THE MATHEMATICS OF MOSAIC ANALYSIS II. FORMULAE FOR INTERACTING FOCI

Robert J. Wyman ¹ and Lawrence Salkoff ¹

¹ Department of Biology, Yale University, New Haven, Connecticut 06511

Mosaic fate mapping requires first a measurement of the frequency of separation (by genotype) of two structures and then a conversion of this frequency of separation to distance (Wyman and Thomas 1982). If the genotype of two structures is visible, the frequency of separation (sturt distance) may be directly obtained. If the genotype is not visible (e.g., for behavioral foci) then the frequency of separation (sturt distance) itself must be calculated. The formulae introduced by Hotta and Benzer (1972) for calculating frequency of separation are appropriate only for a set of mosaics in which each fly has half normal and half mutant tissue. Using these formulae for a set of mosaics with a different fraction of mutant tissue can give enormously incorrect results.—In this paper we use intuitive lines of reasoning to obtain simple formulae for frequencies of separation that are algebraically equal to the more elaborate Hotta and Benzer (1972) formulae.—We show that when calculating sturt distances, data from a collection of mosaics with a range of malenesses, even if the average maleness is , cannot be lumped together. We prove that applying any formula appropriate for m = to a set of mosaics all of maleness m, and then to a set of maleness 1—m, and then averaging the two results, does give the correct value for sturt distances. In this way all the mapping distances may be obtained.—Another method for locating foci is called "contour mapping". We show that the currently available contour formulae are inaccurate. We suggest that contour maps be drawn using the accurate sturt distances.