Author: Eleni Adam, Tieming Ji, Desh Ranjan
Date: 2026-05-18

# The hummingbird

Eleni Adam, Tieming Ji, Desh Ranjan

#### 18 May 2026

#### Package

hummingbird 1.23.0

# Contents

## 1 Introduction

hummingbird is a package for identifying differentially methylated regions (DMRs) between case and control groups using whole genome bisulfite sequencing (WGBS) or reduced representative bisulfite sequencing (RRBS) experiment data.

The hummingbird package uses a Bayesian hidden Markov model (HMM) for detecting DMRs. It fits a Bayesian HMM for one chromosome at a time. The final output of hummingbird are the detected DMRs with start and end positions in a given chromosome, directions of the DMRs (hyper- or hypo-), and the numbers of CpGs in these DMRs.

## 2 Functions

The hummingbird package contains the following three functions:

1. hummingbirdEM: This function reads input data, sets initial values, executes the Expectation-Maximization (EM) algorithm for the Bayesian HMM and infers the best sequence of methylation states.

It takes three parameters as input: the control group data, the case group data and the bin size. A call to this function looks like: hummingbirdEM( experimentInfoControl, experimentInfoCase, binSize = 40), where experimentInfoControl and experimentInfoCase, respectively contain input data for the control and case groups. This input data includes number of methylated reads and number of unmethylated reads for each CpG position for an entire chromosome. Their format needs to be that of a SummarizedExperiment object. In section 3 (Sample Dataset), we provide detailed information on how to organize data into a SummarizedExperiment object. The third parameter binSize is the user desired bin size. Our default bin size is 40 base pairs. A smaller bin size leads to more accurate DMR boundary prediction. A larger bin size leads to faster computational time. The default bin size is chosen by balancing these two factors. More detailed information on the statistical model and how to choose a good bin size can be found in Ji (2019).

2. hummingbirdPostAdjustment: This function is usually executed after executing hummingbirdEM. It allows the researchers to place three additional requirements on DMRs: 1) the minimum length of a DMR, 2) the minimum number of CpGs in a DMR, and 3) the maximum distance (in base pairs) between any two adjacent CpGs in a DMR.

The hummingbirdPostAdjustment function has six parameters. A call to this function looks like: hummingbirdPostAdjustment( experimentInfoControl, experimentInfoCase, emInfo, minCpGs = 10, minLength = 500, maxGap = 300), where experimentInfoControl and experimentInfoCase take the same input data as the function hummingbirdEM; emInfo are results from running the function hummingbirdEM; minCpGs, minLength, maxGap are the aforementioned three extra requirements. Their default values are 10, 500, and 300, respectively.

3. hummingbirdGraph: This function generates observation and prediction graphs for a user specified region. It is usually called after executing hummingbirdEM and hummingbirdPostAdjustment functions.

The function hummingbirdGraph needs five parameters. A call to this function would appear as: hummingbirdGraph(experimentInfoControl, experimentInfoCase, postAdjInfoDMRs, coord1, coord2), where experimentInfoControl and experimentInfoCase are input data as in hummingbirdEM. postAdjInfoDMRs are the reads in the detected DMRs from the results of the function hummingbirdPostAdjustment and coord1 and coord2 are the start and end genomic positions for plotting. The execution of this function produces two figures, which we call the observation figure and the prediction figure. The observation figure shows bin-wise average methylation rate for case and control groups. The prediction figure shows bin-wise prediction, where “0” denotes a predicted normal bin; “1” denotes a predicted hypermethylated bin; and “-1” denotes a predicted hypomethylated bin.

## 3 Sample Dataset

A sample dataset, called “exampleHummingbird”, is provided with the package as an example.

Specifically, it is partial data of chromosome 29 in the large offspring syndrome (LOS) study described in Chen Z. et al (2017). The raw FASTQ files of the WGBS experiment from this study are publicly available at Gene Expression Omnibus (GEO) database with accession no. GSE93775.

