While biodiesel production from photosynthesizing algae is a promising form of alternative energy, the process is water and nutrient intensive. I designed a mathematical model for a photobioreactor system that filters the reactor effluent and returns the permeate to the system so that unutilized nutrients are not wasted, addressing these problems. The model tracks soluble and biomass components that govern the rates of the processes within the photobioreactor (PBR). It considers light attenuation and inhibition, nutrient limitation, preference for ammonia consumption over nitrate, production of soluble microbial products (SMP) and extracellular polymeric substance (EPS), and competition with heterotrophic bacteria that predominately consume SMP. I model a continuous photobioreactor + microfiltration system under nine unique operation conditions - three dilution rates and three recycling rates. I also evaluate the health of a PBR under different dilution rates for two values of qpred. I evaluate the success of each run by calculating values such as biomass productivity and specific biomass yield. The model shows that for low dilution rates (D = <0.2 d-1) and high recycling rates (>66%), nutrient limitation can lead to a PBR crash. In balancing biomass productivity with water conservation, the most favorable runs were those in which the dilution rate and the recycling rate were highest. In a second part of my thesis, I developed a model that describes the interactions of phototrophs and their predators. The model also shows that dilution rates corresponding to realistic PBR operation can washout predators from the system, but the simulation outputs depend heavily on the accuracy of parameters that are not well defined.