Modeling Population Dynamics of Old-World

Agrarian Empires

Jim BennettUniversity of Washington

First Int’l Workshop on Computational History, Dublin, June 2014

Modeling Agrarian Empires

• Quest: Build composite ‘generative’ (agent-based) model(s) that account for spatio-temporal history of Old World empires from 1500BCE to 1500CE.

• This talk: Investigate historical demographic constraints on those models using actual empire location and timing.

• Empire data: Imperial data from Turchin, Currie, Turner, Gavrilets 2014. Many thanks!!

Exogenous asserting of empires removes issue of how, when and where empires arose.

Exogenous asserting of empires removes issue of how, when and where empires arose.

At the start of a quantitative and theoretical science, after having amassed and organized much ‘botany’ of examples, there are attempts to make 1st order models that capture what appear as large scale regularities, hopefully with descriptions of causal force for prediction. History has not been without attempts. Our tools now involve non-linear systems theory and its required use of computers (since our intuitions are poor, which partially explains some of the lack of success of previous efforts).

This talk investigates how well the underpinnings of cliodynamics can predict and inform our understanding of large-scale demographic issues.

At the start of a quantitative and theoretical science, after having amassed and organized much ‘botany’ of examples, there are attempts to make 1st order models that capture what appear as large scale regularities, hopefully with descriptions of causal force for prediction. History has not been without attempts. Our tools now involve non-linear systems theory and its required use of computers (since our intuitions are poor, which partially explains some of the lack of success of previous efforts).

This talk investigates how well the underpinnings of cliodynamics can predict and inform our understanding of large-scale demographic issues.

Old-World Agrarian Empires

QuickTime™ and a decompressor

are needed to see this picture.

31 centuries of data for ‘large’ empires.(actually contains nomadic empires but we ignore those for this talk)

Green are agrarian locations, expanded in 300 and 700CE per PNAS

2500 agricultural regions (out of 5800), each 1degree lat/lon square (1Mha)

Next some quick statistics about them that constrain any plausible generative model over this time.

31 centuries of data for ‘large’ empires.(actually contains nomadic empires but we ignore those for this talk)

Green are agrarian locations, expanded in 300 and 700CE per PNAS

2500 agricultural regions (out of 5800), each 1degree lat/lon square (1Mha)

Next some quick statistics about them that constrain any plausible generative model over this time.

Empire Size in TimeJust agrarian, not nomadic (whose size is large as well)Not all small polities

Note a small number of medium size empires early, then 500BCE large empires show up, the around 500CE lots of small empires (in the Roman Empire time)

Empires > 200regions: Persia, Han, RE, Yuan, Ming.

Conjecture: Empires greater than the increasing trend of small empire (from 10 rising to 75 regions) are empires made of acquired provinces with dispersed hierarchical control.

Just agrarian, not nomadic (whose size is large as well)Not all small polities

Note a small number of medium size empires early, then 500BCE large empires show up, the around 500CE lots of small empires (in the Roman Empire time)

Empires > 200regions: Persia, Han, RE, Yuan, Ming.

Conjecture: Empires greater than the increasing trend of small empire (from 10 rising to 75 regions) are empires made of acquired provinces with dispersed hierarchical control.

Empire Longevity

235 Large Agrarian Empires in 3Ky

The scalloping is an artifact of stochastic interpolation

The longest lived empires are quite small and obscure:Axum Alodia Sindh Meroe Magadah

Mean age compares well with Sirag if you take his secular cycle as an empire dynasty but mixing concepts here.

The scalloping is an artifact of stochastic interpolation

The longest lived empires are quite small and obscure:Axum Alodia Sindh Meroe Magadah

Mean age compares well with Sirag if you take his secular cycle as an empire dynasty but mixing concepts here.

Extant EmpiresQuiet for the first 1KyThen picks up 500BCELots after the fall of RM in Europe, not so much elsewhere

235 total in dataset (and missing small ones). There are bits of big ones on borders with deserts and steppes that appear small but aren’t. Happens since we we limit regions to agrarian locale ala PNAS

Nearly identical with Sirag 2012

Quiet for the first 1KyThen picks up 500BCELots after the fall of RM in Europe, not so much elsewhere

235 total in dataset (and missing small ones). There are bits of big ones on borders with deserts and steppes that appear small but aren’t. Happens since we we limit regions to agrarian locale ala PNAS

Nearly identical with Sirag 2012

(Old) World Population

Kaplan et al, Holocene 2010

From a paper estimating land use and CO2 loading throughout the holo

McEvedy&Johnson within the gray band

1500CE = 400BP1500BCE = 3400BP

From a paper estimating land use and CO2 loading throughout the holo

McEvedy&Johnson within the gray band

1500CE = 400BP1500BCE = 3400BP

Kaplan et al, Holocene 2010

Uniform Empire K Conjecture

• Each ‘hinterland’ agrarian region has a natural carrying capacity Kh.

