# Data model¶

The correlated genealogical trees that describe the shared ancestry of a set of samples are stored concisely in tskit as a collection of easy-to-understand tables. These are output by coalescent simulation in msprime or can be read in from another source. This page documents the structure of the tables, and the different methods of interchanging genealogical data to and from the tskit API. We begin by defining the basic concepts that we need and the structure of the tables in the Data model section. We then describe the tabular text formats that can be used as simple interchange mechanism for small amounts of data in the Text file formats section. The Binary interchange section then describes the efficient Python API for table interchange using numpy arrays. Finally, we describe the binary format used by tskit to efficiently store tree sequences on disk in the Tree sequence file format section.

## Definitions¶

To begin, here are definitions of some key ideas encountered later.

tree

A “gene tree”, i.e., the genealogical tree describing how a collection of genomes (usually at the tips of the tree) are related to each other at some chromosomal location. See Nodes, Genomes, or Individuals? for discussion of what a “genome” is.

tree sequence

A “succinct tree sequence” (or tree sequence, for brevity) is an efficient encoding of a sequence of correlated trees, such as one encounters looking at the gene trees along a genome. A tree sequence efficiently captures the structure shared by adjacent trees, (essentially) storing only what differs between them.

node

Each branching point in each tree is associated with a particular genome in a particular ancestor, called “nodes”. Since each node represents a specific genome it has a unique time, thought of as its birth time, which determines the height of any branching points it is associated with. See Nodes, Genomes, or Individuals? for discussion of what a “node” is.

individual

In certain situations we are interested in how nodes (representing individual homologous genomes) are grouped together into individuals (e.g. two nodes per diploid individual). For example, when we are working with polyploid samples it is useful to associate metadata with a specific individual rather than duplicate this information on the constituent nodes. See Nodes, Genomes, or Individuals? for more discussion on this point.

sample

The focal nodes of a tree sequence, usually thought of as those that we have obtained data from. The specification of these affects various methods: (1) TreeSequence.variants() and TreeSequence.haplotypes() will output the genotypes of the samples, and Tree.roots only return roots ancestral to at least one sample. (See the node table definitions for information on how the sample status a node is encoded in the flags column.)

edge

The topology of a tree sequence is defined by a set of edges. Each edge is a tuple (left, right, parent, child), which records a parent-child relationship among a pair of nodes on the on the half-open interval of chromosome [left, right).

site

Tree sequences can define the mutational state of nodes as well as their topological relationships. A site is thought of as some position along the genome at which variation occurs. Each site is associated with a unique position and ancestral state.

mutation

A mutation records the change of state at a particular site ‘above’ a particular node (more precisely, along the branch between the node in question and its parent). Each mutation is associated with a specific site (which defines the position along the genome), a node (which defines where it occurs within the tree at this position), and a derived state (which defines the mutational state inherited by all nodes in the subtree rooted at the focal node). In more complex situations in which we have back or recurrent mutations, a mutation must also specify its ‘parent’ mutation.

migration

An event at which a parent and child node were born in different populations.

population

A grouping of nodes, e.g., by sampling location.

provenance

An entry recording the origin and history of the data encoded in a tree sequence.

ID

In the set of interconnected tables that we define here, we refer throughout to the IDs of particular entities. The ID of an entity (e.g., a node) is defined by the position of the corresponding row in the table. These positions are zero indexed. For example, if we refer to node with ID zero, this corresponds to the node defined by the first row in the node table.

sequence length

This value defines the coordinate space in which the edges and site positions are defined. This is most often assumed to be equal to the largest right coordinate in the edge table, but there are situations in which we might wish to specify the sequence length explicitly.

A tree sequence can be stored in a collection of eight tables: Node, Edge, Individual, Site, Mutation, Migration, Population, and Provenance. The Node and Edge tables store the genealogical relationships that define the trees, and the Individual table describes how multiple genomes are grouped within individuals; the Site and Mutation tables describe where mutations fall on the trees; the Migration table describes how lineages move across space; and the Provenance table contains information on where the data came from. Only Node and Edge tables are necessary to encode the genealogical trees; Sites and Mutations are optional but necessary to encode polymorphism (sequence) data; the remainder are optional. In the following sections we define these components of a tree sequence in more detail.

