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Changelog

[1.0.3] - 2021-XX-XX

New features:

  • Support for running full ARG simulations with gene conversion ({pr}1801, {issue}1773, {user}JereKoskela).

[1.0.2] - 2021-06-29

Improved Demes support and minor bugfixes.

New features:

  • Support for Demes input and logging in the msp simulate CLI ({pr}1716, {user}jeromekelleher).
  • Add Demography.to_demes method for creating a Demes demographic model from an msprime demography ({pr}1724, {user}grahamgower).
  • Improved mapping of Demes models to Demography objects ({pr}1758, {pr}1757, {pr}1756 {user}apragsdale).
  • Improved numerical algorithms in DemographyDebugger ({pr}1788, {user}grahamgower, {user}petrelharp).

Bugfixes:

  • Raise an error if running full ARG simulations with gene conversion ({issue}1774).

[1.0.1] - 2021-05-10

Minor feature release with experimental Demes support.

  • Change the semantics of Admixture events slightly so that ancestral populations that are inactive, are marked as active ({pr}1662, {issue}1657, {user}jeromekelleher, {user}apragsdale)

  • Initial support for Demes via the Demography.from_demes method. ({pr}1662, {issue}1675, {user}jeromekelleher, {user}apragsdale)

[1.0.0] - 2021-04-14

Msprime 1.0 is a major update, recommended for all users. It introduces new APIs and many new features, which still retaining compatibility with nearly all existing code.

New features:

  • Add new top-level functions sim_ancestry and sim_mutations, intended as long term replacements for simulate and mutate.
  • Add new Demography class as a replacement for the 0.x population_configurations, migration_matrix and demographic_events parameters to simulate. Many new features to improve ease of use and to help avoid errors.
  • Change the underlying simulation from working in discrete genetic coordinates and translating to physical coordinates, to simulating directly in physical coordinates. This fixes some long standing bugs and makes it far simpler to add features such as gene conversion. ({user}daniel-goldstein)
  • Support discrete or continuous genomes in simulations directly.
  • Gene conversion ({user}fbaumdicker)
  • Selective sweeps and low-level infrastructure for the structured coalescent ({user}andrewkern, {user}gbinux)
  • Multiple merger coalescent models ({user}jerekoskela, {user}shajoezhu, {user}TPPSellinger)
  • Different ploidy levels for coalescent models ({user}jerekoskela)
  • Functions to parse species trees and set up simulation models according to the species tree. ({user}mmatschiner {issue}893 {issue}929 {issue}931)
  • Add an modern array oriented RateMap class as to replace the RecombinationMap class ({user}jeromekelleher, {user}grahamgower, {user}hyanwong).
  • Functions to compute the likelihood of a particular ARG realisation under the coalescent with recombination ({user}jerekoskela).
  • Mutations are assigned times ({user}petrelharp)
  • Finite sites mutations ({user}petrelharp)
  • Several instances of matrix mutation models: JC69, GTR, HKY, F84, BLOSUM62, PAM. ({user}GertjanBisschop, {user}petrelharp).
  • An implementation of the SLiM mutation model ({user}petrelharp)
  • An infinite alleles mutation model ({user}jeromekelleher)
  • Methods to track the possible location of lineages, and compute the coalescence rates over time ({user}apragsdale, {user}petrelharp {user}grahamgower).
  • Two new CLI commands, msp ancestry and msp mutations which correspond to the sim_ancestry and sim_mutations functions. These can be pipelined using stdin/stdout. ({user}winni2k, {user}jeromekelleher)
  • Complete provenance recording of all arguments to simulate and mutate. Adds argument record_provenance to simulate, which allows recording of provenances to be disabled, for example when they are large. ({user}benjeffery {pr}914).
  • Add replicate_index to simulate, allowing output of a single tree sequence from a set of replicates. ({user}benjeffery {pr}914).
  • Details of the simulation are written to the DEBUG log periodically. This can help debug long-running simulations. ({user}jeromekelleher, {pr}1080).
  • Binary wheels for PyPI ({user}benjeffery)

Breaking changes:

