Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance
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O R I GI N A L A R T IC L E
Meng Gao
Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance
Received: 4 September 2012 / Accepted: 8 January 2013 / Published online: 16 February 2013 The Ecological Society of Japan 2013
Abstract Spatial point pattern is an important tool for describing the spatial distribution of species in ecology. Negative binomial distribution (NBD) is widely used to model spatial aggregation. In this paper, we derive the probability distribution model of event-to-event nearest neighbor distance (distance from a focal individual to its n-th nearest individual). Compared with the probability distribution model of point-to-event nearest neighbor distance (distance from a randomly distributed sampling point to the n-th nearest individual), the new probability distribution model is more flexible. We propose that spatial aggregation can be detected by fitting this probability distribution model to event-to-event nearest neighbor distances. The performance is evaluated using both simulated and empirical spatial point patterns. Keywords Spatial point pattern Æ Negative binomial Æ Distance sampling Æ Barro Colorado Island, Panama
Introduction In ecology, the spatial point pattern, which is obtained by mapping the locations of each individual as points in space, is a very important tool for describing the spatial distribution of species (Legendre and Fortin 1989). Spatial analysis of point patterns is helpful in revealing the underlying ecological mechanisms behind the spatial distribution patterns (Condit et al. 2000; Stoyan and Penttinen 2000; John et al. 2007). There are three generally accepted types of spatial point patterns: regular, random, and aggregated (Pielou 1960). To detect spatial Electronic supplementary material The online version of this article (doi:10.1007/s11284-013-1029-x) contains supplementary material, which is available to authorized users. M. Gao (&) Key Laboratory of Coastal Zone Environmental Processes, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai, Shandong 264003, China E-mail: [email protected]
patterns, quadrat sampling is one useful method in ecology. Quadrats are randomly thrown on the space and then the number of individuals gained in the each quadrat is counted. The quadrat count data can be well fitted by three discrete probability distribution models, generalized binomial distribution, Poisson distribution, and negative binomial distribution (NBD). They correspond to regular, random, and aggregated spatial point patterns, respectively (Bliss and Fisher 1953; Pielou 1960; Boswell and Patil 1970; He and Gaston 2000; Grevstad 2010; Zillio and He 2010). Poisson distribution usually serves as a null model of complete spatial randomness. Particularly, NBD are the most widely used models as aggregated populations have been found to be very common in nature (Pielou 1960, 1961; He and Gaston 2000). The detection of spatial distribution was firstly implemented by computing kinds
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