<table><caption>**Table 2.** Sociopolitical instability in the Eastern Empire, 285–700 CE
(data from Williams and Friell 1999)</caption><thead><tr><td>Year</td><td>Event</td></tr></thead><tbody><tr><td>306–309</td><td>Galerius intervenes in Western infighting with limited success</td></tr><tr><td>311–313</td><td>Galerius dies, Maximin and Licinius compete for control of East</td></tr><tr><td>316–317</td><td>Licinius fights Constantine, peace and compromise</td></tr><tr><td>324–325</td><td>Licinius fights Constantine again, surrenders and later is killed</td></tr><tr><td>351–353</td><td>After a series of civil wars and coups in the West, Eastern emperor Constantius II goes to war and wins the entire empire</td></tr><tr><td>353</td><td>Gallus, Caesar of the East, is executed for irresponsible governance</td></tr><tr><td>364</td><td>Empire is split once again, Valens rules East</td></tr><tr><td>365–366</td><td>Revolt of Procopius</td></tr><tr><td>378</td><td>Valens killed at Adrianople</td></tr><tr><td>387–395</td><td>Theodosius I intervenes in Western infighting</td></tr><tr><td>450</td><td>Pulcheria and Marcian openly dispute succession with Chrysaphius</td></tr><tr><td>471</td><td>Zeno and the Isaurian faction displace the king-maker, Aspar</td></tr><tr><td>474</td><td>Leo II allegedly poisoned by Isaurian faction</td></tr><tr><td>475</td><td>Riots force Zeno to flee Constantinople, usurpers fight amongst themselves</td></tr><tr><td>476</td><td>Zeno besieges Constantinople</td></tr><tr><td>479</td><td>Revolt of Marcian the Younger</td></tr><tr><td>484</td><td>Revolt of the Samaritans</td></tr><tr><td>484–488</td><td>Revolt of Illus</td></tr><tr><td>492–497</td><td>The Isaurian War</td></tr><tr><td>512–515</td><td>Balkan Rebellion</td></tr><tr><td>532</td><td>Nika Riots</td></tr><tr><td>565</td><td>Clandestine succession engineered by Callinicus</td></tr><tr><td>574</td><td>Abdication of Justin II due to insanity</td></tr><tr><td>582</td><td>Alleged poisoning of Tiberius II</td></tr><tr><td>588</td><td>Mutiny on the Persian front</td></tr><tr><td>602</td><td>Mutiny on the Danube and murder of Maurice by Phocas</td></tr><tr><td>608–610</td><td>Civil war and murder of Phocas by Heraclius</td></tr><tr><td>602–628</td><td>Persian-Byzantine Wars</td></tr><tr><td>634–718</td><td>Arab Conquests</td></tr></tbody></table>

It is important to note, that for all the losses inflicted on the population by the Justinianic plague in 541 and recurrent plague outbreaks in the following decades, there was no successful and permanent coup against an emperor until the year 602. This lies in sharp contrast to the tumultuous elite dynamics found in the West in the fourth and fifth centuries.

One more measure of the Eastern Imperial cycle ought to be mentioned here. If susceptibility to foreign invasion is indeed a symptom of secular crisis and depression, it is also reflected in the history of the Eastern Empire. It is interesting to note that between the periods 296–502 and 502–628, the incidence of Persian invasions of Byzantine territory increased eightfold, despite
the fact that the former period was nearly twice as long as the latter (Fig. 3). Afterward both the Eastern Empire and Persia collapsed from exhaustion and were overwhelmed by the Arab Conquests that soon burst upon the East.

<figure><img src="image_74.png" /><figcaption>Fig. 3. Persian incursions into Byzantine territory (data from Lee 1993)</figcaption></figure>

One might ask whether the defeat in the Battle of Adrianople in 378, in which the Eastern emperor Valens was defeated and killed by the Goths, provides a counter-example. The incident is often treated as a milestone in accounts of the decline of the Roman Empire. Yet the year 378 falls within the Eastern expansion phase. A simple explanation is that secular cycles do not dictate the outcome of individual battles, which are determined by a tangled web of variables: tactics, supply, numerical strength, weather, topography, and countless others. The military defeat in 378 did not signal the secular decline of the Eastern Empire. It is testament to the high social cohesion of the region that after the Battle of Adrianople, despite the death of an emperor, Gothic forces were unable to take Constantinople, or indeed even the nearest town (Ward-Perkins 2005: 35).

In general, it appears that the Eastern Empire from 285-700 experienced a secular cycle that fits well with the basic model (except for its length – approximately 400 years). To summarise, there was expansion in the fourth century, stagflation beginning somewhere in the fifth century, a crisis after the mid-sixth century, and depression in the upheavals of the seventh.
A Possible Western Disintegrative Trend (c. 350–400 CE)

The Third Century Crisis resulted in a great deal of elite conflict and a decline of the general population. By 285 the population was low enough to begin expanding again. Historiography is coloured by debate on when this expansion came to an end. A number of historians have argued that there was very little decline around the year 400 and see a ‘cultural transition’, while still others refuse to see any decline or collapse whatsoever.<fnref n="2" /> Studies arguing for various shades of continuity and cultural transition tend to downplay signs of economic decay and the violent nature of many Germanic incursions, arguing for a ‘natural’ and ‘organic’ process. There was indeed a Western recovery after 285 continuing well into the fourth century. However, for some reason that recovery failed to match the trends seen in the Eastern Empire. Within the period 350–400 population recovery stalled. Settlement patterns suggest that the population stagnated, declined, and fell to levels that can only be described as catastrophic, particularly in Belgica and North Gaul (Fig. 4).

While the consensus among historians is that rural settlement patterns in the Eastern Empire undoubtedly indicate a form of growth, there are some reasons for caution when it comes to settlement patterns in the West. Rural sites were sometimes big, suggesting that many of them were possibly ‘commercial’ farms, rather than family farms. Thus, the decline in the number of settlements in Western Europe may only tell us about the health of one sector of the economy: the sector that was ‘tied into commercial relations’ and produced for the market. Of course, this argument ignores the fact that even if all rural sites that have been excavated over the years were larger farms, an index of economic development might at least to some extent imply trends in demography. While signs of settlement abandonment are not perfect indicators of depopulation and must be used with caution, there is not yet an alternative explanation for this trend that decisively discounts depopulation as a factor, much less proving that the population remained stable. The best arguments put forward now only indicate that settlement occupation ‘does not necessarily’ indicate a depopulation and abandonment of land (Chavarría and Lewit 2004: 31).<fnref n="3" />

<footnote n="2">² While the works are too numerous to list here, authors include: W. Goffart, R. W. Mathisen, P. Amory, D. Shanzer, G. W. Bowersock, and T. Lewit. Merovingian continuity also figures heavily in the controversial thesis of Henri Pirenne. While refreshing, stimulating, and dominating in academic settings, it has had very little impact on popular perception of the era.</footnote>

<footnote n="3">³ In general, the world does not distinguish between growth in the first half of the fourth century and signs of decline in the second half, but assign grow to the entire period (see also Chavarría 2004). The fourth century trends in Spain, however, particularly in South Spain, seem to differ greatly from those seen in Britain, Belgica, Gaul, and Italy, and the work is largely preoccupied with explaining trends of the fifth century.</footnote>
<figure><img src="image_75.png" /><figcaption>**Fig. 4.** Proportion of rural settlements that were completely depopulated (showing losses from peak levels c. 350; data from Lewit 1991)</figcaption></figure>

Another objection is that the degree of depopulation inferred from settlement patterns appears to be too high. What could cause it: a plague similar in magnitude to the Black Death, impact of Germanic invasions, or mass migration to the cities? There is no evidence for any of such explanations. Massive immigration to the cities is further implausible given that cities were falling into decline in this period. However, few historians have yet taken into account demographic-structural theory, which suggests that depopulation often does not require a gigantic catastrophe, but happens more or less gradually as part of a disintegrative phase.

The economic evidence displays the same trend as the decline of rural settlements. After a brief period of recovery in the 300s, the Western economy apparently fell to a nadir point which was lower than anything seen in the disintegrative phase of the previous century (Table 3). Iron production may have recovered c. 300–350, but it fell to an all-time low by the year 400. Thus, only one-tenth of iron sites in Britain survived (Jones and Mattingly 2002: 180–196). A study of mines in the Iberian Peninsula shows that of 173 Roman mines in Spain, fewer than 21 were operating in the late 300s, and this number shrank again to only two in the 400s (Domergue 1990: 215–224). An impressive group of iron forges in southwest Gaul, which began recovering as early as the third century, did not make it out of the fourth (Cauuet *et al.* 1993: 68–69, 123–125).
In eastern Gaul, another iron production site shows the same pattern. It was active between the first and fourth centuries, but charcoal dated by radiocarbon fails to show any operation past 400 (Mangin 1992: 222–242).

Gold mines follow a similar pattern. The coins at Tharsis in Iberia are dated no later than 350, while at Vipasca there is only evidence of dwindling occupation in the fourth century with nothing beyond. At Rio Tinto, a small settlement had coins from the reign of Honorius possibly dating as late as the 420s, but no later. In Britain gold mines were active until c. 383. In Dalmatia, mining halted during the Third Century Crisis, revived on a small scale in the fourth century, but by 400 these mining operations had ceased altogether.<fnref n="4" />

It is unlikely that these large mines were replaced by ‘small-scale’ sites producing at the same level – or anywhere near it. Atmospheric pollution from mining descended on Greenland and became packed down under layers of snow and ice, with the spring thaw dividing one year from the next, similarly to growth rings in a tree trunk.

<table><caption>**Table 3.** Last known mining and smelting activity from the West to the East</caption><thead><tr><td>Year</td><td>Location</td></tr></thead><tbody><tr><td>300s</td><td>Lusitania, North Hispania</td></tr><tr><td>300s</td><td>Forest of Dean, Britannia</td></tr><tr><td>300s</td><td>Weald, Britannia</td></tr><tr><td>Early 300s</td><td>Les Martyrs, Southwest Gaul</td></tr><tr><td>417</td><td>Bituriges, Central Gaul</td></tr><tr><td>By 400</td><td>Autun, East Gaul</td></tr><tr><td>417</td><td>Sardinia</td></tr><tr><td>417</td><td>Noricum</td></tr><tr><td>By 400</td><td>Illyricum</td></tr><tr><td>360</td><td>Dalmatia</td></tr><tr><td>By 550</td><td>Attica, Greece</td></tr><tr><td>By 550</td><td>Pangaios, Greece</td></tr><tr><td>500s</td><td>Inner Egypt</td></tr><tr><td>600s</td><td>Red Sea Coast</td></tr><tr><td>400–600</td><td>Cilicia</td></tr><tr><td>600s</td><td>Cappadocia</td></tr><tr><td>530</td><td>Armenia</td></tr></tbody></table>

*Source:* see Domergue 1990: 215–224; Cauuet *et al.* 1993: 68–69, 123–125; Mangin 1992: 222–242; Hong *et al.* 1994: 1841–1843; Edmondson 1989: 84–102.

<footnote n="4">⁴See J. C. Edmondson 1989: 84–102. While the research plainly shows the closure of most western mines by 400, the author stresses a fifth-century ‘restructuring’ to ‘small-scale’ production for ‘local economies’. It is revealing that no such ‘restructuring’ happened anywhere in the East (see *Ibid.*: 92).</footnote>
Ice cores taken from Greenland allow us to devise a timeline for hemispheric pollution from lead production. They show that lead was being produced at around 80,000 tons per year at the height of Roman power. Production peaked around the time of the Principate's expansion phase, when it attained a level not reached again until 1800. The 300–350 recovery did not reach peak Antonine levels, and after the West's collapse production shrunk from 80,000 tons to only a few thousand tons per year (Hong et al. 1994: 1841–1843). Copper mining and smelting emissions show the same trend. The Roman period marked a sharp rise in copper production to a peak of 15,000 tons per year in the first century CE and fell to 2000 tons in the fifth century before declining further (Hong et al. 1996: 246–249). The lead figures are corroborated by another unusual source, a Swiss peat bog, which also serves as an archive of atmospheric metal deposition. The surface layers are isolated from groundwater and surface water and receive inorganic solids from atmospheric deposition. As a result the peat bog is a record of changing lead and scandium levels for the entire Holocene. In conclusion, the peak of Roman mining was in the first century CE. Production remained high until it declined in the third century, with a possible recovery thereafter, but production slowly dwindled in the fourth century to an early medieval nadir (Shotyk et al. 1998: 1635–1640).

The number of shipwrecks discovered in the Western Mediterranean drops significantly for those dated in the late fourth century (Fig. 5). What is more, the number of shipwrecks found at the bottom of the sea and dated by archaeologists follows precisely the same pattern as what has been predicted for both the Principate and Dominate secular cycles. The number of shipwrecks found in the entire third century is only 49 per cent that of the second century. The period 300–350 indicates a recovery in shipping but 350–399 yields less than 13 per cent of the ships that sunk in the preceding fifty years. The entire fifth century yields only 37 per cent of the fourth century total, including the decline period (Parker 1992: 13–15). The use of shipwrecks as an indicator of total volume must be done with caution, however, but it demonstrates an interesting parallel to the prevailing trend in other areas.<fnref n="5" />

In addition to many rural sites being abandoned, many others show a decline in condition. Slap-dash architecture and make-shift alterations from

<footnote n="5">⁵ Andrew Wilson (2009: 219–229) points out that the decline may have much to do with the shift from the use of amphorae to barrels for containing wine. Wilson also treats the second century peak as a statistical anomaly and distributes them among other periods, by using a range of probability for a wreck sinking in a particular year rather than using Parker's midpoint. This shifts the peak to the first century CE. In the same book, see William Harris ('A Comment on Andrew Wilson: "Approaches to Quantifying Roman Trade"', *Ibid.*: 259–260), who points out that neither textual nor material evidence on land leads us to suspect a decline of trade after 100 CE and that the barrel hypothesis seems inadequate, since it is likely many regions of the Roman Empire were suffering deforestation at that time. Harris also points out that metal ingots in shipwrecks follow a contradictory trend from the amphorae first century peak.</footnote>
the fourth and fifth centuries are often seen in villas. Certain parts of sites were
abandoned while only sections of them remain occupied. At Horath in the
Hunsrück, for instance, the principal building was definitely abandoned with
only the annexed buildings being used. The same was the case at Famechon in
Picardy. Even more, at Emptinne-Champion in Belgium, only part of the cen-
tral building was occupied while the rest of the villa and the baths were de-
serted or even demolished (van Ossel and Ouzoulias 2000: 144–147).

<figure><img src="image_76.png" /><figcaption>Fig. 5. The number of shipwrecks in the Western Mediterranean (data from Parker 1992: 13–15)</figcaption></figure>

Cellars were reused as bakeries or filled up with debris, a kitchen was used as a boiler room, Roman living rooms were partly buried or transformed into fire-pits, an ornate gallery full of mosaics was used as a tool workshop, and a high quality building was transformed into a cowshed, and central heating was abandoned (van Ossel and Ouzoulias 2000: 147–148; Wightman 1985: 257). The utilitarian use of villas may well indicate a form of living that is closer to a subsistence level and it almost certainly indicates a drop in the number of inhabitants at the site. However, alternative explanations involving ‘cultural choice’ have been put forth, along with the argument that a wood building is not inherently better than one built of stone, which is a convenient argument since it leaves no evidence and one is free to imagine as an elaborate a building as one pleases (for instance, Etienne Louis 2004).<fnref n="6" />

<footnote n="6">⁶ The works of T. Lewit will be highlighted later on.</footnote>
Paleopathology, or the medical examination of ancient corpses, shows the deterioration of Western villas was matched by the deterioration of people's health. Exhumations from a site at Saint-Martin-de-Fontenay, modern Calvados, in west Gaul shows that in the fourth century CE the life expectancy was 31.5 years. This was paralleled by a site at Frénouville which in the fourth century had a life expectancy of 32. The results of the dig at Calvados show the period that was marked by ‘socio-economic troubles’. A low life expectancy was accompanied by poor dental conditions, indicating malnutrition. Roughly 30 per cent of the teeth of intact mandibles were either rotten or missing. With an average age of 31.5 this is considerable. There were also a number of anatomical peculiarities indicating intense muscular strain on the legs, the front of which had bones that were almost grotesquely bowed inward (Pilet et al. 1994: 80–81, 93–96, 123–125, 145). A reduced stature might be attributed to poor nutrition caused by population pressure. Population pressure mounts up in the second century as is predicted for the Principate cycle, and it is subsequently relieved during the devastation of the third. The Dominate expansion phase of the fourth century witnesses population growth again, with pressure reducing the average stature, while the depopulation of the fifth century appears to have led to record heights.

A useful survey of settlement abandonment was devised by Tamara Lewit (1991). Lewit looked at two hundred rural sites from several regions in the West and determined when they were occupied. She then gave the proportions for each half-century in the form of a percentage of the highest level of occupation. In the same fashion, Lewit also determined the percentage of the other sites which were still expanding or ‘remaining prosperous’. Lewit’s survey remains one of the best quantitative works on rural settlements, even two decades later.<fnref n="7" /> A re-examination of her numbers reveals an interesting pattern.

<footnote n="7">⁷ Nevertheless, Lewit herself is a staunch advocate of continuity. Lewit's presentation of the percentages downplays the idea of gradual but severe decline in the late fourth century, even though some of the regions seem to indicate it. She is incredulous at depopulation after 400. She advances an array of arguments to explain where all the people went and how continuity was maintained. Of course, if there was a more gradual decline from 350, it defeats necessity of such explanations. Subsequent works of Lewit follow the same theme of continuity (Lewit 2003, 2009). For a critique of this article see Bowes and Gutteridge 2005.</footnote>
<figure><img src="image_77.png" /><figcaption>**Fig. 6.** Average heights (cm) of men and women from a sample of 9477 skeletons from the first century to the nineteenth (data from Koepke and Baten 2005)</figcaption></figure>

In Lewit's presentation, the settlement abandonment percentages were taken from a peak index, whenever the peak occurred, whether it was the first century, as it was for Italy, the second century, where most regional peaks occurred, or the fourth century, where South Gaul and South Spain evidently peaked. These multiple indexes unfortunately detract from the clarity of the presentation. Accordingly I will use a second century index for all regions. The two of the seven regions that exceeded their second century levels will simply score over 100 (Table 4).