  • Require Python 3.7+.
  • The class form for specifying models (e.g., msprime.StandardCoalescent()) no longer take a reference_size argument. ({user}jeromekelleher, {pr}1028).
  • The simulate function only takes one positional argument, and all other arguments are keyword-only.
  • The msp CLI has been stripped of all existing sub-commands except for simulate. The old sub-commands are provided by the tskit CLI or the TreeSequence API in tskit.
  • The end_time option now allows events up to and including the specified max time. Previously, events occurred strictly before the max time. ({user}apragsdale, {issue}1304, {pr}1521)
  • The class msprime.Population now refers to the new demography API. This may break old code that depends on the tskit table entities being exported from msprime (other classes are now formally deprecated and will raise a warning; see the deprecations section).
  • The semantics of start_time and exponential growth models has changed; previously, exponential population size changes would be calculated starting at the simulation start_time at the beginning of the simulation. Now population growth rates are always computed from time 0 (unless other events occur). The old semantics, if needed, can be recovered by setting the growth_rate to 0 in the initial population declaration and adding a population parameters change event at the start_time to change the growth_rate to the desired value.

Performance improvements

  • Much better simulation performance for models with large numbers of populations ({user}jeromekelleher, {pr}1069).
  • Significant performance improvements for simulating from recombination maps ({user}ivan-krukov, {user}castedo)

Deprecations:

  • Deprecate module attributes that were moved to tskit. ({user}benjeffery, {issue}991, {pr}1158)

[0.7.4] - 2019-12-05

Bug fixes:

  • Fix error in mspms output of tree spans. In previous versions, the length of genome spanned by trees in the newick output was incorrect in certain situations (specifically, when "invisible" recombinations are present so that two or more identical trees are printed out). Thanks to {user}fbaumdicker for spotting the problem. ({user}jeromekelleher, {pr}837, {issue}836)
  • Fix assertion tripped when we have very low recombination rates in the DTWF model. Thanks to {user}terhorst for the bug report. ({user}jeromekelleher, {pr}833, {issue}831).
  • Fix bug in memory allocation when simulating mutations on a tree sequence that already contains many mutations. Thanks to {user}santaci for the bug report. ({user}jeromekelleher, {user}petrelharp, {pr}838, {issue}806)

New features:

  • Add the new Census event, which allows us to place nodes on all extant branches at a given time ({user}gtsambos {pr}799).
  • Improved error reporting for input parameters, in particular demographic events ({pr}829).

Documentation:

  • Improved container documentation ({user}agladstein, {pr}822, {issue}809).
  • Improved developer docs for macs ({user}gtsambos, {user}molpopgen, {pr}805).
  • Clarify meaning of migration matrix ({user}petrelharp, {pr}830).

[0.7.3] - 2019-08-03

Bug fixes:

  • Support for SMC models coupled with the record_full_arg feature was erroneously removed in a previous version ({issue}795). The feature has been reinstated ({pr}796).

[0.7.2] - 2019-07-30

Breaking changes

  • The random trajectory has been changed slightly to improve handling of ancient sampling events ({pr}782). Thus, simulations for a given random seed will not be identical to previous versions, if ancient samples are used.

New features

  • Automated Docker builds ({user}agladstein; {pr}661)
  • Add mean coalescence time to DemographyDebugger ({user}petrelharp; {pr}779).
  • Improve MassMigration descriptions in DemographyDebugger ({user}marianne-aspbury; {pr}791).

Bug fixes:

  • In very, very, very rare cases it was possible to generate a zero waiting time until the next coalescent event, leading to zero branch lengths in the output tree sequence and an error being raised ({user}molpopgen, {user}DL42, {user}jeromekelleher; {issue}783, {pr}785).

[0.7.1] - 2019-06-08

New features

  • Discrete Time Wright-Fisher simulation model ({user}DomNelson).
  • SMC/SMC' simulation models ({user}jeromekelleher).
  • Mixed simulation models ({user}jeromekelleher).
  • Specify end_time to allow early-finish for simulations ({user}jeromekelleher).
  • Calculation of historical coalescence rates in the DemographyDebugger ({user}jgallowa07, {user}petrelharp).
  • Additional information on population sizes in DemographyDebugger ({user}andrewkern).
  • Remove support for Python 2 ({user}hugovk).
  • Allow specifying metadata for populations ({user}jeromekelleher).

Bug fixes:

  • Various minor bug and doc fixes from {user}hyanwong, {user}petrelharp, {user}brianzhang01, {user}mufernando and {user}andrewkern.

