Abstract

With the help of rapidly developing sequencing technologies, an increasing number of microbiome datasets are generated and analysed. At present, diversity analysis of taxonomic profiling data is mainly conducted using composition-based methods, which ignores the interactions between community members and limits the study of community dynamics.The goal of *mina* is to provide a framework for microbial community analysis based on higher order community structures to better understand the principles that govern the establishment of those communities. In addition, a bootstrap-permutation based network comparison method was developed to compare global and local ecological networks and to statistically assess their dissimilarity. *mina* package version: 1.13.0

The package is used for microbial profiling data analysis, including community similarity / dissimilarity / distance calculation and network comparison.

*mina* package expects count data (e.g. OTU table or ASV table) to represent community profiling results and a descriptive table which indicates the information of each sample. In the quantitative table, each row contains one composition in the community and each column represents one profiled sample. In the descriptive table, same samples as rows in quantitative table should be included in the column “**Sample_ID**”.

Using `new()`

to create a new object and then import data into the object. The new object could be generated and slots could be imported simultaneously:

```
library(mina)
#>
#> Attaching package: 'mina'
#> The following object is masked from 'package:base':
#>
#> norm
# maize_asv2 and maize_des2 are subset of maize_asv and maize_des
maize <- new("mina", tab = maize_asv2, des = maize_des2)
```

Please be aware that the descriptive table have to contain a column called “**Sample_ID**” which includes the same samples indicated in the quantitative tables. See an example here:

```
head(maize_des)
#> Sample_ID Host_genotype Compartment Soil Management
#> 1 RT_1H 1_B73 root DEMO NK
#> 2 RT_2H 1_B73 root DEMO NK
#> 3 RT_3H 1_B73 root DEMO NK
#> 4 RT_7H 2_DK105 root DEMO NK
#> 5 RT_8H 2_DK105 root DEMO NK
#> 6 RT_9H 2_DK105 root DEMO NK
```

For the quantitative table, each column correspond to one sample indicated in the descriptive table and each row represent one composition in the community.

Typically the analysis of microbial community data includes estimating within and between sample diversities (alpha- and beta-diversity) based on compositions. By counting the number of observed compositions and evaluating the evenness of their distribution, alpha diversity of each community is quantified. Distance or dissimilarity between samples calculated from counts differentiation of compositions is used to indicate the beta diversity of community.

Due to the varied sequencing depth, it is essential to normalize the data before the analysis of the diversity. Rarefaction and normalization by total sum are available here. For rarefaction, to reduce the random effect, multiple times bootstrap is recommended. The normalized table will be stored in the same *mina* object automatically when it were given as input.

```
# check available normalization methods
? norm_tab_method_list
# normalized by total sum
maize <- norm_tab(maize, method = "total")
# normalized by rarefaction
maize <- norm_tab(maize, method = "raref", depth = 5000)
#> 270 samples removed for low depth
# normalized by rarefaction and bootstrap 9 times
maize <- norm_tab(maize, method = "raref", depth = 5000, multi = 9)
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
```

When given a matrix for normalization, the normalized matrix will be returned.

```
# normalized by total sum
maize_asv_norm <- norm_tab(maize_asv2, method = "total")
# normalized by rarefaction
maize_asv_norm <- norm_tab(maize_asv2, method = "raref", depth = 5000)
#> 270 samples removed for low depth
# normalized by rarefaction and bootstrap 99 times
maize_asv_norm <- norm_tab(maize_asv2, method = "raref", depth = 5000,
multi = 9)
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
#> 270 samples removed for low depth
```

Based on the normalized quantitative table, distance / dissimilarity could be calculated between pairwise samples and used for beta-diversity analysis.

```
# check available dissimilarity parameters
? com_dis_list
# tidy the norm tab, intial tab and des tab
maize <- fit_tabs(maize)
# community dissimilarity calculation, Bray-Curtis used in example
maize <- com_dis(maize, method = "bray")
# TINA dissimilarity in Schmidt_et_al_2016
# maize <- com_dis(maize, method = "tina")
```

For *TINA* dissimilarity described in Schmidt *et al.* 2017, in `com_dis()`

function, *Spearman* correlation and weighted Jaccard was used by default, to calculate *TINA* with other options, use function `tina()`

.

To evaluate the biological meaningful variance to noise ratio, the percentage of variance that could not be explained by any factors was calculated.

```
# get the unexplained variance ratio of quantitative table according to the
# group information indicated in descriptive table.
com_r2(maize, group = c("Compartment", "Soil", "Host_genotype"))
#> [1] 0.521
# use tables as input
maize_dis <- dis(maize)
get_r2(maize_dis, maize_des, group = c("Compartment", "Soil", "Host_genotype"))
#> [1] 0.521
```

PCoA (Principle Coordinate Analysis) is usually used for the visualization of beta-diversity of microbial community data. By using different color and shape, samples from different conditions are compared.

```
# dimensionality reduction
maize <- dmr(maize)
# plot the community beta-diversity
# separate samples from different conditions by color, plot PCo1 and PCo2
p1 <- com_plot(maize, match = "Sample_ID", color = "Compartment")
# plot PCo3 and PCo4
p2 <- com_plot(maize, match = "Sample_ID", d1 = 3, d2 = 4, color =
"Compartment")
# in addition, separate samples from different soil type by shape
p3 <- com_plot(maize, match = "Sample_ID", color = "Compartment", shape =
"Soil")
# plot PCo1 and PCo4
p4 <- com_plot(maize, match = "Sample_ID", d1 = 1, d2 = 4, color =
"Compartment", shape = "Soil")
```

When using dissimilarity matrix as input, the `dmr()`

function is used to reduce the dimension of data and `pcoa_plot()`

is used for plotting.

