Reaction- diffusion equations were first applied by Fisher (1930) to model the spread of an allele in a spatial version of natural selection. I will consider spatial patterns that emerge for both continuous-time and discrete-time diffusion when natural selection is also frequency dependent. It is shown that the existence of these patterns in discrete- time depends critically on how diffusion is incorporated into the biological model. This result means that care must be taken when interpreting data from corresponding computer simulations.