
9 |
|
25 |
4 |
85 (86) |
94-95 |
8 |
9 |
|
26 |
4 |
91 (86) |
94-95 |
8 |
9 |
|
27 |
3 |
16 (84) |
93-94 |
9 |
10 |
|
28 |
4 |
72 (86) |
95-96 |
9 |
10 |
|
29 |
5 |
85 (86) |
95-96 |
9 |
10 |
|
30 |
4 |
91 (86) |
95-96 |
9 |
10 |
|
31 |
3 |
16 (84) |
94-95 |
10 |
11 |
|
32 |
Pooled |
45 (84) |
93-95 |
10 |
10-12 |
|
33 |
4 |
72 (86) |
96-97 |
10 |
11 |
|
34 |
4 |
85 (86) |
96-97 |
10 |
11 |
|
35 |
4 |
91 (86) |
96-97 |
10 |
11 |
|
36 |
4 |
72 (86) |
97-98 |
11 |
12 |
|
37 |
4 |
85 (86) |
97-98 |
11 |
12 |
|
38 |
4 |
91 (86) |
97-98 |
11 |
12 |
|
39 |
3 |
85 (86) |
98-99 |
12 |
13 |
|
40 |
Pooled |
45, 91, 72(86) |
93-99 |
12 |
13 |
|
41 |
Pooled |
16 (84) |
95-99 |
12 |
13 |
|
42 |
5 |
63 (72) |
90-91 |
14 |
19 |
|
43 |
4 |
70 (72) |
90-91 |
14 |
19 |
|
44 |
4 |
63 (72) |
91-92 |
14 |
20 |
|
45 |
Pooled |
70,72(72) |
91-93 |
14 |
20-21 |
|
46 |
5 |
63 (72) |
92-93 |
14 |
21 |
|
47 |
3 |
63 (72) |
93-94 |
14 |
22 |
|
48 |
Pooled |
70,72(72),59,61,63,70,72(72) |
90-91,93-95 |
14 |
22-23 |
|
49 |
4 |
54 (68) |
90-91 |
14 |
23 |
|
50 |
Pooled |
54,57,59,61,63, 70,72(72) |
91-93,95-97 |
14 |
24-25 |
|
51 |
4 |
54 (68) |
92-93 |
14 |
25 |
|
52 |
Pooled |
54,59,61 |
93-95 |
14 |
26-27 |
|
53 |
3 |
54 (68) |
94-95 |
14 |
27 |
|
54 |
Pooled |
54,59,61 |
96-96,97-99 |
14 |
28-31 |
†Out of 5 stages,
not including seed bank. Matrices with 3 of 5 stages having n
6 were maintained individually (with pooled data for stages with n <
6). Matrices with 2 or fewer of 5 stages with n
6 were pooled as shown.
‡Only appropriate combinations of population and year were used.
NA = Data gathered from seed bank experiments or from observations of burned populations.
Part 2. Matrices for Eryngium cuneifolium. Each matrix is specific for a population (or from experiments/scenarios for time-since-fire 0, 1, 3) unless indicated as pooled (see Appendix C part 1 for information on matrices). Time since fire (tsf) is shown for each matrix. Stages (rows, columns) are detailed in Table 3 and Fig. 1. Sample size per stage is indicated in the last row of each matrix.
Double entries for fertility transitions (top row, last three columns) show these two alternatives:
First row: fertility transitions derived from plants used to create bootstrapped confidence intervals. We use these values only in graphs showing bootstrapped confidence intervals around means. These values differ from those in the second row because (in addition to rounding error) bootstrapping simulations could not use plants with missing size and survival data. The differences in finite rates of increase produced by the fertility differences are minor, less than 3% in 52 of 54 matrices, and less than 1% in 47 of 54 matrices. These differences do not explain the bootstrap bias.
Second row: fertility transitions for all available plants, used to calculate finite rates of increase and in stochastic simulations.
Eryngium cuneifolium, tsf 0, matrix 1
0.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Eryngium cuneifolium, tsf 1, matrix 2
0.5
0
0
0
0
0
0.0025
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Eryngium cuneifolium, tsf 2, matrix 3
0.5
29.920
0
0
0.000
0.000
0.0025
0
0
0
0
0
0
0.158
0.000
0.000
0.000
0.000
0
0.026
0.000
0.000
0.000
0.000
0
0.158
0.000
0.000
0.000
0.000
0
0.263
0.000
0.000
0.000
0.000
38
Eryngium cuneifolium-Site 57, 1995–1997, tsf 3–4, matrix 4 (pooled)
339.507
458.334
1336.807
0.5
0
0
442.101
461.199
1321.530
0.0025
0
0
0
0
0
0
0.250
0.500
0.000
0.000
0.000
0
0.000
0.125
0.222
0.200
0.040
0
0.000
0.250
0.444
0.267
0.000
0
0.125
0.000
0.111
0.333
0.920
8
8
9
15
25
Eryngium cuneifolium-Site 72(86), 1990–1991, tsf 5, matrix 5
