This thesis attempts to provide new insight into some population-dynamical problems and also proposes a new perspective on certain models of ecological communities. Following a short introduction into the field of mathematical modelling of population dynamics, the first chapter investigates the paradoxical Hydra Effect, the increase of mean population size as a response to an increase in mortality rate, in a class of simple predator-prey models. The main result is that a Hydra Effect occurs if and only if the system dynamics are oscillatory, which has interesting implications for the theory of optimal harvesting and biocontrol of invasive species. The second chapter discusses how coordinate transformations change the structure of intraguild predation food webs, establishing a close connection of certain cases of intraguild predation to simpler community modules such as exploitative competition and food chains. These results and possible generalizations of them could have wide-ranging implications for the question of how structural properties of food webs determine population-dynamical properties such as ecological stability and persistence. The last chapter presents numerical investigations of how random environmental fluctuations affect the spatiotemporal dynamics of oscillatory reaction-diffusion models, such as classical predator-prey and simple lambda-omega systems. These results in particular question whether travelling waves arising from these models can explain similar spatiotemporal waves found in natural populations.