<table><caption>**Table 4.** Index of rural settlements occupied by region and by period (2nd Century Index) (data from Lewit 1991)</caption><thead><tr><th>Region</th><th>200-250</th><th>250-300</th><th>300-350</th><th>350-400</th><th>400-500</th></tr></thead><tbody><tr><td>Britain</td><td>98</td><td>94</td><td>98</td><td>79</td><td>47</td></tr><tr><td>Belgica</td><td>91</td><td>43</td><td>55</td><td>36</td><td>19</td></tr><tr><td>North Gaul</td><td>82</td><td>45</td><td>64</td><td>55</td><td>9</td></tr><tr><td>South Gaul</td><td>94</td><td>73</td><td>104</td><td>104</td><td>73</td></tr><tr><td>North Spain</td><td>96</td><td>61</td><td>93</td><td>96</td><td>54</td></tr><tr><td>South Spain</td><td>109</td><td>100</td><td>109</td><td>100.5</td><td>67</td></tr><tr><td>Italy</td><td>90</td><td>71</td><td>85</td><td>81</td><td>71</td></tr></tbody></table>
The period 200–250 CE shows a decline from the second century peak, probably due to the Antonine Plague that initiated the crisis phase of the Principate. The period 250–300 CE clearly reflects a deep decline of the worst infighting of the Third Century Crisis and secular depression phase. It is interesting to note that a region like Britain, which avoided the bulk of the fighting of this phase, only declines modestly, more like a mild recoil from the carrying capacity than a severe decline from a manmade crisis. The period 300–350 CE witnesses a universal period of growth and recovery, which heralds the beginning of the Dominate expansion phase. Then in the period 350–400 CE this growth is dramatically cut off, in contrast to what we know of settlements in the Eastern Empire. In Britain, Belgica, North Gaul, and Italy there is slight or even considerable decline well before the Germanic invasions. There are, of course, regional variations. South Gaul evidently sees no growth but only stagnation, while Spain sees stagnation or even mild growth. Lewit's figures for South Spain were inflated, based on only one study where 25 per cent of sites surveyed in the Guadalquivir valley possessed no earlier pottery. This contrasts dramatically with the drop in the fifth century. So instead an average between the two periods is taken. Also Lewit inflates the figures for Britain by 8 points after 350 because she does not accept the absence of post-350 coins as conclusive, and so counts them all as occupied. Here the original figure of 79 is up-held. Either way it demonstrates decline from the previous period *well before the Germanic invasions*.

It is important to note that the occupation index includes those settlements that declined, but were not totally abandoned after the second century. Lewit also gave figures for settlements that were expanding or were 'remaining prosperous' in each fifty year period. The remainder from these two categories shows the percentage of settlements that were neither expanding nor stagnating, that is, contracting: either showing signs of decline, partial abandonment, or destruction. The fourth century figures for Britain, Belgica, and North Gaul are worth noting (Table 5).

<table><caption>**Table 5.** Percentage of occupied but contracting rural settlements (data from Lewit 1991)</caption><thead><tr><th>Region</th><th>200-250</th><th>250-300</th><th>300-350</th><th>350-400</th><th>400-500</th></tr></thead><tbody><tr><td>Britain</td><td>8</td><td>20</td><td>16</td><td>38</td><td>N/A</td></tr><tr><td>Belgica</td><td>18</td><td>57</td><td>45</td><td>64</td><td>N/A</td></tr><tr><td>North Gaul</td><td>10</td><td>60</td><td>37</td><td>44</td><td>N/A</td></tr><tr><td>South Gaul</td><td>19</td><td>29</td><td>0</td><td>12</td><td>N/A</td></tr><tr><td>North Spain</td><td>3</td><td>40</td><td>4</td><td>11</td><td>N/A</td></tr><tr><td>South Spain</td><td>3</td><td>20</td><td>9</td><td>0</td><td>N/A</td></tr><tr><td>Italy</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td><td>N/A</td></tr></tbody></table>
Lewit states that it is startling that the 400s saw such a rapid decline because: (1) it followed a period of continued occupation, which is only partly true, (2) it contrasts sharply with archaeological signs of growth in 300–350 in the Eastern Empire, and (3) it would require a massive depopulation surpassing the devas- tation of the Black Death to ‘account for the abandonment of nearly every farm [sic] in North-West Europe within the space of about twenty years’ (Lewit 1991: 37–38). Fortunately, the theory of secular cycles answers each of these points. First, the third and fourth centuries were not periods of continued occu- pation but one of fluctuating population levels due to the rise and fall of secular cycles (Fig. 7). Second, the prosperity of the Eastern Empire does not dictate a similar pattern in the West, since it is becoming increasingly clear that the Dominate cycle evolved differently in the East. The reasons for this difference are dealt with below: a lowered carrying capacity and the East-West disparity in elite dynamics. Third, no holocaust like the Black Death would have been necessary, if the decline in the West had begun earlier than 400, as has been demonstrated with Lewit's own figures. The demographic-structural theory pre- sents an alternative, more gradual, and therefore more conceivable, explanation for depopulation.

## Why did the Western Roman Empire Fall?

The key factor in the West's decline may have been elite overproduction. The demographic structural theory states that a disproportionate amount of sur- viving elites next to a reduced common population can complicate an attempt at population recovery. The historical record shows that while the East in the fourth and fifth centuries had low inequality, low elite numbers, and mostly provincial elites, each with a modest amount of wealth, the Western Empire remained throughout the fourth century glutted with vast masses of elites and the hyper-rich. This disparity may well have played a role in the decline of the West as well as the survival of the East. At any rate, it is too glaring a differ- ence to be ignored.
<figure><img src="image_78.png" /><figcaption>**Fig. 7.** Dynamics of rural settlement occupation for each major region in Western Europe (data from Lewit 1991)</figcaption></figure>

Firstly, we do know that the early fourth century saw an impressive boom in large villa estates, which might indicate the concentration of land into the hands of the few. The standard explanation, the retreat of the aristocracy to the countryside, is unlikely. Instead this pattern could be explained by an early fourth century stagflation dynamic (Chavarría and Lewit 2004: 26–29). We also know something about the immense inequality gap between elite and commoner at this time. The Late Antique historian, Olympiodorus (c. 380 – ? CE), tells us that the richest senators of the West had yearly incomes of four thousand pounds of gold a year, while mid-level senators had around one thousand pounds a year. A commoner, by comparison, could scratch together perhaps five *solidi* in a year's toil, or less than one-fourteenth of a pound of gold.<fnref n="8" /> It is interesting to note this disparity of wealth outstrips inequality ratios for the stagflation period of the Principate and also the most extravagant periods of later French or English history. Additionally, wealthy Roman nobleman Quintus Aurelius Symmachus (c. 340–405) spent around two thousand pounds of gold at one go, on the celebration of his son's praetorship, by personally financing the games in Rome. This ritual was common among the Roman elite in Late

<footnote n="8">⁸ For senatorial incomes see Olympiodorus, in Photius, *Bibliotheca* (1920), frag. 44. For the estimate for a peasant's income see Ward, Heichelheim, and Yeo 1999: 446. This astounding inequality ratio and disparity of wealth is also dealt with in Turchin 2006: 160–161.</footnote>
Antiquity whenever a family member achieved such a distinction, and it was
a social obligation to match or even surpass the displays of splendour and con-
sumption of a rival family (Olympiodorus 1920).

St. Melania the Younger (c. 383–439) came from a foremost senatorial
family. She married her cousin, Pinian, around 399. After a miscarriage of two
children they found religion, took vows of celibacy, and gave up their worldly
possessions. Pinian is said to have held an annual income of 120,000 ‘pieces’ of
gold, on top of his wife’s income of about the same amount (Gerontius 1984: 15).
‘Pieces of gold’ has in the past been interpreted as either pounds or *solidi*. If
more realistically interpreted as *solidi*, that amounts to 1666 pounds annually,
and that roughly equates with what Olympiodorus tells us about the average
senatorial income. If multiplied by two, for it appears Melania held a comparab-
le income separate of Pinian, the total income comes to around 3332 pounds
of gold annually. This point has been debated among historians. Whether or not
Melania and Pinian held a mid-level or a combined upper level senatorial in-
come, it nevertheless appears that when they sold their lands, the sale temporar-
ily caused panic and a fiscal crisis in the property market (Wickham 2005: 29).
Apparently one of the estates sold by Melania in North Africa was larger than
the nearest town, Thagaste, birthplace of St. Augustine (Gerontius 1984: 21).
The presence of such trans-regional hyper-rich is certainly at variance with
what one would typically expect to see of elite dynamics in a supposedly inte-
grative period.

The paucity of sources from this period makes it next to be impossible to
find similar quantitative data for the late fourth century. However, various writ-
ten testimonies confirm the income figures of Olympiodorus and those for
Melania the Younger. For instance, Ammianus Marcellinus (c. 325–390),
a prominent imperial official and the principal historian of the period, came to
Rome from Antioch and was disgusted with the decadence he saw. He writes of
a certain number of idle and frivolous senators, who gorged themselves with
food at luxurious banquets. They spent large sums of money on exotic dancers
and prostitutes.

During a food shortage in Rome, all foreigners were expelled from the city,
while the senators lobbied for three thousand dancers and ladies of negotiable
virtue to remain. The Roman elite gave hugely expensive shows featuring dra-
matic actors. The elite were given to the habit of conspicuous consumption, and
clothed themselves in effete, elaborately designed silk and dyed robes. They
lined the streets with gold plated statues of themselves and their ancestors.
At the baths, they were attended by as many as fifty servants. Now, some histo-
rians have suggested that Ammianus was just ‘rephrasing late antique com-
monplaces’ but that is precisely the point. They were commonplaces for a rea-
son. Ammianus would hardly need to set up a stock figure to decry elite con-
sumption unless there was something to decry. Furthermore, it is worthwhile
to remember that where secular cycles are concerned, it is not so much the specifics of elite behaviour that are important, or the amount of elite wealth in an absolute sense, but the gap between the rich and the poor. And that gap appears to have been very large indeed.

Elites, like the extremely influential Petronius Probus, found political power absolutely vital to protect himself and his clan in their many quarrels with hostile families and rival factions. Ammianus describes Probus as a man known for his family, influence and great wealth throughout the world and his possession of multiple estates, some of which he appropriated 'unjustly'. It was obviously an atmosphere not only of decadence but of intense intraelite competition. This is confirmed by the many court intrigues, plots, and violent coups that characterise the entire era (Table 6). Furthermore, positions like the quaestorship or praetorship, once prestigious and influential offices along the *cursus honorum* had by the fourth century become largely meaningless titles, ceremonially bestowed on the sons of rich men when they came of age. The only real responsibility of the office was to throw a public celebration on its assumption. This confronts one with the notion that the senatorial class was filled with the idle rich, and only a fraction of them stood a chance of gaining any real power.<fnref n="9" /> As it happened, the richest Western families, the Anicii, the Caeonii, the Petronii, the Symmachi, and a handful of others, owned the vast bulk of estates throughout the regions of the Western Empire, and played a very dangerous game of faction, which often came at the expense of the state.

<table><caption>**Table 6.** Sociopolitical instability in the Western Roman Empire, 285–476 CE (from Wood 1994)</caption><thead><tr><th>Year</th><th>Event</th></tr><tr><th>1</th><th>2</th></tr></thead><tbody><tr><td>285</td><td>Diocletian beats Carinus in battle, wrests power from him</td></tr><tr><td>303–311</td><td>Largest and bloodiest persecutions of Christians</td></tr><tr><td>305</td><td>Diocletian retires, Maximian forced to retire</td></tr><tr><td>306</td><td>Maxentius' rebellion, Severus is betrayed by his army</td></tr><tr><td>309</td><td>Maximian fails to overthrow Maxentius and flees to Constantine's court</td></tr><tr><td>310</td><td>Maximian betrays Constantine, later kills him; riots in Rome</td></tr><tr><td>312</td><td>Constantine invades Italy</td></tr><tr><td>313</td><td>Licinius gains control of the East</td></tr><tr><td>316–317</td><td>Constantine fights Licinius, a truce is declared</td></tr><tr><td>320</td><td>Licinius persecutes Christians</td></tr><tr><td>324</td><td>Civil war, battles of Adrianople, Hellespont, Chrysopolis</td></tr><tr><td>324–325</td><td>Licinius sent to live as private citizen but soon hung</td></tr><tr><td>326</td><td>Constantine executes his son and wife</td></tr><tr><td>340</td><td>Constantine II wars with Constans for control of the West and is killed</td></tr></tbody></table>

<footnote n="9">⁹ Ammianus Marcellinus 1973: 14.6.7–19 27.11.1–3, and 28.4.8–18. For an excellent analysis of this source, see Matthews 1975: 1–20.</footnote>
<table><thead><tr><th>1</th><th>2</th></tr></thead><tbody><tr><td>350</td><td>Western ruler Constans is assassinated and usurped by Magnentius</td></tr><tr><td>351</td><td>Constantius wars with Magnentius, Battle of Mursa Major in Pannonia</td></tr><tr><td>353</td><td>Battle of Mons Seleucus in South Gaul, Magnentius kills himself</td></tr><tr><td>355</td><td>Attempted usurpation in Gaul (Claudius Silvanus)</td></tr><tr><td>360–361</td><td>Julian proclaimed ruler of the West, Constantius dies on the way to fight</td></tr><tr><td>361–363</td><td>Julian drastically reduces bureaucracy, executes many elites</td></tr><tr><td>364</td><td>Jovian dies, unclear by murder or natural causes</td></tr><tr><td>372</td><td>Valentinian I, emperor of the West, suppresses usurpation attempt</td></tr><tr><td>375</td><td>Valentinian II and Gratian have joint rule</td></tr><tr><td>383</td><td>Gratian assassinated by usurper Magnus Maximus</td></tr><tr><td>383–388</td><td>Civil war. Theodosius I emperor of the East fights Maximus and restores Valentinian II to the throne</td></tr><tr><td>392</td><td>Valentinian II is found hanged in his room, Arbogast selects Eugenius as emperor of the West</td></tr><tr><td>393–394</td><td>Theodosius I elevates his son Honorius as Western emperor instead; war</td></tr><tr><td>395–423</td><td>Honorius rules the West as a puppet of his generals, principally Stilicho till he was ousted in 408; Honorius fights several attempts at usurpation</td></tr><tr><td>405–410</td><td>Sack of Rome, loss of much of the West</td></tr><tr><td>423–425</td><td>Joannes usurps the Western throne, civil war with the infant Valentinian III</td></tr><tr><td>425–433</td><td>Valentinian is ruled by the faction of his mother, supplanted by the faction of Flavius Aetius</td></tr><tr><td>439</td><td>Loss of North Africa</td></tr><tr><td>454</td><td>Valentinian III treacherously murders Aetius</td></tr><tr><td>455</td><td>Valentinian III is murdered by Aetius' former faction, Petronius Maximus buys the loyalty of the army and becomes emperor, then is swiftly murdered, a few days later the Vandals take Rome by sea and subject it to a severe four days looting and pillage, much worse than in 410, Avitus becomes emperor, Visigoths invade Spain</td></tr><tr><td>c. 457</td><td>Avitus overthrown by a coup of his generals, Majorian becomes emperor</td></tr><tr><td>461</td><td>Majorian tries to institute reforms that threaten wealth of the nobility, he is killed and his fellow general Ricimer sizes power with senator Libius Severus as his puppet</td></tr><tr><td>465–467</td><td>Severus dies, Ricimer rules West without an emperor, then elevates Anthemius as his puppet</td></tr><tr><td>472</td><td>Anthemius, having defied Ricimer and fought a war against him, is killed, Ricimer elevates another puppet, Olybrius, both men die of apparently natural causes in 472</td></tr><tr><td>473</td><td>Gundobad, a nephew of Ricimer, elevates Glycenius, an unknown</td></tr><tr><td>474</td><td>Julius Nepos, Eastern emperor Leo I's choice, deposes Glycenius</td></tr><tr><td>475</td><td>Nepos overthrown by general Orestes, who appoints the ill-fated Romulus Augustulus</td></tr></tbody></table>
The historical record seems to imply that in the Western Empire, unlike the East, the elites never really disappeared. The elite classes undoubtedly lost some of their numbers in the wars of the Third Century Crisis, but it is questionable whether this decrease was enough to significantly reduce elite competition. Conversely, it appears that the events of the third century were enough to accomplish this in the East. A combination of the Persian invasions, civil war, the plague in the East from the 250s to 270s cited by Zosimus, the conquest of the Palmyrene Empire, the summary execution of much of its elite, and the sacking of Palmyra itself, seems to have been sufficient to quell the 'over-mighty subject' of the Eastern Empire for nearly two centuries.<fnref n="10" /> As already stated above, most elites operated on a provincial scale, large estates were rare, and the number of middle and small landholdings was high.

