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Simulate random phylogenetic trees

Project description

Ngesh, simulation of random phylogenetic trees with characters

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ngesh is a Python library for simulating random phylogenetic trees and related data (characters, states, branch length, etc.). It is intended for benchmarking phylogenetic methods, especially in historical linguistics, and for providing dummy trees for their development and debugging. The generation of random phylogenetic trees also goes by the name of "simulation methods for phylogenetic trees" or just "phylogenetic tree simulation".

Please remember that ngesh is a work-in-progress and a library intended to be a simple drop-in for cases where random trees are needed; for complex methods, see the alternatives listed below or consult the bibliographic references.

In detail, with ngesh:

  • trees can be generated according to user-specified birth and death ratios (and the death ratio can be set to zero, resulting in a birth-only tree)
  • speciation events default to two descendants, but the number of descendants can be randomly drawn from a user-defined Poisson process (allowing to model hard politomies)
  • trees will have random topologies and, if necessary, random branch-lengths
  • trees can be limited in terms of number of extant leaves, evolution time (as related to the birth and death parameters), or both
  • non-extant leaves can be pruned from birth-death trees
  • character evolution can be simulated in relation to branch lengths, with user-specified ratios for mutation and horizontal gene transfer, with different rates of change for each character
  • trees can be generated from user-provided seeds, so that the random generation can be maintained across executions (and, in most cases, the execution should be reproducible also on different machines and different vestions of Python)
  • nodes can optionally receive unique labels, either sequential ones (like "L01", "L02", and "L03"), random human-readable names (like "Sume", "Fekobir", and "Tukok"), or random biological names approximating the binomial nomenclature standard (like "Sburas wioris", "Zurbata ceglaces", and "Spellis spusso")
  • trees can be returned as ETE tree objects or exported in a variety of formats, such as Newick trees, ASCII representation, tabular textual listings, etc.

How does ngesh work?

For each tree, an event_rate is computed from the sum of the birth and death rates. At each iteration, which takes place after an random expovariant time from the event_rate, one of the extant nodes is selected for an "event": either a birth or a death from the proportion of each rate. All other extant leaves have their distances updated with the event time.

The random labels follow the expected methods for random text generation from a set of patterns, taking care to generate names as universally readable (if not pronounceable) as possible.

missing on character generation


In any standard Python environment, ngesh can be installed with:

pip install ngesh

The pip installation will also fetch the dependencies ete3 and numpy, if necessary.

How to use

You can test your installation from the command line with the ngesh command, which will return a different random small birth-death tree in Newick format each time it is called:

$ ngesh
(Saorus getes:1.31562,((Voces earas:1.07567,(Dallao spettus:0.703609,Sburas wioris:0.703609)1:0.372063)1:0.464667,(Zurbaza ceglaces:0.527431,(Amduo vizoris:0.345862,Uras wiurus:0.345862)1:0.18551)1:1.00897)1:2.1707);

$ ngesh
((Ollio zavis:0.698453,(Spectuo sicui:0.596731,((Ronis mivulis:0.0431014,Vaporus conomattas:0.0431014)1:0.413634,Rizarus urrus:0.456735)1:0.139996)1:0.101722)1:3.17827,(Deses mepus:2.22061,(Ovegpuves wiumoras:1.88469,(Easas ecdebus:0.201891,Muggas lupas:0.201891)1:1.6828)1:0.335918)1:1.65611);

The same command line tool can refer to values provided in a textual configuration file. Here, we generate the Nexus data for a reproducible Yule tree (note the 12345 seed) with a birth ratio of 0.75, at least 8 leaves with "human" labels, and 10 presence/absence characters:

$ cat my_tree.conf 

$ ngesh -c mine.conf --seed 12345

begin data;
  dimensions ntax=15 nchar=25;
  format datatype=standard missing=? gap=-;
Foro        1011000101010010100100100
Meno        1100100101010010010010001
Vuea        1100110001010100001001001
Vegevo      1100100101010010010010100
Bufuri      1100110001010100001001001
Novake      1100110001010100001001001
Fonulip     1100110001010100001001001
Omih        1101001001010011000100100
Onegro      1101000011010010001100100
Rolsoa      1100100100110010010100100
Wigu        1101001001010010001100100
Teozu       1101001001010011000100010
Kabu        1100100101001010010100100
Timebbed    1100100101010010010010100
Okuna       1100110001010100001001001

Parameters set in a configuration file can be overridden at the command line. The ASCII representation of the topology of the same tree can be obtained with:

