Journal of Experimental Marine Biology and Ecology 366 (2008) 16–27 Contents lists available at ScienceDirect Journal of Experimental Marine Biology and Ecology journal homepage: www.elsevier.com/locate/jembe Animal-sediment relationships re-visited: Characterising species' distributions along an environmental gradient using canonical analysis and quantile regression splines Marti J. Anderson ⁎ Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand article info abstract Keywords: Benthic soft-sediment organisms generally show strong relationships with the grain-size characteristics of Canonical analysis of principal coordinates the sediments they inhabit. These relationships, when characterised from field data, tend to be asymmetrical, Predictive models non-linear and heteroscedastic, due to the existence of multiple other potentially important and interacting Quantile regression splines factors, some of which are inevitably unmeasured. For multivariate data, canonical analysis of principal Sediment texture coordinates (CAP) can be used to isolate particular gradients of interest, despite the presence of other Soft-sediment assemblages potentially important factors. For univariate abundance data, models focusing on upper quantiles of species' Species-environment relationships distributions can ameliorate the problem of heterogeneity induced by other variables. Here, a multivariate model of the relationship between benthic inter-tidal estuarine soft-sediment assemblages (sampled over a period of 3 years from 70 sites across the Auckland region) and the percentage of mud in the sediments was generated using CAP. To characterise changes in assemblage structure, quantile regression splines (of the 0.95 quantile) were used to model each of the twenty most abundant individual taxa along the gradient in percentage mud. This approach provided an effective instrumental quantitative predictive model of species' turnover, while allowing for the asymmetric, non-linear animal-sediment relationships and heterogeneous scatter observed in species' abundances along the mud gradient. © 2008 Elsevier B.V. All rights reserved. 1. Introduction complex, since a number of subsidiary parameters are influenced by sediment characters and the subsidiary factors may in fact be the The strong association between the structure of benthic marine soft- limiting ones.” sediment communities and the texture of the sediments they inhabit is a Models of species' abundances along environmental gradients well-known phenomenon, as outlined in the landmark paper by John S. have seen a fairly long history of development (e.g., see the review by Gray (1974). Professor Gray's work on animal-sediment relationships has Austin, 2007). Species have been thought to show unimodal response provided a touchstone for many soft-sediment ecologists (e.g., Constable, patterns along environmental gradients, and symmetric unimodal or 1999; Ellingsen, 2002; Ysebaert et al., 2002; Thrush et al., 2003). gaussian models have been used to estimate their optima and Although the existence of animal-sediment relationships in these tolerances (ter Braak, 1985, 1986). However, there is no compelling habitats is undisputed, many other factors can also play important reason why models should necessarily be symmetric; indeed, many roles in structuring the temporal and spatial heterogeneity of soft- species show asymmetric responses (or, albeit less commonly, multi- sediment assemblages. These may include (but are certainly not modal patterns) along gradients. This has led to the use of more limited to): predation (Peterson and Skilleter, 1994; Hines et al., 1997), flexible response functions, including splines and generalized bioturbation (Levinton, 1995), physical disturbance (Probert, 1984; additive models (GAMs, Hastie and Tibshirani, 1990; Leathwick Thrush and Dayton, 2002), sedimentation (Peterson, 1985; Norkko et al., 2005; Zhu et al., 2005; Yee, 2006). Not only do species- et al., 2002), pollution (Gray,1992; Gray et al.,1990) or factors affecting environment relationships tend to be inherently asymmetric and colonisation (Zajac et al., 1998; Hewitt et al., 2003; Lundquist et al., nonlinear, they also tend to show heterogeneous scatter. The variance 2006). In order specifically to model and characterise animal- calculated from the abundances of a particular species at each fixed sediment relationships, scientists may need to take other factors point along the environmental gradient will differ at different points. into account, either through modeling or by using a carefully targeted Specifically, variances are inevitably smaller where mean abundance stratified sampling strategy. In the words of Gray (1974): “… values are small, where environmental