In Table 1, there are errors in the formulas for some of the utility functions such as CP-optimality, CPD-optimality, K-optimality, EK-optimality, Sequential CP-optimality, Sequential D-optimality, Sequential ED-optimality, the Maximin utility, and the Morris-Mitchell utility. There is also an error in Equation (17) of the S1 Appendix for the Morris-Mitchell utility. Please see the correct Table 1 here. The changes are explained by a document, S1 File, attached to this correction notice. The document also presents annotated code from the SSNdesign R package to show that no results are affected and that the correct versions of the utility functions were implemented in the first instance.

In the Application column, OP stands for ‘optimal design’, and AD stands for ‘adaptive design’. In the Empirical column, × means No; ✓ means Yes; and n/a means ‘not applicable’. Here, is a vector of covariance parameters from a geostatistical model; denotes the expected Fisher Information Matrix of the covariance parameters; denotes the estimates of the fixed effects; is the covariance matrix of the fixed effects; denotes the universal kriging (UK) variance at prediction site , and is the set of all prediction sites; represents a summary statistic from the existing design after previous design steps; is the distance between sites and in a design, which can be measured as Euclidean distance or hydrological distance along the stream network [10]; for , is the -th smallest of the unique non-zero distances between pairs of sites in a design, and is the number of unique pairs of sites separated by the distance ; and is a weighting power. Both and depend on covariance parameters . In the empirical utility functions, the covariance parameters are estimated from data simulated using the prior draws (see [16]), and the “hats” on and indicate the estimated covariance parameters were used to compute these quantities.