In the West, third century fighting seems to have been no less severe. The establishment of the Gallic Empire in 260 did not prevent elite infighting within that kingdom. Postumus ruled for eight years before he was murdered, and he was followed by five more rulers within the short space of six years. However, at the end of that period, Aurelian reconquered the entire Gallic Empire by cutting a deal with Tetricus II. In exchange for surrendering himself and his claim to the territory, Tetricus was granted a high political office in Italy. It is possible this clemency was extended to a number of other Western elites. The Gallic Empire fell in short order. The same clemency did not apply to the elites of the Palmyrene empire, which saw many of them executed, even while many of its towns were spared, and although Zenobia herself allegedly survived by blaming the war on the influence of her fellows.<fnref n="11" />

Yet it is possible that Western elite competition did not end with the accession of Diocletian. He obtained the imperial purple by overthrowing Carinus in a violent contest. There is no evidence to suggest that a decisive amount of elites perished in the Battle of the Margus (285) which decided the issue. It is true Diocletian reigned through a largely peaceful period. But on closer examination, we see that he ruled for only one year alone, and then forged the Tetrarchy. On the one hand, this may be seen as a more efficient way of administering a sprawling empire, but, on the other hand, it may be seen as a power-sharing deal among the elites. As it was, the peace brought about by the Tetrarchy did not long outlast the retirement of its founder. Furthermore, Diocletian is known for making the bureaucracy larger and taxing higher than ever before. According to the criteria, these are the traits of a stagflation phase, not the dawning of a new expansion (Turchin and Nefedov 2009: 34). If the period 285–305 was one of dubious expansion and tenuous stability in the West,

<footnote n="10">¹⁰ For the mysterious plague which is said to have struck the Romans in their campaigns against Persia in the 250s and 270s, see Zosimus 1982, vol. 1: 8–14, and 26.</footnote>

<footnote n="11">¹¹ For an excellent summary of the events of the Third Century Crisis see Loriot and Nony 1997: 9–17.</footnote>
the period 305–325 was characterised by open elite competition and a number of violent clashes. It is noteworthy that the vast majority of such fighting took place in the Western provinces, while the East remained relatively tame. In fact, as Table 6 shows, this chaotic procession of violent elite competition in the West apparently did not cease until the overthrow of Romulus Augustulus and the ‘official’ end of the Western Roman Empire in 476.

The incidence of coin hoarding has been demonstrated by Peter Turchin to coincide with periods of socio-political instability. The quantity of coin finds from four excavated sites Britain, the most thoroughly studied province, shows that hoarding peaked during the severest phase of the Third Century Crisis, c. 260–274, when the Gallic and Palmyrene empires split off from the Roman (Fig. 8). The reign of Diocletian marked a low point in coin hoarding, but there was a rise during the wars of Constantine. The wars of his heirs were a period of extremely active hoarding, surpassed only by the worst fighting of the Third Century Crisis. There was only a slight contraction in hoarding during the usurpations and executions of the 350s and 360s. Hoarding decreased slightly in the reign of Valentinian I and was restored to peaceful levels during the reign of Valentinian II and Gratian, but then rose again by the end of the civil war that followed Gratian's assassination. Hoarding stayed relatively high right through to the turn of the disastrous fifth century.

<figure><img src="image_79.png" /><figcaption>**Fig. 8.** Dynamics of British coin hoards at four sites, in percentages of the total between 96 and 402 CE (data from Duncan-Jones 2004)</figcaption></figure>
These four sites demonstrate the near parity between the mid fourth century hoarding peak and that seen in the worst phase of the Third Century Crisis. Added to these are the average dates from 151 sites in Britain for the fourth century alone and they seem to exhibit a similar pattern (Fig. 9).

Church-building in Rome yields a different but interesting pattern for elite dynamics in the West (Fig. 10). While Gaul in section two exhibited a fourth century peak in general economic growth before collapsing in the early fifth century, elite-laden Rome shows growth to a peak in church-building well into the 400s. It might be wondered why these building projects were underway long after the West had begun to collapse. This is not so confusing when seen in the context of elite dynamics. The fifth century peak is entirely due to private patronage of the wealthy Roman elite (Fig. 10). In the fourth century, wealthy individuals slowly ceased funding traditional civic architecture. Instead conspicuous consumption began in church-building, on supposed 'religious grounds' to demonstrate the extent of one's devotion. This was nascent in the fourth century, with only two of twelve churches being built by private patronage, but reached fever pitch in the fifth.

<figure><img src="image_80.png" /><figcaption>**Fig. 9.** Dynamics of British coin hoards at 151 sites, in percentages of the total between 294 and 400 CE (data from Ryan 1983)</figcaption></figure>

While Gaul collapsed into a frontier zone in the early 400s, Rome did not fall completely until 476. Most of the church-building happened in the period of elite-overproduction and infighting that did not cease until the deposition
of Romulus Augustulus in 476. There was no fifth century construction or ad-aptation definitively dated after 476, with only one possibly dated prior to 483, and then nothing again until 514–523. Then in the sixth century there was a contraction in the number of churches built, especially of those built by pri-vate patronage. This stands in stark contrast to the fifth century where roughly half of the church-building in Rome was done by private patronage. This might indicate the continued wealth stratification and conspicuous consumption of the elite right up to the total collapse of the Empire. It certainly would accord with the continuous infighting we see right up to 476.

By contrast to the West, the East had very few hyper-rich and saw a rela-
tively stable chain of succession, after it was divided between Valentinian I and
Valens in 364. When Valens was killed at Adrianople in 378 he was replaced
by Theodosius I, an immensely powerful emperor, who ruled the East for near-
ly two decades and even expanded his influence into the West.

<figure><img src="image_81.png" /><figcaption>**Fig. 10.** Numbers of churches built in Rome per century (Randsborg 1991, who uses data from Ward-Perkins 1984)</figcaption></figure>

The reign of Arcadius lasted another decade, 395–408 and the reign of Theodo-
sius II lasted an impressive forty-two years until 450. As was stated before, no
successful and permanent coup was staged against an Eastern Emperor until the
year 602. That the West should have the monopoly on super-rich elites, and that
the East should be extremely prosperous and stable throughout the fourth cen-
tury and beyond, while the West crumbled and collapsed, is hardly a coincidence.

## Conclusion

In summary, I submit that the evidence from various quarters indicates that the Eastern Empire underwent expansion and stagflation in the fourth, fifth, and early sixth centuries as part of a more typical secular cycle. That is why it survived. The Eastern Empire enjoyed an expansion phase c. 285–450, when the population and elite numbers were low. The stagflation phase spanned c. 450–541, when large estates began to appear again, when elites became more numerous and powerful, and the frequency of elite infighting and socio-political instability increased.

<figure><img src="image_82.png" /><figcaption>Fig. 11. Churches built in Rome by patronage (data from Ward-Perkins 1984)</figcaption></figure>

The Justinianic Plague struck in 541 and reduced the common population, gradually halting the expansion of the Eastern Empire, and culminating in the usurpations and civil wars of the seventh century. This was followed shortly thereafter by collapse in the Arab Conquests. By and large, the Eastern Empire enjoyed a full secular cycle c. 285–700, marked by the typical phases of expansion, stagflation, crisis, and depression predicted by the theory.

Conversely, the Western Empire enjoyed only a temporary and failed attempt at expansion and recovery in the early fourth century. Even though the
population in 285 was low enough to begin another integrative phase, and grew
admirably c. 300–350, the same force that kept the West in secular depression
in the Third Century Crisis still existed in the fourth century: elite dynamics. In
fact the inequality ratio was on an unprecedented scale in human history. West-
ern elite infighting raged continually throughout the fourth century, in stark
contrast to the relative stability of the East. A recovery in the West seems likely
after 285, but it probably did not last much after 350. What is more, elite in-
fighting appears to have carried on throughout this period of recovery. This is
significant since the most decisive variable which defines a period of secular
‘depression’ following a population crisis is the elite infighting which prevents
a full demographic recovery.

Therefore, within the confines of the theory of secular cycles, the Domi-
nate conforms to the predictions laid out for it. It exhibits a number of trends
which perhaps explain the total collapse of the West and the survival of the
East. In evaluating these trends, we explore in new ways the well-travelled evi-
dence and the age-old question: what caused the decline and fall of the Roman
Empire? Future studies along these lines may revolutionise the historiography
of Late Antiquity and irrevocably alter the discussion of questions left unan-
swered by older scholarship.

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# 6 Modeling Malthusian Dynamics in Pre-industrial Societies: Mathematical Modeling

Sergey A. Nefedov

## Abstract

The discussion about the Malthusian character of pre-industrial economies that has arisen in the recent years extensively uses simple mathematical models. This article analyzes some of these models to determine their conformity with Malthusian postulates. The author suggests two models that are more adequate for the description of Malthusian patterns.

**Keywords:** Malthusianism, economic and mathematical models, population oscillations, population growth, consumption dynamics, demographic crisis, Cliodynamics.

Until recently, most economic historians have tended toward the opinion that medieval economies in Eurasia had a Malthusian nature (Allen 2008: 951). However, following the publication of Lee and Anderson's (2002) work, many came to dispute this opinion. A discussion has arisen about how the available data confirm the Malthusian relationship between demographic dynamics and consumption (i.e., real wages). This discussion has largely involved simple mathematical models of Malthusian economics.

In 1980, Lee published the first and most popular of these models. This model describes the relationship between the real wage, $w_t$ (consumption), and labor resources, $N_t$ (population), using the following equation:

$$w_t = \exp(\mu + \rho t + \varepsilon_t) N_t^{-\eta}. \qquad (\text{Eq. 1})$$

Or, in logarithmic form:

$$\ln w_t = \mu + \rho t - \eta \ln N_t + \varepsilon_t. \qquad (\text{Eq. 2})$$

Here, $t$ is time; $\mu$, $\rho$, $\eta$ are some non-negative constants; and $\varepsilon_t$ is a variable that takes into account the climatic effect and other exogenous parameters. The factor $\rho$ describes capital increase and technological advances, thus Malthusian economics features $\rho = 0$. If we take into account that $\varepsilon_t = 0$ in the ideal case, the model can be expressed with quite a simple equation: $w_t = C N_t^{-\eta}$, where $C$ is some certain constant. The drawbacks of this equation are evident: a small population $N_t$ results in a consumption rate close to infinity, while in
a large population the consumption becomes too small to ensure subsistence. Additionally, this equation only shows the relationship between population and consumption. The model contains no feedback to demonstrate how consumption influences population growth.

Wood (1998) has suggested one feedback option. Wood derives his equation from the same Eq. 1 as Lee, but formulates it as follows:

$$w_t = \theta (S_t/N_t)^\eta. \qquad (\text{Eq. 1a})$$

Here, $\theta$ is the minimum per capita consumption rate, and $S_t$ is the maximum population that can subsist in the given territory when the consumption equals $\theta$. $S_t$ can grow through technological advances, but the Malthusian case features a constant $S_t$, $S_t = S_0$. Wood believes that the birth rate $b_t$ and death rate $d_t$ can be described with the following equations:

$$b_t = \beta_0 + \beta_1 \ln w_t + \beta_2 d_t, \qquad (\text{Eq. 3})$$

$$d_t = \delta_0 + \delta_1 \ln w_t + \delta_2 b_t, \qquad (\text{Eq. 4})$$

where $\beta_0, \beta_1, \beta_2, \delta_0, \delta_1$, and $\delta_2$ are certain constants. Thus, the equation below describes population growth:

$$dN_t/dt = (b_t - d_t)N_t, \qquad (\text{Eq. 5})$$

Deriving $b_t$ and $d_t$ from the system of Eqs 3 and 4 and inserting them into Eq. 5 yields:

$$dN_t/dt = (b_t - d_t)N_t = (c_0 + c_1 \ln w_t)N_t,$$

where $c_0$ and $c_1$ are certain constants. Substituting Eq. 1a here produces:

$$dN_t/dt = (c_2 + c_3 \ln N_t)N_t, \qquad (\text{Eq. 6})$$

where $c_2$ and $c_3$ are certain constants. The differential Eq. 6 has the time-independent solution $N_t = N_0 = \exp(-c_2/c_3)$; its chart will be a horizontal line. According to the theorem of the unique existence of the solution, no other solutions (integral curves) may cross this horizontal line. The derivative $dN_t/dt$ is positive below this line, in the area $0 < N_t < N_0$; the solutions monotonically increase and the integral curves approximate the horizontal line. The derivative $dN_t/dt$ is negative above this line; the solutions monotonically decrease and the integral curves approximate the horizontal line from above. Finally, the solutions cannot oscillate: the population cannot first feature growth and then loss due to 'Malthusian crisis'. Wood justifies this behavior of his model stating that Malthusian crises 'are not a necessary feature of Malthusian systems... This conclusion is contrary to the belief of many economic historians (e.g., Le Roy Ladurie 1974: *passim*; Postan and Hatcher 1985: 69) though not to anything that Malthus himself ever wrote' (Wood 1998: 110).

Malthus did, however, write about population loss, depopulation:

> The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work them-
selves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world (Malthus 1798: 61).

Wood's model does not, therefore, describe the population dynamics envisioned by Malthus himself. It is nonetheless used in many studies dedicated to the analysis of the Malthusian economics in traditional societies.

Sometimes an iterative version of this model is used, implying calculations on an annual basis. Eq. 1a in the version put forth by Møller and Sharp (2009) has logarithmic form:

$$ \ln w_t = c_0 - c_1 \ln N_t + \ln A. \qquad (\text{Eq. 2a}) $$

Birth and death rates are calculated from the simplified equations:

$$ b_t = a_0 + a_1 \ln w_t, \qquad (\text{Eq. 3a}) $$

$$ d_t = a_2 - a_3 \ln w_t. \qquad (\text{Eq. 4a}) $$

The population $N_t$ is related to the population $N_{t-1}$ in the previous year through the following relationship:

$$ \ln N_t = \ln N_{t-1} + b_{t-1} - d_{t-1}. \qquad (\text{Eq. 7}) $$

Here, $A$, $c_0$, $c_1$, $a_0$ ... $a_3$ are certain constants. Inserting Eqs 3a and 4a into Eq. 7 gives:

$$ \begin{aligned} \ln N_t &= \ln N_{t-1} + (a_1 + a_3) \ln W_{t-1} + a_0 - a_2 = \\ &= \ln N_{t-1} + (a_1 + a_3)(c_0 - c_1 \ln N_{t-1} + \ln A) + a_0 - a_2 = u \ln N_{t-1} + \ln v, \end{aligned} $$
where $u$ and $v$ are certain constants. The resulting equation is:

$$ N_t = v(N_{t-1})^u. \qquad (\text{Eq. 8}) $$

This equation generates a series of population values. If the population at the initial moment equals 1 million (i.e., $N_1 = 1$), then $N_2 = v$, $N_3$ equals $v$ raised to a power of $1 + u$, $N_3$ equals to $v$ raised to a power of $1 + u + u^2$, etc. If $|u| > 1$, then $N_t \to \infty$, which is impossible under the condition of limited resources in the Malthusian theory. If $0 < u < 1$, then $N_t$ monotonically tends to a finite bound. Finally, the case $-1 < u < 0$ produces a very specific series in which the population increases in even years and decreases in odd years (or vice versa). Thus, the Møller-Sharp model has the same drawback as Wood's initial model: it cannot describe long-term population oscillations.

Another iterative version of the model is that developed by Ashraf and Galor (2011). Beginning with Eq. 1a, the authors of this model take into consideration the number of adults and children, and optimize expenses. They, nevertheless, ultimately come to the same Eq. 8.

One more version of Wood's model is that of Voigtlander and Voth (2009). They use Eq. 1a, but replace Eqs 3 and 4 with Eqs 3a and 4a:

$$ b_t = b_0 (w_t / \theta)^m, \qquad (\text{Eq. 3a}) $$

$$ d_t = d_0 (w_t / \theta)^n, \qquad (\text{Eq. 4a}) $$
where $b_0$ and $d_0$ are certain constants. Inserting Eq. 1a into Eq. 5 yields:

$dN_t/dt = (b_t - d_t)N_t = (b_0(S_0/N_t)^{\eta m} - d_0(S_0/N_t)^{\eta m})N_t = q(p - N_t^{\eta(m-n)})N_t^{1-\eta m}$, (Eq. 6a)
where $p$ and $q$ are certain constants. The differential Eq. 6a has the time-independent solution $N_t = N_0 = p^{1/\eta(m-n)}$, which represents a horizontal line. As with the above model, the solution curves that are beneath this line monotonically increase, and those lying above the line monotonically decrease. Thus, this model has the same limitation as Wood's model and its other derivatives: it does not offer oscillating solutions.

Brander and Taylor (1998) have suggested another popular model. This model analyzes some abstract renewable resource consumed in the course of human activities. For example, it might be forest resources or soil yield. $S_t$ is the available amount of this resource (in year $t$), and $K$ denotes its reserve in nature. The equation for consumption of this resource is as follows:

$$dS_t/dt = rS_t(1 - S_t/K) - uS_tN_t \quad (\text{Eq. 8})$$

where $r$ and $u$ are certain constants. The first term on the right side describes the process of natural resource renewal; the second term describes resource depletion owing to economic activity. The population is given by the following equation:

$$dN_t/dt = (d + v S_t)N_t \quad (\text{Eq. 9})$$

where $d$ and $v$ are constants, and $d < 0$ in this case. This equation shows that natural population growth depends on the availability of resource $S_t$.

Brander and Taylor have shown that the system of Eqs 8 and 9 has oscillating solutions: when the resource is abundant, the population grows, when it is exhausted, the population decreases until the resource is renewed. Brander and Taylor refer to their model as ‘Malthusian-Ricardian’. Initially, the model was intended to describe the economy of Easter Island, but afterwards it got wider application as a sufficiently general model of Malthusian economics (e.g., Maxwell and Reuveny 2000; D’Alessandro 2007). It is worth noting, however, that resource $S_t$ in the Brander–Taylor model is not the harvest gathered by farmers. According to Brander and Taylor, the crop is denoted by the term $uS_tN_t$ and it is *deducted* from the resource $S_t$. According to Szulga (2012), such a model describes a society of gatherers (or hunters) rather than an agrarian society. However, Malthus mainly studied agricultural economies. Thus, the Brander–Taylor model cannot be referred to as a ‘Malthusian-Ricardian’ one.

