This work attempts to explain the relationships between natural selection, information theory, and statistical inference. In particular, a geometric formulation of information theory known as information geometry and its deep connections to evolutionary game theory inform the role of natural selection in evolutionary processes. The goals of this work may be stated as (1) to show that a significant collection of important results in evolutionary dynamics can be interpreted elegantly in the context of information theory, and (2) to generalize the framework to study dynamics other than the replicator equation. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]