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Fig. 1. Example of a simulated population in Scenario 2. The study area contains a total of 500 10×10 km squares. (A) A given proportion of these squares were chosen to contain damaged trees; the rest contained no damaged trees. Subfigures B-D show a single such 10×10 km square, with damaged trees indicated by black spots. Subfigure B shows a square containing 238 tree damage aggregation centres at the initial time point (TP1). Subfigure C shows an increment in which the intensity of all of the aggregation centres is increased, and 38 of them have increased in radius. Subfigure D shows the resulting population of damaged trees at a subsequent time point (TP2).

Table 1. Parameters for the simulations of damaged trees in Scenario 1, with values set for simulated alternatives of damage level at an initial time point, TP1, and increases to a subsequent time point, TP2.
TP1 Sparse Medium
Min no. trees ha–1 0.5 5
Max no. trees ha–1 2.5 20
Increase Small Large Small Large
Min new trees ha–1 0.05 9 0.5 38
Max new trees ha–1 0.4 20 2 48
Table 2. Parameters for simulations of damaged trees in Scenario 2, with values set for simulated alternatives of damage level at an initial time point, TP1, and increases to a subsequent time point, TP2.
TP1 Sparse Medium
Min no aggregation centres square–1 200 500
Max no aggregation centres square–1 800 1500
Min aggregation centres radius (m) 5 5
Max aggregation centres radius (m) 50 50
Min no trees ha–1 within aggregation centres 100 250
Max no trees ha–1 within aggregation centres 200 350
Increase Small Large Small Large
Prob. change trees ha–1 in aggregation centres 0.55 0.55 0.35 0.55
Min change (relative to TP1) 3 10 5 10
Max change (relative to TP1) 6 20 10 20
Prob. change in aggregation centres radius 0.15 0.15 0.05 0.15
Min relative change in aggregation centres radius 1.5 1.5 1.5 1.5
Max relative change in aggregation centres radius 2.0 2.0 2.0 2.0
Table 3. Mean number of damaged trees ha–1, between square variance and mean within square variance for 100 simulated squares for each alternative of damage level in Scenario 1 and Scenario 2.
  Level at TP1 Level of
increase 		Mean
(trees ha–1) 		Between square
variance 		Mean within square variance
Scenario 1
TP1 Sparse Small 1.5 0.4 6.1
Large 1.4 0.4 5.6
Medium Small 11.6 17.0 44.3
Large 12.7 15.8 48.3
Increase Sparse Small 0.2 0.0 0.8
Large 9.4 4.5 36.2
Medium Small 1.2 0.2 4.8
Large 35.6 31.4 130.2
TP2 Sparse Small 1.8 0.4 6.9
Large 10.8 5.2 41.5
Medium Small 12.8 17.2 48.8
Large 48.3 33.8 170.1
Scenario 2
TP1 Sparse Small 2.1 0.6 67.2
Large 2.0 0.6 63.2
Medium Small 8.2 5.9 518.8
Large 8.9 6.5 565.1
Increase Sparse Small 5.9 4.9 705.6
Large 17.0 42.2 7 046.6
Medium Small 22.2 42.1 9 131.3
Large 75.6 490.9 63 190.1
TP2 Sparse Small 8.0 9.0 1 073.0
Large 19.0 52.5 8 051.9
Medium Small 30.4 79.0 12 241.5
Large 84.4 609.2 72 560.0
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Fig. 2. Relative standard errors of estimators of the number of damaged trees ha–1 at a subsequent time point (TP2) (subfigs. A and C) and the increase, small and large increment, between the initial time point (TP1), at sparse and medium level, and TP2 (subfigs. B and D) for Scenario 1. Subfigures A and B show results obtained when using a sample consisting of a single year’s panel (n = 100), while subfigures C and D show results obtained using the full sample (N = 500).

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Fig. 3. Relative standard errors of estimators of the state at the initial time point (TP1; subfigs. A and B) and the increment, small and large, from TP1 to a subsequent time point (TP2; subfigs. C and D) in relation to the number of damaged trees ha–1 in Scenario 1 for the sparse (subfigs. A and C) and medium (subfigs. B and D) levels of tree damage at TP1. Results are shown for the full sample (N = 500) and a single year’s panel (n = 100).

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Fig. 4. The power to detect an increase in the number of damaged trees per hectare that exceeds 1 new damaged tree ha–1 in Scenario 1 (subfigs. A and C) and Scenario 2 (subfigs. B and D). Subfigs. A and B show the results for the sub-scenario with a sparse initial damage level while subfigs. B and D show the results for the sub-scenario with an intermediate initial damage level. Results are shown for a small and a large increment between the initial time point (TP1) and a subsequent time point (TP2). Data for the sub-scenario involving a small increment between TP1 and TP2 are omitted in the left hand figure, since the increase never exceeded 1 tree ha–1 in this case.