Up to this point, I have confined my discussion to the analysis of simple Malthusian economics models that contain no more than two differential equations. Naturally, more complicated models do exist (e.g., Usher 1989; Komlos and Artzrouni 1990; Chu and Lee 1994; Galor and Weil 2000; Lee and Tuljapurkar 2008) that allow for better behavioral freedom and offer oscillating solutions, as well. Many such models have been constructed within the framework of cliodynamic studies actively carried out in Russia and the USA (e.g., Tsirel 2004; Korotaev, Malkov, and Khaltourina 2005, 2006; Korotaev, Malkov,
and Grinin 2007; Turchin 2007, 2009; Malkov 2009). However, almost all models described in the literature feature the same drawback: they contain uncertain coefficients whose values are unknown and cannot be determined in principle. The more complicated the model, the more uncertain coefficients it contains. Meanwhile, these coefficients determine the model behavior, and different coefficient values result in different population dynamics. Owing to this, an uncertainty originates: as coefficient values are unknown, it is also unknown which of the possible behavioral variants corresponds to the historical reality and which of them could not possibly have been realized.

In the remainder of this article, I would like to discuss two simple models that contain no uncertain parameters and, in my opinion, are sufficiently adequate for description of Malthusian population dynamics. In the first, $N_t$ is the population in the year $t$, as above; $K_t$ is corn stock after the harvest estimated in terms of minimum annual rations (1 ration approximately equals 240 kg of corn); and $r$ is the natality under the favorable conditions. The area under cultivation and the harvest depend on the population, and with the population growth they tend to some constant determined by the maximum area under cultivation maintained by the agricultural community. We will consider that the harvest is determined by the equation $P_t = aN_t/(N_t + d)$, where $a$ and $d$ are certain constants. To describe the population dynamics we use the standard logistic equation:

$$dN_t/dt = rN_t(1 - N_t / K_t). \qquad (\text{Eq. 10})$$

$K_t$ in this logistic equation denotes the carrying capacity (i.e., the maximum size of population that may live in this territory). In our case, this population size corresponds to the number of minimum annual rations in storage. Annually, $N_t$ rations are consumed, and the stock growth will be equal to:

$$dK_t/dt = P_t - N_t = aN_t/(N_t+d) - N_t. \qquad (\text{Eq. 11})$$

Thus, we have the simplest system of two differential Eqs 10 and 11. This system has an equilibrium state, when the population and stock remain constant, namely in the point $K_0 = N_0 = a - d$.

If $N$ in the equation for $dP/dN$ tends to 0, we will obtain the harvest $a/d$ (number of rations) gathered by one farmer in favorable conditions (when the population is small and he or she is able to cultivate the maximum area). Thus, the value $q = a/d$ shows how many households one farming family can support. The history of agricultural societies shows that $q$ usually varies within the limits $1.2 < q < 2$. We can express $a$ and $d$ in terms of $q$ and $N_0$:

$$d = N_0/(q - 1), \quad a = qN_0/(q - 1).$$

$N_0$ can be conventionally set equal to 1 and there are two constants in this model, $r$ and $q$ that have physical significance and vary within the known limits: $0.01 < r < 0.02$, $1.2 < q < 2$. The usual methods used for investigation of dynamic systems allow us to determine that system of Eqs 10 and 11 originates dying oscillations. The first oscillations can have differ-
ing periods; however, when the curve approaches the equilibrium state, the period is close to:

$$T = 2\pi / \sqrt{(r - r/q - r^2/4)}.$$

The period *T* decreases when *r* and *q* increase, and increases accordingly when these values decrease (Table 1 and Fig. 1).

<table><caption>**Table 1.** Period of oscillations with various *r* and *q* (in years)</caption><tr><td>q/r</td><td>0.01</td><td>0.02</td></tr><tr><td>1.2</td><td>154</td><td>110</td></tr><tr><td>2.0</td><td>89</td><td>63</td></tr></table>

Thus, the period of oscillations in this model is comparable to the duration of secular demographic cycles observed in the history of many states (Turchin and Nefedov 2009).

<figure><img src="image_83.png" /><figcaption>**Fig. 1.** Example of calculations using the model ($r = 0.01$; $p = 1.2$)</figcaption></figure>

The dynamics of the agricultural population according to this model have an oscillating nature. In theory these oscillations die out and the system tends to the equilibrium state, but various random impacts and influences neglected herein (e.g., catastrophic crop failure) disturb the system equilibrium, after which a new series of dying oscillations begins. The peculiar feature of the agricultural society is that its economic dynamics substantially depend on such a random value as the crop yield. The random factors that impact such systems are generally assumed to be exogenous; however, the dependence on crop yield variations is an intrinsic, endogenous feature of agricultural production. Therefore, one arrives at the conclusion that a special random value describing crop yield must be incorporated into the ideal model of the Malthusian cycle. This can be conveniently done within the iterative model where the calculations are made from year to year.
For convenience, I consider production years that start with the harvest, not a specific calendar date. The population size $N_t$ at the beginning of year $t$ is expressed in terms of the number of households or families (conventionally assuming that a household population is 5 people). In theory (i.e., when there is enough land for cultivation), a farming household cultivates a standard parcel of land (e.g., a Middle Eastern 'çiftlik') and one can measure the maximum possible area of arable land in terms of standard parcels $S$. When the number of households $N_t$ exceeds $S$, two families can live on some parcels.

Let $a_t$ represent the annual crop yield $t$, expressed in terms of minimum family corn rations that can be gathered on a standard parcel. We will express the crop yield in the form $a_t = a_0 + d_t$, where $a_0$ is the average crop yield, $d_t$ is a random value that accepts values from the segment $(-a_1, a_1)$. The value $a_1$ is less than $a_0$ and the crop yield $a_t$ varies within the interval of $a_0 - a_1$ to $a_0 + a_1$. With the units of measure that I have assumed, the harvest $Y_t$ (number of rations) can be expressed in the following simple form:

$$Y_t = a_t N_t \text{ if } N_t < S, \text{ and } Y_t = a_t S \text{ if } N_t > S.$$

If there is corn surplus in the year $t$, that is per-capita production $y_t = Y_t/N_t$ exceeds some value of 'satisfactory consumption' $p^1$ ($p^1 > 1$), then the farmers do not consume the entire corn produced, but lay up some surplus portion in store (for simplicity sake we will assume that they lay up half the surplus). However, it is worth noting that, owing to the storage conditions, the household stock $Z_t$ cannot grow to infinity and is limited by certain value $Z^0$. If there are surpluses exceeding this value, they all are consumed. If the year is lean and the production $y_t$ falls below the level $p^1$, the farmers take corn from the stock, increasing the consumption, if possible, up to the level $p^1$. If the stock is not sufficient, it is consumed in full.

The population growth rate $r_t$ is determined as the ratio of the population $N_{t+1}$ in the following year to the population $N_t$ in the previous year. The growth rate $r_t$ depends on the consumption $p_t$. When the consumption is equal to the minimum normal rate ($p_t = 1$), the population remains constant ($r_t = 1$). I designate the maximum natural growth $r^0$, and the consumption rate needed to ensure it $-p^0$. I believe that $r^0 = 1.02$, that the maximum population growth is 2% yearly. When $1 < p_t < p^0$, population growth is linearly dependent on consumption, and in the case when $p_t > p^0$, it does not increase ($r = r^0$). For $p_t < 1$, the dependence of $r_t$ on $p_t$ is taken as $r_t = p_t$ (i.e., in case of crop failure the surviving population will be equal to the number of rations and all people that do not have a sufficient annual food reserve will perish from starvation). Consequently, the population in the following year will be $N_{t+1} = r_t N_t$.

Considering the typical case from the Middle East or Russia in the sixteenth to eighteenth centuries, in which each family could obtain two minimal rations from one standard parcel, one can assume $a_0 = 2$ for the numerical experiment. The scatter of crop yield (ratio $a_1/a_0$) was large enough (e.g., it was about 60% of average crop yield in Egypt). Hence, it appears that one can as-
sume $a_1 = 1.2$. As for the random value $d_t$, it may be approximated using
squared uniform distribution: if $w$ is a value uniformly distributed over the
segment (-1.1), then this random value can be taken as $d_t = a_1 w^2$ sign ($w$) (Ne-
fedov and Turchin 2007). The maximum number of standard parcels $S$ can be
conventionally assumed to equal 1 million, and the maximum stock to equal
ten-year ones ($Z^0 = 10$). Here, I consider a case in which farmers call upon the
experience gained by preceding generations and start laying the crop up in stor-
age as soon as the per-capita production exceeds 1.05 of the minimum level
($p^1 = 1.05$). This calculation has an idealized character, allowing one to assume
$N_1 = 0.8$ as the initial population value (in year $t = 1$). As the calculation results
depend on a random value (i.e., crop yield), they will vary with each program
run. Despite this variation, one can qualitatively observe a pattern of demo-
graphic cycles that seems typical: population growth periods alternating with
demographic catastrophes. The duration of this cycle is, as in the previous
model, 80–200 years (Fig. 2).

<figure><img src="image_84.png" /><figcaption>**Fig. 2.** Example of calculation using this model for $r^0 = 1.02$, $p^0 = 2$, $a_0 = 2$, $a_1 = 1.2$, $p_1 = 1.05$</figcaption></figure>

Naturally, this model describes just the basic mechanism of the demographic
cycle omitting many details (e.g., the existence of the state and military elite,
the emergence of large landowners). Such factors are taken into account in
other models (e.g., Nefedov and Turchin 2007) and the calculations made using
these models show that the qualitative pattern of cycles changes insignificantly
compared to the suggested model. On the whole, it seems quite certain that the availability of corn stock in farms allows for long-term economic stabilization. Population growth results in stock depletion, however, and, sooner or later, major harvest failures provoke catastrophic starvations followed by events like epidemics, uprisings of starving people, and/or invasions by external enemies seeking to take advantage. As a result, the population size can decrease even by half and a new demographic cycle starts. While the model calculations suggest that this new cycle might start immediately after the catastrophe, in real life such crises as wars and uprisings have some inertia and impede economic revival. In such cases, stabilization is delayed.

Finally, it is worth noting that after the publication of Wood's model economic historians came to see Malthusian economics as a system wherein the population size cannot exceed the carrying capacity and, consequently, the 'Malthusian crisis' is not possible. For example, Read and LeBlanc (2003: 59) '... suggest that there is a standard model for the pattern of human population growth and its relationship to carrying capacity (K), namely, that most of the time human populations have low to nonexistent rates of growth... The model is often implicit and may simply assert that, until recently, population sizes have always been well below K and growth rates very low'. But Le Roy Ladurie, Postan, Hatcher and many other economic historians insist that 'Malthusian crises' were quite common phenomena in lived history, a fact acknowledged by Wood himself. The models described in this article show that the inevitability of similar crises arises from the simple laws that govern the functioning of agrarian economies.

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7

A Trap at the Escape from the Trap?
Some Demographic Structural Factors
of Political Instability in Modernizing
Social Systems*<fnref n="1" />

Andrey V. Korotayev, Sergey Yu. Malkov,
and Leonid E. Grinin

Abstract

The escape from the ‘Malthusian trap’ is shown to tend to generate in a rather systematic way quite serious political upheavals. Some demographic structural mechanisms that generate such upheavals have been analyzed, which has made it possible to develop a mathematical model of the respective processes. The forecast of political instability in Sub-Saharan African countries in 2015–2050 produced on the basis of this model is presented.

**Keywords:** modernization, instability, Malthusian trap, mathematical model-
ing, youth bulge, urbanization, Africa, demographic dynamics, demographic
transition, political dynamics, political demography.

Malthusian Trap as a Factor of Political Instability

What is that trap which we mention in the title of this article (and at whose es-
cape we claim another trap to be detected)? It is the so-called ‘Malthusian trap’.
The Malthusian trap<fnref n="2" /> is a rather typical for pre-industrial societies situation
when the growth of output (as it is accompanied by a faster demographic
growth) does not lead in the long-range perspective to the increase in per capita

<footnote>* This research has been supported by the Russian Science Foundation (Project No 14-11-00634).</footnote>

<footnote n="1">¹ This is a modified and extended version of the article originally published in *Cliodynamics* (A Trap at the Escape from the Trap? Demographic-Structural Factors of Political Instability in Modern Africa and West Asia. *Cliodynamics* 2(2) (2011): 1–28. URL: http://escholarship.org/uc/item/79t737gt).</footnote>

<footnote n="2">² Using the terminology of non-linear dynamics one can also denote it as *the low-level equilibrium attractor* (cf. Nelson 1956).</footnote>
output and the improvement of living conditions of the majority of population that remains close to the bare survival level (see, e.g., Malthus 1798, 1978 [1798]; Artzrouni and Komlos 1985; Steinmann and Komlos 1988; Komlos and Artzrouni 1990; Steinmann, Prskawetz, and Feichtinger 1998; Wood 1998; Kögel and Prskawetz 2001; Grinin, Korotayev, and Malkov 2008; Grinin and Korotayev 2009; Grinin et al. 2009; Grinin 2010).

In complex pre-industrial societies the Malthusian trap was one of the main generators of state breakdowns (see, e.g., Korotayev and Khaltourina 2006; Korotayev, Malkov, and Khaltourina 2006b; Chu and Lee 1994; Nefedov 2004; Turchin 2003, 2005a, 2005b; Turchin and Korotayev 2006; Turchin and Nefedov 2009; Usher 1989; Grinin and Korotayev 2009; Grinin, Korotayev, and Malkov 2008; Grinin et al. 2009; Grinin 2007; Korotayev 2006; Korotayev, Komorova, and Khaltourina 2007; Kulpin 1990; Malkov 2002, 2003, 2004; S. Malkov and A. Malkov 2000; S. Malkov, Kovalyov, and A. Malkov 2000; Malkov et al. 2002; Malkov, Selunskaya, and Sergeyev 2005; Malkov and Sergeyev 2002, 2004a, 2004b; Mugruzin 1986, 1994; Nefedov 1999–2010; Nefedov and Turchin 2007; Turchin 2007; van Kessel-Hagesteijn 2009).

A typical example is provided by the last (Qing) of the ‘secular’ (see Korotayev, Malkov, and Khaltourina 2006b; Turchin and Nefedov 2009) cycles of Chinese political-demographic dynamics. In 1700–1850 China managed to achieve rather impressive economic results (due to, say, introduction of some New World crops [first of all, maize and sweet potatoes], development of new varieties of previously known cultivated plants, agricultural labor intensification, land reclamation, etc. [Ho 1955; 1959: 173–174, 180, 185–189; Lee 1982; Bray 1984: 452, 601; Perkins 1969: 39–40; Dikarev 1991: 69–70; Fairbank 1992: 169; Lavely and Wong 1998: 725–726; Lee and Wang 1999: 37–40; Mote 1999: 750, 942; Nefedov 2000a: 17; Myers and Wang 2002: 599, 634–636; Rowe 2002: 479; Zelin 2002: 216–218; van Kessel-Hagesteijn 2009]). As a result of these innovations the carrying capacity of land during this cycle was raised to a radically new level, which also resulted in a rather significant growth of the Chinese GDP.

Thus, according to Maddison's (2001, 2010) estimations, between 1700 and 1850 the GDP of China grew almost threefold (see Fig. 1).
<figure><img src="image_85.png" /><figcaption>**Fig. 1.** Economic macrodynamics of China, 1700–1850 (GDP, millions of 1990 international dollars, purchasing power parities)</figcaption></figure>

*Data source:* Maddison 2001, 2010.

However, the Chinese population grew during the same period of time more than fourfold (see Fig. 2).

<figure><img src="image_86.png" /><figcaption>**Fig. 2.** Population of China, millions, 1700–1850</figcaption></figure>

*Note:* estimates of Zhao and Xie (1988: 539–540).

As a result, by 1850 we observe a rather significant decline of per capita GDP (see Fig. 3).
<figure><img src="image_87.png" /><figcaption>**Fig. 3.** Relative dynamics of GDP, population, and per capita GDP in Qing China, 1700–1850 (100 = 1700 level)</figcaption></figure>

The decline in the level of life of the majority of Chinese (mainly resultant just from the point that the Chinese population growth rates exceeded the rates of economic growth) can be traced on the basis of a significant number of independent data series. For example, Fig. 4 reflects the dynamics of average real daily wages of unskilled workers in this country. As we see, quite predictably, as a result of population growth rates being higher than GDP growth rates, the average real daily wages (that were not high at all even at the beginning of the respective period [see Korotayev and Khaltourina 2006 for comparisons]) dropped to the level of bare physiological survival by the end of the period in question.

Population growth rate being higher than the growth rate of GDP, Qing China experienced a catastrophic decline in the level of life of the majority of Chinese population, which is confirmed by the data of Chinese genealogies (*chia-p'u*) (see Fig. 5).

It worth stressing that in this case we are dealing with a really mass source (for example, Fig. 5 was compiled on the basis of several hundred thousand Chinese genealogies). It also appears necessary to take into account the point that representatives of really low class strata had rather poor chances to get into the abovementioned genealogies. Thus, the data in Fig. 5 reflects the dynamics of the level of life not of the real low class strata, but rather of the Qing ‘middle classes’, whose members were represented in these genealogies on a really mass scale.
<figure><img src="image_88.png" /><figcaption>**Fig. 4.** Population and food consumption in China in the Qing period</figcaption></figure>

*Note:* consumption (daily wages, liters of rice);
population (millions).

*Source:* Adopted from Nefedov 2003: 5. The data on daily wages are from Chao 1986: 218–219. The data on population are from Zhao and Xie 1988: 541–542.