$ ngesh -c mine.conf --seed 12345 -o ascii

      /-|      /-Onegro
     |  |   /-|
     |   \-|   \-Wigu
     |     |
     |      \-Teozu
   /-|   /-Kabu
  |  |  |
  |  |  |            /-Novake
  |  |  |           |
  |  |  |         /-|      /-Okuna
  |  |  |        |  |   /-|
  |   \-|        |   \-|   \-Fonulip
  |     |      /-|     |
  |     |     |  |      \-Bufuri
  |     |     |  |
--|     |   /-|   \-Vuea
  |     |  |  |
  |     |  |  |   /-Meno
  |      \-|   \-|
  |        |      \-Rolsoa
  |        |
  |        |   /-Vegevo
  |         \-|
  |            \-Timebbed

The package is, however, designed to be used as a library. If you have PyQt5 installed (which is not listed as a dependency), the following code will pop up the ETE Tree Viewer on a random tree:

python3 -c "import ngesh ; ngesh.display_random_tree()"

random tree

The main functions for generation are gen_tree(), which returns a random tree topology, and add_characters(), which simulates character evolution in a provided tree. As they are separate tasks, it is possible to just generate a random tree or to simulate character evolution in an user provided tree.

The full documentation is available in the functions docstring (which can be visualized with print(ngesh.gen_tree.__doc__) and print(ngesh.add_characters.__doc__)) or directly in the source code. The code snipped below shows a basic tree generation, character evolution, and output flow; the parameters for generation are the same listed in the docstrings and in the following below.

$ ipython3

In [1]: import ngesh

In [2]: tree = ngesh.gen_tree(1.0, 0.5, max_time=3.0, labels="human")

In [3]: print(tree)

  |  |   /-Defomze
  |   \-|
  |      \-Gegme
  |      /-Bo
  |   /-|
  |  |   \-Peoni
     |   /-Riuzo

In [4]: tree = ngesh.add_characters(tree, 10, 3.0, 1.0)

In [5]: print(ngesh.tree2nexus(tree))

begin data;
  dimensions ntax=7 nchar=15;
  format datatype=standard missing=? gap=-;
Hoale      100111101101110
Butobfa    101011101110101
Defomze    101011110110101
Riuzo      100111101101110
Peoni      110011101110110
Bo         110011101110110
Gegme      101011101110101

Integrating with other software

Integration is easy due to the various export functions. For example, it is possible to generate random trees with characters for which we know all details on evolution and parameters, and generate Nexus files that can be fed to phylogenetic software such as MrBayes or BEAST2 to either check how they perform or how good is our generation in terms of real data.

Let's simulate phylogenetic data for an analysis using BEAST2 through BEASTling. We start with a birth-death tree (lambda=0.9, mu=0.3), with at least 15 leaves, and 100 characters whose evolution is modelled with the default parameters and a string seed "jena" for reproducibility; the tree data is exported in "wordlist" format:

$ cat examples/example_ngesh.conf 

$ ngesh -c examples/example.conf --seed jena > examples/example.csv

$ head examples/example.csv 

We can now use a minimal BEASTling configuration and generate an XML input for BEAST2. Let's assume we want to test how well our pipeline performs when assuming a Yule tree when the data actually includes extinct taxa. The results here presented are not expected to perfect, as we will use a short chain length to make it faster and a model which is different from the assumptions used for generation (besides the fact of the default parameters for horizontal gene transfer being a bit too aggressive).

$ cat examples/example_beastling.conf 
[model example]

$ beastling example_beastling.conf 

$ beast example.xml 

We can proceed normally here: use BEAST2's treeannotator (or similar software) to generate a summary tree, which we store in examples/summary.nex, and plot the results with figtree (or, again, similar software).

Let's plot our summary tree and compare the results with the actual topology (which we can regenerate with the earlier seed).

summary tree

$ ngesh -c examples/example_ngesh.conf --seed jena --output newick > examples/example.nw

original tree

The results are not excellent given the limits we set for quick demonstration, but it still capture major information and subgroupings (as clearer by the radial layout below) -- manual data exploration show that at least some of the errors, including the group in the first split, are due to horizontal gene transfer. For an analysis of the inference performance we would need to improve the parameters above and repeat the analysis on a range of random trees, including studying the log of character changes (including borrowings) involved in this particular random tree.

summary tree radial

TODO: Compare trees (Robinson-Foulds symmetric difference?)

The files used and generated in this example can be found in the /examples directory.

Parameters for tree generation

The parameters for tree generation, as also given by ngesh -h, are:

  • birth: The tree birth rate (l)
  • death: The tree death rate (mu)
  • max_time: The stopping criterion for maximum evolution time
  • min_leaves: The stopping criterion for minimum number of leaves
  • labels: The model for textual generation of random labels (None, "enum" for a simple enumeration, "human" for randomly generated names, and "bio" for randomly generated specie names)
  • num_chars: The number of characters to be simulated
  • k_mut: The character mutation gamma k parameter
  • th_mut: The character mutation gamma th parameter
  • k_hgt: The character HGT gamma k parameter
  • th_hgt: The character HGT gamma th parameter
  • e: The character general mutation e parameter

What does "ngesh" mean?

