Rank abundance relations in evolutionary dynamics of random replicators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 3, 2008, Pages

  Yoshino, Yoshimi ^a   Galla, Tobias ^b,c   Tokita, Kei ^a  

^a OSAKA UNIVERSITY   (Japan)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FORESTRY; IMAGE SEGMENTATION; INTEGRAL EQUATIONS; MECHANICS; NORMAL DISTRIBUTION; RANDOM PROCESSES; STATISTICAL MECHANICS;

EVOLUTIONARY DYNAMICS; FINITE SYSTEM SIZE; FOOD WEBS; HIGHER-ORDER; IN DEPENDENCE; INTERACTION MATRICES; MULTI-SPECIES; NONEQUILIBRIUM STATISTICAL MECHANICS; ORDER PARAMETERS; REPLICATORS; SKEWED DISTRIBUTIONS; SPECIES ABUNDANCE DISTRIBUTION; STABLE SPECIES; STATIONARITY; TRUNCATED NORMAL;

FLOW INTERACTIONS;

EID: 53449096815     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.031924     Document Type: Article

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64. We here note that upon writing ωi =ln (xi) for the octave to which a species with concentration xi >0 belongs, and G (ω) for the "density of species" per octave ω, one has /ω ω+1 G (ω′) d ω′ = / eω eω+1 F (x) dx, so that one realizes by substitution that G (ω) = eω F (eω) =xF (x), which motivates our plotting of xF (x) in a log-linear scale. Note that for convenience we do not use a base of two in this context, but choose natural logarithms instead. This amounts to no more than an overall rescaling by a constant factor.