<figure><img src="image_89.png" /><figcaption>**Fig. 5.** Regional life expectancy from 1500 to 1800</figcaption></figure>

*Note:* ‘The figures indicate the average age at death of the population already having reached the Chinese age of 15’ (Heijdra 1998: 437); hence, the present diagram does not take into account those numerous representatives of respective populations who died before reaching this age. It is perfectly clear that, if this part of the population were taken into account, the values of the average age at death would be radically lower. However, the present diagram gives important information on the relative dynamics of this very important indicator.

*Source:* Heijdra 1998: 437, fig. 9.3.
As we see, at the beginning of the Qing cycle the average age at death among the middle strata of the Chinese population was rather high – 55–60 years; however, by the end of the period in question the value of the respective indicator falls to explicitly low values (around 45 years), whereas it seems appropriate to emphasize that we are not dealing here with the lowest strata of the Chinese population. Another impressive feature is a striking synchronicity of the decline of the average age at death in various regions of China in the course of the Qing sociodemographic cycle.

The fact that the excess of demographic growth rates over GDP growth rates led in Qing China to a catastrophic decline in the level of life of the majority of population is confirmed by the data on dynamics of female infanticide (see Fig. 6).

<figure><img src="image_90.png" /><figcaption>**Fig. 6.** Crude birth rates in Daoyi, 1774–1864 (per 1,000 married women aged 15–45)</figcaption></figure>

*Source:* Lee, Campbell, and Tan 1992: 164, fig. 5.5.

Fig. 6 displays the results of processing of data taken from one of the Qing registration offices that registered births of both boys and girls. As we see, even in the beginning of the period covered by Fig. 6 the situation was far from problem-free – the office used to register just about 5 new-born girls per 10 new-born boys. However, by the late 1840s the situation became simply catastrophic – the office tended to register 1–2 new-born girls per 10 new-born boys.

It appears necessary to note that the historical economic research in this field has revealed for the Qing China the presence of rather strong and significant correlations between the levels of prices of basic food commodities and the levels of female infanticide (see, e.g., Lee, Campbell, and Tan 1992: 158–175).
This, of course, suggests that the catastrophic growth of female infanticide was connected with the catastrophic decline of the living standard of the Chinese population majority.<fnref n="3" />

The catastrophic decline of the majority's level of life in China quite naturally led to the growth of dissatisfaction with the government, which in 1850–1870 produced a series of rebellions (the Taiping Rebellion was the largest among them [see, e.g., Ilyushechkin 1967; Larin 1986; Nepomnin 2005: 395–444; Perkins 1969: 204; Kuhn 1978; Liu 1978 etc.]); this was apparently the bloodiest internal political collapse in the history of the humankind with the total number of dead being estimated as high as 118 (one hundred and eighteen!) million people (Huang 2002: 528). It worth noting that the majority of them died not as a result of direct violence, but because of diseases, famine, floods, etc. that took place in direct connection with the abovementioned events. The most destructive results were produced by the break of the dams by the Yellow River in 1853. As a result the great Chinese river changed its course (before these events it flew to the ocean south of the Shandung Peninsular, and afterwards it began to flow north of it), and a large part of densely populated Northern China was literally washed down. Numerous people died directly as a result of the flood, still more were left without sustenance, had to fled to the cities where the Qing government totally exhausted by the Taiping War had no resources to provide them with food. As a result, millions of undernourished people died of diseases and famine (see, e.g., Kuhn 1978 for more details).

It should be emphasized that even the catastrophic change of the Yellow River course had evident Malthusian causes. The point is that in the preceding period the growing relative overpopulation of the Yellow River valley led to the increasing cultivation of the marginal lands upstream. This resulted in the acceleration of soil erosion and, consequently, the increasing silting of the Yellow River bottom; the bottom was rising more and more that increasingly raised the threat of floods. A whole system of counter-flood dams was built in order to counteract this threat – naturally, their height grew with the rise of the Yellow River bottom. As a result, by the beginning of the Taiping Rebellion the great Chinese river flew in its lower course well above the level of the North Chinese Plain, and in order to prevent its breaking the dams enormous (and constantly growing) resources were needed. After the Taiping rebels<fnref n="4" /> captured the Chinese ‘breadbasket’ in the Lower Yangtze region, the revenues of the Qing budget shrank in the most catastrophic way; this was accompanied by an impetuous increase in military expenses that were necessary to counteract the deadly Taiping onslaught. As a result, the Qing government failed to secure the neces-

<footnote n="3">³ This was already noticed, for example, by Mann: ‘The ... decline in population growth during the nineteenth century owed much to a rise in female infanticide, itself a direct response to declining economic opportunity’ (Mann 2002: 451).</footnote>

<footnote n="4">⁴ Note that the colossal sweep of their rebellion was determined up to a very significant degree just by Malthusian factors.</footnote>
sary (and very costly) support of the extremely complex counter-flood system, and the catastrophic break of the dams by the Yellow River became inevitable (see Korotayev, Malkov, and Khaltourina 2006b: ch. 2 for more details).

Note that Malthus himself considered warfare (including, naturally, internal warfare) as one of the most important results of overpopulation (in addition to epidemics and famines). What is more, he regarded wars, epidemics, and famines (and all of these were observed in China in 1850–1870) as so-called ‘positive checks’ that checked overpopulation in pre-industrial systems (Malthus 1978 [1798]). Thus, in pre-industrial societies bloody political upheavals frequently turned out to be a result of the respective social systems being caught in the Malthusian trap.

By now the students of social systems entrapped in the Malthusian trap have a rather significant number of mathematical models of political-demographic dynamics of such social systems describing the development of bloody political upheavals at the phase of socio-demographic collapse of pre-industrial political-demographic cycles (see, e.g., Korotayev and Khaltourina 2006; Korotayev, Malkov, and Khaltourina 2006b; Usher 1989; Chu and Lee 1994; Malkov 2009; Komlos and Nefedov 2002; Turchin 2003, 2005a, 2005b; Nefedov 2004; Turchin and Nefedov 2009; Turchin and Korotayev 2006 *etc*).

Demographic transition and the increase in agricultural productivity due to major technological advances in the recent centuries (see, e.g., Grinin 2006) allowed most states to escape the Malthusian trap. The first phase of the demographic transition is characterized by a decline in mortality due to improved nutrition, sanitation, advancement and spread of modern medical technologies, *etc*. This leads to the acceleration of population growth. In the second phase of demographic transition, the development of medicine in combination with other processes (especially with mass education among women) leads to a wide-spread use of family planning technologies and, as a result, to a decrease of population growth rates (see, e.g., Chesnais 1992; Korotayev, Malkov, and Khaltourina 2006a).

However, these modernization processes started later in Sub-Saharan Africa than in the rest of the world; and even in the recent decades the Malthusian trap tended to produce state breakdowns in this region.

For example, in the period preceding the fall of Mengistu Haile Mariam's regime, from 1981 to 1991, Ethiopia's GDP grew by 12.5 %, but during the same period the population grew by 40 %. As a result, GDP per capita fell from very low $608 to catastrophic $500. Another dramatic fall occurred in per capita calorie intake: 1831 kcal/day in 1981 was already very low, 1657 in 1991 was below physiological minimum (see Table 1).
<table><caption>**Table 1.** Ethiopian economic-demographic dynamics, 1981–1991</caption><thead><tr><th rowspan="2">Year</th><th colspan="2">Economic growth 1: total GDP production</th><th colspan="2">Demographic growth: population</th><th colspan="2">Economic growth 2: per capita GDP</th><th rowspan="2">Per capita calorie intake</th></tr><tr><th>international dollars 2005, PPP, blns</th><th>% of 1981 level</th><th>mlns</th><th>% of 1981 level</th><th>international dollars 2005</th><th>% of 1981 level</th></tr></thead><tbody><tr><td>1981</td><td>21.76</td><td>100</td><td>35.8</td><td>100</td><td>607.85</td><td>100</td><td>1831</td></tr><tr><td>1986</td><td>22.50</td><td>103.4</td><td>42.1</td><td>117.6</td><td>534.24</td><td>87.9</td><td>1711</td></tr><tr><td>1991</td><td>24.47</td><td>112.5</td><td>49.7</td><td>138.7</td><td>492.85</td><td>81.1</td><td>1657</td></tr></tbody></table>

Sources: World Bank 2014; FAO 2014.

<figure><img src="image_91.png" /><figcaption>**Fig. 7.** Ethiopian economic-demographic dynamics, 1981–1991</figcaption></figure>
<figure><img src="image_92.png" /><figcaption>**Fig. 8.** Per capita food consumption, Ethiopia, 1981–1991, kcal/day</figcaption></figure>

Such a low level of per capita food consumption means that a large part of a country's population is on the edge of serious starvation. In this situation, many inhabitants of this country might choose joining rebels (or bandits; in fact, as it is well known that rebels could be quite easily transformed into bandits, and *vice versa*). It can be quite a rational choice when continuation of usual ways of obtaining subsistence means an almost unavoidable hungry death, whereas joining rebels/bandits gives at least some realistic survival chances (see Korotayev and Khaltourina 2006 for more details). We do not say that this was the only cause of the fall of Mengistu Haile Mariam's regime, but we believe that this factor definitely contributed to this fall.

**Some Features of Political-Demographic Dynamics of Modernizing Systems**

Against this background it appears interesting to consider a few cases of major political upheavals in recent decades.

**Albania – Sociopolitical Collapse of 1997**

*In 1997 Albania was swept by a wave of violent riots caused by the collapse of financial pyramids, as a result of which hundreds thousand Albanians lost all their savings. As is well known, many postsocialist European countries confronted this sort of problem (like the famous collapse of the MMM pyramid in Russia), but nowhere did this lead to a sociopolitical collapse comparable with the Albanian one:*

By early March 1997, Albania was in chaos... The army and police had mostly deserted. Armories had been looted..., evacuation of foreign nationals and mass emigration of Albanians to Italy began. The govern-
ment's authority... had evaporated. When Tirana fell into civil disorder
in late March, the government resigned... Some 2,000 people were
killed... Almost one million weapons were looted... Large parts of the
country were... outside of the government's control (Jarvis 1999: 18).

The order in the country was only restored after the deployment of foreign (first of all, Italian) troops (Ibid.: 17). With a view to what we have already considered in the previous section, it appears rather seductive to suppose a certain 'Malthusian' component in the above-described events. Indeed, in the 1960s – 1990s Albania was the poorest European country with anomalously high (by European standards) birth and fertility rates (see, e.g., Korotayev et al. 2010). Within such a context there seem to be all the possible grounds to expect the development of a classical Malthusian scenario: population growing faster than output – decline of per capita food consumption to the level of bare survival (or even below) – social explosion.

Against this background it appears interesting to consider the actual dy-
namics of per capita food consumption in Albania in the three decades preced-
ing the sociopolitical collapse of 1997 (see Fig. 9).

<figure><img src="image_93.png" /><figcaption>Fig. 9. Per capita food consumption in Albania, 1961–1996, kcal/day</figcaption></figure>

Data source: FAO 2014.

As we see, for the period in question the dynamics of this indicator in Albania
turned out to be almost contrary to the ones predicted by the Malthusian scenario.
Still in the early 1960s in Albania the problem of malnutrition was very serious and the average per capita food consumption was below the norm of 2300–2400 kcal/day recommended by the WHO (see, e.g., Naiken 2002).

However, in the 1960s and 1970s Albania managed to achieve evident successes in the solution of the food problem; in the late 1960s – early 1970s in this country the per capita food consumption exceeded the norm recommended by the WHO – and afterwards it has never dropped below it. In the late 1970s and early 1980s the growth rate of this indicator slowed down, and in 1983–1991 a certain trend towards its decline was observed, which, of course, reflects very serious economic difficulties that were experienced by Albania in the last years of the ‘communist’ period of its history (see, e.g., Sandstrom and Sjöberg 1991). However, even in 1991 (the hardest year in Albania) per capita food consumption did not drop below the norm recommended by the WHO. On the other hand, after 1991 Albania managed to achieve new successes in solving the food problem, and in 1993–1996 per capita food consumption in Albania reached record values for the whole Albanian history; by 1997 it was closer to what would be more appropriately called ‘overeating’ rather than ‘undernourishment’ level.

In any case, we may maintain with a high degree of confidence that with respect to Albania in 1961–1997 it appear impossible to speak about anything like a drop of per capita food consumption to the level of bare survival as a result of the population growing faster than output. It appears much more appropriate to say that these were precisely those years when Albania managed to escape quite successfully from the Malthusian trap.<fnref n="5" />

## South Korea – The 1980 Kwangju Uprising

After the end of the Korean War the largest popular uprising in South Korea took place in 1980 in the city of Kwangju (with 300 thousand participants, about 2000 dead, 5 divisions of regular army taking part in the suppression of the rebellion, etc.). This uprising was accompanied by a series of popular riots in neighboring cities (Lewis 2002).

Against this background, the dynamics of per capita food consumption in South Korea in the two decades preceding the abovementioned popular rebellion looks rather noteworthy (see Fig. 10).

<footnote n="5">⁵ Naturally, the 1997 sociopolitical collapse led to a certain decline in the average per capita food consumption (below 2700 kcal per day), which was still above the level recommended by the WHO; whereas later the growth of this indicator resumed (FAO 2014).</footnote>
<figure><img src="image_94.png" /><figcaption>**Fig. 10.** Per capita food consumption in South Korea, 1961–1980, kcal/day</figcaption></figure>

As we see, South Korea was another country that in the early 1960s encountered the undernourishment problem, the average per capita food consumption being below the norm recommended by the WHO. On the other hand, this was another country that in the 1960s and the early 1970s managed to achieve very noticeable achievements in solving the food problem; note that these achievements were even more considerable than in Albania, it was already in the mid-1960s that the average per capita food consumption in this country exceeded the norm recommended by the WHO (and it has never gone below that level afterwards). After 1973 the growth rate of this indicator in South Korea decreased, and in the late 1970s its certain (though quite insignificant) decline was observed. It does not seem to be a coincidence that this occurred simultaneously with the start of the period of an especially rapid growth of the South Korean economy (the so-called ‘Korean economic miracle’) when an unusually high proportion of the South Korean GDP was used for the gross capital formation purposes (see, e.g., Akaev 2010); hence, an unusually low GDP share was left for the consumption purposes. In the meantime, it appears necessary to stress that, notwithstanding some (incidentally, very small) decline of the per capita food consumption in the late 1970s, the value of this indicator remained at a very high (about 3000 kcal per day) level by the start of the abovementioned popular rebellion.
In any case, with respect to South Korea in 1961–1980 we again get across
the case when it is impossible to note any fall of per capita food consumption to
the level of bare survival as a result of the population growth rates exceeding
the output growth rates. We rather get across one more case when a social sys-
tem escaped rather successfully from the Malthusian trap just in the decades
preceding a social explosion.

Egypt – 1977 ‘Bread Riots’

The largest political unrest in Egypt after 1952 took place in 1977 (the so-called
‘Bread Riots’). The participants were chanting

يَا بَاطِلَ الْعَبْدِورِ
قَبِيدِنَّ الْفَطْسِورِ؟

Yā batl al-‘ubūr! Fēn al-futūr?’ ‘Hero of the Crossing, where is our breakfast?’
(addressing President Sadat).

The riots took place in all the large Egyptian cities, several hundred thousand people participated in them, not less than 800 fell victim (see, e.g., Hirst 1977). Seemingly, we should deal here with nothing else than Malthusian scenario, as the protesters clearly complained about food insufficiency, while in the 1960s – 1970s the Egyptian population was growing exceedingly fast (see Fig. 11).

<figure><img src="image_95.png" /><figcaption>**Fig. 11.** Egyptian population dynamics, thousands of people, 1836–1989</figcaption></figure>

*Data sources: for 1950–2005:* Maddison 2001, 2010; U.S. Bureau of the Census 2010; *World Bank 2014; for 1897–1950:* Craig 1917; Cleveland 1936: 7; *Nāmiq 1952; McCarthy 1976:* 31–3; Vasilyev 1990: 205; *for 1800–1897:* Panzac’s (1987) estimates.