For the microbial community research, diversity analysis capture only static features and co-occurrence networks are typically inferred to indicate dynamics of the system.

Correlation will be calculated according to the covariance of compositions across samples. When significance test is applied, `rcorr()`

from `Hmisc`

.

```
# check available adjacency matrix
? adj_method_list
# Pearson and Spearman correlation
maize <- adj(maize, method = "pearson")
# Pearson and Spearman correlation with significance test
maize <- adj(maize, method = "spearman", sig = TRUE)
```

Also the function could be applied to matrix directly, the correlation between pairwise rows will be calculated.

By removing the non-significant(waiting for update) and weak correlations, the network of each adjacency matrix is generated and closely related nodes will be inferred by clustering methods. In the package, Markov Cluster Algorithm (MCL, Dongen, 2000) and Affinity Propagation (AP, Frey *et al*, 2007) are implemented for network clustering.

```
# check available network clustering methods
? net_cls_list
#> No documentation for 'net_cls_list' in specified packages and libraries:
#> you could try '??net_cls_list'
# network clustering by MCL
maize <- net_cls(maize, method = "mcl", cutoff = 0.6)
#> 199 components are removed for clustering.
# network clustering by AP
maize <- net_cls(maize, method = "ap", cutoff = 0.6, neg = FALSE)
#> 199 components are removed for clustering.
```

Also it is possible to give a adjacency matrix directly and got the generated cluster data frame.

By accumulating the relative abundance of compositions belong to the same network clusters, the higher-order feature quantitative table is obtained and could be used for further diversity analysis. Besides, compositions belong to the same phylogenetic group could also be grouped together as new quantitative table.

According to the network cluster assignments, compositions belong to the same higher order level group are accumulated by summing up their relative abundances.

Same diversity analysis could be applied to cluster table and compared with composition based table.

To compare the network of communities, pairwise distance between adjacency matrix, which present all connection information, are calculated. By substrate adjacency matrix (**A**) by the degree matrix (**D**), Laplacian matrix is obtained and the corresponding eigenvector and eigenvalues are calculated. Spectral distance then defined as the Euclidean distance between first *k* eigenvalues. Alternatively, Jaccard distance between matrix is implemented as dividing the sum of matrix contrast by the sum of larger absolute value between two adjacency matrices.

To be able to test the significance of distances between matrices, a bootstrap-permutation based method is developed. By subsampling and bootstrap, true correlation adjacency matrices were constructed from subset of original data. Then the metadata of samples is randomly swapped as permutated datasets, from which the pseudo correlation coefficient is calculated. By comparing the true adjacency matrices with the pseudo ones, the significance of distance is obtained.

```
# compare the networks from different compartments
maize <- fit_tabs(maize)
maize <- bs_pm(maize, group = "Compartment")
# only get the distance, no significance test
maize <- bs_pm(maize, group = "Compartment", sig = FALSE)
```

When the composition number is big, the bootstrap-permutation could take very long time, thus pre-filtering is needed. `g_size`

is the minimum number of samples for groups defined by `group`

. Conditions with less than `g_size`

would be removed for later analysis and this is set as 88 by default. `s_size`

is the sub-sampling size for bootstrap and permutation, 30 by default. `s_size`

should definitely smaller than `g_size`

and preferably smaller than half of it. Also compositions appear in less than specific percentage of samples could be filtered by setting the occupancy threshold `per`

and `rm`

. By default, the compositions which present in less than 10% samples would be filtered. When the quantitative matrix is too big, one could choose to output the bootstrap and permutation results separately for each comparison.

```
# set the size of group to remove consitions with less sample
# also larger s_size will lead to more stable results but will consume more
# computation and time resource
maize <- bs_pm(maize, group = "Compartment", g_size = 200, s_size = 80)
# remove the compositions appear in less than 20% of samples
maize <- bs_pm(maize, group = "Compartment", per = 0.2)
# set the bootstrap and permutation times. Again the more times bootstrap
# and permutation, the more reliable the significance, with increased
# computation and time resource.
maize <- bs_pm(maize, group = "Compartment", bs = 11, pm = 11)
# output the comparison separately to the defined directory
bs_pm(maize, group = "Compartment", bs = 6, pm = 6,
individual = TRUE, out_dir = out_dir)
```

After getting the true and pseudo adjacency matrices, Spectral and Jaccard distance defined before is then calculated and p value is obtained by comparing the *F* (the real distance) and *Fp* (the pseudo distance) following the formula: p = \(\frac { C_{F_p > F} + 1 }{ N_{dis} + 1 }\) For the individual generated network comparison results, the distance calculation is implemented by the function `net_dis_indi()`

. Same methods are available.

```
# check the available methods
? net_dis_method_list
# calculate the distances between matrices
maize <- net_dis(maize, method = "spectra")
maize <- net_dis(maize, method = "Jaccard")
# check the ditance results and significance (if applicable)
dis_stat(maize)
# the comparison stored separately in previous step
ja <- net_dis_indi(out_dir, method = "Jaccard")
dis_stat(ja)
spectra <- net_dis_indi(out_dir, method = "spectra")
dis_stat(spectra)
```