In the course of a study on the effects of the mechanical shearing of DNA, Eugene Nester, A. T. Ganesan, and Joshua Lederberg studied the transfer, by transformation, of sheared DNA from a wild type strain of Bacillus subtilis (his2^+ aro3^+ try2^+ aro1^+ tyr1^+ aro2^+) to strains of bacteria carrying a series of mutations (E. W. Nester, A. T. Ganesan, and J. Lederberg. 1963. Proceedings of the National Academy of Sciences 49:61-68). They reported the following rates of cotransformation between his2^+ and the other genes (expressed as cotransfer rate), shown here.

Genes Rate of cotransfer
his2+ and aro34 0.015
his2+ and try2+ 0.10
his2+ and aro1+ 0.12
his2+ and tyr1+ 0.23
his2+ and ar02+ 0.05

On the basis of these data, which gene is farthest from his2^+? Which gene is closest to his2^+?