• Conjecture: Once occupied by an empire, the carrying capacity increases to some uniform Ke

• Protection provides stability, infrastructure investment, redistribution, etc.

• Net birth rate ße also increases

• Can we estimate Kh, Ke, and ße?

• Assuming logistic growth: Ṗ = ße(1 - P/Ke)P

To a first approximation.

The interesting bit in the conjecture is that Ke is uniform across time and space.

And that the increase is *rapid* -- like immediate

To a first approximation.

The interesting bit in the conjecture is that Ke is uniform across time and space.

And that the increase is *rapid* -- like immediate

Medieval England 1150-1300

• Natural experiment: Seigniorial system on an island; no war

• Experiment ended with natural famine (1312) and plague (1348)

• Opinion varies about whether rebellion or intensification would have occurred; assume rebellion (there were grumblings).

• Population: 1M to 3M (Campbell 2000) (or 3M to 6M, Postan)

• 12Ma (4Mha) supported population spread over 16-20Mha (1Mha = 1 region)

• Wheat production at peak implies ~3M/4Mha or 750K/planted region carrying capacity (or Ke ~250K/region)

• Logistic growth implies net birth rate of ße ~1.75%

Scaling an Anachronism

• At peak: 2500 agricultural regions

• Ke ~250K => 500M max population in 1500CE

• At start: 1800 agricultural ‘hinterland’ regions

• 100M in 1500BCE => Kh ~60K

100M 1500BCE

500M 1500CE

Simulation:Initially all ag regions have Ph and Kh and beta_h.If region becomes empire, change K to Ke and beta to beta_e, else (back to hinterland) hange K to Kh and beta to beta_h. Grow (or cull) current population logistically

Simulation:Initially all ag regions have Ph and Kh and beta_h.If region becomes empire, change K to Ke and beta to beta_e, else (back to hinterland) hange K to Kh and beta to beta_h. Grow (or cull) current population logistically

Scale Medieval England to Old World:

Given ße =1.75% and (ßh = 0%) what is predicted population?

Predicted Population

McEvedy & Jones via Kremer 1993

Note that this is *maximum* since there is no death except when an empire segment falls back to hinterland.No famine, plague, war

Not dealing with nomadic empires or Americas

So uniform K is false but not too far off...Suggest if a generative model can get the spatial and temporal pace correct, population will largely follow

Note that this is *maximum* since there is no death except when an empire segment falls back to hinterland.No famine, plague, war

Not dealing with nomadic empires or Americas

So uniform K is false but not too far off...Suggest if a generative model can get the spatial and temporal pace correct, population will largely follow

Area Under EmpireShown here with a linear stochastic interpolation between centuries.

Population is largely correlated with area pacing, modulo famines and plagues

Shown here with a linear stochastic interpolation between centuries.

Population is largely correlated with area pacing, modulo famines and plagues

Regional Population Data

Krumhardt, 2010

Of course there were variations, which, in this model, implies different Ke or beta. We opt for the former and estimate different Ke:

Of course there were variations, which, in this model, implies different Ke or beta. We opt for the former and estimate different Ke:

Population with Regional Ke

Original is blue, regional is cyan based on matching M&J values.But BUG: These values are after death...BUG: Since there is no death, this is an underestimate except for Americas, etc! But everyone needs to scale K proportionally?

Decline in the last 500yr due to lower Russia Ke. Otherwise Asia largely offsets Mesopotamia.

Why do we fall short? Probably K is off (rice intensification ala Geertz?) even more especially later. Tom will be working on this...

Also, likely a higher birth rate in earlier medieval times, ironically, since we chose ME as our starting point.

Except: No death yet....

Original is blue, regional is cyan based on matching M&J values.But BUG: These values are after death...BUG: Since there is no death, this is an underestimate except for Americas, etc! But everyone needs to scale K proportionally?

Decline in the last 500yr due to lower Russia Ke. Otherwise Asia largely offsets Mesopotamia.

