In field surveys, ecologists make observations at different spatial locations, hereafter referred to as “sites”. The aim is often to relate biological response variables (e.g., the growth of individuals, the abundance of a species, or the structure of ecological communities) to explanatory environmental variables (e.g., soil characteristics, herbivore abundance).

Ecologists know from experience that physical as well as biological variables observed in nature display spatial patterns. Patterns may result either from deterministic processes or from processes causing spatial autocorrelation, or both; the distinction is explained below. As we will see in this paper, some types of spatial pattern make it difficult to accurately detect and quantify the biological responses, which are of primary interest. The effects of spatial structures in general, and of spatial autocorrelation in particular, on statistical tests of significance, have been described elsewhere (see, e.g., Bivand 1980, Cliff and Ord 1981, Haining 1990, or Legendre and Legendre 1998 for a review). It is our purpose here to determine the consequences of particular sampling designs on the detection of biological responses in the face of some common types of spatial patterning in the data.

Rather than analysing actual data sets, we chose the simulation approach because the use of simulations allows us to compare the outcome of the analysis to “the truth”, which we know because we have generated it. The analysis of real data sets is usually limited in terms of the number of data sets available with all the necessary variables; it is also limited by the fact that one does not know whether the null hypothesis (H_{0}: there is no effect of the environmental variable on the response variable) or the alternative hypothesis (H_{1}: there is an effect) is true in any particular case. Monte Carlo simulations allow researchers to know the exact relationship between variables in the data. No doubt exists as to whether it is H_{0} or H_{1} which is true in each particular simulated data set (Milligan 1996).

We used stochastic simulations designed to produce surfaces of responses. These surfaces may incorporate 1) deterministic (e.g., physical) spatial patterns in the environmental variable to which the biological entities are responding, 2) spatial autocorrelation in the underlying environmental variable, and 3) spatial autocorrelation in the biotic responses. Each pair of surfaces was generated using a particular set of parameter values, and was replicated 1000 times. By analysing these replicates, we can explore the consequences of using various sampling designs for our ability to detect true biotic responses, and to conclude that there is no biotic response when none is present while different types of spatial pattern are present.

The simulations were used in this paper to address three questions formulated below. In these simulations, we generated the processes described above that may give rise to spatial structures: deterministic spatial structures and spatial autocorrelation in the explanatory variables, plus spatial autocorrelation in the ecological response variable.

The questions addressed in this paper are: a) What is the effect (in terms of type I error) of spatial autocorrelation on the statistical tests of correlation and regression analysis, which are commonly used by ecologists to analyse field survey data? b) Can we eliminate the effect of spatial autocorrelation by the design of the survey? Which designs provide the most power? c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis? To answer this question, we used ordinary correlation analysis and compared it to a modified t-test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation.