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Biological invasions are a significant driver of human-induced global change and many ecosystems sustain sympatric invaders. Interactions occurring among these invaders have important implications for ecosystem structure and functioning, yet they are poorly understood. Here we apply newly developed metrics derived from stable isotope data to provide quantitative measures of trophic diversity within populations or species. We then use these to test the hypothesis that sympatric invaders belonging to the same functional feeding group occupy a smaller isotopic niche than their allopatric counterparts. Two introduced, globally important, benthic omnivores, Louisiana swamp crayfish (Procambarus clarkii) and carp (Cyprinus carpio), are sympatric in Lake Naivasha, Kenya. We applied our metrics to an 8-year data set encompassing the establishment of carp in the lake. We found a strong asymmetric interaction between the two invasive populations, as indicated by inverse correlations between carp abundance and measures of crayfish trophic diversity. Lack of isotopic niche overlap between carp and crayfish in the majority of years indicated a predominantly indirect interaction. We suggest that carp-induced habitat alteration reduced the diversity of crayfish prey, resulting in a reduction in the dietary niche of crayfish. Stable isotopes provide an integrated signal of diet over space and time, offering an appropriate scale for the study of population niches, but few isotope studies have retained the often insightful information revealed by variability among individuals in isotope values. Our population metrics incorporate such variation, are robust to the vagaries of sample size and are a useful additional tool to reveal subtle dietary interactions among species. Although we have demonstrated their applicability specifically using a detailed temporal dataset of species invasion in a lake, they have a wide array of potential ecological applications.