In this regard it seems reasonable to view the actual dynamics of per capita
food consumption in Egypt in the 1960s and 1970s (see Fig. 12).
<figure><img src="image_96.png" /><figcaption>**Fig. 12.** Per capita food consumption in Egypt, 1961–1982, kcal/day
*Source:* FAO 2014.</figcaption></figure>

Evidently, Malthusian scenario does not work here. Indeed, in the early 1960s the problem of undernourishment was still quite acute for Egypt, and per capita consumption was lower than the WHO recommended norm of 2300–2400 kcal/person/day (Naiken 2002). In the mid-1960s Egypt reached this level, but could not exceed it before 1974. After 1973 per capita food consumption increased rapidly, getting over 3000 kcal/day in 1982 (next year after Sadat's death) and never after decreasing beyond this level. Thus, the problem of over-eating became more relevant for Egypt than the one of undernourishment. This success should be attributed to the *Infitah* economic reforms launched by Sadat administration in 1974 (see, e.g., Weinbaum 1985: 215–216). Indeed, though population grew by 36.1 % from 1970 to 1982, Egyptian GDP grew by 141.1 % during the same period, the major part of this growth taking place during *Infitah*. As a result, GDP per capita grew almost twofold, which correlated with the similarly rapid growth in per capita consumption (see Table 2 and Fig. 13).
<table><caption>**Table 2.** Egyptian economic-demographic dynamics in the 'Sadat epoch' (1970–1982)</caption><thead><tr><th rowspan="2">Year</th><th colspan="2">Economic growth 1: GDP production</th><th colspan="2">Demographic growth: population</th><th colspan="2">Economic growth 2: GDP per capita production</th><th rowspan="2">Per capita food consumption</th></tr><tr><th>Bln international dollars 1990, PPP</th><th>% from 1970 level</th><th>Millions of people</th><th>% from 1970 level</th><th>International dollars 1990</th><th>% from 1970 level</th></tr></thead><tbody><tr><td>1970</td><td>42.1</td><td>100.0</td><td>33.6</td><td>100.0</td><td>1 254</td><td>100.0</td><td>2355</td></tr><tr><td>1971</td><td>43.9</td><td>104.2</td><td>34.2</td><td>101.8</td><td>1 283</td><td>102.3</td><td>2341</td></tr><tr><td>1972</td><td>44.7</td><td>106.1</td><td>34.8</td><td>103.7</td><td>1 284</td><td>102.4</td><td>2361</td></tr><tr><td>1973</td><td>45.9</td><td>109.1</td><td>35.5</td><td>105.7</td><td>1 294</td><td>103.2</td><td>2376</td></tr><tr><td>1974</td><td>47.7</td><td>113.2</td><td>36.2</td><td>107.9</td><td>1 317</td><td>105.0</td><td>2443</td></tr><tr><td>1975</td><td>52.5</td><td>124.7</td><td>37.0</td><td>110.1</td><td>1 421</td><td>113.3</td><td>2481</td></tr><tr><td>1976</td><td>60.6</td><td>144.0</td><td>37.7</td><td>112.4</td><td>1 606</td><td>128.1</td><td>2555</td></tr><tr><td>1977</td><td>68.5</td><td>162.8</td><td>38.8</td><td>115.5</td><td>1 767</td><td>140.9</td><td>2600</td></tr><tr><td>1978</td><td>73.8</td><td>175.3</td><td>40.0</td><td>119.2</td><td>1 844</td><td>147.0</td><td>2702</td></tr><tr><td>1979</td><td>79.6</td><td>189.1</td><td>41.3</td><td>122.9</td><td>1 930</td><td>153.9</td><td>2811</td></tr><tr><td>1980</td><td>88.2</td><td>209.5</td><td>42.6</td><td>127.0</td><td>2 069</td><td>165.0</td><td>2887</td></tr><tr><td>1981</td><td>91.7</td><td>217.9</td><td>44.2</td><td>131.6</td><td>2 076</td><td>165.5</td><td>2992</td></tr><tr><td>1982</td><td>101.5</td><td>241.1</td><td>45.7</td><td>136.1</td><td>2 223</td><td>177.2</td><td>3067</td></tr></tbody></table>

Data source: Maddison 2001, 2010; FAO 2014.

<figure><img src="image_97.png" /><figcaption>**Fig. 13.** Egyptian economic-demographic dynamics in the 'Sadat epoch' (1970–1982)</figcaption></figure>
Thus, ‘bread riots’ occurred in Egypt at that very time when the country was successfully escaping from the Malthusian trap.

**Syria – The 1982 Hama Rebellion**

In Syria after the end of the Second World War the largest popular rebellion took place in 1982 in Hama. The rebellion was suppressed with regular army units, aviation, artillery, and tanks. According to some estimates, the number of dead reached 40 thousand, including 1000 soldiers of regular army (see, e.g., Fisk 1990; Friedman 1998; Wiedl 2006).

After the cases considered above the picture of dynamics of per capita food consumption in Syria in the two decades preceding the Hama rebellion should not look surprising. Yet, with respect to this country the ‘counter-Malthusian’ dynamics looks especially impressive – indeed, in the nine years preceding the rebellion the per capita food consumption in Syria was growing continuously and very rapidly (see Fig. 14).

<figure><img src="image_98.png" /><figcaption>**Fig. 14.** Per capita food consumption in Syria, 1961–1982, kcal/day</figcaption></figure>

Source: FAO 2014.

In general, as we see, in the two decades preceding the largest popular rebellion in its post-war history Syria had escaped the Malthusian trap in a rather successful way, having moved within a historically very short period quite far from the level of explicit undernourishment of the early 1960s and reaching by 1982 a level that could be more accurately characterized as overeating.
## Civil War in El Salvador

In 1980 a civil war began in El Salvador; it continued till 1992 and led to the death of 75 thousand inhabitants of this country – a colossal number for a country with total population of about 4.5 mln people at the moment of the civil war start (see, e.g., Montgomery 1995).

In the meantime, the per capita food consumption dynamics in El Salvador looked as follows (see Fig. 15):

<figure><img src="image_99.png" /><figcaption>**Fig. 15.** Per capita food consumption in El Salvador, 1961–1992, kcal/day</figcaption></figure>

*Source:* FAO 2014.

We obviously see here a picture that is generally similar to the cases observed above; however, it has some noticeable nuances. As we see, still in the early 1960s the majority of the Salvadorian population confronted the most serious (in comparison with all the other cases considered above) undernourishment problems. The situation with food consumption somehow improved in this country in the 1960s. However, it improved in the most significant way just in the decade that preceded directly the outbreak of the Salvadorian civil war. It was just the year of the civil war start when per capita food consumption in this country reached the level recommended by the World Health Organization.
Civil War in Liberia

In 1989 a civil war started in Liberia which continued up to 2003. About 200,000 – 300,000 Liberians were killed (of the total population slightly more than 2 mln at the war start) (Frenkel 1999; Huband 1998; Williams 2006). General dynamics of per capita food consumption in Liberia during 3 decades preceding the civil war looked as follows (see Fig. 16):

<figure><img src="image_100.png" /><figcaption>**Fig. 16.** Per capita food consumption, Liberia, 1961–1989, kcal/day</figcaption></figure>

Source: FAO 2014.

Thus, in the 1960s – 1980s (before civil war) per capita food consumption tended to grow in Liberia. While in the early 1960s there was some undernourishment, in the 1980s per capita consumption was thoroughly higher than the recommended norm of 2300–2400 kcal/day. Besides, in the year of civil war start *Liberia occupied the FIRST place in Tropical Africa according to the level of per capita food consumption* (see Fig. 17).
<figure><img src="image_101.png" /><figcaption>**Fig. 17.** Average per capita food consumption (kcal/day) in various countries of Tropical Africa in 1989 (i.e., in the year of the Liberian civil war start)</figcaption></figure>

Source: FAO 2014.

Liberian case is among the most tragic ones, as not only did the country ‘stumble’ at the escape from the Malthusian trap, but also fell back into the trap again (see Fig. 18).
<figure><img src="image_102.png" /><figcaption>**Fig. 18.** Per capita food consumption in Liberia, 1984–2005, kcal/day
*Source:* FAO 2014.</figcaption></figure>

Thus, in 2005 per capita food consumption had not yet approached the pre-war level and was significantly lower than even the early 1960s level. After civil war started, an unfavorable mechanism of positive feedback formed in Liberia, as civil war destroyed economy, which reduced the per capita consumption, which increased the unrest and worsened the civil war. During the short breaks the renewed (even before economy restoration) rapid demographic growth did not allow for any remarkable improvement in living standards (nor in per capita consumption) or even led to its worsening, which resulted in new unrests and new stages of civil war. Currently Liberia is again trying to escape from the Malthusian trap, but there is no warranty against its getting into ‘a trap at the escape from the Malthusian trap’ once more.

**Civil War in Côte d'Ivoire**

One of the most recent civil wars in Africa occurred in Côte d'Ivoire in 2002 (Akokpari 2007). Per capita food consumption dynamics thereby looked as follows (see Fig. 19):
<figure><img src="image_103.png" /><figcaption>**Fig. 19.** Per capita food consumption, Côte d'Ivoire, 1961-2003, kcal/day</figcaption></figure>

Source: FAO 2014.

Thus, undernourishment problem was solved in the 1960s, and at the civil war start per capita food consumption was stably higher than the WHO recommended norm. Besides, in the civil war start year Côte d'Ivoire rated among the top Tropical African countries according to per capita food consumption indicator (see Fig. 20).
<figure><img src="image_104.png" /><figcaption>**Fig. 20.** Average per capita food consumption (kcal/day) in various countries of Tropical Africa in 2002 (i.e., in the year of the civil war start in Côte d'Ivoire)</figcaption></figure>

Source: FAO 2014.

**Islamic Revolution in Iran**

Against the background of the material considered above the dynamics of per capita food consumption in Iran in the years preceding the successful Islamic Revolution of 1979 in Iran should not look really surprising (see Fig. 21).
<figure><img src="image_105.png" /><figcaption>**Fig. 21.** Per capita food consumption in Iran, 1961–1979, kcal/day</figcaption></figure>

Source: FAO 2014.

This diagram suggests that the system of socioeconomic reforms (the so-called ‘White Revolution’ [see, e.g., Abrahamian 2008: 123–154]) started by the last Iranian Shah Mohammad Reza Pahlavi in 1963 brought conspicuous positive results. Indeed, the Iranian population grew very rapidly in the years preceding the Iranian Revolution. For example, between 1965 and 1979 it grew from 25 to almost 38 million (see, e.g., Maddison 2001, 2010), that is by about 50 %. However, in the same period of time the agricultural output in Iran grew by more than 100 % (see Fig. 22).
<figure><img src="image_106.png" /><figcaption>**Fig. 22.** Dynamics of agricultural output in Iran, 1965–1979 (in millions of constant 2000 dollars)</figcaption></figure>

Source: World Bank 2014.

In the meantime Iranian GDP in this period grew by more than 150 %, as a result of which per capita GDP increased by 75 % (Maddison 2001; 2010). Hence, the salient positive trend of per capita food consumption dynamics in Iran reflects up to a rather high degree the real economic successes that were achieved by this country as Mohammad Reza Pahlavi's administration was implementing the system of socioeconomic reforms known as the ‘White Revolution’.

**Civil War in Algeria**

Let us consider in some greater detail the structural-demographic dynamics of Algeria 1962–1991, that is in the period after independence and before the start of the civil war (1992–2002) which can be characterized as a failed Islamic revolution (Kepel 2004: 164–180, 247–266). Per capita consumption dynamics in Algeria during the two decades preceding the civil war looked as follows (see Fig. 23):
<figure><img src="image_107.png" /><figcaption>**Fig. 23.** Per capita food consumption, Algeria, 1962–1991, kcal/day</figcaption></figure>

Sources: FAO 2014; Zinkina 2010: 260.

Obviously, the dynamics observed is just contrary to the one that could be ex-
pected on the basis of the Malthusian trap assumption. Indeed, in the first years
after independence the Algerian population was far below the WHO norm and
greatly undernourished. Only in 1973 did it manage to go over the critical level of
1850 kcal/day. However, there was no unrest in this period. By the late 1970s
Algeria exceeded the WHO 2300–2400 kcal/day recommended level and did not
fall below this level any more. By the late 1980s it was more than 2800 kcal/day.
This dynamics correlates very well with the rapid growth of agricultural labor
productivity proving the significant success achieved by Algeria in the moderniza-
tion of agriculture (see Fig. 24).
<figure><img src="image_108.png" /><figcaption>**Fig. 24.** Labor productivity in Algerian agriculture, 1962–1991 (constant 2000 dollars per agricultural worker)</figcaption></figure>

Source: World Bank 2014.

**A Trap at the Escape from the Malthusian Trap: Empirical Data**

During the three decades preceding the start of the civil war Algeria successfully came out of the Malthusian trap; in fact, as we shall see below, this very escape to a large extent generated the forces that played a crucial role in the genesis of the Algerian civil war.

By definition, the escape from the Malthusian trap implies the solution of the famine problem, which in its turn implies a significant decrease in the death rates. Indeed, for countries with per capita consumption up to 2900 kcal/day there is a strong negative correlation observed between this indicator and the crude death rate (see Fig. 25 and Table 3).
<figure><img src="image_109.png" /><figcaption>**Fig. 25.** Correlation between per capita food consumption and crude death rate (according to 1995 data for countries with consumption up to 2900 kcal/day)</figcaption></figure>

Note: *r* = -0.64, *R*² = 0.41, *p* << 0.0001. Source: SPSS 2010.

<table><caption>**Table 3.** Regression analysis</caption><thead><tr><th rowspan="2">Model</th><th colspan="2">Non-standardized<br>coefficient</th><th>Standardized<br>coefficient</th><th rowspan="2">t</th><th rowspan="2">Statistical significance<br>(p)</th></tr><tr><th>B</th><th>Stat. error</th><th>β</th></tr></thead><tbody><tr><td>(Constant)</td><td>38</td><td>5.1</td><td></td><td>7.45</td><td>&lt;&lt; 0.0001</td></tr><tr><td>Per capita food<br>consumption,<br>kcal/day</td><td>-0.012</td><td>0.002</td><td>-0.639</td><td>-5.45</td><td>&lt;&lt; 0.0001</td></tr></tbody></table>

*Dependent variable:* Crude death rate (per 1000)

As escape from the Malthusian trap usually occurs at the first stage of demographic transition, the results of regression analysis imply that this escape (usually accompanied by more than 1000 kcal/day growth in per capita consumption) must be accompanied by population growth rates increase by not less than one per cent, which implies a very significant acceleration. This can be seen in Algeria. The escape from the Malthusian trap was accompanied by a dramatic fall in death rate (see Fig. 26).
<figure><img src="image_110.png" /><figcaption>**Fig. 26.** Crude death rate (per 1000) dynamics in Algeria, 1960–1992</figcaption></figure>

Source: World Bank 2014.

Thus, in three decades preceding the start of the civil war the Algerian death rates declined threefold! During the most of this period birth rate was stably high, so population growth rates were increasing and started to decline only in the mid-1980s, but in 1991 (civil war start) they were still very high (2.4 % or 600,000 a year) (see Figs 27 and 28).

<figure><img src="image_111.png" /><figcaption>**Fig. 27.** Relative population growth rates, Algeria, 1970–1983, % a year</figcaption></figure>

Source: Maddison 2001, 2010.
<figure><img src="image_112.png" /><figcaption>**Fig. 28.** Absolute population growth rates, Algeria, 1970–1985, thousands per year</figcaption></figure>

Source: Maddison 2001, 2010.

Naturally, such an impetuous population growth would almost inevitably create serious structural strains in any social system. However, within the Algerian social system this was not the only generator of structural strains.

Within socioeconomic systems escaping from the Malthusian trap per capita consumption growth correlates in an especially strong way with the decrease of infant and child mortality (see Figs 29 and 30):

<figure><img src="image_113.png" /><figcaption>**Fig. 29.** Correlation between per capita food consumption and infant mortality rate (per 1000 live births) according to 1995 data, for countries with less than 2900 kcal/day</figcaption></figure>

Note: r = -0.69, R² = 0.475, p << 0.0001 (for interval < 2700 kcal the value of r achieves -0.74).

Source: SPSS 2010.
<figure><img src="image_114.png" /><figcaption>**Fig. 30.** Correlation between per capita food consumption and (under-five) child mortality rate (per 1000) according to 1995, data for countries with less than 2900 kcal/day</figcaption></figure>

Note: $r = -0.68$, $R^2 = 0.46$, $p < 0.0001$ (for interval < 3000 kcal value of r achieves -0.7).

Source: SPSS 2010.

Predictably, Algerian escape from the Malthusian trap was also accompanied by a precipitous fall of infant and child mortality rates (Figs 31 and 32):

<figure><img src="image_115.png" /><figcaption>**Fig. 31.** Infant mortality, Algeria, 1960–1995, per 1000 live births</figcaption></figure>

Source: World Bank 2014.
<figure><img src="image_116.png" /><figcaption>**Fig. 32.** Under-five mortality, Algeria, 1960–1995, per 1000</figcaption></figure>

Source: World Bank 2014.

Thus, while crude death rate in Algeria in 1960–1995 decreased threefold, infant mortality declined almost fourfold during the same period, while child (under-five) mortality fell almost fivefold!

Thus, at the first phase of demographic transition (that tends to coincide with the escape from the Malthusian trap) death rate declines dramatically (Vishnevski 1976, 2005; Chesnais 1992; Korotayev, Malkov, and Khaltourina 2006a), the greatest decline occurring in infant and under-five mortality, while birth rates still remain high. Thus, out of six-seven children born by a woman, five-six children survive up to reproductive age, not two or three as earlier. This leads not only to the demographic explosion, but also to the formation of the ‘youth bulge’, as the generation of children turns out to be much larger in number than their parents’ generation. Thus, in Algeria the share of youth cohort in the total population greatly increased at the escape from the Malthusian trap (see Fig. 33).

<figure><img src="image_117.png" /><figcaption>**Fig. 33.** Youth cohort (aged 15–24) in the population of Algeria, 1970–2005, with a forecast up to 2015, %</figcaption></figure>

Source: UN Population Division 2010.
A number of researchers, first of all Goldstone (1991, 2002), regard the rapid growth of the youth share in population as a major factor of political instability.

For example, Goldstone maintains that ‘the rapid growth of youth can un-
dermine existing political coalitions, creating instability. Large youth cohorts are
often drawn to new ideas and heterodox religions, challenging older forms of
authority. In addition, because most young people have fewer responsibilities
for families and careers, they are relatively easily mobilized for social or politi-
cal conflicts. Youth have played a prominent role in political violence through-
out recorded history, and the existence of a ‘youth bulge’ (an unusually high
proportion of youths aged 15–24 years relative to the total adult population) has
historically been associated with times of political crisis. Most major revolu-
tions ... [including] most twentieth-century revolutions in developing coun-
tries – have occurred where exceptionally large youth bulges were present’
(Goldstone 2002: 10–11; see also Goldstone 1991; Moller 1968; Mesquida and
Weiner 1999; Heinsohn 2003; Fuller 2004).

Let us consider the ‘youth bulge’ factor in Algeria in more detail. This will
allow specifying some other channels of this factor's impact upon the political
instability genesis. First of all consider the dynamics of absolute number of
young Algerians (see Fig. 34).

