--- _id: '5421' abstract: - lang: eng text: 'Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are: (1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure). (2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.' alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Martin full_name: Nowak, Martin last_name: Nowak citation: ama: Chatterjee K, Ibsen-Jensen R, Nowak M. The Complexity of Evolution on Graphs. IST Austria; 2014. doi:10.15479/AT:IST-2014-190-v2-2 apa: Chatterjee, K., Ibsen-Jensen, R., & Nowak, M. (2014). The complexity of evolution on graphs. IST Austria. https://doi.org/10.15479/AT:IST-2014-190-v2-2 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Martin Nowak. The Complexity of Evolution on Graphs. IST Austria, 2014. https://doi.org/10.15479/AT:IST-2014-190-v2-2. ieee: K. Chatterjee, R. Ibsen-Jensen, and M. Nowak, The complexity of evolution on graphs. IST Austria, 2014. ista: Chatterjee K, Ibsen-Jensen R, Nowak M. 2014. The complexity of evolution on graphs, IST Austria, 27p. mla: Chatterjee, Krishnendu, et al. The Complexity of Evolution on Graphs. IST Austria, 2014, doi:10.15479/AT:IST-2014-190-v2-2. short: K. Chatterjee, R. Ibsen-Jensen, M. Nowak, The Complexity of Evolution on Graphs, IST Austria, 2014. date_created: 2018-12-12T11:39:14Z date_published: 2014-04-18T00:00:00Z date_updated: 2023-02-23T12:26:33Z day: '18' ddc: - '000' - '005' department: - _id: KrCh doi: 10.15479/AT:IST-2014-190-v2-2 file: - access_level: open_access checksum: 42f3d8b563286eb0d903832bd9a848d3 content_type: application/pdf creator: system date_created: 2018-12-12T11:54:16Z date_updated: 2020-07-14T12:46:50Z file_id: '5538' file_name: IST-2014-190-v2+2_main_full.pdf file_size: 443529 relation: main_file - access_level: open_access checksum: 0c9a2fd822309719634495a35957e34d content_type: application/pdf creator: kschuh date_created: 2019-09-06T07:30:20Z date_updated: 2020-07-14T12:46:50Z file_id: '6852' file_name: IST-2014-190-v1+1_main_full.pdf file_size: 440911 relation: main_file file_date_updated: 2020-07-14T12:46:50Z has_accepted_license: '1' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: '27' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '190' related_material: record: - id: '5432' relation: later_version status: public - id: '5440' relation: later_version status: public status: public title: The complexity of evolution on graphs type: technical_report user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 year: '2014' ...