We present an ecological model called SPEAD wherein various phytoplankton compete for nutrients. Phytoplankton in SPEAD are characterized by two continuously distributed traits: optimal temperature and nutrient half-saturation. Trait diversity is sustained by allowing the traits to mutate at each generation. We show that SPEAD agrees well with a more classical discrete model for only a fraction of the cost. We also identify realistic values for the mutation rates to be used in future models.