[0.7.1b1] - 2019-05-31

Early release making DTWF code available to beta testers.

[0.7.0] - 2019-02-19

Separation of tskit from msprime. Msprime is now solely dedicated to simulating the coalescent, and all infrastructure for working with succinct tree sequences is now provided by tskit. To ensure compatibility, msprime now imports code from tskit under the old names, which should ensure that all code continues to work without changes.

New features

  • Ability to record the full ARG ({user}jerekoskela; {issue}665)

Bug fixes:

  • Fix deprecation warning ({issue}695).

[0.7.0a1] - 2019-01-14

Alpha release for testing the tskit/msprime split.

[0.6.2] - 2018-12-04

Minor bugfix release.

New features:

  • Add provenance recording option to simplify (#601)
  • Minor performance improvement (#598)

Bug fixes:

  • Fix performance regression in replication (#608)

[0.6.1] - 2018-08-25

Significant features for integration with forwards-time simulators plus improvements and bugfixes.

Breaking changes:

  • Change in the semantics of how populations are treated by simplify. By default, populations that are not referenced will now be removed from the data model. This can be avoided by setting filter_populations=False.
  • Simplify now raises an error if called on a set of tables that contain one or more migrations.

New features:

  • The simulate() function now supports a from_ts argument allowing msprime to complete the ancestry in tree sequences generated by forward simulations (#503, #541, #572, #581).
  • Add start_time and end_time parameters to the mutate function (#508).
  • Add reduce_to_site_topology argument to simplify. This allows us to find the minimal tree sequence that would be visible from a given set of sites, and is also a useful compression method if we are only interested in the observed sequences. (#545, #307).
  • Simplify generalised to support individuals, and the filter_populations, filter_individuals and filter_sites parameters added to allow filtering of unreferenced objects from the data model. (#567).
  • Default random seeds are now generated from a sequence initialised by a system source of randomness (#534). Random seeds should also be safely generated across multiple processes.
  • Full text I/0 support for Individuals and Populations (#498, #555)
  • Substantially improved performance in msprime.load for large tables and significant refactoring of C code (#559, #567, #569).
  • Improved performance of generating genotypes (#580).
  • Formal schema for tree sequence provenance (#566, #583).
  • Many updates to documentation.

Bug fixes:

  • Throw a more intelligible error during simulation if a topology is produced where the time of a parent is equal to the time of the child. (#570, #87).
  • Pickle supported in the TableCollection object. (#574, #577).

Deprecated:

  • The filter_zero_mutation_sites parameter for simplify has been deprecated in favour of filter_sites.

[0.6.0] - 2018-06-20

This release is focused on ensuring interoperability with the forthcoming SLiM 3.0 release, which has support for outputting tree sequences in msprime's .trees format. The release represents a substantial step towards the goal of separating the tskit code from msprime. It removes the troublesome HDF5 dependency in favour of the much simpler kastore library.

The principle new features are the mutate() function which allows us to easily add mutations to any tree sequence, preliminary support for Individuals and Populations within the data model, and the addition of the new TableCollection object as the central structure in the Tables API.

Breaking changes:

  • Files stored in the HDF5 format will need to upgraded using the msp upgrade command.

New features:

  • The mutate function (#507).
  • Removed HDF5 library dependency. Now use the embedded kastore library for storing data.
  • Numpy and h5py are now install time dependencies, solving some installation headaches.
  • The new TableCollection type gives much tighter integration with the low-level library. Functions like sort_tables and simplify_tables are now methods of this class. The load_tables function has been replaced by TableCollection.tree_sequence. These functions still work, but are deprecated.
  • Preliminary support for Individual and Population types in the Tables API and for TreeSequences.
  • Add 'root' argument to SparseTree.newick and support for arbitrary node labels (#510).
  • Larger numbers of alleles now supported via 16-bit genotypes (#466).
  • Substantially improved simplify performance when there is a large number of sites (#453).

Bug fixes:

  • Fix bug in tree drawing with many roots (#486)
  • Fix segfault in accessing trees with zero roots (#515)
  • Fix bug where DemographyDebugger was modifying the input sample sizes (#407)

Deprecated:

  • sort_tables is deprecated in favour of TableCollection.sort().
  • simplify_tables is deprecated in favour of TableCollection.simplify().
  • load_tables is deprecated in favour of TableCollection.tree_sequence().