Why do we fall short? Probably K is off (rice intensification ala Geertz?) even more especially later. Tom will be working on this...

Also, likely a higher birth rate in earlier medieval times, ironically, since we chose ME as our starting point.

Except: No death yet....

Asia, India: 1.20Ke

Mesopotamia: 0.75Ke

Russia: 0.30Ke

Structural Demographics

Demographic pressures that stressThe established structure of social/economic sectors that cause

Immiseration then asabiya “bubbles” that(when channeled via sector “elites”) lead to“Acute” collective acts (wars, coalitions, investment, etc.).These acts and consequences are recorded in history,

often as havoc.These actions “reset” demography and sector structure.

Conjecture: Empire histories are composed of repeated “secular cycles” of:

the majorthe major

Empire experiences growth again under new ‘contract’; collapse if contract fails.

Agrarian sector structure: wealth production (farming) and protection (warrior/elites)

Go slowGoldstone ‘the major’What are basic economic sectors -- these could be extended

Asabiya and immiseration via Turchin

Go slowGoldstone ‘the major’What are basic economic sectors -- these could be extended

Asabiya and immiseration via Turchin

Modeling Secular CyclesInformed by Turchin’s HD and SC arguments. No detailed economics,

just the result.

This differs from HD, replacing fiat immediate and drastic collapse with a different collapse fiat structure of Fathers and Sons with some stochastic elements

Region miserable at 90%KEmpire miserable at 80% regions miserableStochastic rebellion (4%/y)Rebellion triggers F/S cycle3-5 alternating *generations* of war/uneasy peaceF: exponential death rate of 1%/y Sons: .2%/yReformation always follows rebellionuntil empire collapses or is annexed

This yields ~30-50% haircut for each F/S bout, which seems excessive but empirically it yields ~250yr (10g) cycles (after an initial longer startup cycle). LIkely unreported ‘collateral damage’?

Thus we tune it to previously reported (HD/SC) SC period to see impact...In this run we have the first cycle taking ~440y, the second ~250y, the third >200y (not complete).

The alternatives are a ‘saturated’ but tolerated world of no growth, having gone through their frontier and several SCs before having everything under control and prescribed. If you are insular geographically (mountains, no emigration, no internal major metaethnic differences )this could allow you to go stable but otherwise a pesky neighbor will instigate mischief. Egypt, China?

Informed by Turchin’s HD and SC arguments. No detailed economics, just the result.

This differs from HD, replacing fiat immediate and drastic collapse with a different collapse fiat structure of Fathers and Sons with some stochastic elements

Region miserable at 90%KEmpire miserable at 80% regions miserableStochastic rebellion (4%/y)Rebellion triggers F/S cycle3-5 alternating *generations* of war/uneasy peaceF: exponential death rate of 1%/y Sons: .2%/yReformation always follows rebellionuntil empire collapses or is annexed

This yields ~30-50% haircut for each F/S bout, which seems excessive but empirically it yields ~250yr (10g) cycles (after an initial longer startup cycle). LIkely unreported ‘collateral damage’?

Thus we tune it to previously reported (HD/SC) SC period to see impact...In this run we have the first cycle taking ~440y, the second ~250y, the third >200y (not complete).

The alternatives are a ‘saturated’ but tolerated world of no growth, having gone through their frontier and several SCs before having everything under control and prescribed. If you are insular geographically (mountains, no emigration, no internal major metaethnic differences )this could allow you to go stable but otherwise a pesky neighbor will instigate mischief. Egypt, China?

Old World with Secular Cycles

QuickTime™ and a decompressor

are needed to see this picture.

Movie30s 1c political boundariescyan integrative, magenta misery, red FSusing previous K/P/beta assumptions

Movie30s 1c political boundariescyan integrative, magenta misery, red FSusing previous K/P/beta assumptions

Population with Secular Cycles

Cyan: world pop with regional KeBlack: same with secular cycles

Cyan: world pop with regional KeBlack: same with secular cycles

Rebellion Starts

236 Rebellions in 3Ky

Migration as Relief Valve• Internal migration from more- to less-saturated

regions

• Move where the jobs/opportunities are:

• Frontier added (hinterland) or depleted annexed empires

• Natural inertia: Stay near extended family and familiar land

• Only a fraction move unless forced.

