Description:

This Python code computes higher-order interactions such as 2-way, 3-way,…, n-way interaction coordinates and some circuits in the n-species (or loci in genetics) case taking as input 2^n experimental measurements. These interactions are described in A.L Gould et al's work on High-dimensional microbiome interactions shape host fitness .

Instructions:

• To compute the above mentioned interactions insert manually experimental data and standard error measurements in the epistasis.py file and run. Currently, the program is set to work in the 5-species case, but it can be altered easily to analyze interactions in the n-species case.

• This code can also compute the intervals in which the results of the above interactions are contained by knowing the intervals in which the starting measurments are contained: for instance, average measurement +/- SE.

  • Example: if each measurment w_X belongs to the interval [w_X-SE,w_X+SE], then our code coutputs the bounds of the interval [a,b] containing for instance the 2-way interaction

    w_00000+w_00011-w_00001-w_00010 .

    Similarly, the code computes all other intervals for the various higher-order interactions described above.

Dependencies:

• NumPy: Python interface to store and operate on numerical arrays
• Itertools: Python module used to creat iterators

The epistasis.py file uses the code contained in the following files:

• Fourier.py: module written to compute interactions coordinates inside n-dimensional hypercubes, as described in equation 8 in Epistasis and shapes of fitness landscapes
• Circuits.py: generates all 2 and 3 dimensional circuit interactions inside n-dimensional hypercubes.
• Slicing.py: generates all possible contexts for circuit and interaction coordinates.
• Utlis.py: minor module with additional codes used in the above files.

Observation:

The code builds on: Python sequences. In particular tuple/list/dict comprehensions, generators and 'yield from' idioms have been extensively applied to delegate a lot of data manipulation to Python. Only simple mathematical operators are used (inner product, matrix product). Elementary interval arithmetics.

References:

• A.L Gould et al, High-dimensional microbiome interactions shape host fitness
• N. Beerenkinkel et al, Epistasis and shapes of fitness landscapes

Authors:

Korasidis Nikolaos [email protected], Lamberti Lisa [email protected]

Initial release: August 2018