Interval arithmetic

Version Compatibility

Reference examples tested with: bedtools 2.31+, pybedtools 0.10+, pyranges 0.1+ (or 1.0+ - see note), bioframe 0.7+.

Before using code patterns, verify installed versions match. If versions differ:

• CLI: bedtools --version then bedtools <subcommand> --help to confirm flags
• Python: pip show <package> then help(module.function) to check signatures

pyranges has a major-version API split: pyranges 0.x and the 1.0 rewrite (package pyranges1) differ in method names and return shapes. Verify with import pyranges; pyranges.__version__ before pasting v0 idioms. If code throws an error, introspect the installed package and adapt rather than retrying.

Interval Arithmetic

"Which of my peaks overlap promoters, and how do I combine/subtract/annotate interval sets?" -> Apply exact, deterministic set operations to sorted interval files, guarding the preconditions (prior sort, the -sorted chromosome-order contract, -split) that otherwise corrupt the answer.

• CLI: bedtools intersect -a a.bed -b b.bed -u, bedtools merge, bedtools subtract, bedtools map -c 4 -o mean
• Python: a.intersect(b, u=True), a.merge() (pybedtools); pr_a.overlap(pr_b) (pyranges); bf.overlap(df1, df2) (bioframe)

The Single Most Important Modern Insight -- The Arithmetic Is Exact; the Danger Is the Silent Preconditions

The set operations themselves are exact and deterministic - bedtools, pyranges, and bioframe compute identical geometry on the same 0-based half-open intervals. The bugs are never in the arithmetic; they hide in four preconditions that fail quietly, returning a plausible wrong answer with exit code 0:

1. merge, map, closest, groupby require prior sort. merge only collapses records that are adjacent in file order - on unsorted input, overlapping intervals survive un-merged and downstream counts are wrong, with no warning.
2. -sorted requires sorted input in a shared chromosome order. It swaps intersect's in-memory interval tree for a low-memory chromosome sweep. Modern bedtools (>=~2.25) detects unsorted or differently-ordered -sorted input and errors out (exit 1: ... is not sorted / chromomsome sort ordering ... is inconsistent); older versions silently swept past overlaps and under-reported. Pass -g genome.txt to pin the expected chromosome order (reproducible, and it catches the subtler missing-chromosome cases). The mismatch that stays SILENT on every version is a chromosome-NAME difference (chr1 vs 1), which returns an empty result with no error.
3. -split changes whether the count is exons or the spanning envelope. A BED12 record or spliced BAM read (CIGAR N) spans introns; without -split bedtools intersects the whole intron-spanning envelope, silently inflating RNA-seq overlaps. With -split it intersects only the blocks (exons).
4. A raw overlap count is not association. Long features, clustered features, and uneven coverage all inflate it; the number means nothing without a null. bedtools fisher is a weak analytic screen, not the answer - route rigorous significance to overlap-significance.

Tool Taxonomy

Tool	Role	Mechanism	When
bedtools	CLI interval algebra (reference implementation)	streaming sweep on sorted input; in-memory tree otherwise	shell pipelines, large files, reproducible one-liners
pybedtools	Python wrapper over bedtools	shells out to the bedtools binary; BedTool objects, flags as kwargs	inside a Python script; need exact bedtools parity; chaining with pandas
pyranges	pure-Python vectorized engine	native NumPy/pandas PyRanges; no bedtools dependency	large in-memory joins, no bedtools install, dataframe-native; mind the v0/v1 split
bioframe	functions on a plain pandas DataFrame	vectorized pandas merges; columns chrom/start/end	data already in pandas / the cooler-Hi-C ecosystem

All three Python engines compute the same overlaps; the porting bugs are about default strand handling and return shape (pyranges overlap vs join vs intersect; bioframe overlap with how=), not geometry.

Decision Tree by Scenario

Scenario	Recommended	Why
Quick overlap on the command line	bedtools intersect -u	no Python overhead; reproducible one-liner
Inside a pandas/Python pipeline	pybedtools or pyranges/bioframe	stays in-process; pyranges/bioframe need no bedtools binary
Whole-genome-scale intersect	intersect -sorted -g genome.txt	low-memory sweep; modern bedtools errors on a sort/order mismatch, -g pins the expected chromosome order
Spliced reads / BED12 vs exons	add -split	otherwise the intron-spanning envelope is intersected (RNA-seq inflation)
Are two SV/CNV calls the same event?	-f 0.5 -r (50% reciprocal)	one-sided fractions let a giant interval swallow a tiny one
Transfer/aggregate B values onto A	bedtools map -c COL -o OP	columnar alternative to intersect -wo | groupby
Build consensus peakset from replicates	cat | sort | merge -d N	collapses replicate peaks within N bp
Multi-sample shared-region map	multiinter / unionbedg	presence/absence (intervals) or stacked signal matrix
Is the overlap more than chance?	-> overlap-significance	raw count is length/coverage-confounded; needs a permutation null
Peaks not yet called	-> chip-seq/peak-calling or atac-seq/atac-peak-calling	this category operates on existing intervals

