Beyond baci: optimization of environmental sampling designs through monitoring and simulation

The detection of anthropogenic disturbances requires appropriate sampling design and powerful statistical tests. This study illustrates how simulations of environmental disturbances may be used to improve the capability of any given sampling design to detect impacts of a specified magnitude. Here, real data on the abundance of algae and invertebrates are used to simulate the effects of environmental disturbances on two rocky shores in the northwest Mediterranean. Natural populations were sampled eight times between 1995 and 1996 in mid‐shore habitats on each of two shores. Four sites were sampled at each of three different levels on the shore each time. Three replicate quadrats were sampled in each site. This design was rearranged to create two “Impacted” and two “Control” sites at each level on each shore. The first four times were used as “Before” data; the latter four times represented a series of “After” data. Two different approaches were used to simulate environmental impacts. The first was based on the methodology developed in the context of Beyond BACI designs, and consisted in altering the mean abundance of organisms of known amounts at the “Impacted” sites for the “After” series of data. Simulated data were generated by multiplying the real values by random variates obtained from binomial distributions of means 0.8, 0.5, and 0.2, to simulate reductions in mean abundance to 0.8, 0.5, and 0.2, respectively. These data were analyzed using analysis of variance following the logic of Beyond BACI designs. A Monte Carlo procedure was also developed based on the linear model of the Beyond BACI design, using real estimates of spatial and temporal variance of the red alga Rissoella verruculosa. Power of the Before/After vs. Control/Impact (B × I) interaction was calculated from sets of 1000 simulations under the alternative hypothesis of an impact causing a reduction in mean abundance of the alga to 0.5. Power curves were generated for the B × I interaction using different combinations of number of sites, number of times, and number of replicate plots, thereby providing a direct way of optimizing the sampling design. In most cases impacts were detected as significant changes from before to after the simulated disturbances in the differences between the impacted and control sites. The probability of detecting an impact was not consistent between the two shores, and it also changed in relation to level on the shore. Statistical power was large for several of the tests involved in the detection of the simulated impacts. Sample size was also calculated for different combinations of Type I and Type II errors, indicating that the sample size required to design powerful environmental sampling programs can be maintained within a range of acceptable and logistically feasible sampling efforts for these rocky shores. In some cases it was not possible to proceed with calculation of power and sample size using classical procedures based on non‐central F distributions, due to the impossibility of providing an error term with a single component of variation. The Monte Carlo procedure developed here solved this problem, providing a tool of potential wide application for the design and optimization of environmental sampling programs.