### Nodes, Genomes, or Individuals?¶

The natural unit of biological analysis is (usually) the individual. However, many organisms we study are diploid, and so each individual contains two homologous copies of the entire genome, separately inherited from the two parental individuals. Since each monoploid copy of the genome is inherited separately, each diploid individual lies at the end of two distinct lineages, and so will be represented by two places in any given genealogical tree. This makes it difficult to precisely discuss tree sequences for diploids, as we have no simple way to refer to the bundle of chromosomes that make up the “copy of the genome inherited from one particular parent”. For this reason, in this documentation we use the non-descriptive term “node” to refer to this concept – and so, a diploid individual is composed of two nodes – although we use the term “genome” at times, for concreteness.

Several properties naturally associated with individuals are in fact assigned to nodes in what follows: birth time and population. This is for two reasons: First, since coalescent simulations naturally lack a notion of polyploidy, earlier versions of tskit lacked the notion of an individual. Second, ancestral nodes are not naturally grouped together into individuals – we know they must have existed, but have no way of inferring this grouping, so in fact many nodes in an empirically-derived tree sequence will not be associated with individuals, even though their birth times might be inferred.

## Table definitions¶

### Table types¶

#### Node Table¶

A node defines a monoploid set of chromosomes (a “genome”) of a specific individual that was born at some time in the past: the set of chromosomes inherited from a particular one of the individual’s parents. (See Nodes, Genomes, or Individuals? for more discussion.) Every vertex in the marginal trees of a tree sequence corresponds to exactly one node, and a node may be present in many trees. The node table contains five columns, of which flags and time are mandatory:

Column

Type

Description

flags

uint32

Bitwise flags.

time

double

Birth time of node

population

int32

Birth population of node.

individual

int32

The individual the node belongs to.

binary

The time column records the birth time of the individual in question, and is a floating point value. Similarly, the population column records the ID of the population where this individual was born. If not provided, population defaults to the null ID (-1). Otherwise, the population ID must refer to a row in the Population Table. The individual column records the ID of the Individual individual that this node belongs to. If specified, the ID must refer to a valid individual. If not provided, individual defaults to the null ID (-1).

The flags column stores information about a particular node, and is composed of 32 bitwise boolean values. Currently, the only flag defined is NODE_IS_SAMPLE = 1, which defines the sample status of nodes. Marking a particular node as a “sample” means, for example, that the mutational state of the node will be included in the genotypes produced by TreeSequence.variants().

Bits 0-15 (inclusive) of the flags column are reserved for internal use by tskit and should not be used by applications for anything other than the purposes documented here. Bits 16-31 (inclusive) are free for applications to use for any purpose and will not be altered or interpreteted by tskit.

See the Node requirements section for details on the properties required for a valid set of nodes.

For convenience, the text format for nodes decomposes the flags value into its separate values. Thus, in the text format we have a column for is_sample, which corresponds to the flags column in the underlying table. As more flags values are defined, these will be added to the text file format.

The metadata column provides a location for client code to store information about each node. See the Metadata section for more details on how metadata columns should be used.

Note

The distinction between flags and metadata is that flags holds information about a node that the library understands, whereas metadata holds information about a node that the library does not understand. Metadata is for storing auxiliarly information that is not necessary for the core tree sequence algorithms.

#### Individual Table¶

An individual defines how nodes (which can be seen as representing single chromosomes) group together in a polyploid individual. The individual table contains three columns, of which only flags is mandatory.

Column

Type

Description

flags

uint32

Bitwise flags.

location

double

Location in arbitrary dimensions

parents

int32

Ids of parent individuals

binary

See the Individual requirements section for details on the properties required for a valid set of individuals.

The flags column stores information about a particular individual, and is composed of 32 bitwise boolean values. Currently, no flags are defined.

Bits 0-15 (inclusive) of the flags column are reserved for internal use by tskit and should not be used by applications for anything other than the purposes documented here. Bits 16-31 (inclusive) are free for applications to use for any purpose and will not be altered or interpreteted by tskit.

The location column stores the location of an individual in arbitrary dimensions. This column is ragged, and so different individuals can have locations with different dimensions (i.e., one individual may have location [] and another [0, 1, 0]. This could therefore be used to store other quantities (e.g., phenotype).

The parents column stores the ids of other individuals that are the parents of an individual. This column is ragged such that an individual can have any number of parents.

The metadata column provides a location for client code to store information about each individual. See the Metadata section for more details on how metadata columns should be used.

Note

The distinction between flags and metadata is that flags holds information about a individual that the library understands, whereas metadata holds information about a individual that the library does not understand. Metadata is for storing auxiliarly information that is not necessary for the core tree sequence algorithms.

