In this thesis analytical and simulation techniques are applied to problems in biological evolution. The thesis is divided into four parts. Firstly, chapter two investigates anomalies that occur in the Penna bit-string model of ageing, an influential model of mutation accumulation and selection. These anomalies result in unusual demographic distributions and can lead to the so-called Eve effect. The anomalies are characterised along with their associated demographic distributions. It is argued that the anomalies are similar in nature to the well known first-passage problem. Secondly, chapter three uses evolutionary game theory to investigate the evolution of harmful mating tactics in hermaphrodites. These tactics benefit the function of the sperm donor at the expense of sperm recipient. The model predicts evolutionary stable values of resource allocation between sexual functions, and the level of harm. The analysis provides support for empirical observations and makes predictions about the effects of harmful mating tactics on population evolution. Thirdly, chapter four considers the sustainability of the two main types of sexual reproduction; hermaphroditism and dioecy (male and female individuals). By use of stochastic spatial simulations it is demonstrated that hermaphroditism can have an even greater advantage over dioecy than predicted by mean-field analysis. This result provides support for the observation that hermaphroditism is associated with sedentary species. Finally, chapter five considers the evolution of gynodioecy, a breeding system of plants in which populations consist of hermaphrodite and female individuals. It is both a common and widespread polymorphism, and has been identified in many species of ecological and economic interest. Mean-field calculations and stochastic spatial simulations are used to identify the conditions necessary for gynodioecy to evolve.