Intersect - the Workhorse

The output-mode flags do not change what overlaps; they change what gets printed (the #1 source of confusion). Full flag semantics are in usage-guide.md.

bedtools intersect -a peaks.bed -b genes.bed -u            # whole A, once, if it overlaps >=1 B
bedtools intersect -a peaks.bed -b genes.bed -v            # A features with NO overlap (set difference)
bedtools intersect -a peaks.bed -b genes.bed -c            # per-A count of B hits (0 if none)
bedtools intersect -a peaks.bed -b genes.bed -wa -wb       # whole A + whole B, one line per pair ("join")
bedtools intersect -a peaks.bed -b genes.bed -loj          # left outer join: every A, NULL B if none
bedtools intersect -a peaks.bed -b genes.bed -wo           # A+B+bp-of-overlap, only A with overlap
bedtools intersect -a peaks.bed -b genes.bed -wao          # like -wo but A-with-no-overlap kept (B=., overlap=0)

import pybedtools

a = pybedtools.BedTool('peaks.bed')
b = pybedtools.BedTool('genes.bed')
a.intersect(b, u=True)            # flags become kwargs
a.intersect(b, wa=True, wb=True)
a.intersect(b, c=True)

Subtract, Merge, Complement, Cluster

bedtools subtract -a a.bed -b b.bed             # clip the overlapping portions out of A (A can fragment)
bedtools subtract -a a.bed -b b.bed -A          # drop the ENTIRE A feature if any part overlaps B
bedtools sort -i a.bed | bedtools merge -d 0    # collapse overlapping + book-ended; -d 0 is the default
bedtools sort -i a.bed | bedtools merge -c 4,5 -o distinct,sum   # summarize columns while merging
bedtools complement -i a.bed -g genome.txt      # the gaps: genome NOT covered by A (genome file required)
bedtools sort -i a.bed | bedtools cluster -d 0  # assign a cluster id to overlapping/adjacent features

Valid -o operations: sum, min, max, absmin, absmax, mean, median, mode, antimode, stdev, sstdev, collapse, distinct, count, count_distinct, first, last. merge -d 0 merges overlapping and book-ended (touching) features but NOT a 1 bp gap; -d 1 does.

Map - Transfer Values, and Groupby - Aggregate

Goal: Summarize a column of overlapping B features onto each A interval (e.g. mean signal per gene).

Approach: For each sorted A interval, map collects overlapping B features and applies an aggregation -o to a B column -c; groupby is the single-file SQL-style aggregator after an intersect -wo.

bedtools map -a genes.bed -b scores.bedgraph -c 4 -o mean      # both inputs MUST be sorted
bedtools intersect -a genes.bed -b peaks.bed -wo \
  | bedtools groupby -g 1,2,3,4 -c 13 -o sum                   # group on A cols, sum the overlap-bp col

import pybedtools

genes = pybedtools.BedTool('genes.bed').sort()
scores = pybedtools.BedTool('scores.bedgraph').sort()
genes.map(scores, c=4, o='mean')

Multi-Sample: Multiinter and Unionbedg

bedtools multiinter -header -names s1 s2 s3 -i s1.bed s2.bed s3.bed   # which files cover each sub-interval
bedtools unionbedg -header -names s1 s2 s3 -i s1.bg s2.bg s3.bg       # stack bedGraph signal into a matrix

multiinter is the interval presence/absence map (build a consensus by filtering its num/list columns); unionbedg is its signal-track analog.

Jaccard and Fisher - Mechanics Only

jaccard is a single similarity scalar |A n B| / |A u B| in [0,1], useful for all-vs-all dataset clustering - it is NOT a significance test (no p-value). fisher builds a 2x2 table and returns a Fisher p, but it estimates the in-neither cell from a mean-interval-size/genome-size heuristic, ignores genome structure, and is prone to inflation - treat it as a fast triage screen only.

bedtools jaccard -a a.bed -b b.bed -g genome.txt        # both sorted; reports jaccard + n_intersections
bedtools fisher  -a a.bed -b b.bed -g genome.txt         # weak analytic null; validate any low p by simulation

For a defensible enrichment p-value (size-preserving permutation in an accessible workspace, GAT/regioneR/LOLA/GREAT), route to overlap-significance.