#### Edge Table¶

An edge defines a parent-child relationship between a pair of nodes over a specific sequence interval. The edge table contains five columns, all of which are mandatory except metadata:

Column

Type

Description

left

double

Left coordinate of the edge (inclusive).

right

double

Right coordinate of the edge (exclusive).

parent

int32

Parent node ID.

child

int32

Child node ID.

binary

Each row in an edge table describes a half-open genomic interval [left, right) over which the child inherited from the given parent. The left and right columns are defined using double precision floating point values. The parent and child columns specify integer IDs in the associated Node Table.

The metadata column provides a location for client code to store information about each edge. See the Metadata section for more details on how metadata columns should be used.

See the Edge requirements section for details on the properties required for a valid set of edges.

#### Site Table¶

A site defines a particular location along the genome in which we are interested in observing the allelic state. The site table contains three columns, of which position and ancestral_state are mandatory.

Column

Type

Description

position

double

Position of site in genome coordinates.

ancestral_state

text

The state at the root of the tree.

binary

The position column is a floating point value defining the location of the site in question along the genome.

The ancestral_state column specifies the allelic state at the root of the tree, thus defining the state that nodes inherit if no mutations intervene. The column stores text character data of arbitrary length.

The metadata column provides a location for client code to store information about each site. See the Metadata section for more details on how metadata columns should be used.

See the Site requirements section for details on the properties required for a valid set of sites.

#### Mutation Table¶

A mutation defines a change of allelic state on a tree at a particular site. The mutation table contains five columns, of which site, node and derived_state are mandatory.

Column

Type

Description

site

int32

The ID of the site the mutation occurs at.

node

int32

The node this mutation occurs at.

parent

int32

The ID of the parent mutation.

time

double

Time at which the mutation occurred.

derived_state

char

The allelic state resulting from the mutation.

binary

The site column is an integer value defining the ID of the site at which this mutation occurred.

The node column is an integer value defining the ID of the first node in the tree below this mutation.

The time column is a double precision floating point value recording how long ago the mutation happened.

The derived_state column specifies the allelic state resulting from the mutation, thus defining the state that the node and any descendant nodes in the subtree inherit unless further mutations occur. The column stores text character data of arbitrary length.

The parent column is an integer value defining the ID of the mutation whose allelic state this mutation replaced. If there is no mutation at the site in question on the path back to root, then this field is set to the null ID (-1). (The parent column is only required in situations where there are multiple mutations at a given site. For “infinite sites” mutations, it can be ignored.)

The metadata column provides a location for client code to store information about each site. See the Metadata section for more details on how metadata columns should be used.

See the Mutation requirements section for details on the properties required for a valid set of mutations.

#### Migration Table¶

In simulations, trees can be thought of as spread across space, and it is helpful for inferring demographic history to record this history. Migrations are performed by individual ancestors, but most likely not by an individual whose genome is tracked as a node (as in a discrete-deme model they are unlikely to be both a migrant and a most recent common ancestor). So, tskit records when a segment of ancestry has moved between populations. This table is not required, even if different nodes come from different populations.

Column

Type

Description

left

double

Left coordinate of the migrating segment (inclusive).

right

double

Right coordinate of the migrating segment (exclusive).

node

int32

Node ID.

source

int32

Source population ID.

dest

int32

Destination population ID.

time

double

Time of migration event.

binary

The left and right columns are floating point values defining the half-open segment of genome affected. The source and dest columns record the IDs of the respective populations. The node column records the ID of the node that was associated with the ancestry segment in question at the time of the migration event. The time column is holds floating point values recording the time of the event.

The metadata column provides a location for client code to store information about each migration. See the Metadata section for more details on how metadata columns should be used.

See the Migration requirements section for details on the properties required for a valid set of mutations.

#### Population Table¶

A population defines a grouping of individuals that a node can be said to belong to.

The population table contains one column, metadata.

Column

Type

Description

binary

The metadata column provides a location for client code to store information about each population. See the Metadata section for more details on how metadata columns should be used.

See the Population requirements section for details on the properties required for a valid set of populations.

#### Provenance Table¶

Todo

Document the provenance table.

Column

Type

Description

timestamp

char

Timestamp in ISO-8601 format.

record

char

Provenance record.

Each table (excluding provenance) has a metadata column for storing and passing along information that tskit does not use or interpret. See Metadata for details. The metadata columns are binary columns.

When using the Text file formats, to ensure that metadata can be safely interchanged, each row is base 64 encoded. Thus, binary information can be safely printed and exchanged, but may not be human readable.

The tree sequence itself also has metadata stored as a byte array.