[0.5.0] - 2018-02-26

This is a major update to the underlying data structures in msprime to generalise the information that can be modelled, and allow for data from external sources to be efficiently processed. The new Tables API enables efficient interchange of tree sequence data using numpy arrays. Many updates have also been made to the tree sequence API to make it more Pythonic and general. Most changes are backwards compatible, however.

Breaking changes:

  • The SparseTree.mutations() and TreeSequence.mutations() iterators no longer support tuple-like access to values. For example, code like

    for x, u, j in ts.mutations():

    : print("mutation at position", x, "node = ", u)

    will no longer work. Code using the old Mutation.position and Mutation.index will still work through deprecated aliases, but new code should access these values through Site.position and Site.id, respectively.

  • The TreeSequence.diffs() method no longer works. Please use the TreeSequence.edge_diffs() method instead.

  • TreeSequence.get_num_records() no longer works. Any code using this or the records() iterator should be rewritten to work with the edges() iterator and num_edges instead.

  • Files stored in the HDF5 format will need to upgraded using the msp upgrade command.

New features:

  • The API has been made more Pythonic by replacing (e.g.) tree.get_parent(u) with tree.parent(u), and tree.get_total_branch_length() with tree.total_branch_length. The old forms have been maintained as deprecated aliases. (#64)
  • Efficient interchange of tree sequence data using the new Tables API. This consists of classes representing the various tables (e.g. NodeTable) and some utility functions (such as load_tables, sort_tables, etc).
  • Support for a much more general class of tree sequence topologies. For example, trees with multiple roots are fully supported.
  • Substantially generalised mutation model. Mutations now occur at specific sites, which can be associated with zero to many mutations. Each site has an ancestral state (any character string) and each mutation a derived state (any character string).
  • Substantially updated documentation to rigorously define the underlying data model and requirements for imported data.
  • The variants() method now returns a list of alleles for each site, and genotypes are indexes into this array. This is both consistent with existing usage and works with the newly generalised mutation model, which allows arbitrary strings of characters as mutational states.
  • Add the formal concept of a sample, and distinguished from 'leaves'. Change tracked_leaves, etc. to tracked_samples (#225). Also rename sample_size to num_samples for consistency (#227).
  • The simplify() method returns subsets of a large tree sequence.
  • TreeSequence.first() returns the first tree in sequence.
  • Windows support. Msprime is now routinely tested on Windows as part of the suite of continuous integration tests.
  • Newick output is not supported for more general trees. (#117)
  • The genotype_matrix method allows efficient access to the full genotype matrix. (#306)
  • The variants iterator no longer uses a single buffer for genotype data, removing a common source of error (#253).
  • Unicode and ASCII output formats for SparseTree.draw().
  • SparseTree.draw() renders tree in the more conventional 'square shoulders' format.
  • SparseTree.draw() by default returns an SVG string, so it can be easily displayed in a Jupyter notebook. (#204)
  • Preliminary support for a broad class of site-based statistics, including Patterson's f-statistics, has been added, through the {}SiteStatCalculator, and its branch length analog, {}BranchLengthStatCalculator. The interface is still in development, and is expected may change.

Bug fixes:

  • Duplicate site no longer possible (#159)
  • Fix for incorrect population sizes in DemographyDebugger (#66).

Deprecated:

  • The records iterator has been deprecated, and the underlying data model has moved away from the concept of coalescence records. The structure of a tree sequence is now defined in terms of a set of nodes and edges, essentially a normalised version of coalescence records.
  • Changed population_id to population in various DemographicEvent classes for consistency. The old population_id argument is kept as a deprecated alias.
  • Changed destination to dest in MassMigrationEvent. The old destination argument is retained as a deprecated alias.
  • Changed sample_size to num_samples in TreeSequence and SparseTree. The older versions are retained as deprecated aliases.
  • Change get_num_leaves to num_samples in SparseTree. The get_num_leaves method (and other related methods) that have been retained for backwards compatibility are semantically incorrect, in that they now return the number of samples. This should have no effect on existing code, since samples and leaves were synonymous. New code should use the documented num_samples form.
  • Accessing the position attribute on a Mutation or Variant object is now deprecated, as this is a property of a Site.
  • Accessing the index attribute on a Mutation or Variant object is now deprecated. Please use variant.site.id instead. In general, objects with IDs (i.e., derived from tables) now have an id field.
  • Various get_ methods in TreeSequence and SparseTree have been replaced by more Pythonic alternatives.

