You are monitoring a quantitative trait in a population of butterflies over multiple generations. your professor tells you that the trait is evolving by natural selection in this population. however, there is no change in mean fitness over time. what type(s) of selection could be occurring in this population and how could you tell what type of selection is happening

In the given population, epistasis or frequency-dependent selection would have been taking place. In frequency-dependent selection, selection of a genotype relies upon its frequency in population. It is further divided into two types, that is, positive and negative frequency-dependent selection.  

In negative frequency-dependent selection rare genotypes are selected, while in positive frequency-dependent selection more common genotypes are selected. The other possibility is epistasis, in which the fitness of genotypes relies upon the non-additive influences over the multiple loci.  

allowed for the prediction of the properties of missing elements.

you didn't give any options but heres what i can tell you: an inference is likely to change based on additional observations. the latter is something that you have seen or sensed using your sensory organs while the former is like a conclusion out from what you have observed.