### Valid tree sequence requirements¶

Arbitrary data can be stored in tables using the classes in the Tables and Table Collections. However, only a TableCollection that fulfils a set of requirements represents a valid TreeSequence object which can be obtained using the TableCollection.tree_sequence() method. In this section we list these requirements, and explain their rationale. Violations of most of these requirements are detected when the user attempts to load a tree sequence via tskit.load() or TableCollection.tree_sequence(), raising an informative error message. Some more complex requirements may not be detectable at load-time, and errors may not occur until certain operations are attempted. These are documented below. We also provide tools that can transform a collection of tables into a valid collection of tables, so long as they are logically consistent, as described in Table transformation methods.

#### Individual requirements¶

Individuals are a basic type in a tree sequence and are not defined with respect to any other tables. Individuals can have a reference to their parent individuals, if present these references must be valid or null (-1).

Individuals must be sorted such that parents are before children. Sorting a set of tables using TableCollection.sort() will ensure that this requirement is fulfilled.

#### Node requirements¶

Given a valid set of individuals and populations, the requirements for each node are:

• population must either be null (-1) or refer to a valid population ID;

• individual must either be null (-1) or refer to a valid individual ID.

An ID refers to a zero-indexed row number in the relevant table, and so is “valid” if is between 0 and one less than the number of rows in the relevant table.

There are no requirements regarding the ordering of nodes with respect to time.

Sorting a set of tables using TableCollection.sort() has no effect on nodes.

#### Edge requirements¶

Given a valid set of nodes and a sequence length $$L$$, the simple requirements for each edge are:

• We must have $$0 \leq$$ left $$<$$ right $$\leq L$$;

• parent and child must be valid node IDs;

• time[parent] > time[child];

• edges must be unique (i.e., no duplicate edges are allowed).

The first requirement simply ensures that the interval makes sense. The third requirement ensures that we cannot have loops, since time is always increasing as we ascend the tree.

To ensure a valid tree sequence there is one further requirement:

• The set of intervals on which each node is a child must be disjoint.

This guarantees that we cannot have contradictory edges (i.e., where a node a is a child of both b and c), and ensures that at each point on the sequence we have a well-formed forest of trees. Because this is a more complex semantic requirement, it is not detected at load time. This error is detected during tree traversal, via, e.g., the TreeSequence.trees() iterator.

In the interest of algorithmic efficiency, edges must have the following sortedness properties:

• All edges for a given parent must be contiguous;

• Edges must be listed in nondecreasing order of parent time;

• Within the edges for a given parent, edges must be sorted first by child ID and then by left coordinate.

Violations of these requirements are detected at load time. The TableCollection.sort() method will ensure that these sortedness properties are fulfilled.

#### Site requirements¶

Given a valid set of nodes and a sequence length $$L$$, the simple requirements for a valid set of sites are:

• We must have $$0 \leq$$ position $$< L$$;

• position values must be unique.

For simplicity and algorithmic efficiency, sites must also:

• Be sorted in increasing order of position.

Violations of these requirements are detected at load time. The TableCollection.sort() method ensures that sites are sorted according to these criteria.

#### Mutation requirements¶

Given a valid set of nodes, edges and sites, the requirements for a valid set of mutations are:

• site must refer to a valid site ID;

• node must refer to a valid node ID;

• time must either be UNKNOWN_TIME (a NAN value which indicates the time is unknown) or be a finite value which is greater or equal to the mutation node’s time, less than the node above the mutation’s time and equal to or less than the time of the parent mutation if this mutation has one. If one mutation on a site has UNKNOWN_TIME then all mutations at that site must, as a mixture of known and unknown is not valid.

• parent must either be the null ID (-1) or a valid mutation ID within the current table

Furthermore,

• If another mutation occurs on the tree above the mutation in question, its ID must be listed as the parent.

For simplicity and algorithmic efficiency, mutations must also:

• be sorted by site ID;

• when there are multiple mutations per site, mutations should be ordered by decreasing time, if known, and parent mutations must occur before their children (i.e. if a mutation with ID $$x$$ has parent with ID $$y$$, then we must have $$y < x$$).

Violations of these sorting requirements are detected at load time. The TableCollection.sort() method ensures that mutations are sorted according site ID, but does not at present enforce that mutations occur after their parent mutations.

Mutations also have the requirement that they must result in a change of state. For example, if we have a site with ancestral state of “A” and a single mutation with derived state “A”, then this mutation does not result in any change of state. This error is raised at run-time when we reconstruct sample genotypes, for example in the TreeSequence.variants() iterator.

Note

As tskit.UNKNOWN_TIME is implemented as a NaN value, tests for equality will always fail. Use tskit.is_unknown_time to detect unknown values.