Per-Method Failure Modes

Merge without sorting first

Trigger: bedtools merge (or cluster/map/groupby) on unsorted input. Mechanism: merge only collapses records adjacent in file order. Symptom: overlapping intervals survive un-merged; counts wrong, no error. Fix: bedtools sort -i in.bed | bedtools merge.

-sorted on unsorted or differently-ordered input

Trigger: intersect -sorted on unsorted input or files in different chromosome orders. Mechanism: the sweep walks both files in lockstep assuming a shared order. Symptom: modern bedtools (>=~2.25) errors out (... is not sorted / chromomsome sort ordering ... is inconsistent, exit 1); pre-2.25 returned a silently smaller set. Fix: sort every input identically and pass -g genome.txt to pin the order; on an old bedtools, suspect this when a result is surprisingly small.

Missing -split on spliced features

Trigger: intersecting BED12 / spliced BAM without -split. Mechanism: the intron-spanning envelope is treated as solid. Symptom: intronic positions "overlap" exons; RNA-seq overlap inflated/smeared. Fix: add -split whenever an operand is BED12 or a spliced alignment and exon-level truth is required.

-f vs -F swapped, or default 1 bp overlap

Trigger: thresholding the wrong set, or no -f at all. Mechanism: -f is a fraction of A, -F a fraction of B (default -f 1e-9 = any 1 bp); A and B play asymmetric roles. Symptom: a tiny peak "inside" a 2 Mb gene by one base; swapping -a/-b changes counts. Fix: threshold the small set; use -r for "same event" concordance.

complement/shuffle without a genome file

Trigger: complement (or closest/map order assumptions) without -g. Mechanism: bedtools cannot know where chromosomes end. Symptom: error, or gaps/coordinates that run past chromosome ends. Fix: pass a correct -g genome.txt built from the same assembly.

chrom-naming mismatch (chr1 vs 1)

Trigger: BED uses chr1, genome/other file uses 1. Mechanism: chromosomes never match. Symptom: empty/zero output, no error. Fix: harmonize naming across all inputs and the genome file.

Quantitative Thresholds

Threshold	Source	Rationale
Overlap fraction -f (state explicitly)	analysis choice	default -f 1e-9 (1 bp) is rarely the biological question; threshold the small set
50% reciprocal overlap (-f 0.5 -r)	SV/CNV field convention	"are these the same event"; one-sided lets a big interval swallow a small one
Merge -d (e.g. 100 bp for replicate consensus)	replicate-merge convention	collapses near-coincident replicate peaks; tune per assay/resolution
merge -d 0 (default)	bedtools default	merges overlapping + book-ended, NOT a 1 bp gap (use -d 1 for that)

Common Errors

Error / symptom	Cause	Solution
Empty intersect output	chrom naming mismatch (chr1 vs 1)	harmonize naming across files + genome.txt
merge left overlaps behind	input not sorted	sort before merge/cluster/map/groupby
-sorted errors or (old bedtools) returns too few	unsorted or mismatched chromosome order	sort all inputs identically; add -g genome.txt to pin order
RNA-seq overlap looks inflated	missing -split on BED12/spliced BAM	add -split
Negative start / past-chromosome-end	wrong/missing -g genome.txt	pass a correct chrom-sizes file
pyranges AttributeError	0.x vs 1.0 API mismatch	check pyranges.__version__; use matching method names

References

• Quinlan AR, Hall IM. 2010. BEDTools: a flexible suite of utilities for comparing genomic features. Bioinformatics 26:841-842.
• Dale RK, Pedersen BS, Quinlan AR. 2011. Pybedtools: a flexible Python library for manipulating genomic datasets and annotations. Bioinformatics 27:3423-3424.
• Stovner EB, Sætrom P. 2020. PyRanges: efficient comparison of genomic intervals in Python. Bioinformatics 36:918-919.
• Open2C, Abdennur N, Fudenberg G, Flyamer IM, Galitsyna AA, Goloborodko A, Imakaev M, Venev SV. 2024. Bioframe: operations on genomic intervals in pandas dataframes. Bioinformatics 40:btae088.

Related Skills

• bed-file-basics - BED format, coordinate systems, and the conversions this skill depends on
• overlap-significance - Whether an overlap count exceeds a matched null (permutation, GAT/regioneR/LOLA/GREAT)
• proximity-operations - closest, window, flank, slop for adjacency rather than membership
• coverage-analysis - per-base depth and bedGraph signal feeding map/unionbedg
• gtf-gff-handling - exon/feature models whose -split behavior this skill depends on
• chip-seq/peak-calling - source of the peak BED files these operations consume
• atac-seq/consensus-peakset - replicate merge via merge/multiinter