Douglas R. White
This presentation is the property of its rightful owner.
Sponsored Links
1 / 32

Douglas R. White Andrey Korotayev Daria Khaltourina Secular Cycles and Millennial Trends PowerPoint PPT Presentation


  • 79 Views
  • Uploaded on
  • Presentation posted in: General

Douglas R. White Andrey Korotayev Daria Khaltourina Secular Cycles and Millennial Trends Irvine, 2004. Where: N (t) - population r - rate of natural growth C - maximum carrying capacity. Nefedov’s Model of Agrarian Demographic Cycle. Q(t) = F[P(t)]A F(P) = Q/A = ksps

Download Presentation

Douglas R. White Andrey Korotayev Daria Khaltourina Secular Cycles and Millennial Trends

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Douglas R. White

Andrey Korotayev

Daria Khaltourina

Secular Cycles and Millennial Trends

Irvine, 2004


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Where:

N (t) - population

r - rate of natural growth

C - maximum carrying capacity


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Nefedov’s Model of Agrarian Demographic Cycle

Q(t) = F[P(t)]A

F(P) = Q/A = ksps

Q = kspsA.

A(P)= kP , if kP< Am

A(P)= Am , if kP > Am

AF(Y) = kY , if kY < Am - AT

AF(Y) = Am - AT , if kY > Am - AT

M = ksqAF

P0 = p0Y(t)

W=M+P0

u = (X (t) – M) /Y (t)

Half of the surplus is stored for future consumption:

pc = (u+ p0)/2 if u > p0 and (u+ p0)/2 < pm

pc = pm if (u+ p0)/2 > pm

If u<p0 , then X(t) < W.

P1 = pcY(t)

W1=M+P1

Zp = X(t) – W1

l = l0+ dl0

Q = ksps AF = ksql AF = lM

X(t+1) = lM – H + X(t) – W1


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

R. Pearl's Model

Y – population

r - the rate of natural growth in favorable conditions

C - capacity of an ecological niche or the maximal population at available food resources

by

In the model

is replaced with

where n is a parameter of compensation suggested by

J. Maynard Smith and M. Slatkin


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

If X(t)<W

X (t) - the quantity of grain after harvest (crop and stocks)

W - is the quantity of grain needed to cover minimum consumption and seed

The peasants have grain deficits.

Then the peasants lack sufficient grain in spring sowing even if they consume p0 (the minimal total consumptionper capita).

Then they sell part of their land in order to compensate for the lack of seed grain.

In some cases the landowners have a limited stock of grain and can not buy all the

land sold by the peasants.

Then the peasants reduce their fund of consumption P1 so, that

M+P1 = X(t).

M - the total grain requirements for seed

P1 - total consumption

X (t) - the quantity of grain after harvest (crop and stocks)


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

In this case

u < p0

and consumption per capita equals

p(u)=P1 / Y(t).

During the famineP1< p0 Y(t)

and

Y(t)/C = Y(t)/( P1/p0) = p0Y(t)/ P1 > 1 in (4).

Therefore population is reduced.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

If the famine threatens destruction of a significant part of the population the authorities distribute grain to the peasants, increasing consumption up to pu0 (pu0 < p0).

Na = Da/1.5

Ma = ksqAT

Pa0 = p0Ya (t)

Pa= pua Ya (t)