<figure><img src="image_118.png" /><figcaption>**Fig. 34.** Dynamics of young (aged 15–24) Algerian population, thousands, 1970–1995</figcaption></figure>

Source: UN Population Division 2010.

Thus, number of Algerian youths was growing explosively at the eve of the civil
war, more than doubling within 20 years (1970–1990). In 1980–1995 it grew by
65 %. Accordingly, in order to prevent catastrophic unemployment, new
workplaces had to be created at a proportionate rate, which is difficult even for
a fast-growing economy. If an economy is not growing as fast, unemployment
rockets up (in Algeria it reached 40 % in the late 1980s: Haldane 1989; Zinkina 2010: 261), especially among the youth (i.e., among that very age cohort which is most inclined to aggression). Against such a background it usually becomes more and more difficult to prevent major political upheavals.

There is one more force generated by modernization in general (and the escape from the Malthusian trap, in particular) that can contribute to the genesis of political instability, namely urbanization (see, e.g., Grinin and Korotayev 2009; Grinin 2010). Indeed, the start of escape from the Malthusian trap leads to a stable decline in death rates, stipulating the first phase of demographic transition. The escape itself is achieved through agricultural labor productivity growth (as was mentioned above, in Algeria it grew fivefold during the two decades preceding the civil war).

In general, the escape from the Malthusian trap stimulates urban population growth in several ways. Death rate decline in conjunction with still high birth rates leads to a rapid increase of population growth rates, so excessive rural population appears. This population is pressed out of the rural areas, as labor productivity grows, and less workforce is required for agricultural work. This population may well be supplied with food resources as per capita food production and consumption increases at the escape from the Malthusian trap, so such escape strongly supports the rapid intensification of urbanization processes, allowing for the urbanization levels which could not be achieved in agrarian societies.

Let us consider this with respect to the Algerian case (see Fig. 35).

<figure><img src="image_119.png" /><figcaption>**Fig. 35.** Dynamics of urban population percentage in Algerian, 1970–1990</figcaption></figure>

Source: UN Population Division 2010.
Thus, less than one-third of Algerians resided in cities at the eve of independ-
ence. At the eve of the civil war the urban population constituted more than
a half of the whole population. This increase took place against the background
of a very fast demographic growth. Thus, urban population was growing par-
ticularly fast in absolute numbers (see Fig. 36).

<figure><img src="image_120.png" /><figcaption>**Fig. 36.** Total urban population of Algeria, 1970–1990, thousands</figcaption></figure>

Source: UN Population Division 2010.

Thus, during 30 years preceding the civil war start in Algeria the urban popula-
tion grew fourfold, which evidently could serve as a major destabilizing factor.

The escape from the Malthusian trap engenders a rapid growth of urban population due to both natural increase and rural-urban migrations. This causes social tensions, as jobs and accommodation need to be supplied for the fast-growing mass of people. Besides, rural migrants usually have no skills appropriate for urban settings and can only find unqualified and low-paid jobs, which causes growing discontent among them.

The situation is exacerbated by the fact that most of the rural-urban mi-
grants are usually young. The ‘youth bulge’ and intensive urbanization factors
act together, making the number of young urban population rocket up.<fnref n="6" /> For
example, during 30 years of independence in Algeria its young population grew
almost threefold, while its urban population increased fourfold, so the number
of the urban youth increased by an order of magnitude (which was just a logical
consequence of the country’s escape from the Malthusian trap). Thus, not only
did the most radically inclined part of population rocket up in numbers, but it
also got concentrated in cities (that, we should not forget, are centers of politi-
cal system), which is a serious danger for political stability, especially if eco-
nomic decline occurs.

<footnote n="6">⁶ Note that, as these are young males (rather than females) that tend to migrate from the rural to urban areas, we have an especially explosive growth of young male urban population, which has a particularly destabilizing effect.</footnote>
It appears quite useful to consider the action of the above-described factors at the ‘grassroots’ level. For this we find it appropriate to reproduce Kepel's description of the events in Algeria that preceded the October riots of 1988, which served as an omen of the forthcoming civil war:

> ...A population explosion had thrust the children of the *fellahs* (farmers) into the cities and their outskirts, where conditions were precarious... In 1989, 40 percent of Algeria's population of 24 million were under 15 years of age; the urban population was in excess of 50 percent of the total population... The official unemployment rate was 18.1 percent of the working population, though in reality joblessness was much higher: in 1995 it rose – again officially – to 28 percent. The young urban poor of Algeria were mocked as hittistes – from the Arab word *hit*, ‘wall’. This jibe derived from the image of jobless young men with nothing to do all day but lean against a wall. The joke was that, in a socialist country where in theory everyone was supposed to have a job, the profession of a hittiste consisted in propping up walls that would otherwise collapse. The hittistes were assumed to be passive – unlike the Iranian ones, who were glorified by religious movements and hailed as the messengers of history and the Revelation.

At the time of the October 1988 riots, oil and gas represented 95 percent of the nation's exports and supplied more than 60 percent of the government's yearly budget... The Algerian state was a kind of popular democracy cum oil. The state used its oil revenues to buy social pacification... This balance of power, maintained by subsidies, socialism, repression, and official ideology, was ultimately dependent on the fragile economic equilibrium created by the high price of oil. In 1986, when oil prices collapsed, half of Algeria's budget was wiped out and the whole structure fell down in ruins. Worse, the population explosion had created a demand for... urban infrastructure, housing, and employment that continued to increase... The construction industry in particular had failed spectacularly to keep pace with the housing demand; the result was the kind of slums and overcrowded urban conditions that invariably lead to social eruption.

It was in this deteriorating climate, punctuated by continual strikes, that riots broke out on October 4, 1988. Mobs of impoverished Algerian youths attacked such symbols of the state as buses, road signs, and Air Algeria agencies, along with any automobile that looked expensive... These days... marked the emergence of the young urban poor as a force to be reckoned with. The once ridiculed hittistes had shown that they could seize and hold power in the streets, shaking to its foundations a regime that had excluded them and whose legitimacy they scorned (Kepel 2006: 159–161).

## A Trap at the Escape from the Malthusian Trap: Logical and Mathematical Models

Thus, the emergence of major sociopolitical upheavals at the escape from the Malthusian trap is not an abnormal, but a regular phenomenon. So, a special
explanation is rather needed for exceptions, when social systems managed to
avoid such shocks.

Why should such upheavals be treated as a regular phenomenon? The an-
swer may be summarized as follows:

1) Start of the escape from the Malthusian trap tends to bring about a precipitous death rate decline and, consequently, an explosive acceleration of the population growth rates (which in itself can lead to a certain increase in socio-political tensions).

2) The start of the escape is accompanied by especially strong decreases in infant and under-five mortality, which raises the proportion of the youth in the overall population (and especially in the adult population) – the so-called ‘youth bulge’.

3) This increases sharply the proportion of the part of population most inclined to radicalism.

4) The impetuous growth of the young population requires the creation of enormous numbers of new jobs, which is a serious economic problem, while the youth unemployment growth can have a particularly strong destabilizing effect, creating an ‘army’ of potential participants for various political upheavals, including civil wars, revolutions, and state breakdowns.

5) Escape from the Malthusian trap stimulates a vigorous growth of the ur-
ban population. Besides, excessive population is pressed out from the country-
side by the growth of agricultural labor productivity. Massive rural-urban mi-
gration almost inevitably creates a significant number of those dissatisfied with
their current position, as initially the rural-urban migrants mostly can only get
unskilled low-paid jobs and low-quality accommodation.

6) Escape from the Malthusian trap is achieved through the development of new economic sectors and decline of the old ones. Such structural changes can- not proceed painlessly, as old qualification of workers loses its value and, not having necessary new skills, these workers are obliged to take up low-qualified jobs, which makes them socially discontent.

7) The young people make up the majority of rural-urban migrants, so the ‘youth bulge’ and intensive urbanization factors act together, producing a particularly strong destabilizing effect. Not only does the most radically inclined part of population rocket up in numbers, but it also gets concentrated in major cities / political centers.

8) This can result in serious political destabilization even against the back-
ground of a rather stable economic growth (see Fig. 37). The probability of
political destabilization naturally increases dramatically if an economic crisis
occurs, or if the government loses its legitimacy due to any other causes (such
as military defeats), though the recent ‘Arab Spring’ events have demonstrated
once again in a rather salient way that even this is not really necessary (see,
e.g., Korotayev and Zinkina 2011).
As regards mathematical models describing the formation of the ‘youth bulge’ (that, in combination with some other factors, can lead to major sociopolitical upheavals even against the background of an apparently rather successful escape from the Malthusian trap), they are rather well-developed and are widely used in demographic research.

We can regard a model by Ototsky (2008) as an example. It uses component method (or cohort analysis) to describe mathematically the dynamics of society age structure. The method of components implies dividing the whole population into groups of people of one age, so-called ‘year cohorts’, which are divided into male and female ones for correct estimation of the population reproductive potential. For each cohort their own birth, death, and migration rates are determined. Birth year of people subsumed under the cohort is regarded as a serial number of this cohort. Number of males (or females) in a cohort is expressed in the following way:

$$Nm_t^i = Nm_{t-1}^i - kUm_{t-i} \cdot Nm_{t-1}^i + M_{t-i} \cdot kMmw, t > i, \quad (\text{Eq. 1})$$

where $Nm_t^i$ is a number of males in cohort $i$; $kUm_t$ – age-specific death rate; $M_t$ – age-specific net immigration; $kMmw_t$ – share of males in net immigration; $i$ – cohort serial number (corresponds to the year of people in the cohort); $t$ – year of calculation; $t-i$ – age of people in cohort $i$.

Number of newborn boys (and girls) is calculated with the following equation:

$$Nm_t^i = kRmw \cdot \sum_{j=0}^{60} kR_j \cdot Nw_{t-j} + M_0 \cdot kMmw, \quad t=i, \quad (\text{Eq. 2})$$

where $Nm_t^i$ is a number of newborn boys; $Nw_t$ – number of women in age cohorts; $kR_t^*$ – age-specific birth rates according to cohorts of mothers; $i$ – cohort number (accords to birth year of people in the cohort), for newborns $i = t$; $kRmw_t$ – share of boys in the newborn.

Number of the newborn in an age group is calculated in the following way:

$$R^* = kR^* \sum_{k=l_i}^{n_i} Nw_k, \quad (\text{Eq. 3})$$

where $R^*$ is number of the newborn in mothers' age group; $kR^*$ – age-specific birth rate of mothers' cohort; $Nwk$ – number of women of age $k$; $i$ – age group index (the maximum age in the group); $l_i$ – the minimum age in age group $i$; $n_i$ – the maximum age in age group $i$.
<figure><img src="image_121.png" /><figcaption>**Fig. 37.** 'A trap at the escape from the Malthusian trap'. A cognitive model</figcaption></figure>
General number of the newborn by mother cohorts is calculated with the following equation:

$$R_i = \sum_{g=0}^{i} R^*_{g}. \qquad (\text{Eq. 4})$$

Distribution of age-specific death rates among yearly age cohorts of males and females is calculated through the interpolation of the integral of the number of dead according to age groups:

$$Um^*_{i} = kUm^*_{i} \cdot \sum_{k=1}^{n_i} Nm_k, \qquad (\text{Eq. 5})$$

where Um* is number of men who died within the age group; i – age group index (the maximum age in group); kUm* – age-specific male death rate by age group; Nmk – number of males of age k; lᵢ – the minimum age in an age group; nᵢ – the maximum age in age group.

Integral of dead males by age cohorts:

$$Um_i = \sum_{g=0}^{i} Um^*_{g}. \qquad (\text{Eq. 6})$$

The same way is used to calculate the number of dead females in age group (Uw*ᵢ) and integral number of dead females by cohorts (Uwᵢ).

Age-specific of male and female death rates by age cohorts are calculated as follows:

$$kUm_i = \frac{Um_i}{Nm_i}, \quad kUw_i = \frac{Uw_i}{Nw_i}. \qquad (\text{Eq. 7})$$

Detailed statistical data are needed for making calculations with the model (1)–(7). If detailed data lack or approximate estimations suffice, the analytical McKendrick – von Foerster model can be used (McKendrick 1926; von Foerster 1959). According to it, equations for defining the number of people of age τ at a moment of time t are written in the following form:

$$\frac{\partial u(\tau, t)}{\partial t} + \frac{\partial u(\tau, t)}{\partial \tau} = -d(\tau, t)u(\tau, t), \qquad (\text{Eq. 8}) \\ u(0, t) = 0, \quad \int_{0}^{\infty} u(\tau, t)b(\tau, t)d\tau, \quad u(\tau, 0) = g(\tau),$$

where u(τ,t) is the number of people of age τ at a moment of time t; b(τ,t) is the intensity of childbearing among females of age τ at a moment of time t; d(τ,t) is the age-specific death rate for people of age τ at moment of time t; g(τ) is the age structure of society at the starting moment of time (for simplicity it is implied that the difference between numbers of males and females is negligibly small, and the number of born boys is equal to that of girls, the death rate d(τ,t) is the same for males and females).
Model (8) is capable of describing the emergence of ‘youth bulge’ in a soci-
ety escaping from the Malthusian trap.

Assume that up to some moment of time $t_0$ the society was demographically stable (its age structure did not change, see Fig. 38), while fertility rate was high (7 children per woman) and infant mortality was high, too.

<figure><img src="image_122.png" /><figcaption>**Fig. 38.** Initial age structure of the society (simulation)</figcaption></figure>

If at moment $t_0$ infant mortality starts declining and decreases fivefold in 30 years, then according to Eq. 8 society age structure will substantially change with the unchanged structure of birth rate (see Fig. 39, lines correspond to successive change of the society demographic structure during 55 years from the $t_0$ moment).
<figure><img src="image_123.png" /><figcaption>**Fig. 39.** Change of the age structure with the decrease of infant mortality (simulation)</figcaption></figure>

Obviously, infant mortality decline leads to an increase in proportion of the youth within total population. Thereby a ‘youth bulge’ emerges (see Fig. 40 reflecting the change of percentage of population aged 15–24 in the overall population starting from $t_0 + 20$ years).

<figure><img src="image_124.png" /><figcaption>**Fig. 40.** Change of the youth (population aged 15–24) proportion in the total population with infant mortality decline (simulation)</figcaption></figure>
Obviously, despite their simulation character the results of calculations corre-
late with the empirical data rather well (see Fig. 33 above).

The excessive young population not required in the rural areas moves to cit-
ies searching for better life, which affects the development of socioeconomic
and political processes in the society. The result of these processes depends on
particular conditions. In any case, it is a critical period in the life of any society
escaping from the Malthusian trap.

Figs 41 and 42 represent the results of calculations on urban population
growth and urban population percentage increase with an assumption that the
increasing demographic pressure in rural areas presses the excessive population
(and especially the young population) to move to the urban areas with probabil-
ity about 0.5 (calculations are presented for the same conditions as in Figs 38-
40 starting from t₀ + 20 years).

<figure><img src="image_125.png" /><figcaption>**Fig. 41.** Urban population growth under the impact of migration inflow from rural areas (simulation)</figcaption></figure>
<figure><img src="image_126.png" /><figcaption>**Fig. 42.** Increase in proportion of urban population under the impact of intensifying rural-urban migration (simulation)</figcaption></figure>

Naturally, mass rural-urban migration is possible only in conditions of general economic growth when some ‘surplus’ product appears which allows to feed the growing urban population. In order to account for this condition we can use the general dynamic urbanization equation developed in our earlier works (see, e.g., Korotayev 2006):

$$ \frac{du}{dt} = aSu (u_{\lim} - u), \qquad (\text{Eq. 8}) $$

where $u$ is the proportion of urban population (‘urbanization index’); $S$ is per capita ‘surplus’; $a$ is a constant; $u_{\lim}$ is the maximum possible urban population proportion (which can be estimated as lying between 0.8–0.9 and in this context may be viewed as the ‘saturation level’; in calculations presented below this value was taken as 0.9).

The sense of this equation is as follows: urbanization being low, the probability of a rural resident migrating to town is the higher, the greater urban population proportion. Indeed, the higher this proportion, the greater the probability of having some relative or acquaintance in town, who will be able to supply the rural migrant with the necessary information and initial support (an ordinary peasant will hardly decide to move ‘into nowhere’). However, urban population growth rates slow down when approaching the saturation level.

Besides, both in our equation and in real life urbanization rates depend also on the level of economic development, which in our equation is calculated through the per capita surplus. Indeed, if rural areas do not produce surplus, urbanization becomes impossible, while in order for it to start (and accelerate) significant economic growth is required. It also requires the labor productivity
growth, for example, in agriculture, which would allow feeding the urban population, on the one hand, and creating a surplus of workforce in agriculture encouraging the rural residents to move to cities, on the other.

Uniting Eqs 1 and 8 into a system we obtain a mathematical description of the young urban population dynamics.

