Effects of sample design and landscape features on a measure of environmental heterogeneity
Environmental heterogeneity, an important influence on organisms and ecological processes, can be quantified by the variance of an environmental characteristic over all locations within a study extent. However on landscapes with autocorrelation and gradient patterns, estimating this variance from a sample of locations may lead to errors that cannot be corrected with statistical techniques. We analytically derived the relative expected sampling error of sample designs on landscapes with particular gradient pattern and autocorrelation features. We applied this closed-form approach to temperature observations from an existing study. The expected heterogeneity differed, both in magnitude and direction, amongst sample designs over the study site's likely range of autocorrelation and gradient features. We conducted a simulation study to understand the effects of (i) landscape variability and (ii) design variability on an average sampling error. On 10 000 simulated landscapes with varying gradient and autocorrelation features, we compared estimates of variance from a variety of structured and random sample designs. While gradient patterns and autocorrelation cause large errors for some designs, others yield near-zero average sampling error. Sample location spacing is a key factor in sample design performance. Random designs have larger range of possible sampling errors than structured designs due to the potential for sample arrangements that over- and under-sample certain areas of the landscape. Furthermore, when implementing a new sample design to quantify environmental heterogeneity via variance, we recommend using a simple structured design with appropriate sample spacing. For existing designs, we recommend calculating the relative expected sampling error via our analytical derivation.