In this section, we will use this example data to demonstrate how to organize data in a correct format for our hummingbird package. Our package requires R version 4.0 and Rcpp package.

    library(GenomicRanges)
    library(SummarizedExperiment)
    library(hummingbird)
    data(exampleHummingbird)

First, we use “abnormUM”, “abnormM”, “normM”, and “normUM”, respectively, to denote four matrices that contain numbers of unmethylated reads for the abnormal group, numbers of methylated reads for the abnormal group, numbers of methylated reads for the normal group, and the numbers of unmethylated reads for the normal group. For each of these four matrices, each row is a CpG position, and each column is a biological replicate (for example, a patient, a mouse, etc.). In the LOS study, the abnormal group has four cattle and the normal group has four cattle also. Thus, these four matrices each contain four columns. We require these four matrices to only contain commonly shared CpGs at the same genomic positions. CpGs that are not shared by all biological replicates are removed before analysis. The following shows the first 6 rows from the normM matrix.

    head(normM)

    ##      [,1] [,2] [,3] [,4]
    ## [1,]    8    7   12   10
    ## [2,]    4    4    2    4
    ## [3,]    0    1    0    4
    ## [4,]    2    2    0    2
    ## [5,]    1    1    1    1
    ## [6,]    8    0    0    7

Our Bayesian HMM does not have a requirement of minimum number of biological replicates in each treatment group. The case group (or abnormal group) and control group (or normal group) can have either one or more replicates. The two groups can have unequal number of replicates.

Second, we use vector pos to contain genomic positions of these CpGs in the abovementioned four matrices – “abnormUM”, “abnormM”, “normM”, and “normUM”.

    head(pos)

    ##      [,1]
    ## [1,]  271
    ## [2,]  331
    ## [3,]  363
    ## [4,]  386
    ## [5,]  418
    ## [6,]  464

To use the hummingbird package, we need to put the four matrices and vector pos in two SummarizedExperiment objects, one for the case group and one for the control group. This can be done as follows:

    pos <- pos[,1]
    assaysControl <- list(normM = normM, normUM = normUM)
    assaysCase <- list(abnormM = abnormM, abnormUM = abnormUM)
    exampleSEControl <- SummarizedExperiment(assaysControl,
                                            rowRanges = GPos("chr29", pos))
    exampleSECase <- SummarizedExperiment(assaysCase,
                                        rowRanges = GPos("chr29", pos))

exampleSEControl and exampleSECase are ready for use by the hummingbird package.

To display data in the SummarizedExperiment object, we can do the following.

The CpG positions are:

    rowRanges(exampleSEControl)

    ## UnstitchedGPos object with 4746 positions and 0 metadata columns:
    ##          seqnames       pos strand
    ##             <Rle> <integer>  <Rle>
    ##      [1]    chr29       271      *
    ##      [2]    chr29       331      *
    ##      [3]    chr29       363      *
    ##      [4]    chr29       386      *
    ##      [5]    chr29       418      *
    ##      ...      ...       ...    ...
    ##   [4742]    chr29    399795      *
    ##   [4743]    chr29    399802      *
    ##   [4744]    chr29    399833      *
    ##   [4745]    chr29    399864      *
    ##   [4746]    chr29    399987      *
    ##   -------
    ##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

    rowRanges(exampleSECase)

    ## UnstitchedGPos object with 4746 positions and 0 metadata columns:
    ##          seqnames       pos strand
    ##             <Rle> <integer>  <Rle>
    ##      [1]    chr29       271      *
    ##      [2]    chr29       331      *
    ##      [3]    chr29       363      *
    ##      [4]    chr29       386      *
    ##      [5]    chr29       418      *
    ##      ...      ...       ...    ...
    ##   [4742]    chr29    399795      *
    ##   [4743]    chr29    399802      *
    ##   [4744]    chr29    399833      *
    ##   [4745]    chr29    399864      *
    ##   [4746]    chr29    399987      *
    ##   -------
    ##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

The matrices containing the methylated and unmethylated read count data of the normal group are as follows:

    head(assays(exampleSEControl)[["normM"]])

    ##      [,1] [,2] [,3] [,4]
    ## [1,]    8    7   12   10
    ## [2,]    4    4    2    4
    ## [3,]    0    1    0    4
    ## [4,]    2    2    0    2
    ## [5,]    1    1    1    1
    ## [6,]    8    0    0    7

    head(assays(exampleSEControl)[["normUM"]])

    ##      [,1] [,2] [,3] [,4]
    ## [1,]    4    7    2    4
    ## [2,]   12   11   11   10
    ## [3,]   10   10    8    7
    ## [4,]    8   11   10   13
    ## [5,]    7   11    6   17
    ## [6,]    8    9    7    8

The matrices containing the methylated and unmethylated read count data of the abnormal group are as follows:

    head(assays(exampleSECase)[["abnormM"]])

    ##      [,1] [,2] [,3] [,4]
    ## [1,]   10    7   10   13
    ## [2,]    6    2    6    8
    ## [3,]    3    0    3    0
    ## [4,]    0    1    1    0
    ## [5,]    1    1    2    2
    ## [6,]    6    4    8    7

    head(assays(exampleSECase)[["abnormUM"]])

