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Recently, arguments inspired by algorithmic information theory (AIT) and Kolmogorov complexity have been invoked to uncover simplicity bias in GP maps, an exponentially decaying upper bound in phenotype probability with the increasing phenotype descriptional complexity. This means that phenotypes with many genotypes assigned via the GP map must be simple, while complex phenotypes must have few genotypes assigned. Here, we use similar arguments to bound the probability P(x \u2192 y) that phenotype x, upon random genetic mutation, transitions to phenotype y. The bound is P(x\u2192y)\u22722\u2212aK~(y|x)\u2212b, where K~(y|x) is the estimated conditional complexity of y given x, quantifying how much extra information is required to make y given access to x. This upper bound is related to the conditional form of algorithmic probability from AIT. We demonstrate the practical applicability of our derived bound by predicting phenotype transition probabilities (and other related quantities) in simulations of RNA and protein secondary structures. Our work contributes to a general mathematical understanding of GP maps and may facilitate the prediction of transition probabilities directly from examining phenotype themselves, without utilizing detailed knowledge of the GP map.<\/jats:p>","DOI":"10.1098\/rsif.2022.0694","type":"journal-article","created":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T03:05:39Z","timestamp":1670987139000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Predicting phenotype transition probabilities via conditional algorithmic probability approximations"],"prefix":"10.1098","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4423-3255","authenticated-orcid":true,"given":"Kamaludin","family":"Dingle","sequence":"first","affiliation":[{"name":"Cambridge CB2 1TN, UK 1","department":["Department of Chemical Engineering and Biotechnology, Cambridge University"]},{"name":"Pasadena, CA 91125, USA 2","department":["Department of Computing and Mathematical Sciences, California Institute of Technology"]},{"name":"32093, Kuwait 3","department":["Department of Mathematics and Natural Sciences, Centre for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9757-5967","authenticated-orcid":true,"given":"Javor K.","family":"Novev","sequence":"additional","affiliation":[{"name":"Cambridge CB2 1TN, UK 1","department":["Department of Chemical Engineering and Biotechnology, Cambridge University"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2613-0041","authenticated-orcid":true,"given":"Sebastian E.","family":"Ahnert","sequence":"additional","affiliation":[{"name":"Cambridge CB2 1TN, UK 1","department":["Department of Chemical Engineering and Biotechnology, Cambridge University"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ard A.","family":"Louis","sequence":"additional","affiliation":[{"name":"Oxford OX1 2JD, UK 4","department":["Department of Physics, Rudolf Peierls Centre for Theoretical Physics, Oxford University"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2022,12,14]]},"reference":[{"key":"2026010520262651500_RSIF20220694C1","volume-title":"Arrival of the fittest: solving evolution\u2019s greatest puzzle","author":"Wagner","year":"2014"},{"key":"2026010520262651500_RSIF20220694C2","doi-asserted-by":"crossref","first-page":"20170275","DOI":"10.1098\/rsif.2017.0275","article-title":"Structural properties of genotype\u2013phenotype maps","volume":"14","author":"Ahnert","year":"2017","journal-title":"J. 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