[0.4.0] - 2016-10-16

Major release providing new functionality and laying groundwork for upcoming functionality.

Breaking changes:

  • The HDF5 file format has been changed to allow for non-binary trees and to improve performance. It is now both smaller and faster to load. However, msprime cannot directly load tree sequence files written by older versions. The msp upgrade utility has been developed to provide an upgrade path for existing users, so that files written by older versions of msprime can be converted to the newer format and read by version 0.4.x of msprime.

  • The tuples returned by the mutations method contains an element. This will break code doing things like

    for pos, node in ts.mutations():

    : print(pos, node)

    For better forward compatibility, code should use named attributes rather than positional access:

    for mutation in ts.mutations():

    : print(mutation.position, mutation.node)

  • Similarly, the undocumented variants method has some major changes:

    1. The returned tuple has two new values, node and index in the middle of the tuple (but see the point above about using named attributes).
    2. The returned genotypes are by default numpy arrays. To revert to the old behaviour of returning Python bytes objects, use the as_bytes argument to the variants() method.

New features:

  • Historical samples. Using the samples argument to simulate users can specify the location and time of all samples explicitly.
  • HDF5 file upgrade utility msp upgrade
  • Support for non-binary trees in the tree sequence, and relaxation of the requirements on input tree sequences using the read_txt() function.
  • Integration with numpy, with zero-copy access to the low-level C API.
  • Documented the variants() method that provides access to the sample genotypes as either numpy arrays or Python bytes objects.
  • New LdCalculator class that allows very fast calculation of r^2 values.
  • Initial support for threading.
  • The values returned mutations() method now also contain an index attribute. This makes many operations simpler.
  • New TreeSequence.get_time() method that returns the time a sample was sampled at.

Performance improvements:

  • File load times substantially reduced by pre-computing and storing traversal indexes.
  • O(1) implementation of TreeSequence.get_num_trees()
  • Improved control of enabled tree features in TreeSequence.trees() method using the leaf_lists and leaf_counts arguments.

Bug fixes:

  • Fixed a precision problem with DemographyDebugger. #37
  • Segfault on large haplotypes. #29

[0.3.2] - 2016-07-21

Feature release adding new import and export features to the API and CLI.

  • New TreeSequence.write_records and TreeSequence.write_mutations methods to serialise a tree sequence in a human readable text format.
  • New msprime.load_txt() method that parses the above formats, and allows msprime to read in data from external sources.
  • New TreeSequence.write_vcf method to write mutation information in VCF format.
  • Miscellaneous documentation fixes.

[0.3.1] - 2016-06-24

Feature release adding population related methods to the API.

  • New TreeSequence.get_population(sample_id) method.
  • New TreeSequence.get_samples(population_id) method.
  • Added the optional samples argument to the TreeSequence.get_pairwise_diversity method.
  • Fixed a potential low-level buffer overrun problem.

[0.3.0] - 2016-05-31

Bugfix release affecting all users of the Python API. Version 0.2.0 contained a confusing and inconsistent mix of times and rates being expressed in both coalescent units and generations. This release changes all times and rates used when describing demographic models to generations, and also changes all population sizes to be absolute. In the interest of consistency, the units of the trees output by msprime are also changed to generations. This is a major breaking change, and will require updates to all scripts using the API.

This release also include some performance improvements and additional functionality.

Mspms users are not affected, other than benefiting from performance improvements.

Breaking changes:

  • Time values are now rescaled into generations when a TreeSequence is created, and so all times associated with tree nodes are measured in generations. The time values in any existing HDF5 file will now be interpreted as being in generations, so stored simulations must be rerun. To minimise the chance of this happening silently, we have incremented the file format major version number, so that attempts to read older versions will fail.
  • Growth rate values for the PopulationConfiguration class are now per generation, and population sizes are absolute. These were in coalescent units and relative to Ne previously.
  • GrowthRateChangeEvents and SizeChangeEvents have been replaced with a single class, PopulationParametersChange. This new class takes an initial_size as the absolute population size, and growth_rate per generation. Since the change in units was a breaking one, potentially leading to subtle and confusing bugs, we decided that the name refactoring would at least ensure that users would need to be aware that the change had been made. This API should now be stable, and will not be changed again without an excellent reason.
  • MigrationRateChangeEvent has been renamed to MigrationRateChange and the migration rates are now per-generation.
  • MassMigrationEvent has been renamed to MassMigration, and the values of source and destination swapped, fixing the bug in issue #14.
  • The TreeSequence.records() method now returns an extra value, potentially breaking client code.