#### Migration requirements¶

Given a valid set of nodes and edges, the requirements for a value set of migrations are:

• left and right must lie within the tree sequence coordinate space (i.e., from 0 to sequence_length).

• time must be strictly between the time of its node and the time of any ancestral node from which that node inherits on the segment [left, right).

• The population of any such ancestor matching source, if another migration does not intervene.

To enable efficient processing, migrations must also be:

• Sorted by nondecreasing time value.

Note in particular that there is no requirement that adjacent migration records should be “squashed”. That is, we can have two records m1 and m2 such that m1.right = m2.left and with the node, source, dest and time fields equal. This is because such records will usually represent two independent ancestral segments migrating at the same time, and as such squashing them into a single record would result in a loss of information.

#### Population requirements¶

There are no requirements on a population table.

#### Provenance requirements¶

The timestamp column of a provenance table should be in ISO-8601 format.

The record should be valid JSON with structure defined in the Provenance Schema section (TODO).

### Table transformation methods¶

In several cases it may be necessary to transform the data stored in a TableCollection. For example, an application may produce tables which, while logically consistent, do not meet all the requirements for a valid tree sequence, which exist for algorithmic and efficiency reasons; table transformation methods can make such a set of tables valid, and thus ready to be loaded into a tree sequence.

In general, table methods operate in place on a TableCollection, directly altering the data stored within its constituent tables. Some of the methods described in this section also have an equivalant TreeSequence version: unlike the methods described below, TreeSequence methods do not operate in place, but rather act in a functional way, returning a new tree sequence while leaving the original unchanged.

This section is best skipped unless you are writing a program that records tables directly.

#### Simplification¶

Simplifying a tree sequence is an operation commonly used to remove redundant information and only retain the minimal tree sequence necessary to describe the genealogical history of the samples provided. In fact all that the TreeSequence.simplify() method does is to call the equivalent table transformation method, TableCollection.simplify(), on the underlying tables and load them in a new tree sequence.

Removing information via TableCollection.simplify() is done by discarding rows from the underlying tables. Nevertheless, simplification is guaranteed to preserve relative ordering of any retained rows in the Site and Mutation tables.

The TableCollection.simplify() method can be applied to a collection of tables that does not have the mutations.parent entries filled in, as long as all other validity requirements are satisfied.

#### Sorting¶

The validity requirements for a set of tables to be loaded into a tree sequence listed in Table definitions are of two sorts: logical consistency, and sortedness. The TableCollection.sort() method can be used to make completely valid a set of tables that satisfies all requirements other than sortedness.

This method can also be used on slightly more general collections of tables: it is not required that site positions be unique in the table collection to be sorted. The method has two additional properties:

• it preserves relative ordering between sites at the same position, and

• it preserves relative ordering between mutations at the same site.

TableCollection.sort() does not check the validity of the parent property of the mutation table. However, because the method preserves mutation order among mutations at the same site, if mutations are already sorted so that each mutation comes after its parent (e.g., if they are ordered by time of appearance), then this property is preserved, even if the parent properties are not specified.

#### Table indexes¶

To efficiently iterate over the trees in a tree sequence, tskit uses indexes built on the edges. To create a tree sequence from a table collection the tables must be indexed; the TableCollection.build_index() method can be used to create an index on a table collection if necessary.

Todo

Add more details on what the indexes actually are.

#### Removing duplicate sites¶

The TableCollection.deduplicate_sites() method can be used to save a tree sequence recording method the bother of checking to see if a given site already exists in the site table. If there is more than one site with the same position, all but the first is removed, and all mutations referring to the removed sites are edited to refer to the first (and remaining) site. Order is preserved.

#### Computing mutation parents¶

If each edge had at most only a single mutation, then the parent property of the mutation table would be easily inferred from the tree at that mutation’s site. If mutations are entered into the mutation table ordered by time of appearance, then this sortedness allows us to infer the parent of each mutation even for mutations occurring on the same branch. The TableCollection.compute_mutation_parents() method will take advantage of this fact to compute the parent column of a mutation table, if all other information is valid.

#### Computing mutation times¶

In the case where the method generating a tree sequence does not generate mutation times, valid times can be provided by TableCollection.compute_mutation_parents(). If all other information is valid this method will assign times to the mutations by placing them at evenly spaced intervals along their edge (for instance, a single mutation on an edge between a node at time 1.0 and a node at time 4.0 would be given time 2.5; while two mutations on that edge would be given times 2.0 and 3.0).

