# Identity by descent¶

The TreeSequence.ibd_segments() method allows us to compute segments of identity by descent.

Note

This documentation page is preliminary

Todo

Relate the concept of identity by descent to the MRCA spans in the tree sequence.

## Examples¶

Let’s take a simple tree sequence to illustrate the TreeSequence.ibd_segments() method and associated Identity classes:

import tskit
import io
from IPython.display import SVG

nodes = io.StringIO(
"""\
id      is_sample   time
0       1           0
1       1           0
2       1           0
3       0           1
4       0           2
5       0           3
"""
)
edges = io.StringIO(
"""\
left    right   parent  child
2     10     3       0
2     10     3       2
0     10     4       1
0     2      4       2
2     10     4       3
0     2      5       0
0     2      5       4
"""
)

SVG(ts.draw_svg())


### Definition¶

A pair of nodes (u, v) has an IBD segment with a left and right coordinate [left, right) and ancestral node a iff the most recent common ancestor of the segment [left, right) in nodes u and v is a, and the segment has been inherited along the same genealogical path (ie. it has not been broken by recombination). The segments returned are the longest possible ones.

Consider the IBD segments that we get from our example tree sequence:

segments = ts.ibd_segments(store_segments=True)
for pair, segment_list in segments.items():
print(pair, list(segment_list))

(0, 1) [IdentitySegment(left=2.0, right=10.0, node=4), IdentitySegment(left=0.0, right=2.0, node=5)]
(0, 2) [IdentitySegment(left=2.0, right=10.0, node=3), IdentitySegment(left=0.0, right=2.0, node=5)]
(1, 2) [IdentitySegment(left=0.0, right=2.0, node=4), IdentitySegment(left=2.0, right=10.0, node=4)]


Each of the sample pairs (0, 1), (0, 2) and (1, 2) is associated with two IBD segments, representing the different paths from these sample pairs to their common ancestor. Note in particular that (1, 2) has two IBD segments rather than one: even though the MRCA is 4 in both cases, the paths from the samples to the MRCA are different in the left and right trees.

### Data structures¶

The result of calling TreeSequence.ibd_segments() is an IdentitySegments class:

segments = ts.ibd_segments()
print(segments)

╔════════════════════╗
║IdentitySegments    ║
╠══════════════╤═════╣
║Parameters:   │     ║
║max_time      │  inf║
║min_span      │    0║
║store_pairs   │False║
║store_segments│False║
║Results:      │     ║
║num_segments  │    6║
║total_span    │ 30.0║
╚══════════════╧═════╝


By default this class only stores the high-level summaries of the IBD segments discovered. As we can see in this example, we have a total of six segments and the total span (i.e., the sum lengths of the genomic intervals spanned by IBD segments) is 30.

If required, we can get more detailed information about particular segment pairs and the actual segments using the store_pairs and store_segments arguments.

Warning

Only use the store_pairs and store_segments arguments if you really need this information! The number of IBD segments can be very large and storing them all requires a lot of memory. It is also much faster to just compute the overall summaries, without needing to store the actual lists.

segments = ts.ibd_segments(store_pairs=True)
for pair, value in segments.items():
print(pair, "::", value)

(0, 1) :: IdentitySegmentList(num_segments=2, total_span=10.0)
(0, 2) :: IdentitySegmentList(num_segments=2, total_span=10.0)
(1, 2) :: IdentitySegmentList(num_segments=2, total_span=10.0)


Now we can see the more detailed breakdown of how the identity segments are distributed among the sample pairs. The IdentitySegments class behaves like a dictionary, such that segments[(a, b)] will return the IdentitySegmentList instance for that pair of samples:

seglist = segments[(0, 1)]
print(seglist)

IdentitySegmentList(num_segments=2, total_span=10.0)


If we want to access the detailed information about the actual identity segments, we must use the store_segments argument:

segments = ts.ibd_segments(store_pairs=True, store_segments=True)
segments[(0, 1)]

IdentitySegmentList([IdentitySegment(left=2.0, right=10.0, node=4), IdentitySegment(left=0.0, right=2.0, node=5)])


The IdentitySegmentList behaves like a Python list, where each element is an instance of IdentitySegment.

Warning

The order of segments in an IdentitySegmentList is arbitrary, and may change in future versions.

Todo

More examples using the other bits of the IdentitySegments API here

### Controlling the sample sets¶

By default we get the IBD segments between all pairs of sample nodes.

#### IBD within a sample set¶

We can reduce this to pairs within a specific set using the within argument:

Todo

More detail and better examples here.

segments = ts.ibd_segments(within=[0, 2], store_pairs=True)
print(list(segments.keys()))

[(0, 2)]


#### IBD between sample sets¶

We can also compute IBD between sample sets:

segments = ts.ibd_segments(between=[[0,1], [2]], store_pairs=True)
print(list(segments.keys()))

[(0, 2), (1, 2)]


See the TreeSequence.ibd_segments() documentation for more details.
The max_time and min_span arguments allow us to constrain the segments that we consider.