{"paper":{"title":"Exactly solvable dynamics of the Eigen and the Crow-Kimura models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"q-bio.PE","authors_text":"Andrei Akmetzhanov, David B. Saakian, Olga Rozanova","submitted_at":"2009-08-12T05:11:25Z","abstract_excerpt":"We introduce a new way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the $1/N$-accuracy, where $N$ is genome length. For smooth and monotonic fitness function this approach gives two dynamical phases: smooth dynamics, and discontinuous dynamics. The latter phase arises naturally with no explicit singular fitness function, counter-intuitively. The Hamilton-Jacobi method yields straightforward analytical results for the models that utilize fitness as a func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1615","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}