# Pedigrees¶

Pedigrees describe parent-offspring relationships between individuals, and can be provided as input to constrain simulations of genetic ancestry (see the Fixed pedigree section for details). In this section we describe the data structures used to encode pedigrees in msprime, and the utilities used to create input pedigrees.

## Pedigree encoding¶

Msprime uses the tskit node and individual tables to encode pedigree information. Each individual is defined by a row in the individual table, and this row index is the individual’s id. Pedigree relationships are defined using the parents column, which contains the IDs of an individual’s parents. Further information is stored in the nodes associated with the individual.

Note

It is important to note that sample status, time, and population information is associated with an individual’s nodes (see the Ploidy section for details), which is an artefact of tskit’s node-centric design.

It is possible to specify a pedigree model directly using tskit APIs, but it is simpler to use the PedigreeBuilder utility class (or the Simplified file format). In the following example we build a simple trio:

pb = msprime.PedigreeBuilder()
pedigree = pb.finalise()
# TODO replace with display(pedigree) when its implemented in tskit
# https://github.com/tskit-dev/tskit/issues/2093
print(pedigree)

TableCollection

Sequence Length: -1.0
Time units: generations

Individuals
╔══╤═════╤════════╤═══════╤════════╗
╠══╪═════╪════════╪═══════╪════════╣
║0 │    0│        │ -1, -1│     b''║
║1 │    0│        │ -1, -1│     b''║
║2 │    0│        │   0, 1│     b''║
╚══╧═════╧════════╧═══════╧════════╝

Nodes
╔══╤═════╤══════════╤══════════╤══════════╤════════╗
╠══╪═════╪══════════╪══════════╪══════════╪════════╣
║0 │    0│         0│         0│1.00000000│     b''║
║1 │    0│         0│         0│1.00000000│     b''║
║2 │    0│         0│         1│1.00000000│     b''║
║3 │    0│         0│         1│1.00000000│     b''║
║4 │    1│         0│         2│0.00000000│     b''║
║5 │    1│         0│         2│0.00000000│     b''║
╚══╧═════╧══════════╧══════════╧══════════╧════════╝

Edges
╔══╤════╤═════╤══════╤═════╤════════╗
╠══╪════╪═════╪══════╪═════╪════════╣
╚══╧════╧═════╧══════╧═════╧════════╝

Sites
╔══╤════════╤═══════════════╤════════╗
╠══╪════════╪═══════════════╪════════╣
╚══╧════════╧═══════════════╧════════╝

Mutations
╔══╤════╤════╤════╤═════════════╤══════╤════════╗
╠══╪════╪════╪════╪═════════════╪══════╪════════╣
╚══╧════╧════╧════╧═════════════╧══════╧════════╝

Migrations
╔══╤════╤═════╤════╤══════╤════╤════╤════════╗
╠══╪════╪═════╪════╪══════╪════╪════╪════════╣
╚══╧════╧═════╧════╧══════╧════╧════╧════════╝

Populations
╔══╤════════════════════════════════════╗
╠══╪════════════════════════════════════╣
║0 │{'description': '', 'name': 'pop_0'}║
╚══╧════════════════════════════════════╝

Provenances
╔══╤═════════╤══════╗
║id│timestamp│record║
╠══╪═════════╪══════╣
╚══╧═════════╧══════╝


The pedigree returned by the finalise() method contains the pedigree information defined by the calls to add_individual(). For this trio, we began by adding the parents, and because they are founders, we don’t provide any information about their parents. Each call to add_individual() returns the integer ID of newly added individual.

### Requirements¶

This section lists the detailed requirements of the low-level encoding for the tskit node and individual tables.

Warning

Most of this information is only of interest if you are constructing these tables by hand. For most purposes it’s best to use either the PedigreeBuilder API or the Simplified file format.

• Each individual must have exactly two parents. Unknown parents are indicated using -1 (thus, a founder individual will have parents=[-1, -1].

• Each individual must be associated with exactly two nodes.

• All nodes associated with an individual must have the same time and population values. (These are referred to as the individual’s time and population, as a shorthand.)

• An individual’s time must be less than all its parent’s times.

It is often useful to associate metadata with individuals when building a pedigree. This allows us to either directly store information about the individuals for later analysis, or to store an identifier to facilitate matching with existing records.

In this example we update our simple trio by associating a string identifier with each individual. We use the tskit.MetadataSchema.permissive_json() function here to create a schema, as this is an easy and quick way to get a functional metadata schema. Much more sophisticated approaches are possible, however: please see the tskit metadata documentation for more information.

pb = msprime.PedigreeBuilder(
pedigree = pb.finalise()
display(pedigree.individuals)

00-1, -1{'name': 'mom'}
200, 1{'name': 'child'}

## Simplified file format¶

The methods described in Pedigree encoding are general and allow for arbitrary metadata to be associated with individuals. It is often convenient to work with a text based representation of the pedigree, which is supported by the parse_pedigree() function. The Format definition section defines the columns and requirements for this file format.

See the Basic example and subsequent sections for examples.

### Format definition¶

This section describes the detailed rules for the pedigree text file format.

The first line of the file must be a header starting with a # character, listing the included columns separated by white space.

