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RILs are useful for preliminary mapping of any trait that differs between the parental strains used to generate the population. The great thing about RILs is that the same mapping population can be maintained and used over and over again to map all kinds of different traits. They can also reveal multiple loci contributing to any trait of interest. The downside is that they are less statistically powerful for analyzing effects of any one particular locus, because each RIL also harbors potentially confounding background genetic variation.
NILs are most useful when you have a candidate gene or one particular locus of interest. They will allow you to measure the effect of allelic variation at that locus only, while eliminating background genetic variation. NILs are more powerful than RILs but can only be used to study one locus at a time. Furthermore, you can't generate useful NILs until you have a candidate locus to "zoom in on," which typically comes from previous RIL studies.