## Correlation between Young Urban Population Growth Rates and Intensity of Internal Violent Conflicts: A Cross-National Test

Our cross-national test indicates that violent internal conflicts should be expected in cases when the young urban population grows by more than 30 % during 5 years; if this indicator exceeds 45 % it turns out very difficult for corresponding countries to avoid such upheavals (see Table 4 and Figs 43–45):

<table><caption>**Table 4.** Correlation between the maximum growth rates of young urban population (% per five-year periods) and internal violent conflicts' intensity, 1960–2005</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Internal violent conflict intensity</th></tr><tr><th>1 (low, &lt; 500 violent deaths)</th><th>2 (medium and high, 500–100 000)</th><th>3 (very high &gt; 100 000)</th></tr></thead><tbody><tr><td rowspan="8">The maximum (for 1960–2005) young urban population growth rates, % per five-year period</td><td>0 (Very low, &lt; 15 %)</td><td>8<br><b>88.9 %</b></td><td>1<br><b>11.1 %</b></td><td>0</td></tr><tr><td>1 (Low, 15–20 %)</td><td>3<br><b>60.0 %</b></td><td>2<br><b>40.0 %</b></td><td>0</td></tr><tr><td>2 (Medium, 20–30 %)</td><td>14<br><b>53.8 %</b></td><td>12<br><b>46.2 %</b></td><td>0</td></tr><tr><td>3 (High, 30–45 %)</td><td>14<br><b>26.4 %</b></td><td>26<br><b>49.1 %</b></td><td>13<br><b>24.5 %</b></td></tr><tr><td>4 (Very high, &gt; 45 %)</td><td>0</td><td>18<br><b>52.9 %</b></td><td>17<br><b>47.1 %</b></td></tr></tbody></table>

Note: $p = 0.59$ ($p \ll 0.0001$); $\gamma = 0.74$ ($p \ll 0.0001$). Values of the young urban population growth rates have been calculated on the basis of the UN database (UN Population Division 2010). Data there are provided for data points separated by five-year periods; so, this stipulated our choice of five-year periods. For sources on internal conflict intensity see notes to Table 5. Only countries with not less than one million population in 1960 are accounted for in this Table, in Table 5, and in Figs 43–45.
<figure><img src="image_127.png" /><figcaption>**Fig. 43.** Percentage of countries with low (< 500 violent deaths) intensity of internal violent conflicts (for 1960–2005 period) in respective groups</figcaption></figure>

<figure><img src="image_128.png" /><figcaption>**Fig. 44.** Percentage of countries with very high (> 100,000 violent deaths) intensity of internal violent conflicts (for 1960–2005) in respective groups</figcaption></figure>
<table><thead><tr><th></th><th>0</th><th>0</th><th>0</th><th>13</th><th>16</th></tr></thead><tbody><tr><td></td><td>Very low, &lt; 15 %</td><td>Low, 15-20 %</td><td>Medium, 20-30 %</td><td>High, 30-45 %</td><td>Very high, &gt; 45 %</td></tr></tbody></table>

The maximum (for 1960-2005) young urban population growth rate (% increase per five-year period)

<caption>**Fig. 45.** Distribution of countries with an especially high (> 100,000 violent deaths) intensity of violent internal conflicts (for 1960-2005 period) among respective groups</caption>

<table><caption>**Table 5.** Internal political conflicts of 1960-2005 that resulted in especially numerous (> 100,000) violent deaths</caption><thead><tr><th>No</th><th>Country</th><th>Year of the beginning</th><th>Year of the end</th><th>Event</th><th>Violent deaths</th></tr></thead><tbody><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td></tr><tr><td>1</td><td>Algeria</td><td>1992</td><td>2002</td><td>Islamist rebellion, civil war</td><td>~100,000</td></tr><tr><td>2</td><td>Angola</td><td>1975</td><td>2002</td><td>Civil war</td><td>~550,000</td></tr><tr><td>3</td><td>Afghanistan</td><td>1978</td><td>*</td><td>Afghan revolution, civil wars (complicated by foreign interventions)</td><td>~1,800,000</td></tr><tr><td>4</td><td>Bangladesh</td><td>1971</td><td>1971</td><td>War for independence from West Pakistan</td><td>~1,250,000</td></tr><tr><td>5</td><td>Burma/ Myanmar</td><td>Before 1960</td><td>*</td><td>Civil wars</td><td>~130,000</td></tr><tr><td>6</td><td>Bosnia and Herzegovina</td><td>1992</td><td>1995</td><td>The Bosnian civil war</td><td>~175,000</td></tr><tr><td>7</td><td>Burundi</td><td>1993</td><td>1993</td><td>Civil war, mass killings of hutu and tutsi (mainly hutu were killed)</td><td>~200,000<sup>**</sup></td></tr><tr><td>8</td><td>Vietnam</td><td>1965</td><td>1973</td><td>Civil war in South Vietnam with interventions on the part of the USA and North Vietnam</td><td>~1,700,000</td></tr></tbody></table>
<table><thead><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr></thead><tbody><tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td></td></tr><tr><td>9</td><td>Guatemala</td><td>1960</td><td>1996</td><td>Civil war</td><td>~200,000</td><td></td></tr><tr><td>10</td><td>Congo, Dem. Rep. (Zaire)</td><td>1960</td><td>1965</td><td>Congolese crisis</td><td>~100,000</td><td></td></tr><tr><td></td><td></td><td>1998</td><td>2009</td><td>Civil wars</td><td>~3,800,000</td><td></td></tr><tr><td>11</td><td>Indonesia</td><td>1965</td><td>1966</td><td>Coup attempt, mass executions</td><td>~400,000</td><td></td></tr><tr><td>12</td><td>Iraq</td><td>1961</td><td>*</td><td>Kurd upsurges in the north, Shia insurrections in the south, political upheavals of the 2000s</td><td>~100,000</td><td></td></tr><tr><td>13</td><td>Iran</td><td>1978</td><td>1979</td><td>Islamic revolution</td><td>~100,000</td><td></td></tr><tr><td>14</td><td>Yemen</td><td>1962</td><td>1970</td><td>Revolution and civil war</td><td>~100,000</td><td></td></tr><tr><td>15</td><td>Cambodia</td><td>1970</td><td>1991</td><td>Civil wars and their consequences (complicated by foreign interventions)</td><td>~2,500,000</td><td></td></tr><tr><td>16</td><td>China</td><td>1966</td><td>1969</td><td>'Cultural revolution'</td><td>From 2,000,000 to 7,000,000</td><td></td></tr><tr><td>17</td><td>Laos</td><td>1960</td><td>1973</td><td>Civil war within the Second Indo-china War</td><td>From 70,000 to 250,000</td><td></td></tr><tr><td>18</td><td>Liberia</td><td>1989</td><td>1997</td><td>Civil wars</td><td>~150,000</td><td></td></tr><tr><td>19</td><td>Lebanon</td><td>1975</td><td>1990</td><td>Civil war complicated by numerous cases of foreign intervention</td><td>~150,000</td><td></td></tr><tr><td>20</td><td>Mozambique</td><td>1975</td><td>1992</td><td>Civil war</td><td>~1,000,000</td><td></td></tr><tr><td>21</td><td>Nigeria</td><td>1966</td><td>1970</td><td>Coup, civil war of Biafra</td><td>From 600,000 to 1,000,000</td><td></td></tr><tr><td>22</td><td>Rwanda</td><td>1994</td><td>1994</td><td>Civil war, mass killings of the Tutsi</td><td>~937,000**</td><td></td></tr><tr><td>23</td><td>Somalia</td><td>1991</td><td>*</td><td>Civil war, state breakdown, chaos, anarchy</td><td>~400,000**</td><td></td></tr><tr><td rowspan="3">24</td><td rowspan="3">Sudan</td><td>1955</td><td>1972</td><td>Civil war</td><td>~500,000</td><td></td></tr><tr><td>1983</td><td>*</td><td>Civil war</td><td>~1,900,000</td><td></td></tr><tr><td>2003</td><td>*</td><td>Darfur conflict</td><td>From 70,000 to more than 180,000</td><td></td></tr><tr><td>25</td><td>Uganda</td><td>1979</td><td>1986</td><td>Civil wars</td><td>~300,000**</td><td></td></tr><tr><td>26</td><td>The Philippines</td><td>Since 1972</td><td>*</td><td>War against guerillas</td><td>From 50,000 to 150,000</td><td></td></tr></tbody></table>
<table><thead><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>27</td><td><strong>Chad</strong></td><td>1965</td><td>1997</td><td>Civil wars</td><td>From 50,000 to 100,000</td></tr><tr><td>28</td><td><strong>Eritrea</strong></td><td>1962</td><td>1992</td><td>War for independence and internal conflicts</td><td>~1,400,000</td></tr><tr><td>29</td><td><strong>Ethiopia</strong></td><td>1962</td><td>1992</td><td>Civil wars</td><td>~1,400,000<sup>7</sup></td></tr></tbody></table>

Note: * Events unfinished, violence continuing in some form.

Sources: Grinin and Korotayev 2009; Bercovitch and Jackson 1997; Clodfelter 1992; Crowder, Fage, and Oliver 1986; Lorraine 1995; Palmowski 1997; Project Ploughshares 2008; Rummel 1994; Small and Singer 1982; Totten 1997; Wallechinsky 1995; White 2010a; 2010b.

The research reveals that for 1960–2005 period the probability of major internal violent political conflicts in countries with very low (less than 15 % increase per five years) young urban population growth rates was very low. For countries with intermediate values of these rates (20–30 % increase per five years) the probability of such conflicts was close to 50 %, that is one chance out of two. However, even for this group of countries there was not a single occurrence of a particularly violent internal political upheaval in the given period. In countries with high (30–45 % increase per five years) young urban population growth rates the probability of avoiding the major internal political upheavals falls down to a very low level (about one chance out of four). Besides, the probability of particularly violent civil wars becomes very high in these countries (also about one chance out of four).

However, particularly deep internal political problems were encountered in those countries in which the young urban population growth rates were very high (> 45 % increase per five years) in the period under consideration. Out of 34 countries of this group NOT A SINGLE ONE managed to avoid major political shocks. Besides, the risk of particularly violent civil war occurrence was very high for these countries (about one chance out of two).

## Forecasting the Dynamics of Sociopolitical Instability in the African Countries in 2020–2050

The results obtained in our research can well be used for predicting the risks of sociopolitical instability for the countries being on the verge of escaping from the Malthusian trap, in the process of escape, or having escaped from it recently.

Working out of such forecasts is currently made remarkably easier by the fact that UN Population Division has developed urbanization dynamics fore-

<footnote n="7">⁷ General number of deaths in Ethiopia and Eritrea in 1962–1992.</footnote>
casts for all the African countries, as well as age structure dynamics forecasts up to 2050 (UN Population Division 2010). Synthesis of these predictions allowed us to make a synthetic forecast regarding the dynamics of structural-demographic instability for the African countries in this period.

It is noteworthy that in our prediction only ‘positive results’ are really significant (i.e. the results revealing the presence of high political instability risk in a certain country in a certain period). We are inclined to interpret such results as an evidence of a real risk of political instability in the given place at the given time (if, of course, respective governments do not undertake adequate measures in proper time). On the other hand, in our opinion, ‘negative results’ cannot be viewed as a guarantee of absence of political upheavals in the given country up to 2050 (as we do not claim that the reasons of violent political upheavals can be reduced to structural-demographic factors only).

* * *

Our forecast has produced rather different results for different Subsaharan African countries.

No serious demographic structural risks of the type in questions are forecasted after 2015 for some Subsaharan countries (especially in Southern Africa). Let us regard, for example, the forecast for Botswana (see Fig. 46):

<figure><img src="image_129.png" /><figcaption>**Fig. 46.** Young urban population dynamics (thousands) in Botswana, forecast up to 2050</figcaption></figure>

No serious structural-demographic risks of this type are forecasted for many countries of Tropical Africa, for example, Gabon (see Fig. 47):
<figure><img src="image_130.png" /><figcaption>**Fig. 47.** Young urban population dynamics (thousands) in Gabon, forecast up to 2050</figcaption></figure>

While in the Gabon case the young urban population growth curve quite clearly demonstrates the absence of major structural-demographic risks, for some other Tropical African countries it is necessary (in order to detect it) to carry out an analysis of time series generated by our forecast. A bright example here is represented by the Ghana case (see Fig. 48).

<figure><img src="image_131.png" /><figcaption>**Fig. 48.** Young urban population dynamics (thousands) in Ghana, forecast up to 2050</figcaption></figure>

Indeed, in application to Ghana the forecasted situation may seem truly threatening, as by 2050 the young urban population there is likely to grow almost threefold (i.e., 200 %; while in the cases considered above this growth did not exceed 50 %).
However, a simple analysis of the corresponding time series shows that the situation is not so threatening. Indeed, the forecasted dynamics of relative growth rates of the young urban population has the following shape (Fig. 49).

<figure><img src="image_132.png" /><figcaption>**Fig. 49.** Forecasted dynamics of relative growth rates of the young urban population in Ghana up to 2050, % per five-year periods</figcaption></figure>

Thus, in the following decade urban youth relative growth rates are forecasted to be decreasing in Ghana up to a quite safe level of less than 14 % during five years; in the 2020s these rates are going to stabilize (at the same rather safe level), while after 2030 they will decline further on. A similar dynamics is demonstrated by the absolute growth rates of the young urban population (see Fig. 50).

<figure><img src="image_133.png" /><figcaption>**Fig. 50.** Forecasted dynamics of absolute growth rates (in thousands) of the young urban population in Ghana up to 2050, per five-year periods</figcaption></figure>
Thus, no increase in absolute growth rates of the young urban population is forecasted in Ghana for the next decade. According to the same forecast, a certain increase in these rates is expected in the 2020s, but it will be very moderate (25 % during ten years). After 2030 the absolute growth rates are forecasted to start declining, and by the 2040s they are expected to fall below the current level.

However, the forecast indicates the presence of high structural-demographic risks for a wide range of Tropical African countries (see Table 6 below for a full list). Fortunately, in no case the urban youth growth rates are forecasted to exceed the critical level of 45 % per five years (let us remember that in the recent decades not a single country which crossed this level managed to avoid major internal sociopolitical conflicts, while in half of the cases particularly violent internal political upheavals occurred). Along with that, a number of tropical African countries are forecasted to get into a very dangerous zone of 30–45 % (let us remember that in the recent decades only a quarter of countries found in this zone managed to avoid major internal political conflicts, while in a quarter of cases particularly violent internal political upheavals were observed).

Tanzania is among the countries of high structural-demographic risk. The general dynamics of the urban population in this country is forecasted as follows (see Fig. 51):

<figure><img src="image_134.png" /><figcaption>**Fig. 51.** Young urban population dynamics in Tanzania up to 2050, thousands</figcaption></figure>
Thus, in 2005–2050 an almost six-fold increase in the young urban population is forecasted for Tanzania, while in the 2020s the relative growth rates of this indicator will exceed the critical level of 30 % per five years.

However, the most serious structural-demographic risks are predicted for
Niger (see Fig. 52):

<figure><img src="image_135.png" /><figcaption>**Fig. 52.** Young urban population dynamics in Niger up to 2050, thousands</figcaption></figure>

Thus, in 2000–2050 the young urban population of Niger will increase by an order of magnitude, while in the second half of the 2010s the relative growth rates of this indicator will exceed the critical level of 30 % per five years, while in the early 2020s they will exceed an even more dangerous level of 40 % during five years. These rates will decrease to relatively safe levels only in the late 2040s (see Fig. 53).
<figure><img src="image_136.png" /><figcaption>**Fig. 53.** Forecasted dynamics of relative growth rates of the young urban population in Niger up to 2050, % per five-year periods</figcaption></figure>

Besides, in Niger an increase by an order of magnitude (in comparison to 2000 level) in the absolute growth rates of the young urban population is forecasted by 2030 (see Fig. 54).

<figure><img src="image_137.png" /><figcaption>**Fig. 54.** Forecasted dynamics of absolute growth rates (in thousands) of the young urban population in Niger up to 2050, per five-year periods</figcaption></figure>
In conclusion, let us present a summary forecast of structural-demographic risks of political destabilization in the Subsaharan African countries up to 2050 (see Table 6).

<table><caption>**Table 6.** Summary forecast of structural-demographic risks of political destabilization in Subsaharan African countries up to 2050</caption><thead><tr><th>Country</th><th>Years of maximum urban youth growth rates</th><th>Urban youth growth rates (% in five years) in those years</th><th>Period of particularly high structural-demographic risks of political destabilization</th><th>Structural-demographic risk level</th></tr></thead><tbody><tr><td>Niger</td><td>2021–2025</td><td>41.8</td><td>2021–2030</td><td>Very high</td></tr><tr><td>Malawi</td><td>2016–2020</td><td>39</td><td>2015–2025</td><td>High</td></tr><tr><td>Burkina Faso</td><td>2021–2025</td><td>38.7</td><td>2021–2030</td><td>High</td></tr><tr><td>Uganda</td><td>2021–2025</td><td>33.1</td><td>2021–2030</td><td>High</td></tr><tr><td>Eritrea</td><td>2021–2025</td><td>32.5</td><td>2021–2030</td><td>High</td></tr><tr><td>Tanzania</td><td>2021–2025</td><td>30.6</td><td>2021–2030</td><td>High</td></tr><tr><td>Kenya</td><td>2021–2025</td><td>30.2</td><td>2021–2030</td><td>High</td></tr><tr><td>Rwanda</td><td>2021–2025</td><td>29.6</td><td>2021–2030</td><td>Medium</td></tr><tr><td>Chad</td><td>2016–2020</td><td>28.5</td><td>2016–2025</td><td>Medium</td></tr><tr><td>Burundi</td><td>2026–2030</td><td>28.1</td><td>2026–2035</td><td>Medium</td></tr><tr><td>Congo, Dem. Rep.</td><td>2016–2020</td><td>27.7</td><td>2016–2025</td><td>Medium</td></tr><tr><td>Mozambique</td><td>2021–2025</td><td>27.4</td><td>2021–2030</td><td>Medium</td></tr><tr><td>Somalia</td><td>2016–2020</td><td>27.4</td><td>2016–2025</td><td>Medium</td></tr><tr><td>Ethiopia</td><td>2016–2020</td><td>26.7</td><td>2016–2025</td><td>Medium</td></tr><tr><td>Gambia</td><td>2016–2020</td><td>26.5</td><td>2016–2025</td><td>Medium</td></tr><tr><td>Sierra Leone</td><td>2016–2020</td><td>25.4</td><td>2016–2025</td><td>Medium</td></tr><tr><td>Madagascar</td><td>2016–2020</td><td>25.2</td><td>2016–2020</td><td>Medium</td></tr></tbody></table>

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