Research Article: A 3-dimensional mathematical model of microbial proliferation that generates the characteristic cumulative relative abundance distributions in gut microbiomes

Date Published: August 8, 2017

Publisher: Public Library of Science

Author(s): Lena Takayasu, Wataru Suda, Eiichiro Watanabe, Shinji Fukuda, Kageyasu Takanashi, Hiroshi Ohno, Misako Takayasu, Hideki Takayasu, Masahira Hattori, Joao B Xavier.


The gut microbiome is highly variable among individuals, largely due to differences in host lifestyle and physiology. However, little is known about the underlying processes or rules that shape the complex microbial community. In this paper, we show that the cumulative relative abundance distribution (CRAD) of microbial species can be approximated by a power law function, and found that the power exponent of CRADs generated from 16S rRNA gene and metagenomic data for normal gut microbiomes of humans and mice was similar consistently with ∼0.9. A similarly robust power exponent was observed in CRADs of gut microbiomes during dietary interventions and several diseases. However, the power exponent was found to be ∼0.6 in CRADs from gut microbiomes characterized by lower species richness, such as those of human infants and the small intestine of mice. In addition, the CRAD of gut microbiomes of mice treated with antibiotics differed slightly from those of infants and the small intestines of mice. Based on these observations, in addition to data on the spatial distribution of microbes in the digestive tract, we developed a 3-dimensional mathematical model of microbial proliferation that reproduced the experimentally observed CRAD patterns. Our model indicated that the CRAD may be determined by the ratio of emerging to pre-existing species during non-uniform spatially competitive proliferation, independent of species composition.

Partial Text

The human gut harbors trillions of microbes belonging to hundreds of species. The structure of the gut microbiome is influenced by individual lifestyle, including dietary habits and host physiology, including disease, resulting in a high degree of interindividual variability in species richness and abundance [1–8]. In addition to many studies of the ecological and biological factors that influence the diversity of human gut microbiomes, several studies have reported the universal features shared among individual gut microbiomes. For instance, some studies found that human gut microbiomes can be classified into a few distinct clusters, called enterotypes, that are characterized by the relative abundance of a few particular taxa [9, 10]. Some groups of the gut species exhibit robust bistable abundance distributions [11]. Host-independent dynamics of the high interindividual variability in the human gut microbiome have also been observed [12]. Although these studies revealed several fundamental features of the structure of the gut microbiome, independent of the high variability, studies that explore the underlying rules and processes that shape the human gut microbiome remain scarce.

Overall, we found that the CRAD indicated that gut microbiomes exhibiting high interindividual variability show robust community structure. We approximated the CRADs by power law functions and estimated the power exponent by MLE (S1 Table), further suggesting that the CRADs underlie universal rule shaping the gut microbiome, independent of host-associated factors such as lifestyle, physiology, or genetic background. Since most of the CRAD variations observed in the various microbial communities could be explained by our mathematical model developed in this study without considering microbial growth rate or interactions, it can be suggested that spatially competitive proliferation of unevenly distributed microbes is the primary process generating CRADs following power law. In addition, subtle proliferation differences between microbial species were amplified to produce large differences over time in the present model. This property of our model would generate a random change in the ranking of the resulting abundant species, even if similar species are involved in the initial stages of proliferation, which is concordant with the high interindividual variability observed in the gut microbiome even for monozygotic twins [33]. The positive correlation of the β value of CRAD with the species richness and the Shannon index that evaluate ecological features of the bacterial community implies that the β value of CRAD can also be used as a novel metric for ecological evaluation of the bacterial community. We found that similar β values were observed in many of a variety of samples analyzed in this study though it is known that the species richness and diversity index are varied by various factors. This ambivalence might be partly due to involvement of various components in community structure such as bacterial interaction and bacterial growth in the CRADs and β values of actual data.




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