#### Recording tables in forwards time¶

The above methods enable the following scheme for recording site and mutation tables during a forwards-time simulation. Whenever a new mutation is encountered:

1. Add a new site to the site table at this position.

2. Add a new mutation to the mutation table at the newly created site.

This is lazy and wrong, because:

1. There might have already been sites in the site table with the same position,

2. and/or a mutation (at the same position) that this mutation should record as its parent.

But, it’s all OK because here’s what we do:

1. Add rows to the mutation and site tables as described above.

2. Periodically, sort, deduplicate_sites, and simplify, then return to (1.), except that

3. Sometimes, to output the tables, sort, compute_mutation_parents, (optionally simplify), and dump these out to a file.

Note: as things are going along we do not have to compute_mutation_parents, which is nice, because this is a nontrivial step that requires construction all the trees along the sequence. Computing mutation parents only has to happen before the final (output) step.

This is OK as long as the forwards-time simulation outputs things in order by when they occur, because these operations have the following properties:

1. Mutations appear in the mutation table ordered by time of appearance, so that a mutation will always appear after the one that it replaced (i.e., its parent).

2. Furthermore, if mutation B appears after mutation A, but at the same site, then mutation B’s site will appear after mutation A’s site in the site table.

3. sort sorts sites by position, and then by ID, so that the relative ordering of sites at the same position is maintained, thus preserving property (2).

4. sort sorts mutations by site, and then by ID, thus preserving property (1); if the mutations are at separate sites (but the same position), this fact is thanks to property (2).

5. simplify also preserves ordering of any rows in the site and mutation tables that do not get discarded.

6. deduplicate_sites goes through and collapses all sites at the same position to only one site, maintaining order otherwise.

7. compute_mutation_parents fills in the parent information by using property (1).

## Tree structure¶

Tree structure in tskit is encoded internally as a “quintuply linked tree”, a generalisation of the triply linked tree encoding used by Knuth and others. Nodes are represented by their integer IDs, and their relationships to other nodes are recorded in the parent, left_child, right_child, left_sib and right_sib arrays. For example, consider the following tree and associated arrays:

node

parent

left_child

right_child

left_sib

right_sib

0

5

-1

-1

-1

1

1

5

-1

-1

0

2

2

5

-1

-1

1

-1

3

6

-1

-1

-1

4

4

6

-1

-1

3

-1

5

7

0

2

-1

6

6

7

3

4

5

-1

7

-1

5

6

-1

-1

Each node in the tree sequence corresponds to a row in this table, and the columns are the individual arrays recording the quintuply linked structure. Thus, we can see that the parent of nodes 0, 1 and 2 is 5. Similarly, the left child of 5 is 0 and the right child of 5 is 2. The left_sib and right_sib arrays then record each nodes sibling on its left or right, respectively; hence the right sib of 0 is 1, and the right sib of 1 is 2. Thus, sibling information allows us to efficiently support trees with arbitrary numbers of children. In each of the five pointer arrays, the null node (-1) is used to indicate the end of a path; thus, for example, the parent of 7 and left sib of 0 are null.

Please see this example for details of how to use the quintuply linked structure in the C API.

Note

For many applications we do not need the quintuply linked trees, and (for example) the left_sib and right_child arrays can be ignored. The reason for using a quintuply instead of triply linked encoding is that it is not possible to efficiently update the trees as we move along the sequence without the quintuply linked structure.

Warning

The left-to-right ordering of nodes is determined by the order in which edges are inserted into the tree during iteration along the sequence. Thus, if we arrive at the same tree by iterating from different directions, the left-to-right ordering of nodes may be different! The specific ordering of the children of a node should therefore not be depended on.

### Accessing roots¶

The roots of a tree are defined as the unique endpoints of upward paths starting from sample nodes (if no path leads upward from a sample node, that node is also a root). Thus, trees can have multiple roots in tskit. For example, if we delete the edge joining 6 and 7 in the previous example, we get a tree with two roots:

node

parent

left_child

right_child

left_sib

right_sib

0

5

-1

-1

-1

1

1

5

-1

-1

0

2

2

5

-1

-1

1

-1

3

6

-1

-1

-1

4

4

6

-1

-1

3

-1

5

7

0

2

-1

-1

6

-1

3

4

7

-1

7

-1

5

5

-1

6

To gain efficient access to the roots in the quintuply linked encoding we keep one extra piece of information: the left_root. In this example the leftmost root is 7. Roots are considered siblings, and so once we have one root we can find all the other roots efficiently using the left_sib and right_sib arrays. For example, we can see here that the right sibling of 7 is 6, and the left sibling of 6 is 7.

