Some Population Problems Involving Pleistocene Man

Birdsell, Joseph Benjamin

doi:10.1101/sqb.1957.022.01.008

Cited by 153 publications

(75 citation statements)

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“…Population number data sets in previously empty islands are available [49] and the average value implied is R 0N = 2.2 [21]. The generation time is T = 1 generation = 32 yr [50].…”

Section: Application To the Neolithic Transition In Europementioning

confidence: 99%

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

Fort

2011

Phys. Rev. E

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It is shown that Lotka-Volterra interaction terms are not appropriate to describe vertical cultural transmission. Appropriate interaction terms are derived and used to compute the effect of vertical cultural transmission on demic front propagation. They are also applied to a specific example, the Neolithic transition in Europe. In this example, it is found that the effect of vertical cultural transmission can be important (about 30%). On the other hand, simple models based on differential equations can lead to large errors (above 50%). Further physical, biophysical, and cross-disciplinary applications are outlined.

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“…Population number data sets in previously empty islands are available [49] and the average value implied is R 0N = 2.2 [21]. The generation time is T = 1 generation = 32 yr [50].…”

Section: Application To the Neolithic Transition In Europementioning

confidence: 99%

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

Fort

2011

Phys. Rev. E

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“…The only time in the past when such rates seem to have occurred is when people colonized new environments where, in terms of their culture, all important resources were essentially unlimited. It is interesting to note that if Birdsell (1957) and Martin (1973) are right about the first peopling of Australia and the New World, under these conditions nomadic huntergatherers have been as capable as sedentary people of sustaining such high growth rates. The problem today is quite different and probably unprecedented; extremely high rates of natural increase are maintained in the face of serious shortages.…”

Section: Pre-industrial Population Trends: Theory and Datamentioning

confidence: 99%

On Causes and Consequences of Ancient and Modern Population Changes¹

Cowgill

1975

American Anthropologist

248

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“…The hatched regions in these figures correspond to likely ranges of the parameters, and have been obtained as follows. Birdsell [24] was able to collect detailed evolution data of two human populations which settled in empty space. A fit of these data (either to an exponential or to logistic curve) yields a 0.032 6 0.003 yr 21 , with 80% confidence level (C.L.).…”

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confidence: 99%

Time-Delayed Theory of the Neolithic Transition in Europe

1999

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The classical wave-of-advance model of the neolithic transition (i.e., the shift from hunter-gatherer to agricultural economies) is based on Fisher's reaction-diffusion equation. Here we present an extension of Einstein's approach to Fickian diffusion, incorporating reaction terms. On this basis we show that second-order terms in the reaction-diffusion equation, which have been neglected up to now, are not in fact negligible but can lead to important corrections. The resulting time-delayed model agrees quite well with observations. [ S0031-9007(98) [11,12]. Thus HRD equations, instead of the usual PRD equations, should be regarded as the first choice from a conceptual perspective. Hyperbolic reaction-diffusion equations have been very recently applied to the spread of epidemics [13], forest fire models [14], and chemical systems [15].An interesting application of PRD equations arose after archaeological data led to the conclusion that European farming originated in the Near East, from where it spread across Europe. The rate of this spread was measured [16], and a mathematical model was proposed according to which early farming expanded in the form of a PRD wave of advance [17]. Such a model provides a consistent explanation for the origin of Indo-European languages [18], and also finds remarkable support from the observed gene frequencies [19]. However, this PRD model predicts a velocity for the spread of agriculture that is higher than that inferred from archaeological evidence, provided that one accepts those values for the parameters in the model that have been measured in independent observations [17]. Here we will analyze this problem by means of a HRD model.Let p͑x, y, t͒ stand for the population density (measured in number of families per square kilometer), where x and y are Cartesian coordinates and t is the time. We assume that a well-defined time scale t between two successive migrations exists. We begin, as usual [20], noting that, between the values of time t and t 1 t, both migrations and population growth will cause a change in the number of families in an area differential ds dx dy, i.e., ͓p͑x, y, t 1 t͒ 2 p͑x, y, t͔͒ds ͓p͑x, y, t 1 t͒ 2 p͑x, y, t͔͒ m ds 1 ͓p͑x, y, t 1 t͒ 2 p͑x, y, t͔͒ g ds ,where the subindices m and g stand for migrations and population growth, respectively. We denote the coordinate variations of a given family during t by Dx and Dy. The effect of migrations on the evolution of p͑x, y, t͒ will be derived here by means of a simple extension of Einstein's model of Fickian diffusion [21]. The migration term in Eq. (1) can be written as ͓p͑x, y, t 1 t͒ 2 p͑x, y, t͔͒ m ds ds Z 12`Z 12`p ͑x 1 Dx, y 1 Dy, t͒f͑Dx, Dy͒dDx dDy 2 dsp͑x, y, t͒ ,where f͑Dx, Dy͒ is the fraction of those families lying at time t in an area ds, centered at ͑x 1 Dx, y 1 Dy͒, such that they are at time t 1 t in an area ds, centered at ͑x, y͒. Therefore, Z 12`Z 12`f ͑Dx, Dy͒dDx dDy 1 ,

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Some Population Problems Involving Pleistocene Man

Cited by 153 publications

References 0 publications

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

On Causes and Consequences of Ancient and Modern Population Changes¹

Time-Delayed Theory of the Neolithic Transition in Europe

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Some Population Problems Involving Pleistocene Man

Cited by 153 publications

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Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

On Causes and Consequences of Ancient and Modern Population Changes1

Time-Delayed Theory of the Neolithic Transition in Europe

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On Causes and Consequences of Ancient and Modern Population Changes¹