Fig. 1. A schematic description of establishing a variogram, modelling a function, and producing maps by kriging. Samples (e.g. to determine ciliate abundance) are collected at points of a sampling grid (a). Variance estimates of ciliate abundances at points separated by a common distance (lag, h) are calculated using the equation (explanations in the text); this is repeated for each lag (three examples of lags are illustrated in a). Each variance estimate is then plotted against its respective lag to produce an empirical variogram (points in b). Then, a model is fit to the variogram data (lines in b), and the model is used to predict abundance at unsampled points and to characterize patches. The parameters of the variogram models are the nugget, the range, and the sill (see text for their interpretation). Three models are the most common: the Gaussian, spherical and exponential (thick, medium, and thin lines, respectively, in b). Models are used to map ciliate abundance by the kriging procedure, with each model producing different predicted distributions (c, d, e): the spherical and exponential produce "fuzzier" images than the Gaussian.

Published as part of Bulit, Celia, 2014, Good Reasons and Guidance for Mapping Planktonic Protist Distributions, pp. 13-27 in Acta Protozoologica 53 (1) on page 17, DOI: 10.4467/16890027AP.14.003.1440, http://zenodo.org/record/8377567