This is an online client for computing higher-order epistatic interactions as detailed in the articles [1] and [2]. It was implemented as polymake extension and can be found online on GitHub. If you found this useful for your scientific work, please cite our paper [1].

The input is a sequence of genotype-phenotype maps, where several phenotypes for the same genotype are considered as independent measurements, thus giving rise to a distribution of phenotypes. Genotypes are 0/1-vectors (i.e., here we are treating the biallelic case only), and phenotypes are real numbers. The entire dataset is supposed to be contained in a single file of type csv (ASCII text, comma separated values). Such files can be exported from standard spreadsheet software.

Download result file

After roughly five minutes, in order to download the results for a previously submitted csv data sheet, please enter your id here:

Data sets examined in our papers [1] and [2]

• Eble data
• Khan data
• Gould data

Explanation of the output

Your input will be rejected

• if it is not of the form as explained above or
• if the number of loci exceeds 7 or
• if the given data is not generic enough, i.e., the genotype-phenotype map doesn't induce a triangulation.

Once passed this check, the epistatic filtration of the input data is computed and the following reports are given back:

• filtrationbars_user_input.pdf: a filtration bar diagram as Fig. 3 in Section 3.4 of [1].
• epistatic+landscape_user_input.pdf: the dual graph of the triangulation with red/blue colored and ordered edges as in Fig. 2(A) of [2].
• critical+spanningtree_user_input.pdf: the spanning tree of the epistatic landscape only featuring the critical edges.
• result.csv: a detailed data sheet explaining the epistatic landscape including the epistatic weights and p-values.

If the given genotypes describe the vertices of the complete n-dimensional cube, various parallel transports are performed, see Section 6.6. and 6.7 of [1]. For each locus i in {1,...,n} the parallel information **0***→**1*** and **1***→**0*** is computed where the digits 0 and 1 are in the i-th place. The results can be found in the folders parallel/locus〈i〉/0+TO+1 (first case) and parallel/locus〈i〉/1+TO+0 (second case):

• the filtrationbars diagram of the source of the parallel transport.
• the epistatic landscape of the source of the parallel transport.
• the targetbars diagram, i.e. the parallel transported filtrationbars diagram.
• two analysis tables (one csv, one pdf) listing the detaild information of the parallel transport.
• Further, the folder parallel/ contains the file parallel_summary_user_input.pdf with a coarse summary of all performed transports.

References

1. Holger Eble, Michael Joswig, Lisa Lamberti, and William B. Ludington: Cluster partitions and fitness landscapes of the Drosophila fly microbiome, J. Math. Biology (2019), no. 79, 861–899, doi: 10.1007/s00285-019-01381-0.
2. Holger Eble, Michael Joswig, Lisa Lamberti, and William B. Ludington: Higher-order interactions in fitness landscapes are sparse, preprint, ArXiv:2009.12277.