Does colorectal cancer significantly influence the assembly of gut microbial communities?

Dataset description

Forty-six gut microbiome samples from patients with CRC and fifty-six gut microbiome samples from healthy individuals were pyro-sequenced successfully by Wang et al. (2012), and the raw data generated by their sequencing operations were downloaded from the Short Reads Archive (accession number SRP005150). We recalculated the OTU (Operational Taxonomic Units) tables with 98% similarity cutoff threshold from the raw data using the Mothur software pipeline (Schloss et al., 2009). We picked 4,868 OTUs in total with a range of 12–266 OTUs per sample. Our recalculated dataset was then divided into 2 groups: the CRC group (the samples from CRC patients) and the control group (the samples from healthy individuals).

The computational procedure for the neutrality test

We used two sampling formulae proposed by Ewens (1972) and Etienne (2005) respectively to test the fitting of neutral theory model to the gut microbiome dataset. The Ewens formula was originally developed for testing the neutrality of gene mutation in molecular biology by Ewens (1972) and later adapted for testing the neutral theory of biodiversity (Hubbell, 2001). The formula describes the probability of species abundance distribution without dispersal limitation. The Etienne (2005) formula added the dispersal limitation to Ewens formula and should perform better if the dispersal limitation plays a significant role in shaping community. Dispersal limitation is controlled by parameter m, which captures the probability of a randomly chosen individual in a local community is replaced by an offspring of a randomly chosen individual from the metacommunity.

To evaluate which of the two formulae is more suited for the gut microbiome dataset, we compared the log-likelihoods computed from both formulae. The better one (with larger likelihood value) was then used to test if the observed microbial community in samples satisfied the neutral theory by comparing the log-likelihoods of the observed microbial community and neural-theoretic (artificially simulated) microbial community. We also expect that the possible difference between Ewens and Etienne log-likelihoods may reveal the existence or lack of dispersal limitation in the gut microbial community.

The Ewens (1972) sampling formula was originally proposed to describe the probability distribution of alleles in gene mutations and later introduced into ecology by Hubbell (2001) to compute the likelihood of the presence of an ecological community consisting of S species with abundance of n₁, n_2…n_s and to measure the compliance of neutral theory prediction. The formula has the following form: (1)${\displaystyle Pr\left(n_1,n_2,\dots ,n_s|\theta ,J\right)=\frac{J!{\theta }^s}{1^{{\varphi }_1}{2}^{{\varphi }_2}\dots J^{{\varphi }_J}{\varphi }_1!{\varphi }_2!\dots {\varphi }_J!\prod _{K=1}^J\left(\theta +K-1\right)}}$ where K is counter variable ranging from 1 to J, J is the number of individuals in the community, S is the number of species in the community, θ is biodiversity parameter, n_i is the abundance of species i, and ϕ_a is the number of species with abundance a. This formula does not include the effect of dispersal limitation, which implies that the immigration rate m =1.

Etienne (2005) proposed a new formula for testing the neutral theory for biodiversity that considers the dispersal limitation explicitly (i.e., m < 1). It has the following form: (2)${\displaystyle P\left(D|\theta ,m,J\right)=\frac{J!}{\prod _{i=1}^S{n}_i\prod _{j=1}^J{\varphi }_j!}\frac{{\theta }^S}{{\left(I\right)}_J}\sum _{A=S}^{J}K\left(D,A\right)\frac{I^A}{{\left(\theta \right)}_A}}$ where m is defined as: (3)${\displaystyle m=\frac{I}{I+j-1}}$ and K(D, A) is defined as: (4)${\displaystyle K\left(D,A\right)=\sum _{\left\{a_1,a_2,\dots ,a_s|\sum _{i=1}^S{a}_i=A\right\}}\prod _{i=1}^S\frac{{\bar{S}}_{\left(n_i,a_i\right)}{\bar{S}}_{\left(a_1,1\right)}}{{\bar{S}}_{\left(n_i,1\right)}}.}$ We compared the performance (measured in D) of two formulae on the dataset to detect the possible effect of dispersal limitation using the following log-likelihood ratio test, (5)${\displaystyle D=-2ln\left(\frac{L_0}{L_1}\right)=-2\left[ln\left(L_0\right)-ln\left(L_1\right)\right]}$ where, L₀ is the null model and L₁ isthe alternative model, D is the deviation that is twice the difference between the log-likelihoods of the two formulae. The p-value computed follows a X²-distribution with the degree of freedom being one.

We used the exact neutrality test method (Etienne, 2007) to test the neutrality of community (i.e., the statistical fitness of the neutral theory model to the dataset). In brief, we first apply the maximum likelihood estimation (MLE) method to estimate the parameters of the neutral model from the observed samples. The de facto standard R package UNTB for testing the neutral theory (Hankin, 2007) was utilized to perform the MLE. Second, for each sample, we simulated 100 artificial communities (datasets) using parameters (θ, I, J) estimated from observed samples and then used Etienne’s formula to calculate the likelihood for each artificial dataset, namely P_s. Finally, we compared the mean value of the likelihoods (P_s) of 100 artificial datasets for each sample and the likelihood (P) of corresponding observed sample using the Chi-squared test under the null hypothesis that there is no significant difference between the probability from observed community and the values computed from the artificial data sets. If no significant difference between P_s and P₀ was detected, the community would be considered neutral.

The comparison of Ewens and Etienne sampling formulae

Detailed results of the gut microbiome calculated with Ewens and Etienne formulae were exhibited in the online supplementary Tables S1 and S2, respectively. The comparison of the performance of two methods shows that Ewens and Etienne formulae made no significant difference in terms of the log-likelihood (p > 0.05) in all the samples we tested. In another word, both methods performed equally well with the dataset. Given that one sample failed to compute the result using Etienne’s formula because of too few species, the Ewens formula was used to test the neutrality in the following analysis.

Ewens’ neutrality exact test and comparison of the diversity parameter (θ)

For each sample, the likelihood (P₀) of observed dataset and the average likelihood (P_s) of corresponding 100 artificially simulated datasets were compared using the log-likelihood ratio test. In total, approximately 3.9% (4/102) samples passed the exact neutrality test. The test results of the samples that passed the neutrality test are listed in Table 1, and the results of the rest samples are listed in the online supplementary Tables. In the CRC group, 6.5% (3/46) satisfied the neutral prediction, and in the control (healthy) group 1.8% (1/56) samples satisfied. The result of the positive rates of neutrality tests from both the healthy (control) and CRC groups is also displayed in Fig. 1. No significant difference between both the groups was detected statistically (p = 0.324). The average diversity parameter θ of each group was calculated and displayed in Fig. 2. The average θ value of CRC group is 42.89 and the average θ value of the control group is 57.13. The CRC group exhibited significantly higher θ value than the control group (p < 0.01).