Universität zu Köln

Park, Su-Chan and Krug, Joachim ORCID: 0000-0002-2143-6490 (2016). delta-exceedance records and random adaptive walks. J. Phys. A-Math. Theor., 49 (31). BRISTOL: IOP PUBLISHING LTD. ISSN 1751-8121

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Abstract

We study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition Y-k > Yk-1 - delta(k-1) with a deterministic sequence delta k > 0 called the handicap. For constant delta(k) equivalent to delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al 2015 Phys. Rev. E 91 042707). Here we explore the behavior for general probability distributions and decreasing and increasing sequences delta(k), focusing in particular on the case when delta(k) matches the typical spacing between subsequent records in the underlying simple record process without handicap. We find that a continuous phase transition occurs only in the exponential case, but a novel kind of first order transition emerges when delta(k) is increasing. The problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes, where delta(k) corresponds to the change of the deterministic fitness component after k mutational steps. The results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Park, Su-Chan UNSPECIFIED UNSPECIFIED UNSPECIFIED Krug, Joachim UNSPECIFIED orcid.org/0000-0002-2143-6490 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-266795
DOI:	10.1088/1751-8113/49/31/315601
Journal or Publication Title:	J. Phys. A-Math. Theor.
Volume:	49
Number:	31
Date:	2016
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1751-8121
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institut für Biologische Physik
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DIMINISHING-RETURNS EPISTASIS; BENEFICIAL MUTATIONS; EVOLUTION; NUMBER Multiple languages Physics, Multidisciplinary; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/26679