Table 1. Nearest neighbor analysis of attack patterns of Ips typographus at three attack densities on Norway spruce logs (90 by 19 cm diam) in southern Norway (8-13 June 1983) | ||||
Neighboring attacks | ||||
---|---|---|---|---|
N1 | N2 | N3 | N4 | |
47 Attacks in log A (0.90 per dm2) | ||||
Expected distance | 5.26 ± 0.79a | 7.89 ± 0.82 | 9.87 ± 0.83 | 11.51 ± 0.84 |
Observed distance | 5.69 ± 0.69 | 8.44 ± 0.73 | 10.23 ± 0.77 | 11.90 ± 0.82 |
c value (Thompson, 1956)b | 1.0645 | 1.3056 | 0.8559 | 0.9115 |
P valuec | 0.287 | 0.192 | 0.392 | 0.362 |
101 Attacks in log B (1.99 per dm2) | ||||
Expected distance | 3.54 ± 0.36a | 5.32 ± 0.38 | 6.64 ± 0.38 | 7.75 ± 0.38 |
Observed distance | 4.22 ± 0.34 | 5.64 ± 0.31 | 6.95 ± 0.30 | 8.21 ± 0.32 |
c value (Thompson, 1956)b | 3.669 | 1.691 | 1.573 | 2.345 |
P valuec | < 0.001** | 0.091 | 0.116 | 0.019* |
179 Attacks in log C (3.17 per dm2) | ||||
Expected distance | 2.81 ± 0.22a | 4.22 ± 0.22 | 5.27 ± 0.23 | 6.15 ± 0.23 |
Observed distance | 3.65 ± 0.20 | 4.82 ± 0.22 | 5.82 ± 0.23 | 6.66 ± 0.24 |
c value (Thompson, 1956)b | 7.646 | 5.284 | 4.754 | 4.399 |
P valuec | < 0.001** | < 0.001** | < 0.001** | < 0.001** |
Table 2. Comparison of observed average distances to the four nearest neighbors (N1-N4) at three densities of Ips typographus attack with the corresponding values obtained from the simulation model in which the minimum allowed distance to N1 was controlled (from O to 4 cm) | |||||||
Average distance to neighbors (cm) | |||||||
---|---|---|---|---|---|---|---|
Neighbor | Observed distance | Theoretical distance (random) | Simulation of minimum allowed distance to N1a | ||||
0 | 1 | 2 | 3 | 4 | |||
47 Attacks in log A (0.90 per dm2 | |||||||
N1 | 5.685 | 5.263 | 5.007 | 5.512 | 5.533* | 5.971 | 6.477 |
N2 | 8.442 | 7.894 | 7.725 | 8.088 | 8.073 | 8.201* | 8.777 |
N3 | 10.230 | 9.868 | 9.688 | 10.042 | 9.884 | 10.148* | 10.519 |
N4 | 11.896 | 11.512 | 11.452 | 11.733 | 11.492 | 11.852* | 11.999 |
101 Attacks in log B (1.99 per dm2 | |||||||
N1 | 4.223 | 3.544 | 3.480 | 3.696 | 3.935* | 4.450 | 5.072 |
N2 | 5.642 | 5.315 | 5.451 | 5.552 | 5.598* | 5.796 | 6.209 |
N3 | 6.953 | 6.644 | 6.874 | 6.675 | 6.901* | 7.120 | 7.288 |
N4 | 8.212 | 7.751 | 7.855 | 7.774 | 7.796 | 8.156* | 8.229 |
179 Attacks in log C (3.17 per dm2 | |||||||
N1 | 3.654 | 2.810 | 2.680 | 3.096 | 3.359* | 3.976 | 4.522 |
N2 | 4.815 | 4.216 | 4.195 | 4.556 | 4.583* | 4.907 | 5.199 |
N3 | 5.822 | 5.269 | 5.227 | 5.539 | 5.560 | 5.733* | 5.931 |
N4 | 6.658 | 6.147 | 6.087 | 6.462 | 6.342 | 6.542* | 6.678 |
Table 3. The quadratic regression of the simulated values in Table 2 and the observed average distances to neighbors in Ips typographus were used to determine the hypothetical minimum allowed distance to the nearest neighbor | ||
Neighbor | Quadratic regression equationa | Calculated minimum allowed distance (X)b in cm |
---|---|---|
47 Attacks in log A (0.90 per dm2 | ||
N1 | Y = 0.0299X2 + 02202X + 5.080 | 2.13(1.04-3.05)c |
N2 | Y = 0.0406X2 + 0.0591X + 7.811 | 328(1.93-4.28) |
N3 | Y = 0.0326X2 + 0.0465X + 9.768 | 3.12(0.98-4.43) |
N4 | Y = 0.0238X2 + 0.0262X + 11.511 | 3.51(0.31-5.25) |
101 Attacks in log B (1.99 per dm2 | ||
N1 | Y = 0.0777X2 + 0.0829X + 3.494 | 2.58(2.19-2.92) |
N2 | Y = 0.0554X2 - 0.0457X + 5.480 | 2.17(0.90-2.85) |
N3 | Y = 0.0519X2 - 0.0804X + 6.821 | 2.55(122-324) |
N4 | Y = 0.0461X2 - 0.0716X + 7.828 | 3.77(3.10-4.31) |
179 Attacks in log C (3.17 per dm2 | ||
N1 | Y = 0.0439X2 + 02810X + 2.702 | 2.45(224-2.65) |
N2 | Y = 0.0114X2 + 0.1905X + 4.239 | 2.61(2.16-3.05) |
N3 | Y = -0.0054X2 + 0.1819X + 5.267 | 3.39(2.61-422) |
N4 | Y = -0.0113X2 + 0.1713X + 6.147 | 4.08(2.78-6.38) |
John A. Byers Department of Animal Ecology, Lund University, SE-223 62 Lund, Sweden Present address: |
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