## Introduction

Spatially explicit data on animal abundances comprise key data for ecologists and are essential for a sound underpinning of conservation and management plans (Underwood 1997; Krebs 2001). Collecting such data is expensive and labour-intensive, and therefore monitoring programmes are practically constrained by the number of sampling units (Andrew & Mapstone 1987; Field, Tyre, & Possingham 2005). Smaller sample sizes reduce the accuracy of the estimates (e.g. total abundances), or the power to detect significant impacts (Quinn & Keough 2005). Hence, it pays selecting a sampling design that minimises the number of sampling units and maximises the accuracy of the estimates (Thompson 1992). Monitoring programmes can have multiple objectives such as describing spatial patterns and temporal trends in species abundance, or impact assessments, and each objective can have a different optimal sampling design. Optimising sampling designs between monitoring objectives that explicitly consider spatial autocorrelation has received little attention so far and is the objective of this paper.

Hitherto, the ecological literature has paid much attention to designing sampling programmes aiming at detecting the impact of a specific treatment in an area (Green 1979; Underwood 1991, 1997; Stewart-Oaten, Bence, & Osenberg 1992; Stewart-Oaten & Bence 2001). So-called beyond BACI designs (before–after control–impact) are now regarded as the most appropriate for spatial sampling for impact assessments (Underwood 1991, 1994; Schmitt & Osenberg 1996). Usually, multiple sites are sampled within an area, several locations per site and several sampling units per location. The results are analysed by nested anova where the overall variance is allocated to different variance components according to the spatial scale of sampling. Such models are powerful for impact assessment, but they ignore spatial autocorrelation that can provide additional biological information (Sokal & Oden 1978b; Kraan *et al.* 2009a,b). As such, the monitoring of spatial autocorrelation warrants to become a monitoring objective itself.

In contrast to the nested anova approach, the geostatistical literature (Diggle & Ribeiro 2007) and some of the ecological literature (Sokal & Oden 1978a,b; Legendre 1993; Keitt *et al.* 2002; Fortin & Dale 2005; Dormann *et al.* 2007) have emphasised explicitly modelling spatial autocorrelation. Usually, spatial autocorrelation is modelled as a declining function of Euclidean distance between sampling units (Cliff & Ord 1981; Upton & Fingleton 1985). Hence, geostatistical approaches advocate model-based inference by estimating an underlying spatial autocorrelation model allowing for predictions at unsampled locations (i.e. mapping, Ripley 1981; Cressie 1993). Another advantage of explicitly modelling spatial autocorrelation is that this provides an understanding of the mechanisms (e.g. competition, landscape structure) underlying the observed spatial distributions (Bergström, Englund, & Bonsdorff 2002; Klaassen *et al.* 2006; de Frutos, Olea, & Vera 2007; Lagos *et al.* 2007; Kraan *et al.* 2009b; van Gils 2010).

The NIOZ Royal Netherlands Institute for Sea Research maintains long-term benthic monitoring programmes for detecting temporal and spatial changes in abundance from either natural or anthropogenic causes (Piersma *et al.* 2001; Beukema & Dekker 2006; van Gils *et al.* 2006a, 2009; Dekker & Beukema 2007; Kraan *et al.* 2007). Additionally, mapping macrobenthic invertebrates enables predictions on the spatial distribution of their predators, such as birds and fish (van Gils *et al.* 2005, 2006b). Currently, the NIOZ monitoring programme is limited to the western Dutch Wadden Sea, but is to be extended to cover the entire Dutch Wadden Sea for monitoring effects of gas extraction. The aim of this study is twofold. First, building on the existing benthic monitoring efforts at NIOZ, we aim to determine an optimal sampling design for monitoring programmes that have multiple conflicting objectives. Second, we apply this sampling design to the Dutch Wadden Sea. We focus on the following objectives: (1) estimation of temporal change and spatial differences in abundance between 2 years or two areas. Because comparisons between years or areas depend on similar analytical principles, they can be combined into one objective. (2) Predicting species abundances at unsampled locations, that is, mapping. Such predictions, using model-based inference, are only as good as the match between the estimated model parameters and the data, and therefore an additional objective was (3) accurately estimating autocorrelation model parameters. Comparisons between sampling designs were based on (1) the minimum detectable difference (MDD) between means of two time periods or areas, (2) the mean prediction error and (3) the estimation bias, that is, the number of times the autocorrelation parameters were inestimable and the difference in simulated and estimated autocorrelation parameters. With respect to these criteria, we compared one novel with four regularly applied sampling designs.