Presented in this document is a class of deterministic models describing the dynamics of two plant species whose characteristics are common to the majority of annual plants that have a seedbank. Formulated in terms of elementary dynamical systems, these models were developed in response to four major questions on the long-term outcomes of binary mixtures of plant species: Is ultimate coexistence possible? If not, which strain will win? Does the mixture approach an equilibrium? If so, how long does the mixture take to attain it? The book gives a detailed account of model construction, analysis and application to field data obtained from long-term trials. In the particular case study modelled, the species involved are two pastural strains whose dynamics have critical agricultural and economic implications for the areas in which they are found, including North America, the Mediterranean region and Australia. This study will be valuable to researchers and students in mathematical biology and to agronomists and botanists interested in population dynamics.