Columns can be listed in any order. Columns from the required columns list below must be included, and only recognised columns can be included in the file.

All other lines in the file are rows defining a particular individual. Each row must contain data for all columns defined in the header, separated by whitespace.

#### Required columns¶

id

A unique string identifier for this individual.

parent0

The parent that will be assigned to parents[0] in the tskit encoding. This must be either a identifier defined in the id column, or the value . (representing missing data).

parent1

The parent that will be assigned to parents[1] in the tskit encoding. The value requirements are identical to the parent0 column.

time

The time value to associate with the individual.

Note

The time column may become optional in later releases.

#### Optional columns¶

is_sample

The sample status of the individual. If equal to 1, the nodes associated with this individual will be marked as samples. If 0 they will not. No other values are supported.

population

The population to associate with the individual. Values must correspond to population identifiers in a supplied Demography object

### Basic example¶

In this example we encode a trio, child, mom and dad:

txt = """\
# id parent0 parent1 time
mom    .   .  1
"""
pedigree = msprime.parse_pedigree(io.StringIO(txt))
display(pedigree.individuals)
display(pedigree.nodes)

001, 2{'file_id': 'child'}
10-1, -1{'file_id': 'mom'}
01000.00000000b''
11000.00000000b''
20011.00000000b''
30011.00000000b''
40021.00000000b''
50021.00000000b''

We have three individuals in our input pedigree, and there is therefore three rows in the individual table. In the tskit encoding, individuals are referred to by their integer ID (the corresponding row in the individual table). Individuals are added to the table in the same order they appear in the file, and therefore child corresponds to ID 0, mom ID 1 and dad ID 2. These ID values are then used in the parents column to describe the pedigree relationships.

Time information about individuals is stored in the node table, where the time of an individual is associated with its two nodes. For example, nodes 0 and 1 correspond to the two genomes of individual 0 (child), and these are both at time 0.

The individual table also includes the original string file_id as metadata to faciliate joining with existing data sources. We can access these IDs as follows:

for id, ind in enumerate(pedigree.individuals):

0 -> child
1 -> mom


### Specifying samples¶

In the previous example we did not specify which of our individuals were the samples (“probands”). In this case, parse_pedigree() assumes that any individual at time 0 is a sample. This is show in the example above in the node table, where we can see that the flags value for both of child’s nodes is 1 (corresponding to tskit.NODE_IS_SAMPLE)

We can override this behaviour by providing an is_sample column:

import io
txt = """\
# id parent0 parent1 time is_sample
mom1     .   .   1 0
mom2     .   .   2 0
"""
pedigree = msprime.parse_pedigree(io.StringIO(txt))
display(pedigree.individuals)
display(pedigree.nodes)

001, 2{'file_id': 'child1'}
10-1, -1{'file_id': 'mom1'}
304, 5{'file_id': 'child2'}
40-1, -1{'file_id': 'mom2'}
01000.00000000b''
11000.00000000b''
20011.00000000b''
30011.00000000b''
40021.00000000b''
50021.00000000b''
61031.00000000b''
71031.00000000b''
80042.00000000b''
90042.00000000b''
100052.00000000b''
110052.00000000b''

Here we have two trios, where the child in the second trio is from the same generation as the parents in the second. We use the is_sample column to specify that child2 is a sample as well as child1.

### Demography information¶

If the founder individuals of the pedigree belong to different populations and we wish to simulate ancestry beyond the pedigree, we must define a demographic model and define the populations that the individuals belong to.

See the Pedigrees and demography section for a full discussion of how demography interacts with fixed pedigree simulations and important caveats.

To do this we must pass the Demography instance defining the demographic model to parse_pedigree(), and include a population column in the file.

import io
txt = """\
# id parent0 parent1 time is_sample population
child1 mom1 dad1 0 1 A
mom1     .   .   1 0 A
dad1     .   .   1 0 A
child2 mom2 dad2 1 1 B
mom2     .   .   2 0 B
dad2     .   .   2 0 B
"""

demography = msprime.Demography()

pedigree = msprime.parse_pedigree(io.StringIO(txt), demography=demography)
display(pedigree.populations)
display(pedigree.individuals)
display(pedigree.nodes)

0{'description': '', 'name': 'A'}
1{'description': '', 'name': 'B'}
2{'description': '', 'name': 'C'}
001, 2{'file_id': 'child1'}
10-1, -1{'file_id': 'mom1'}
304, 5{'file_id': 'child2'}
40-1, -1{'file_id': 'mom2'}
01000.00000000b''
11000.00000000b''
20011.00000000b''
30011.00000000b''
40021.00000000b''
50021.00000000b''
61131.00000000b''
71131.00000000b''
80142.00000000b''
90142.00000000b''
100152.00000000b''
110152.00000000b''

## Visualising pedigrees¶

It is often useful to visualise a (small) pedigree. The following function is used in this documentation, which may be a useful recipe for others:

def draw_pedigree(ped_ts):

G = nx.DiGraph()
for ind in ped_ts.individuals():
time = ped_ts.node(ind.nodes[0]).time
pop = ped_ts.node(ind.nodes[0]).population