Powerful techniques using total variation distance have been developed to give bounds on how close a particular distribution is to the Poisson distribution. These techniques can be exploited in population genetics to give asymptotically efficient estimates of population parameters for models involving selection. This research also studies a mathematical model for the evolution of recombinant DNA. A third problem is to consider the statistical limitation of new technology which may someday be used for DNA sequencing. Interpreting the vast amount of DNA data now available requires mathematical models that take into account statistical variability. Using new probability techniques, this research will develop insight into three scientifically relevant problems in genetics.