The mathematics of mosaic analysis III. Analysis of structures with extent in two dimensions

This paper derives formulae for the use of mosaic analysis to determine the sizes, shapes and locations of structures that are not points but are extended areas on the blastoderm. We consider a male patch of any convex shape and size and a structure of any convex shape and size. The probability that these two intersect in a set of mosaics is simply one-quarter the product of their perimeters. From this perimeter formula we derive equations relating the frequency of mosaicism of a structure to its size and we derive a formula for the mapping of lethal foci. We then develop a method to locate the borders of a focus that covers an area on the blastoderm.