## 1 Introduction  
A vast variety of microbial communities exist in various environments, such as the ocean, soil, and parts of living organisms [1; 2; 3; 4]. However, the majority of the microorganisms in these environments remain uncultured. Recently, next-generation sequencing (NGS) technologies have opened the possibility of performing genetic analyses of these culture-independent microorganisms [5]. Bioinformatics approaches for NGS technologies can promote the understanding of complex microbial communities [6], but the roles of many microorganisms remain to be clarified. The knowledge of bacterial taxonomic composition changes in various environments is essential to understand the roles of their complex communities [7; 8]. Therefore, further investigations of taxonomic compositional variation in microbial communities may highlight the potential roles of several microorganisms.  
The human gut microbiome is a well-studied microbial community [9; 10; 11]. Some gut microbes support the breaking down of proteins, lipids, and carbohydrates into nutrients that humans can efficiently absorb through the gastrointestinal tract [12]. Additionally, several microbes residing in the intestinal tract produce valuable compounds, including vitamins and anti-inflammatory substances [13; 14]. The existence of certain microbial species in the gut microbiome is related to disorders of the host [15; 16]. Therefore, the human gut microbiome is also used as a biomarker in clinical practice [17]. Several gut microbial species maintain symbiotic relationships with their hosts, with respect to surrounding environmental changes [18]. The compositional differences in the microbiome may reflect the changes in their habitat environments. These differences in the human gut microbiome may be related to environmental factors, such as pH [19] and oxygen concentration [20], for each gastrointestinal tract position. For example, there is bias in the types of microbial species, depending on the position in the human gastrointestinal tract [21].  
To detect these taxonomic differences in the types of microbial species, computational frameworks such as edgeR [22] or DESeq2 [23] are often used. These approaches were originally designed for differential gene expression analyses, assuming that most of the features do not change concerning the experimental conditions. However, the taxonomic abundance of microbial species can vary widely under the same conditions. Therefore, these methods based on many invariant factors cannot easily detect the differential taxonomic abundance changes in rare microbes. Furthermore, although the negative values generated by logarithmic transformation in DESeq2 may be set to zero values, this process may ignore many rare species and underestimate the diversity of microbial communities.  
The microbiome includes many rare microorganisms (Operational taxonomic units; OTUs) with a composition ratio of 0.01% or less, but their variation tends to be overlooked due to the lack of appropriate approaches. In this study, we described microorganisms whose composition significantly changed after the diet intervention as outliers. We also defined features with a 0.01% or less compositional ratio as minor components and focused on their relative variations. To detect the compositional changes of complex microbial communities including minor microbial components, we developed a new computational framework called Bacterial Relative Variation Outliers (BRAVO), to evaluate the relative variation for each microbial component. This method detects OTUs with differential taxonomic abundances, based on the relative variation index among samples. BRaVO detects outliers with very low relative abundances. Our approach will shed light on the taxonomic abundance changes including minor components that were often ignored in previous methodologies, and help us understand such complex microbial communities.