The field of ecology has long benefitted from the application of quantitative techniques and models borrowed from other disciplines. There is a distinct need for the use of statistical and mathematical tools to address current, complex population- and species-level ecological questions. This dissertation aims to apply current mathematical and statistical approaches to answer questions regarding population dynamics, migratory behavior, and social learning. Chapter one focuses on the density-dependence of fish reproduction. I present a hierarchical model that leverages data from hundreds of populations to find statistically meaningful parameters at higher taxonomic levels. I find that reproductive density-dependence is tightly clustered within taxonomic groupings, indicating a clear evolutionary history in these population dynamics. In the second chapter, I develop a probabilistic model to look at how migratory knowledge is spread between individuals that migrate in small groups. I focus on small populations at risk of losing migratory behavior in order to ask what aspects of learning behavior, population dynamics, and grouping structure are most important to retaining a migratory culture. My findings highlight the importance of informed leaders, rare, large groups, and regular mixing of group composition towards the preservation of migratory behavior in small populations. In the final chapter, I use reaction-diffusion equations to look at the success of animal movement behaviors on landscapes where resources vary in space and time, and the role that memory plays in this system. I find that, while advective behaviors successfully maintain migratory movement on many landscapes, the addition of memory allows for greater populations when resources become especially scarce. This is even more effective when both behaviors are allowed to work in concert.