    ##      [,1] [,2] [,3] [,4]
    ## [1,]    6    3    3    3
    ## [2,]    9    5    6   12
    ## [3,]   12   11    8   20
    ## [4,]    8   13   12   15
    ## [5,]   10   12   12   19
    ## [6,]    8    7    6   14

## 4 Example

This section uses the abovementioned example dataset to show how to use our hummingbird package to infer methylation states. First, we need to load the hummingbird package and the exampleHummingbird dataset. The exampleHummingbird dataset contains the SummarizedExperiment objects, exampleSEControl and exampleSECase, that are ready for use by the hummingbird package.

    library(hummingbird)
    data(exampleHummingbird)

    emInfo <- hummingbirdEM(experimentInfoControl = exampleSEControl,
                            experimentInfoCase = exampleSECase, binSize = 40)

    ## Reading input...
    ## Bin size: 40.
    ## Total lines: 4746, total replicates in normal group: 4 and in abnormal group: 4
    ## Processing input...
    ## Processing input completed...
    ## Calculation of the initial value...
    ## Initial Value calculated...
    ## EM begins...
    ## Iteration: 1
    ## Iteration: 2
    ## Iteration: 3
    ## Iteration: 4
    ## Iteration: 5
    ## Iteration: 6
    ## Iteration: 7
    ## Iteration: 8
    ## Iteration: 9
    ## Iteration: 10
    ## Iteration: 11
    ## Iteration: 12
    ## Iteration: 13
    ## Iteration: 14
    ## Iteration: 15
    ## Iteration: 16
    ## Iteration: 17
    ## Iteration: 18
    ## Iteration: 19
    ## Iteration: 20
    ## Iteration: 21
    ## Iteration: 22
    ## Calculation of states...
    ## EM converged after 22 iterations.
    ## Saving output...
    ## ****** Program ended. ******

    emInfo

    ## GRanges object with 3296 ranges and 4 metadata columns:
    ##          seqnames        ranges strand |  distance      norm    abnorm
    ##             <Rle>     <IRanges>  <Rle> | <integer> <numeric> <numeric>
    ##      [1]    chr29       271-310      * |        40  0.672414  0.711864
    ##      [2]    chr29       311-350      * |        40  0.258065  0.413793
    ##      [3]    chr29       351-390      * |        40  0.156250  0.104348
    ##      [4]    chr29       391-430      * |        40  0.122449  0.126984
    ##      [5]    chr29       431-470      * |        40  0.333333  0.421875
    ##      ...      ...           ...    ... .       ...       ...       ...
    ##   [3292]    chr29 399671-399710      * |        40  0.250000  0.294118
    ##   [3293]    chr29 399751-399790      * |        80  0.617021  0.555556
    ##   [3294]    chr29 399791-399830      * |        40  0.700000  0.743902
    ##   [3295]    chr29 399831-399870      * |        40  0.448980  0.416667
    ##   [3296]    chr29 399951-399990      * |       120  0.108696  0.268293
    ##          direction
    ##          <integer>
    ##      [1]         1
    ##      [2]         1
    ##      [3]         0
    ##      [4]         0
    ##      [5]         0
    ##      ...       ...
    ##   [3292]         0
    ##   [3293]         0
    ##   [3294]         0
    ##   [3295]         0
    ##   [3296]         0
    ##   -------
    ##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

emInfo is a GenomicRanges object that contains the start and end positions of each bin, the distance between the current bin the bin ahead of it, the average methylation rate of normal and abnormal groups and the predicted direction of methylation change (“0” means a predicted normal bin; “1” means a predicted hypermethylated bin; “-1” means a predicted hypomethylated bin).

hummingbirdPostAdjustment adjusts emInfo such that each detected DMR has a user-defined minimum length, minimum number of CpGs, and maximum gap between adjacent CpGs in each DMR. If the user does not define, the default values are minLength=500, minCpGs=10, and maxGap=300.

    postAdjInfo <- hummingbirdPostAdjustment(
        experimentInfoControl = exampleSEControl,
        experimentInfoCase = exampleSECase,
        emInfo = emInfo, minCpGs = 10,
        minLength = 100, maxGap = 300)