• Assume 10%/year

• Conjecture: Delays the onset of misery and rebellion

On average how much? 1 generation?In fact, it delays misery but doesn’t eliminate rebellions. Ceases to function as you reach saturation.

Forced migration during war is the largest ‘international’ migration/mixing event

After 1500CE much more migration from rural to urban (where the jobs and protection for more are) Required different infrastructure of course

On average how much? 1 generation?In fact, it delays misery but doesn’t eliminate rebellions. Ceases to function as you reach saturation.

Forced migration during war is the largest ‘international’ migration/mixing event

After 1500CE much more migration from rural to urban (where the jobs and protection for more are) Required different infrastructure of course

Migration Mitigates Misery

Note that all previous runs were with migration = .2/2

Reddish colors show the number of ‘miserable’ people in the world.

Blue/red - no migrationCyan/magenta - .2/2 migration

But the number of rebellions does not change BECAUSE unless something happens to drop the population further, the secular cycle logic operates on the replacement empire at its annexed population level, and so continues.

We need war or something else to drop the population on empire exchange but then we’ll still get whatever that pace is assuming it is uniformly applied!

While the number of rebellions doesn’t change, their timing does. On average, they are delayed by 50 years using migration = .2/2

As arable land is saturated, even with migration, we would expect that time to misery decreases but that trend is not clear in this simulation. Perhaps it happens post-1500CE, mitigated by migration to new world and migration to new economic sectors with increased Ke.

Note that all previous runs were with migration = .2/2

Reddish colors show the number of ‘miserable’ people in the world.

Blue/red - no migrationCyan/magenta - .2/2 migration

But the number of rebellions does not change BECAUSE unless something happens to drop the population further, the secular cycle logic operates on the replacement empire at its annexed population level, and so continues.

We need war or something else to drop the population on empire exchange but then we’ll still get whatever that pace is assuming it is uniformly applied!

While the number of rebellions doesn’t change, their timing does. On average, they are delayed by 50 years using migration = .2/2

As arable land is saturated, even with migration, we would expect that time to misery decreases but that trend is not clear in this simulation. Perhaps it happens post-1500CE, mitigated by migration to new world and migration to new economic sectors with increased Ke.

Summary

• The (quasi-)uniform empire K conjecture is surprisingly plausible

• Ke ~ 4 Kh permitting ße ~1.75%

• Regional (and temporal) Ke required for improved accuracy

• No plague, famine, inter-state war

• Generative models that match empire spatial and temporal pace should estimate gross population well.

• Secular cycles with F/S significantly reduces world population (~20% in 1500CE)

• Sirag 2012 observes shortening cycles: Due to saturation?

• Migration mitigates misery, retarding (by ~50y) but not reducing rebellions

• Investigate increased, forced migration during war

Current generative models are too aggressive in time and space leading to initial over- and later under-shoots in population (not shown)

No plague or famine (or war)

Secular cycle modeling uses too-deep haircuts. Alt: Shallower haircut but lower beta that increases during IntAlt: ‘Saturation’ where some empires control rebellions and live at saturation?Secular cycle shortening Sirag 2012 could be accounted for by ‘constant’ rather than fractional haircuts with slowing beta, so pop is not reset

Next steps: With actual data: Famine/plague/K adjustmentsAdd metaethnic data for triggers

Looking ahead, from 1500CE to 1945CE Ke increases to ~8Kh, then from 1945CE to present, it increases (oil and hence fertilizers) to ~400Ke. Also, post 1500CE, the Americas opened up with migration possibilities but they saturated in a few hundred years as well.

Model: formation and growth of empire; the front half of the problem.

Current generative models are too aggressive in time and space leading to initial over- and later under-shoots in population (not shown)

No plague or famine (or war)

Secular cycle modeling uses too-deep haircuts. Alt: Shallower haircut but lower beta that increases during IntAlt: ‘Saturation’ where some empires control rebellions and live at saturation?Secular cycle shortening Sirag 2012 could be accounted for by ‘constant’ rather than fractional haircuts with slowing beta, so pop is not reset

Next steps: With actual data: Famine/plague/K adjustmentsAdd metaethnic data for triggers

Looking ahead, from 1500CE to 1945CE Ke increases to ~8Kh, then from 1945CE to present, it increases (oil and hence fertilizers) to ~400Ke. Also, post 1500CE, the Americas opened up with migration possibilities but they saturated in a few hundred years as well.

Model: formation and growth of empire; the front half of the problem.

Comments and Questions?