With the recent advances in sequencing technology, researchers now have opportunities to study microbiomes associated with various environments. Recent studies have shown that the composition of microbiomes in our bodies and our environments play a significant role in our health. For example, 90% of human DNA is composed of bacterial microbiomes. In this study, we propose a systems biology approach using split graphs to analyze the composition of microbiomes and the impact of such composition on the health and growth of organisms living in associated environments. We focus on a case study related to the composition of microbiomes in fish guts and its impact on various growth parameters for three types of fish. The proposed model explores features in the aquatic ecosystem including correlations among its microorganisms and their abundance levels. The results of the study show that single or groups of bacteria are significantly associated with multiple growth phenotypes in different gut portions of the fish. We also identify bacterial clusters that provide new insight to functional relevance of these bacteria and their contribution to the fish gut microbial ecosystem.