Technically it is just an unique name, but it was derived from one of the Sumerian words for "tree", ĝeš, albeit with an uncommon transcription. The name comes from the library once being a module of a larger system for simulating language evolution and benchmarking related tools, called Enki after the Sumerian god of (among many other things) language and mischief.

The intended pronounciation, as in the most accepted reconstructions, is /ŋeʃ/. But don't strees over it: it is just a unique name.


There are many tools for simulating phylogenetic processes in order to obtain random phylogenetic trees. The most complete is probably the R package TreeSim by Tanja Stadler, which includes many flexible tree simulation functions. In R, one can also use the rtree() function from package ape and the birthdeath.tree() one from package geiger, as well as manually randomizing taxon placement in cladograms.

In Python, some code similar to ngesh and which served as initial inspiration is provided by Marc-Rolland Noutahi on the blog post How to simulate a phylogenetic tree ? (part 1).

A number of on-line tools are also available at the time of writing:


  • Shorter-term

    • Write better documentation of function parameters
    • Add all still unavailable parameters to the command line tool (e.g., setting hard politomies)
    • Automatically generate developer documentation (possibly with Sphinx)
    • Allow generation of unlabelled trees from the command-line (a text generation model is currently mandatory)
    • Look for default parameters that are more closely related to linguistic trees (or, at least, to the Indo-European one)
    • Check if all outputs are complete (e.g., characters are currently missing in the Newick format)
    • Add a command-line option (or a new tool) that allows to write the output to one file and the reference tree to a second one (possibly with the log of character evolution)
    • Check for alternatives for the exponential correction of a character resistance to mutation (e.g. Zipf law), including separating mutation and borrowing rates
    • Allow to exclude non extant taxa from horizontal gene transfer events
    • Add stopping criterion on the global number of nodes (in complement to the number of extant nodes, currently implemented), either absolute or as a range
  • Longer-term

    • Simulation of data problems (incomplete sampling, errors in sequencing/cognate judgment, etc.)
    • Variable birth/death ratios
    • Rewrite the random text generation functions, possibly as actual Python generators
    • Consider replacing or complementing expovariate() in birth/death events with actual random Poisson sampling, allowing additional models
    • Build a simple website
    • Implement parallel character evolution as controlled by a parameter
    • Rewrite functions with too many arguments to accept dictionaries of parameters
    • Implement more models for random character generation, especially those frm genetics (first candidate, a General Time Reversable model with a proportion of invariable sites and a gamma-shaped distribution of rates across sites)
    • Simulate a "donation power" for taxa, making borrowing events globally more likely from a given donor (analogous to cultural influence in linguistics)
    • Allow to guarantee that borrowing events will always result in altered states (it is currently possible that an event will borrow an equal state for a given character, especially considering that we favor borrowing from closer taxa)
    • Implement character simulation for other datatypes, particularly from genetics (currently only standard binary presence/absence)


random tree random tree random tree

How to cite

If you use ngesh, please cite it as:

Tresoldi, Tiago (2019). Ngesh, a tool for simulating random phylogenetic trees. Version 0.2. Jena. Available at:

In BibTeX:

  author = {Tresoldi, Tiago},
  title = {Ngesh, a tool for simulating random phylogenetic trees. Version 0.2},
  howpublished = {\url{}},
  address = {Jena},
  year = {2019},
  doi = {10.5281/zenodo.2619311},


  • Bailey, N. T. J. (1964). The elements of stochastic processes with applications to the natural sciences. John Wiley & Sons.

  • Foote, M., J. P. Hunter, C. M. Janis, and J. J. Sepkoski Jr. (1999). Evolutionary and preservational constraints on origins of biologic groups: Divergence times of eutherian mammals. Science 283:1310–1314.

  • Harmon, Luke J (2019). Phylogenetic Comparative Methods -- learning from trees. Available at: Access date: 2019-03-31.

  • Noutahi, Marc-Rolland (2017). How to simulate a phylogenetic tree? (part 1). Available at: Access date: 2019-03-31

  • Stadler, Tanja (2011). Simulating Trees with a Fixed Number of Extant Species. Systematic Biology 60.5:676-684. DOI:


Tiago Tresoldi (

The author was supported during development by the ERC Grant #715618 for the project CALC (Computer-Assisted Language Comparison: Reconciling Computational and Classical Approaches in Historical Linguistics), led by Johann-Mattis List.

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