Dissecting the Spatial Structure of Ecological Data at Multiple Scales

Abstract

Spatial structures may not only result from ecological interactions, they may also play an essential functional role in organizing the interactions. Modeling spatial patterns at multiple spatial and temporal scales is thus a crucial step to understand the functioning of ecological communities. PCNM (principal coordinates of neighbor matrices) analysis achieves a spectral decomposition of the spatial relationships among the sampling sites, creating variables that correspond to all the spatial scales that can be perceived in a given data set. The analysis then finds the scales to which a data table of interest responds. The significant PCNM variables can be directly interpreted in terms of spatial scales, or included in a procedure of variation decomposition with respect to spatial and environmental components. This paper presents four applications of PCNM analysis to ecological data representing combinations of: transect or surface data, regular or irregular sampling schemes, univariate or multivariate data. The data sets include Amazonian ferns, tropical marine zooplankton, chlorophyll in a marine lagoon, and oribatid mites in a peat bog. In each case, new ecological knowledge was obtained through PCNM analysis.

Contribution of environmental and spatial processes to rocky intertidal metacommunity structure

“…The PCNM approach has two distinct advantages over using direct geographic coordinates or trend-surface (i.e., polynomial) approaches to model spatial dependence. First, all principal coordinates are orthogonal and are therefore uncorrelated independent variables (Borcard and Legendre, 2002, Borcard et al, 2004; in polynomial approaches, spatial variables obviously depend on each other (e.g., x coordinates and square of x coordinates). Second, spatial dependence can be detected over a wider range of scales (Borcard and Legendre, 2002, Borcard et al, 2004.…”

“…First, all principal coordinates are orthogonal and are therefore uncorrelated independent variables (Borcard and Legendre, 2002, Borcard et al, 2004; in polynomial approaches, spatial variables obviously depend on each other (e.g., x coordinates and square of x coordinates). Second, spatial dependence can be detected over a wider range of scales (Borcard and Legendre, 2002, Borcard et al, 2004. Each PCNM variables has a wave-like spatial pattern: the first few PCNM variables exhibit broad-scale amplitude and frequency, and each successive variable resolves finer high-frequency, low-amplitude spatial patterns (Fig.…”

Disentangling the roles of spatial and environmental variables in shaping benthic algal assemblages in rivers of central and northern China

“…Among the three important MEMs for richness, both MEM 8 and 9 represent fine-scale patterns, indicating that regional algal richness was principally driven by autocorrelation processes (e.g., algal dispersal, interactions among individuals/species, etc.) (Borcard et al 2004). On the contrary, community composition was mainly influenced by broad-scale patterns of MEM component 1 and 2, implying that large scale spatial processes such as dispersal limitation or spatially structured environmental gradients might be more important in shaping regional community structure (Sharma et al 2011;Virtanen and Soininen 2012).…”

Segmentação multiresolução variográfica ótima.

“…Muitos destes testes são baseados em análises de vetores de distância, cujo objetivo é a identificação dos efeitos de tendência causados pela autocorrelação espacial, principalmente por meio do arranjo espacial dos dados, a mensuração e quantificação do fenômeno espacial observado, e sua possível influência nos dados coletados. Borcard et al (2004) desenvolveu uma técnica que utiliza mapas simulados com diferentes formas de autocorrelação espacial, em diferentes escalas, para extrair os principais descritores de um fenômeno espacial, técnica denominada Mapas de Moran ou Principal Coordinates of Neighbour Matrices (Seção 2.3.1). A técnica é empregada em Ecologia e Biogeografia para estimar e considerar o efeito da autocorrelação nos dados e melhorar os modelos obtidos (MARROT; GARANT;CHARMANTIER, 2015).…”

“…Também vimos que Borcard et al (2004) desenvolveu uma técnica baseada neste índice, denominada Mapas de Moran ou PCNM. Esta técnica utiliza mapas simulados com diferentes formas de autocorrelação espacial em diferentes escalas para extrair os principais descritores de um fenômeno espacial.…”