Semi‐strong Hybrid Scaling, a new ordination algorithm

Abstract

There is a small group of association measures that appear optimal for comparing sites on the basis of their species composition. These measures can accurately estimate affinity between sites when they are ecologically similar. Once sites share few or no species, these measures always under‐estimate the ‘ecological distance’ between them. A new ordination algorithm called Semi‐strong Hybrid Scaling, SHS, uses these features in an attempt to provide a better configuration of the sites. The new method is evaluated by a direct comparison of the structure in simulated data with the Hybrid method of Faith, Minchin & Belbin (1987). To evaluate SHS and compare it with Hybrid Scaling, 3240 datasets were generated using the COMPAS simulator (Minchin 1987). The data were designed to simulate as closely as possible, what is known of the distribution of species on environmental gradients. The factors included the dimensionality of the data, the number of sites and species, the shape of the species response surfaces, positioning of the sites in the simulation space, carrying capacity and level of noise. Recovery of the simulated site positions by SHS and Hybrid Scaling was evaluated using Procrustes rotation. SHS produced a better recovery in 88% of the datasets.

Seasonal flooding, instream habitat structure and fish assemblages in the Mulgrave River, north-east Queensland: towards a new conceptual framework for understanding fish-habitat dynamics in small tropical rivers

“…Three-dimensional semi-strong hybrid multidimensional scaling (SSHMDS -PATN Version 3.03, Belbin (1991)) was used to explore relationships among the four sites and the wet and dry season samples on the basis of: (i) instream habitat structure (mean value of each habitat variable at each site on each sampling date); (ii) fish abundance (standardised CPUE of each species summed across methods for each site on each sampling date); and (iii) fish biomass (standardised BPUE of each species summed across methods for each site on each sampling date). Combining catch data from different gear types is an effective way to negate biases caused by gear selectivity (Weaver et al 1993).…”

Biogeography of scorpion communities in the southern Carnarvon Basin, Western Australia

“…The group structure apparent in the resulting dendrogram of survey areas was analysed against the quadrat physical attributes, one by one, using the GSTA module of PATN. Kruskal-Wallis K sample test was used to assess the significance of the relationship, and 'Semi-Strong Hybrid MultiDimensional Scaling' (Belbin, 1991) was used to reduce the dimensionality in the data.…”

Circumboreal Gradients in Plant Species and Functional Types

“…Depending on the purpose of the analysis and the nature of the data, MDS may be applied using metric or nonmetric (NMDS) algorithms, both of which exhibit strengths and weaknesses (see also Thessler et al 2005 for NMDS relating floristic to remotelysensed data). In the present case the PATN multivariate software package was applied using a twodimensional semistrong hybrid scaling (SSH) procedure (Belbin 1991(Belbin , 2008. SSH maximizes the advantages of both MDS procedures by allowing combinations of nonmetric (ordinal or monotone), or metric (ratio) scaling.…”