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On the behavior of the leading eigenvalue of Eigen’s evolutionary matricesстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 24 ноября 2021 г.
- Авторы: Semenov Yuri S., Bratus Alexander S., Novozhilov Artem S.
- Журнал: Mathematical Biosciences
- Том: 258
- Год издания: 2014
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 134
- Последняя страница: 147
- DOI: 10.1016/j.mbs.2014.10.004
- Аннотация: We study general properties of the leading eigenvalue w¯(q) of Eigen's evolutionary matrices depending on the replication fidelity q. This is a linear algebra problem that has various applications in theoretical biology, including such diverse fields as the origin of life, evolution of cancer progression, and virus evolution. We present the exact expressions for w¯(q),w¯'(q),w¯''(q) for q = 0, 0.5, 1 and prove that the absolute minimum of w¯(q), which always exists, belongs to the interval (0, 0.5]. For the specific case of a single peaked landscape we also find lower and upper bounds on w¯(q), which are used to estimate the critical mutation rate, after which the distribution of the types of individuals in the population becomes almost uniform. This estimate is used as a starting point to conjecture another estimate, valid for any fitness landscape, and which is checked by numerical calculations. The last estimate stresses the fact that the inverse dependence of the critical mutation rate on the sequence length is not a generally valid fact.
- Добавил в систему: Семенов Юрий Станиславович