Xa (t+1) = (Mal – Ma – Ha)/2 + Xa (t) – Pa

Xr(t+1) = kr (lMa–Ha)/2 – Hr + Xr (t) – Pr

G = (ksql –ksq) Da – Haa )/2

Cr = Pr/p0


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Where: 0.75 – minimal cultivated area per person necessary to maintain minimal level of consumption (ha) (for the Late Han period); 1/2 – the rent is assumed to be one half of the total product; A(t) – cultivated area; AF – the area of land belonging to the farmers; Am – maximum size of area under cultivation; AT – land of the tenants; C – capacity of an ecological niche, or the maximum population at available level of agricultural technology; Cr – maximum number of craftsmen; d – random variable; Da – area of land sold by peasants = area of land passing to new tenants; G – income of landowners; H – total amount of taxes in terms of grain; Ha – total amount of taxes paid by tenants in terms of grain; Hr – total amount of taxes paid by craftsmen in terms of grain; kr – % of landowners' income spent for purchase of craft products; ks – multiple-cropping index (sown area divided by cultivated area); l – real productivity; l0 – the output of grain per sowing, harvest/seeds proportion; lM – crop of the next year; M – total grain requirements for seed; Ma – weight of seed grain of the tenants; Na – peasant population decreases; P(t) – the rural population at period t; p(u) – consumption per capita; P0 – minimum total consumption; p0 – minimum total consumption per capita; P1 – total consumption; Pa – total consumption of tenants; Pa0 – minimal total consumption of tenants; pa0 – minimal total consumption per capita of tenants; pc – consumption per capita; pm – maximum consumption; Pr – total consumption of craftsmen; ps – productivity per hectare; pua – consumption per capita of tenents; Q – crop output measured in kilograms; q – quantity of seed needed per hectare; u – the amount of grain available per capita; W – is the quantity of grain needed to cover minimum consumption and seed; W1 – total grain output is used for consumption and seed; X(t) – quantity of grain after harvest (crop + stocks); Xa(t) – Pa – stocks saved in barns of the tenants; Xa(t) – the quantity of grain after harvest (crop and stocks) that tenants have; Xr – stocks of a grain of handicraftsmen; Y(t) – the number of peasants; Ya(t) – number of tenants; Zp – available grain stock by the time of the following crop.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Economic dynamics in the period Later Han


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Population and consumption in Qing Epoch in China

–▄– – consumption (daily wages, liters of rice)

–♦– – population (millions)


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Population in Early Tang China (the number of households in millions)


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Population in Late Tang China (the number of households in millions)


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Consumption in Babylonia in the 6th – early 5th centuries BC.

The numbers indicate the amount of barley in liters that a blue worker

could buy on his daily wage.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Consumption dynamics in Northern India in the late 16th – 17th centuries.

The numbers indicate the amount of wheat in liters that a unskilled worker

could buy on his daily wage.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

dx/dt = Ax – Bxy

dy/dt = Cxy – Dy

(where x is population density ["prey"] and y is warfare frequency ["predator"])


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

  • Temporal dynamics of prey (solid curve) and predator (broken curve) predicted by the Lotka-Volterra model with parameters a = 0.02, b = 0.02, c = 0.025, and d = 0.1.

  • The scatterplot of relationship between P and N; the straight line is regression.

  • (c) The scatterplot of the relationship between the logarithmic rate of change of P (∆p, defined in the text) and N.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Population dynamics of the caterpillar (larch budmoth) and its predators (parasitic wasps).

(a) Population oscillations of the caterpillar (solid curve) and predators (broken curve).

(b) A scatter plot of the predator against the prey. The solid line is the regression. Broken lines connect consecutive data points, revealing the presence of cycles. (c) A scatter plot of the predator against prey lagged by two years.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Analysis of the Han Chinese data.

a) Population and warfare trajectories.

b) (The trajectory in the population-warfare phase space.

c) The relationship between the warfare rate of change and population density.


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Where:

N - number of inhabitants

t - time

r - population growthrate

K - the population size at which surplus equals zero or "carrying capacity"

W – internal warfare

β - per capita state expenditure rate

S - the accumulated state resources (e.g., in kg of grain)

ρ - the per capita taxation rate at low population density


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Temporal dynamics of population N (solid curve) and internal warfare I (broken curve)


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Trend to the Growth of Population (in millions) in China

200 BCE – 1850 CE

200 BCE 0 500 1000 1500 1850


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Trend to the Growth of the Largest State/Empire Territory Size

(millions of square km) in West Asian/Mesopotamia Centered System

2500 BCE – 550 BCE


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Trend to the Growth of the Largest State/Empire Territory Size (millions of square km) in West Asian/Mesopotamia Centered System

900 BCE – 850 CE


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Trend to the Growth of the Largest State/Empire Territory Size

(millions of square km) in West Asian/Mesopotamia Centered System

2500 BCE – 850 CE


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Trend to the Growth of the Largest State/Empire Territory Size (millions of square km) in East Asian/China Centered System

1900 BCE – 1865 CE

-1900 1000 0 1000 1865


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Population Growth Rate X Territorial Expansion/Aggressive External Warfare


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Relative Consumption Rate X Territorial Expansion/Aggressive External Warfare


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

1 – low in comparison with other phases of respective cycle

2 – intermediate in comparison with other phases of respective cycle

3 – high in comparison with other phases of respective cycle


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

CHINA = overall population of China (millions)

PEKING = population of Peking (tens of thousands)


Douglas r white andrey korotayev daria khaltourina secular cycles and millennial trends

Ch.Gr. = growth rate of the overall population of China

Pek.Gr. = growth rate of Peking population

(r = –.84, p = .078)


  • Login