Beyond pairs: definition and interpretation of third-order structure in spatial point patterns

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KaitoEtal2015Preprint.pdf

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/79235 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/79235 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/79235 archive 351 disk0/00/01/14/88 2016-01-15 08:53:27 2021-08-27 17:25:11 2016-01-15 08:53:27 article show Kaito C. 8579 Dieckmann U. 1668 0000-0001-7089-0393 Sasaki A. 8233 0000-0003-3582-5865 Takasu F. Beyond pairs: definition and interpretation of third-order structure in spatial point patterns pub iis_ecl prog_eep mapped point data; pair correlations; spatial configuration; spatial ecology; triplets Spatial distributions of biological species are an important source of information for understanding local interactions at the scale of individuals. Technological advances have made it easier to measure these distributions as spatial point patterns, specifying the locations of individuals. Extensive attention has been devoted to analyzing the second-order structure of such point patterns by focusing on pairs of individuals, and it is well known that the local crowdedness of individuals can thus be quantified. Statistical measures such as a point pattern's pair correlation function or Ripley's K function show whether a given point pattern is clustered (excess of short-distance pairs) or overdispersed (shortage of short-distance pairs). These notions are naturally defined in comparison with control patterns exhibiting complete spatial randomness, i.e., an absence of any spatial structure. However, here is no rational reason why the analysis of point patterns should stop at the second order. In this paper, we focus on triplets of individuals in an attempt to quantify and interpret the third-order structure of a point pattern. We demonstrate that point patterns with 'bandedness', in which individuals are primarily distributed within bands, can be detected by an excess of thinner triplets at a characteristic spatial scale linked to the band's width. In this context, we show how the generation of control patterns as a reference for gauging a test pattern's triplet frequencies is critical for defining and interpreting the third-order structure of point patterns. Since perfect information on a point pattern's second-order structure typically suffices for its unique reconstruction (up to translation, rotation, and reflection), we conjecture that it is essential to minimally coarse-grain such second-order information before using it to generate control patterns for identifying a point pattern's third-order structure. We recommend the further exploration of this conjecture for future studies. 2015-05 published Elsevier 10.1016/j.jtbi.2015.02.004 XJ-15-074 Journal of Theoretical Biology; 372:22-38 (May 2015) (Published online 10 February 2015) [doi:10.1016/j.jtbi.2015.02.004] 1352 66 267 public Journal of Theoretical Biology 372 22-38 TRUE 1095-8541 FALSE info:eu-repo/semantics/article