conditions are unsuitable. consideration of the relationship of organisms to sediments is Furthermore, the distribution of abundances at a fixed point along the gradient will be strongly right-skewed (long-tailed). All these characteristics are often a consequence of the fact that other ⁎ Tel.: +64 9 373 7599x85052; fax: +64 9 373 7000. unmeasured variables also limit abundances and can interact with E-mail address: [email protected]. the (measured) system in complex ways. Quantile regression 0022-0981/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jembe.2008.07.006 M.J. Anderson / Journal of Experimental Marine Biology and Ecology 366 (2008) 16–27 17 (Koenker and Bassett, 1978; Cade and Noon, 2003; Koenker, 2005)is (in the present case, the environmental gradient of interest is the an effective tool that can be used to ameliorate the heterogeneity percentage of mud in the sediments); (ii) the fact that species caused by such unmeasured factors (Cade et al., 2005). More generally display asymmetric non-linear relationships in their relative specifically, the idea of modeling not the mean but the upper (or abundances along environmental gradients and (iii) the idea that a lower) quantiles not only deals nicely with the intrinsic hetero- model of the outer “envelope” can be more meaningful and useful for geneity, but also aligns directly with the ecological concept of characterising individual species' patterns along a gradient than a limiting factors acting as constraints on organisms (Thomson et al., model based on the mean. 1996; Cade et al., 1999; Lancaster and Belyea 2006). More specifically, using a reasonably large set of monitoring data Recently, Thrush et al. (2003, 2005) modeled the relationship from estuarine intertidal soft-sediment habitats across the Auckland between soft-sediment benthic fauna and the percentage of mud region, the approach taken here consisted of essentially two steps. (b63 µm) in sediments, using data obtained from sampling mud-to- First, a multivariate predictive model of the relationship between sand transects in 19 estuaries and harbours across the North Island of benthic infaunal assemblages and the percentage mud of the New Zealand. It was recognised that the distributions of abundances sediments was generated, using canonical analysis of principal of species along the gradient in percentage mud would be hetero- coordinates (CAP, Anderson and Robinson, 2003; Anderson and Willis, geneous: species might well be functionally able to occur within a 2003). Second, the gradient in assemblage structure for a suite of the particular range of percentage mud, but other factors may come into most abundant species was characterised using quantile regression play so that variation in their abundances within that range would be splines (Koenker, 2005). This approach not only provides a working large. Outside of this range (i.e., for those parts of the mud gradient quantitative model of community change and individual species' where the species has low tolerance), variation would necessarily be responses along an important environmental gradient, it also allows relatively small, due to limited abundance. Thus, Thrush et al. (2003, predictions for future change scenarios, such as expected increases in 2005) modeled the maximum abundances of species along the the percentage mud content of sediments (Thrush et al., 2004), against gradient, rather than modeling their mean abundance. This resulted which future monitoring data can be examined. in a model for each species or taxon that appeared like an “envelope”, clearly allowing for intrinsic heterogeneity along the mud gradient. 2. Methods Here, the animal-sediment relationships of Gray (1974) are re- visited, following also in the footsteps of Thrush et al. (2003, 2005) in 2.1. Sampling design and database an effort to model soft-sediment fauna specifically along a gradient in sediment texture. Several refinements are suggested which specifi- The data used here form part of a monitoring programme, funded cally cater for: (i) the fact that organisms will respond in the field by the Auckland Regional Council (ARC), examining the potential long- simultaneously to multiple gradients, whereas one may wish to focus term effects of urbanization and sediment inputs from surrounding in some cases (for modeling and/or prediction) on only one of these catchments on benthic intertidal estuarine infauna (Anderson et al., Fig. 1. Map showing the positions of the 7 estuaries in the Auckland region included as part of the monitoring programme. 18 M.J. Anderson / Journal of Experimental Marine Biology and Ecology 366 (2008) 16–27 then deflocculated for at least 4 hours (using Calgon 5 g per litre) and wet-sieved. Each fraction