Inhomogeneous spatial point pattern analysis of moso bamboo Phyllostachys edulis

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1 Acta Ecologica Sinica * K Monte-Carlo Inhomogeneous spatial point pattern analysis of moso bamboo Phyllostachys edulis SHI Peijian 1 GUO Shiquan 2 YANG Qingpei 3 * WANG Bing 4 YANG Guangyao 3 FANG Kai 3 1 Institute of Zoology Chinese Academy of Sciences 2 Institute of Educational Science of Longhui County Hunan Province Longhui China 3 Jiangxi Provincial Key Laboratory for Bamboo Germplasm Resources and Utilization Jiangxi Agricultural University Nanchang China 4 Institute of Forest Ecology Environment and Protection Chinese Academy of Forestry Beijing China Abstract Moso bamboo is a plant of significant economic importance. The study of moso spatial distribution is beneficial in order to calculate potential distribution patterns. The spatial distribution of a moso bamboo forest area comprising of varying levels of fertilization was researched using inhomogeneous spatial point pattern analysis. The results show a significant scattered distribution pattern without clustering formation. For obtaining the instensity of moso bamboo the quadratic equation in 2 variables is used to fit the observed data and the goodness-of-fit of moso bamboo instensity is statisfactory. This study illustrates the spatial distribution patterns of moso bamboo as well as the latent potential of varying levels of fertilizer on the spatial distribution of moso bamboo. This has particular significance when considering intensive management practices within bamboo plantations. Moreover in light of the lack of domestic ecosystems research considering heterogeneous point pattern analysis this research aims to extensively popularize the adoption of the methodology throughout domestic ecological research. Key Words inhomogeneous point pattern K function kernel estimation Monte-Carlo simulations moso bamboo 1 2 Ripley K 3 Ripley 2006ABD03A0703 GJJ * Corresponding author. Qingpeiyang@ 126. com

2 K CSR Diggle Chetwynd 4 Cuzick Edwards 5 Diggle Chetwynd 6 Baddeley 7 Ripley K K Diggle 8 Baddeley Gabriel Diggle 9 K 10 Phyllostachys edulis Diggle Chetwynd K ij K ij d = λ - 1 j E n ij n ij i d j d j = 1 j = 2 K 11 d K 22 d K k 11 d = k 22 d = k 12 d D d = K 11 d - K 22 d 0 0 D d 1 2 K^ 11 d = D^ d = K^ 11 d - K^ 22 d n1 n 1 n 1-1 i = 1 n 1 w ij I d ij d j = 1 3

3 16 K^ 22 d = K^ 12 d = n 2 n 2-1 n i = n 1 +1 n1 n n 1-1 n 2-1 n w ij I d ij d j = n 1 +1 i = 1 n n 2 w ij j = n n 1 w ji I d ij d n 1 n 2 n w ij w ji I d ij d 1 0 Diggle Chetwynd D d r - 1 r - 1 D d D d k p k /r p K Baddeley Ripley K K Baddeley Diggle 8 λ x = lim dx 0 λ 2 x y = lim dx 0 dy 0 E N dx { dx } E { } g x y = λ 2 x y λ x λ y N dx N dy dx dy x y λ x 0 g x y = g x - y d K I d = 2π ug u du 0 K I d = πd 2 K I d > πd 2 K I d < πd 2 K I d K^ I d λ = 1 w ij I d ij d n i = 1 j 1 λ x i λ x j Baddeley λ^ h x = n i = 1 κ h x - x i /C h x C h x = A κ h x - u du κ h u = h - 2 κ u /h к u /h u h Baddeley λ^ h x j = n i = 1 i j κ h x j - x i /C h x j

4 A = m m 1 CSR Fig. 1 B1 B R Splancs Spatstat D d Baddeley 3 B1 5m Spatial distribution of moso bamboo 2 D d B2 Fig. 2 Estimated D d of moso bamboo D d B1 B2 λ B1 x y = exp x y x xy y 2 λ B2 x y = exp x y x xy y 2 x y 4 2 P B2 P 4 B2 B1 B2 12

5 Fig. 3 3 Estimated intensity surfaces a. B1 b. B1 c. B2 d. B2 B1 B2 Monte-Carlo 5 5 K I d 5b 5d K I d B2 10m 4 4 B2 Fig. 4 Goodness-of-fit of parametric estimate of intensity surface for group B2 Spatstat

6 K I d Fig. 5 Estimated K I d and envelopes a. B1 K I d b. B1 K I d c. B2 K I d d. B2 K I d /4 8m K Adrian Baddeley Kathleen Buckingham

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