The aim of this paper is to provide general results for predicting progress in a physical mapping project by anchoring random clones, when clones and anchors are not homogeneously distributed along the genome. A complete physical map of the DNA of an organism consists of overlapping clones spanning the entire genome. Several schemes can be used to construct such a map, depending on the way that clones overlap. We focus here on the approach consisting of assembling clones sharing a common random short sequence called an anchor. Some mathematical analyses providing statistical properties of anchored clones have been developed in the stationary case. Modeling the clone and anchor processes as non-homogeneous Poisson processes provides such an analysis in a general non-stationary framework. We apply our results to two natural non-homogeneous models to illustrate the effect of inhomogeneity. This study reveals that using homogeneous processes for clones and anchors provides an overly optimistic assessment of the progress of the mapping project.