## Missing data¶

Missing data is encoded in tskit using the idea of isolated samples. A sample’s genotype is missing at a position if it is isolated and if it has no mutations directly above it at that position. An isolated sample is a sample node (see Definitions) that has no children and no parent, in a particular tree. This encodes the idea that we don’t know anything about that sample’s relationships over a specific interval. This definition covers the standard idea of missing data in genomics (where we do not know the sequence of a given contemporary sample at some site, for whatever reason), but also more generally the idea that we may not know anything about large sections of the genomes of ancestral samples. However, a mutation above an isolated node can be thought of as saying directly what the genotype is, and so renders the genotype at that position not missing.

Consider the following example:

In this tree, node 4 is isolated, and therefore for any sites that are on this tree, the state that it is assigned is a special value tskit.MISSING_DATA, or -1, as long as there are no mutations above the node at that site. Note that, although isolated, because node 4 is a sample node it is still considered as being present in the tree, meaning it will still returned by the Tree.nodes() and Tree.samples() methods. The Tree.is_isolated() method can be used to identify nodes which are isolated samples:

>>> [u for u in tree.samples() if tree.is_isolated(u)]  # isolated samples in this tree
[4]
>>> [u for u in tree.nodes() if not tree.is_isolated(u)]  # topologically connected nodes
[0, 1, 2, 3, 5, 6, 7]


See the TreeSequence.variants() method and Variant class for more information on how missing data is represented in variant data.

## Text file formats¶

The tree sequence text file format is based on a simple whitespace delimited approach. Each table corresponds to a single file, and is composed of a number of whitespace delimited columns. The first line of each file must be a header giving the names of each column. Subsequent rows must contain data for each of these columns, following the usual conventions. Each table has a set of mandatory and optional columns which are described below. The columns can be provided in any order, and extra columns can be included in the file. Note, in particular, that this means that an id column may be present in any of these files, but it will be ignored (IDs are always determined by the position of the row in a table).

We present the text format below using the following very simple tree sequence, with four nodes, two trees, and three mutations at two sites, both on the first tree:

time ago
--------
3            3
┏━━┻━━┓
╋     ╋         2
┃     ╋      ┏━━┻━━┓
0         0     1      0     1

position  0           7          10


A deletion from AT to A has occurred at position 2 on the branch leading to node 0, and two mutations have occurred at position 4 on the branch leading to node 1, first from A to T, then a back mutation to A. The genotypes of our two samples, nodes 0 and 1, are therefore AA and ATA.

### Individual text format¶

The individual text format must contain a flags column. Optionally, there may also be location, parents and metadata columns. See the individual table definitions for details on these columns.

Note that there are currently no globally defined flags, but the column is still required; a value of 0 means that there are no flags set.

The location and parents columns should be a sequence of comma-separated numeric values. They do not all have to be the same length.

An example individual table:

flags       location     parents
0           0.5,1.2      -1, -1
0           1.0,3.4      0, -1
0
0           1.2
0           3.5,6.3      1,2
0           0.5,0.5      3,4
0           0.5          -1,-1
0           0.7,0.6,0.0
0           0.5,0.0


### Node text format¶

The node text format must contain the columns is_sample and time. Optionally, there may also be population, individual, and metadata columns. See the node table definitions for details on these columns.

Note that we do not have a flags column in the text file format, but instead use is_sample (which may be 0 or 1). Currently, NODE_IS_SAMPLE is the only flag value defined for nodes, and as more flags are defined we will allow for extra columns in the text format.

An example node table:

is_sample   individual   time
1           0            0.0
1           0            0.0
0           -1           1.0
0           -1           3.0


### Edge text format¶

The edge text format must contain the columns left, right, parent and child. Optionally, there may also be a metadata column. See the edge table definitions for details on these columns.

An example edge table:

left   right   parent  child
0.0    7.0     2       0
0.0    7.0     2       1
7.0    10.0    3       0
7.0    10.0    3       1


### Site text format¶

The site text format must contain the columns position and ancestral_state. The metadata column may also be optionally present. See the site table definitions for details on these columns.

sites:

position      ancestral_state
2.0           AT
4.0           A


### Mutation text format¶

The mutation text format must contain the columns site, node and derived_state. The time, parent and metadata columns may also be optionally present (but parent must be specified if more than one mutation occurs at the same site). If time is absent UNKNOWN_TIME will be used to fill the column. See the mutation table definitions for details on these columns.

mutations:

site   node    derived_state    time    parent
0      0       A                0       -1
1      0       T                0.5     -1
1      1       A                1       1


### Migration text format¶

The migration text format must contain the columns left, right, node, source, dest and time. The metadata column may also be optionally present. See the migration table definitions for details on these columns.

migrations:

left   right   node   source   dest   time
0.0    0.7     5      2        3      1.0
0.8    0.9     8      3        4      3.0


### Population text format¶

Population tables only have a metadata column, so the text format for a population table requires there to be a metadata column. See the population table definitions for details.

