Patterns in war dynamics (1495-1945), Part II: Results and Methods

2.1 Properties of systemic wars.

 I argue that two fundamentally different types of war can be distinguished: systemic and non-systemic wars. During relatively stable periods, the System produces non-systemic wars. Systemic wars typically follow relatively stable periods and signal the collapse of the international order that was imposed during the relatively stable period. In contrast with non-systemic wars, systemic wars involve all the Great Powers that the System contains at the time of the war and typically have a significant impact on the ‘order’ – the organization – of the System. Systemic wars are responsible for the periodic reorganization of the anarchistic System, for the (re-)alignment of positions of power and influence of states with the order that is imposed.

Based on the two criteria and the judgment of historians regarding the impacts of wars on the System’s order, four systemic wars can be identified during the period 1495-1945 (see Table 1).

Systemic wars (1495-1945)



Systemic war

Period No dataset Levy

Severity (bcd)


1 The Thirty Years’ War 1618-1648 46, 47, 48, 49 1,971,000
2 The French Revolutionary and Napoleonic Wars 1792-1815 84, 85 2,532,000
3 The First World War 1914-1918 107 7,734,300
4 The Second World War 1939-1945 113 12,948,300

Table 1: The table shows the four systemic wars that the System produced during the period 1495-1945, including their severities. Severity is defined as the number of battle-connected deaths (bcd) of military personnel of the Great Powers participating in a war. Data from Levy.


2.2 Properties of cycles.

The identification of four systemic wars makes it possible to identify the four relatively stable periods that typically precede systemic wars. Whereas the System is reorganized during systemic wars, during relatively stable periods, international orders are ‘in place’ (imposed) that regulate interactions between states and ensure a certain predictability in behavior and that the war dynamics of the System stay reasonably contained. Wars that the System produces during relatively stable periods I denote as ‘non-systemic wars’. I define a relatively stable period and the systemic war that follows as a ‘cycle’.

A closer look at the lifespans of the four successive cycles during the period 1495-1945 reveals that except for the lifespan of the second cycle (1648-1815), the lifespans shorten in duration. The severities of successive systemic wars increased ‘at the same time’. The increasing frequencies of cycles and their increasing amplitudes (severities) seem (at least statistically) to be closely related: the correlation coefficient between the lifespans of successive cycles and severities of systemic wars is -0.99.

Cycles (1495-1945)




Lifespan (years)

Total severity (bcd)




153 2,976,000
2 1648-1815 167 7,550,300
3 1815-1918 103 8,484,680
4 1918-1945 27


Table 2: The table shows the main properties of the four cycles that the System produced during the period 1495-1945. Data from Levy .


2.3 Properties of relatively stable periods.

 It is now also possible to identify four relatively stable periods that preceded the four respective systemic wars. During relatively stable periods, ‘stability’ is anchored in and maintained by international orders that are imposed on the System.

As mentioned above, during relatively stable periods, the System produces non-systemic wars. It is possible to distinguish two types of non-systemic wars: non-systemic wars in the System’s core (Europe) that are closely related to a process of integration of the core, which I refer to as ‘integration wars’, and so-called ‘expansion wars’, i.e., non-systemic wars that are related to the expansion of the core to the System’s non-core, or concern autonomous non-core wars.

In Fig 1. the different types of wars are shown, including their respective occurrences during the period 1495-1945.


Figure 1: In this figure, a ‘taxonomy’ of wars is presented, including their respective numbers during the period 1495-1945. It is based on a cyclical perspective and on the different purposes of wars. Two main categories of wars can be distinguished: systemic and non-systemic wars. Depending on their ‘purpose’, non-systemic wars can either be ‘integration wars’ – closely related to the integration of the System’s core (Europe) – or expansion wars, which are manifestations of the expansion of the core (Europe) to the non-core, and of autonomous non-core war dynamics. Depending on the nature of their dynamics, integration wars can be ‘chaotic’ or ‘periodic’ in nature.


In the table and figure below (Table 3, Fig. 2), I specify several properties of relatively stable periods. The war frequencies are calculated by dividing the number of integration wars during relatively stable periods by the respective lifespans of these periods. Great Power status changes concern the number of times states acquired or lost Great Power status during relatively stable periods.

Relatively stable periods (international orders)




Lifespan (years) No. of integr. wars No. of expansion wars War frequency (integr. wars)

No. of Great Power status changes


1 1495-1618 123 45 0 0.37 8
2 1648-1792 144 34 5 0.24 6
3 1815-1914 99 16 4 0.16 2
4 1918-1939 21 2 2 0.10 1

Table 3: This table presents the main properties of relatively stable periods (international orders). Basic data from Levy.

pnas-fig-2Figure 2: This figure shows the development of the number of non-systemic wars, of war frequencies and of Great Power status changes in Europe during the four successive relatively stable periods that can be distinguished, in addition to their lifespans.

Another property that can be quantified concerns the development of state structures – their shapes and sizes – in the System’s core (Europe) during the period 1495-1945.

During that period, Europe developed from a diverse collection of approximately 300 loosely connected ‘units’ with a total population of approximately 83 million in 1495 into a highly connected anarchistic system of approximately 25 ‘standardized’ state-structures, with a total population of approximately 544 million in 1939. Following the First World War (the third systemic war, 1914-1918), the structures of states (shapes and sizes) in Europe reached a more or less permanent state.


2.4 Severities of cycles and release ratios of cycles.

 When cycles are used as units of analysis and when the severities of successive cycles and of their respective components (relatively stable periods and systemic wars) are analyzed, it is possible to acquire a better understanding of the development of certain characteristics of successive cycles. To that end, I introduce the concept of release ratios of cycles.

The release ratio of a cycle specifies what percentage of the total severity of the cycle (the sum of the severities of all non-systemic wars during the relatively stable period of the cycle and of its systemic war) is contributed by the systemic war of the cycle. I consider the release ratio a measure – an indication – of the amount of tensions that are released through systemic war activity during a cycle.

My analysis reveals that (1) the total severity of successive cycles, (2) the severity per year (calculated by dividing the total severity of a cycle by its lifespan), and (3) the release ratios developed steadily, with the exception of the second cycle, which caused a distortion in an otherwise regular trend (see also Supportive Information).

The analysis not only shows that the total severity of the second cycle was relatively high but also that much more tension was released by means of non-systemic wars than during the systemic war that followed (the French Revolutionary and Napoleonic Wars, 1792-1815); the second cycle was clearly an exception.



Figure 3: This figure shows the total severities, the severity/year, and release ratios of successive cycles during the period 1495-1945, basic data from Levy.

If the total severity and the release ratio are ‘corrected’ (respectively to 5,000,000 and 78%) – assuming these properties follow the trend set by the first, third and fourth cycles – the total severities of the four cycles increased exponentially (R2 = 1.00), the release ratio increased linearly (R2 = 0.98), and the severity per year grew by a factor that itself increased exponentially (R2 = 1.00). See also Fig. S2 with a ‘corrected’ version of the second cycle.

As I explain later, the distortions of the second cycle, including the distortion in the lifespan of the second cycle, seem to be related to the ‘abnormal’ nature of non-systemic war dynamics during the period 1657-1763.

To be continued.