Improvements:

  • Added tutorial for demographic events.
  • Added DemographyDebugger class to help view the changes in populations over time.
  • Added population tracking for coalescent events. We can now determine the population associated with every tree node. The relevant information has been added to the HDF5 file format.
  • Improved performance for replication by reusing the same low-level simulator instance. This leads to significant improvements for large numbers of replicates of small simulations. Issue #8.
  • Changed the TreeSequence.records() method to return named tuples.
  • Added get_total_branch_length method. Issue #12.
  • Fixed bug in reading Hapmap files. Issue #13.

[0.2.0] - 2016-05-05

Major update release, adding significant new functionality to the Python API and several breaking changes. All code written for the 0.1.x API will be affected, unfortunately.

Breaking changes:

  • Sample IDs are now zero indexed. In previous versions of msprime, the samples were numbered from 1 to n inclusive, which is not Pythonic. This change has been made to make the API more usable, but will cause issues for existing code.
  • There is now an Ne parameter to simulate(), and recombination, mutation and migration rates are now all per-generation. The keyword arguments have been changed to recombination_rate and mutation_rate, which should mean that silent errors will be avoided. All rates in existing code will need to be divided by 4 as a result of this. This change was made to make working with recombination maps and per generation recombination rates easier.
  • Msprime now uses continuous values to represent coordinates, and the num_loci parameter has been replaced with a new length parameter to simulate(). Internally, a discrete recombination model is still used, but by default the potential number of discrete sites is very large and effectively continuous. True discrete recombination models can still be specified by using the recombination_map argument to simulate.
  • The population_models argument to simulate() has been removed, and replaced with the population_configuration and demographic_events parameters. This was necessary to provide the full demographic model.
  • The HDF5 file format has been updated to accommodate the continuous coordinates, along with other minor changes. As a consequence, simulation results will be somewhat larger. Stored simulations will need to be re-run and saved.
  • Removed the random_seed key from the provenance JSON strings.
  • Removed the simulate_tree() function, as it seemed to offer little extra value.

New features:

  • Simulation of variable recombination rates via arbitrary recombination maps.
  • Full support for population structure and demographic events.
  • API support for replication via the num_replicates argument to simulate().
  • Fully reworked random generation mechanisms, so that in the nominal case a single instance of gsl_rng is used throughout the entire simulation session.
  • Addition of several miscellaneous methods to the TreeSequence API.
  • Added NULL_NODE constant to make tree traversals more readable.

[0.1.10] - 2016-04-21

Bugfix release. Fixes serious issue affecting simulations with small sample sizes.

https://github.com/jeromekelleher/msprime/issues/7

All users of mspms should update immediately and any analyses using a small sample size (< 10) with mutations should be repeated.

Many thanks to Konrad Lohse for identifying the issue.

[0.1.9] - 2016-04-01

Bugfix release. Fixes serious issue affecting random seeds in mspms.

https://github.com/jeromekelleher/msprime/issues/6

All users of mspms should update immediately and any analyses using the -seeds option in mspms should be repeated.

Many thanks to Derek Setter for identifying the issue.

[0.1.8] - 2016-02-17

Transitional release providing population structure support for the ms-compatible command line interface. A considerable amount of low-level plumbing was required to provide the required flexibility. This is currently not visible from the high-level API, but will shortly be made available in the forthcoming 0.2.x series.

The current implementation of migration should work well for small numbers of populations (e.g. < 10), but will not scale well for large numbers of populations.

Changes

  • Added the -I, -m, -ma, -em, -eM, -ema, -eG, -eg, -eN, -en, -ej and -es options to mspms. These should provide full ms compatibility, except for the -es option which is currently limited in scope.
  • Added some extra keys to the low-level configuration JSON in the HDF5 file format to describe the population structure. This will be documented in a future release.
  • Added a {}get_pairwise_diversity method to the TreeSequence class to efficiently calculate the population genetics statistic pi.