Multidelayed random walks: Theory and application to the neolithic transition in Europe

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 70, Issue 3, 2004, Pages 6-

  Fort, Joaquim ^a   Jana, Debnarayan ^b,c   Humet, Josep ^a  

^a UNIVERSITY OF GIRONA   (Spain)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c UNIVERSITY OF CALCUTTA   (India)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; DIFFUSION; ELECTRON TRANSITIONS; ERROR CORRECTION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; PROBABILITY;

BIOPHYSICAL SYSTEMS; MICROSCOPIC MOTION; NEOLITHIC TRANSITIONS; POPULATION DENSITY;

ELEMENTARY PARTICLES;

ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPUTER SIMULATION; DIFFUSION; EUROPE; EVALUATION; EVOLUTION; HISTORY; HUMAN; MIGRATION; MOVEMENT (PHYSIOLOGY); PHYSIOLOGY; POPULATION DYNAMICS; POPULATION GROWTH; SEXUAL BEHAVIOR; STATISTICAL DISTRIBUTION; STATISTICAL MODEL; TIME; VALIDATION STUDY;

COMPUTER SIMULATION; DIFFUSION; EMIGRATION AND IMMIGRATION; EUROPE; EVOLUTION; HISTORY, ANCIENT; HUMANS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MOVEMENT; POPULATION DYNAMICS; POPULATION GROWTH; REPRODUCTIVE BEHAVIOR; STATISTICAL DISTRIBUTIONS; TIME FACTORS;

EID: 42749099704     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.031913     Document Type: Article

References (23)

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7. This causes the additional complication of normalizing probabilities, so in contrast to Refs. we will deal with particle number densities per unit area instead of probabilities (also, in this way the comparison to the simpler, special case in Ref. will be much clearer).
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18. A new analysis of more recent archaeological data [M. Gkiasta, T. Russell, S. Shennan, and J. Steele, AntiquityATQYAF0003-598X 77, 45 (2003)] yields a similar but somewhat higher value for the speed, although its error is not estimated (in contrast, the data in Ref. were used to compute both the time-versus-distance and the distance-versus-time speed errors in Ref.). We plan to analyze the new data in detail in a separate publication.
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21. Note that the value of (Formula presented) is necessary to compute the diffusion coefficient, namely, (Formula presented) for the single-delay model, as done in Refs.
22. Table 5 in Ref., p. 58 gives the age distribution of unmarried people for preindustrial agriculturalists which (neglecting death effects, which we cannot estimate, as a first approximation) allows us to determine the number of people who have left a domestic group as (Formula presented), (Formula presented), (Formula presented), and (Formula presented) (from which our values of (Formula presented) follow directly), with mean ages (Formula presented), (Formula presented), and (Formula presented). Concerning (Formula presented), in the same Ref., p. 67, it is stated that children do not become marriageable (i.e., able to disperse according to the Majangir custom) until they are (Formula presented) old. Note that these values of (Formula presented) and (Formula presented) yield a mean (Formula presented), which (adding about (Formula presented) from the parents’ migration until the child’s birth) is indeed consistent with the value of (Formula presented) for the generation time used in Ref. However, to apply the new model in the present paper, a final correction is necessary. If a son/daughter leaves their parents when he/she is, e.g., (Formula presented) old, to this we should add the time interval from the migration of his/her parents until his/her birth. Since the mean number of children per family for preindustrial agriculturalists is about 6.5 and their average birth interval is close to (Formula presented) (Ref., p. 66), we find that the mean time interval from the migration of the parents until a child's birth is of about (Formula presented). Therefore, we have used (Formula presented) to obtain our values of (Formula presented) in the main text.
23. D. W. Sellen and R. Mace, Curr. Anthropol.CUANAX0011-3204 38, 878 (1997), table 2.10.1086/204677