An example population table:

id   metadata
0    cG9wMQ==
1    cG9wMg==


The metadata contains base64-encoded data (in this case, the strings pop1 and pop1).

## Binary interchange¶

In this section we describe the high-level details of the API for interchanging table data via numpy arrays. Please see the Tables and Table Collections for detailed description of the functions and methods.

The tables API is based on columnar storage of the data. In memory, each table is organised as a number of blocks of contiguous storage, one for each column. There are many advantages to this approach, but the key property for us is that allows for very efficient transfer of data in and out of tables. Rather than inserting data into tables row-by-row (which can be done using the add_row methods), it is much more efficient to add many rows at the same time by providing pointers to blocks of contiguous memory. By taking this approach, we can work with tables containing gigabytes of data very efficiently.

We use the numpy Array API to allow us to define and work with numeric arrays of the required types. Node IDs, for example, are defined using 32 bit integers. Thus, the parent column of an Edge Table’s with n rows is a block 4n bytes.

This approach is very straightforward for columns in which each row contains a fixed number of values. However, dealing with columns containing a variable number of values is more problematic.

### Encoding ragged columns¶

A ragged column is a column in which the rows are not of a fixed length. For example, Metadata columns contain binary of data of arbitrary length. To encode such columns in the tables API, we store two columns: one contains the flattened array of data and another stores the offsets of each row into this flattened array. Consider an example:

>>> s = tskit.SiteTable()
>>> print(s)
0       0.00000000      A
1       0.00000000
2       0.00000000      TTT
3       0.00000000      G
>>> s.ancestral_state
array([65, 84, 84, 84, 71], dtype=int8)
>>> s.ancestral_state.tobytes()
b'ATTTG'
>>> s.ancestral_state_offset
array([0, 1, 1, 4, 5], dtype=uint32)
>>> s.ancestral_state[s.ancestral_state_offset[2]: s.ancestral_state_offset[3]].tobytes()
b'TTT'


In this example we create a Site Table with four rows, and then print out this table. We can see that the second row has the empty string as its ancestral_state, and the third row’s ancestral_state is TTT. When we print out the tables ancestral_state column, we see that its a numpy array of length 5: this is the flattened array of ASCII encoded values for these rows. When we decode these bytes using the numpy tobytes method, we get the string ‘ATTTG’. This flattened array can now be transferred efficiently in memory like any other column. We then use the ancestral_state_offset column to allow us find the individual rows. For a row j:

ancestral_state[ancestral_state_offset[j]: ancestral_state_offset[j + 1]]


gives us the array of bytes for the ancestral state in that row.

For a table with n rows, any offset column must have n + 1 values, the first of which is always 0. The values in this column must be nondecreasing, and cannot exceed the length of the ragged column in question.

## Tree sequence file format¶

To make tree sequence data as efficient and easy as possible to use, we store the data on file in a columnar, binary format. The format is based on the kastore package, which is a simple key-value store for numerical data. There is a one-to-one correspondence between the tables described above and the arrays stored in these files.

By convention, these files are given the .trees suffix (although this is not enforced in any way), and we will sometimes refer to them as “.trees” files. We also refer to them as “tree sequence files”.

Todo

Link to the documentation for kastore, and describe the arrays that are stored as well as the top-level metadata.

### Legacy Versions¶

Tree sequence files written by older versions of tskit are not readable by newer versions of tskit. For major releases of tskit, tskit upgrade will convert older tree sequence files to the latest version.

File formats from version 11 onwards are based on kastore; previous to this, the file format was based on HDF5.

However many changes to the tree sequence format are not part of major releases. The table below gives these versions.

Version number

Commit Short Hash

11.0

5646cd3

10.0

e4396a7

9.0

e504abd

8.0

299ddc9

7.0

ca9c0c5

6.0

6310725

5.0

62659fb

4.0

a586646

3.2

8f44bed

3.1

d69c059

3.0

7befdcf

2.1

a26a227

2.0

7c507f3

1.1

c143dd9

1.0

04722d8

0.3

f42215e

0.1

34ac742