    ## Reading input...
    ## Min CpGs: 10, Min Length: 100, Max gap: 300.
    ## Post Adjustment begins...
    ## Post Adjustment completed...
    ## Output DMRs...
    ## There are 3 DMRs in total. The first 3 are displayed.
    ## Region: Start, End, Length, Direction, CpGs
    ## 1: 98391, 98590, 200, -1, 10
    ## 2: 107991, 108350, 360, -1, 12
    ## 3: 110551, 110870, 320, -1, 10
    ## Saving output...
    ## ****** Program ended. ******

    postAdjInfo$DMRs

    ## GRanges object with 3 ranges and 3 metadata columns:
    ##       seqnames        ranges strand |    length direction      CpGs
    ##          <Rle>     <IRanges>  <Rle> | <integer> <integer> <integer>
    ##   [1]    chr29   98391-98590      * |       200        -1        10
    ##   [2]    chr29 107991-108350      * |       360        -1        12
    ##   [3]    chr29 110551-110870      * |       320        -1        10
    ##   -------
    ##   seqinfo: 1 sequence from an unspecified genome; no seqlengths

postAdjInfo is a list of two GenomicRanges objects, the DMRs and the obsPostAdj. Specifically, the DMRs contains the detected regions based on the user-defined arguments (minLength, minCpGs, and maxGap). It contains the refined DMRs with the start genomic position, the end genomic position, length of the region, direction of predicted methylation change (“0” indicates no significant change, “1” indicates predicted hyper-methylation, and “-1” indicates predicted hypo-methylation), and the number of CpGs. The obsPostAdj object contains methylation status of each CpG site.

At last, we use hummingbirdGraph to visualize observations and predictions for a user-defined genomic region. In the observation plot, the horizontal axis shows genomic positions; the vertical axis displays sample average methylation rates for normal and abnormal groups, respectively, for each bin. The prediction plot displays the sample average difference between the abnormal group and the normal group for each bin. Numbers (“0”, “1”, “-1”) indicate the predictions.

The next two figures (the former is an observation plot and the latter is a prediction plot) visualize the second DMR in the above output.

    hummingbirdGraph(experimentInfoControl = exampleSEControl,
                    experimentInfoCase = exampleSECase,
                    postAdjInfoDMRs = postAdjInfo$DMRs,
                    coord1 = 107991, coord2 = 108350)

## 5 Citation

If you use the hummingbird package, please cite the following paper that includes the statistical model and fitting algorithm:

- Ji (2019) A Bayesian hidden Markov model for detecting differentially methylated regions. Biometrics 75(2):663‐673.

## 6 Reference

Real data from the LOS study are from the following paper:

- Chen et al. (2017) Global misregulation of genes largely uncoupled to DNA methylome epimutations characterizes a congenital overgrowth syndrome. Scientific Reports 7, 12667.

## 7 Session Info

The presented analysis was conducted on:

    sessionInfo()

    ## R version 4.6.0 Patched (2026-05-01 r89994)
    ## Platform: aarch64-apple-darwin23
    ## Running under: macOS Tahoe 26.3.1
    ##
    ## Matrix products: default
    ## BLAS:   /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRblas.0.dylib
    ## LAPACK: /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1
    ##
    ## locale:
    ## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
    ##
    ## time zone: America/New_York
    ## tzcode source: internal
    ##
    ## attached base packages:
    ## [1] stats4    stats     graphics  grDevices utils     datasets  methods
    ## [8] base
    ##
    ## other attached packages:
    ##  [1] hummingbird_1.23.0          SummarizedExperiment_1.43.0
    ##  [3] Biobase_2.73.1              MatrixGenerics_1.25.0
    ##  [5] matrixStats_1.5.0           GenomicRanges_1.65.0
    ##  [7] Seqinfo_1.3.0               IRanges_2.47.1
    ##  [9] S4Vectors_0.51.2            BiocGenerics_0.59.2
    ## [11] generics_0.1.4              BiocStyle_2.41.0
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] Matrix_1.7-5        jsonlite_2.0.0      compiler_4.6.0
    ##  [4] BiocManager_1.30.27 tinytex_0.59        Rcpp_1.1.1-1.1
    ##  [7] magick_2.9.1        jquerylib_0.1.4     yaml_2.3.12
    ## [10] fastmap_1.2.0       lattice_0.22-9      R6_2.6.1
    ## [13] XVector_0.53.0      S4Arrays_1.13.0     knitr_1.51
    ## [16] DelayedArray_0.39.2 bookdown_0.46       bslib_0.11.0
    ## [19] rlang_1.2.0         cachem_1.1.0        xfun_0.57
    ## [22] sass_0.4.10         otel_0.2.0          SparseArray_1.13.2
    ## [25] cli_3.6.6           magrittr_2.0.5      digest_0.6.39
    ## [28] grid_4.6.0          lifecycle_1.0.5     evaluate_1.0.5
    ## [31] abind_1.4-8         rmarkdown_2.31      tools_4.6.0
    ## [34] htmltools_0.5.9