200.118
366.792
1292.923
0.5
0
0
199.618
361.213
1292.762
0.0025
0
0
0
0
0
0
0.600
0.538
0.105
0.043
0.034
0
0.000
0.077
0.211
0.043
0.000
0
0.200
0.077
0.368
0.217
0.085
0
0.000
0.000
0.105
0.696
0.847
0
13
19
23
59
Eryngium cuneifolium-Site 85, 1990–1991, tsf 5, matrix 6
250.147
589.699
2076.223
0.5
0
0
253.087
589.347
2075.785
0.0025
0
0
0
0
0
0
0.600
0.476
0.105
0.000
0.000
0
0.000
0.333
0.132
0.000
0.000
0
0.200
0.048
0.368
0.185
0.053
0
0.000
0.000
0.368
0.778
0.868
3
21
38
27
38
Eryngium cuneifolium-Site 91, 1990–1991, tsf 5, matrix 7
213.876
532.314
1872.315
0.5
0
0
213.876
532.314
1872.603
0.0025
0
0
0
0
0
0
0.600
0.649
0.150
0.000
0.000
0
0.000
0.243
0.250
0.080
0.000
0
0.200
0.000
0.375
0.160
0.000
0
0.000
0.000
0.150
0.560
0.999
2
37
40
25
33
Eryngium cuneifolium-Site 72(86), 1991–1992, tsf 6, matrix 8
384.448
885.282
2689.799
0.5
0
0
654.564
885.010
2588.837
0.0025
0
0
0
0
0
0
0.745
0.278
0.091
0.056
0.014
0
0.071
0.222
0.477
0.278
0.014
0
0.010
0.111
0.227
0.500
0.127
0
0.000
0.056
0.000
0.056
0.662
4
18
5
18
71
Eryngium cuneifolium-Site 85, 1991–1992, tsf 6, matrix 9
352.410
601.744
2149.086
0.5
0
0
335.862
588.372
2105.881
0.0025
0
0
0
0
0
0
0.745
0.375
0.063
0.061
0.000
0
0.071
0.250
0.438
0.273
0.052
0
0.010
0.125
0.250
0.424
0.247
0
0.000
0.000
0.000
0.061
0.597
1
24
16
33
77
Eryngium cuneifolium-Site 91, 1991–1992, tsf 6, matrix 10
309.669
648.940
2706.920
0.5
0
0
333.411
612.888
2603.546
0.0025
0
0
0
0
0
0
0.745
0.344
0.105
0.000
0.000
0
0.071
0.344
0.632
0.235
0.042
0
0.010
0.063
0.158
0.588
0.104
0
0.000
0.000
0.000
0.118
0.813
1
32
19
17
48
Eryngium cuneifolium-Site 57, 1998–1999, tsf 6, matrix 11
384.448
827.398
5066.537
0.5
0
0
490.310
828.624
4839.360
0.0025
0
0
0
0
0
0
0.739
0.500
0.091
0.125
0.000
0
0.076
0.200
0.477
0.250
0.000
0
0.011
0.050
0.227
0.250
0.083
0
0.000
0.000
0.000
0.250
0.667
92
20
4
8
24
Eryngium cuneifolium- Site 16, 1990–1991, tsf 7, matrix 12
156.135
356.880
943.183
0.5
0
0
155.243
351.527
943.055
0.0025
0
0
0
0
0
0
0.556
0.5
0.063
0
0
0
0.056
0.167
0.188
0
0
0
0
0
0.063
0
0.143
0
0
0
0
0.176
0.714
18
12
16
17
7
Eryngium cuneifolium-Site 45, 1990–1991, tsf 7, matrix 13
151.674
284.389
1100.380
0.5
0
0
156.135
284.612
1100.083
0.0025
0
0
0
0
0
0
0.510
0.517
0.1
0.25
0
0
0.031
0
0.4
0
0
0
0.031
0.069
0.1
0.25
0.083
0
0.010
0
0
0.313
0.75
2
29
10
16
36
Eryngium cuneifolium-Site 72(86), 1992–1993, tsf 7, matrix 14
156.135
391.792
1196.712
0.5
0
0
178.440
386.323
1212.500
0.0025
0
0
0
0
0
0
0.391
0.222
0.000
0.000
0.000
0
0.022
0.222
0.000
0.000
0.000
0
0.043
0.167
0.583
0.261
0.000
0
0.000
0.000
0.083
0.565
0.761
46
18
12
23
46
Eryngium cuneifolium-Site 85, 1992–1993, tsf 7, matrix 15
194.962
350.655
1270.323
0.5
0
0
173.087
363.125
1192.871
0.0025
0
0
0
0
0
0
0.583
0.125
0.074
0.023
0.000
0
0.083
0.438
0.222
0.047
0.000
0
0.083
0.250
0.519
0.512
0.000
0
0.083
0.000
0.074
0.326
0.833
12
16
27
43
42
Eryngium cuneifolium-Site 91, 1992–1993, tsf 7, matrix 16
157.447
353.162
1237.641
0.5
0
0
196.284
341.713
1210.715
0.0025
0
0
0
0
0
0
0.722
0.621
0.265
0.000
0.000
0
0.000
0.207
0.147
0.000
0.000
0
0.000
0.034
0.500
0.458
0.051
0
0.000
0.000
0.029
0.375
0.795
18
29
34
24
39
Eryngium cuneifolium-Site 16, 1991–1992, tsf 8, matrix 17
104.090
507.046
702.607
0.5
0
0
104.387
386.323
703.054
0.0025
0
0
0
0
0
0
0.059
0.391
0.000
0.072
0.125
0
0.118
0.261
0.833
0.080
0.250
0
0.000
0.000
0.000
0.376
0.000
0
0.000
0.000
0.000
0.288
0.625
17
23
6
3
8
Eryngium cuneifolium-Site 45, 1991–1992, tsf 8, matrix 18
89.220
183.688
1022.206
0.5
0
0
89.220
183.793
993.019
0.0025
0
0
0
0
0
0
0.643
0.233
0.167
0.176
0.029
0
0.000
0.067
0.167
0.000