Common ecology quantifies human insurgency

Juan Camilo Bohorquez, Sean Gourley, Alexander R. Dixon, Michael Spagat & Neil F. Johnson (2009) doi: 10.1038/nature08631 Common ecology quantifies human insurgency. Nature

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Johnson等人声称发现了量化人类叛乱的共同生态。人类叛乱在事件规模和单位时间事件数量方面都具有明显的长尾特征。Neil F. Johnson也是一个金融物理学家,他的书包括Financial market complexity。


Many collective human activities, including violence, have been shown to exhibit universal patterns1–19. The size distributions of casualties both in whole wars from 1816 to 1980 and terrorist attacks have separately been shown to follow approximate power-law distributions 6,7,9,10. However, the possibility of universal patterns ranging across wars in the size distribution or timing of within conflict events has barely been explored. Here we show that the sizes and timing of violent events within different insurgent conflicts exhibit remarkable similarities. We propose a unified model of human insurgency that reproduces these commonalities, and explains conflict-specific variations quantitatively in terms of underlying rules of engagement. Our model treats each insurgent population as an ecology of dynamically evolving, self-organized groups following common decision-making processes. Our model is consistent with several recent hypotheses about modern insurgency 18–20, is robust to many generalizations 21, and establishes a quantitative connection between human insurgency, global terrorism 10 and ecology 13–17,22,23. Its similarity to financial market models 24–26 provides a surprising link between violent and non-violent forms of human behaviour.



事件的规模采用死亡人员数量来衡量,主要因为死亡人数更容易核实。从累计概率分布来看具有明显长尾特征。根据图1,其中事件规模的幂指数$\alpha \sim 2.5$。




横轴是每天发生暴乱事件的数量$n$, 纵轴是每天叛乱事件数量n的概率分布$p(n)$。其实,它衡量的是单位事件数量的分布,即有多少天发生了n件叛乱事件。

显然有些事件的timing是幂律分布(如Iraq days 0-180),有些是对数正态分布(如Colombia days 0-500、Iraq 540+)。与随机情况相比,作者所提出的模型更好的拟合了真实数据。




  1. Grouping Mechanism (1): ongoing group dynamics within the insurgent population (for example, as a result of internal interactions and/or the presence of an opposing entity such as a state army);
  2. Timing Mechanism (2): group decision-making about when to attack based on competition for media attention.


  1. 在时间点t媒体会广播叛乱事件。【机制2】
  2. 在时间点t媒体报道会改变群体的策略和自信水平【机制2】
  3. 在时间点t群体内部互动(联合或分裂)【机制1】
  4. 机制1构成群体重组,机制2决定自群体在时间点t的攻击决策
  5. 上述过程构成时间点t的叛乱事件数$n_x(t)$

    • 数据分析:
      • 时间点t的事件数量在规模维度上汇总 $\sum_x n_x(t) $, 【size-aggregated】
      • 规模为x的事件数量在时间维度上汇总 $\sum_t n_x (t)$, 【time-aggregated】
  6. 在时间点t更新叛乱事件的新闻


  • 机制1导致了时间维度汇总的事件数量的分布(Figure2)size-aggregated】;
  • 机制2导致了规模维度汇总的时间数量的分布(Figure3)【time-aggregated】。

首先,就机制1而言,叛乱群体内部的互动包括了分裂(fragmentation, $v_{frag}$)与合并(coalesce, $v_{coal}$)两类。

  • 一个群体分裂的概率一般比较小,约为1%。
  • 当两个力量为$s_1$和$s_2$的两个群体合并的时候,他们的力量变为$s_1 + s_2$。


  • 假设所有组参与叛乱的概率相等;
  • 群体力量$s$按时间进行平均的分布即叛乱事件的规模$x$分布。
  • 以上过程导致一个稳定的幂律分布,幂指数围绕2.5左右摇摆。1 2

Supplementary Figure 2

The model is simply a modified version of the well-known and well-studied El Farol problem of Brian Arthur in which potential bar-goers compete for space in a crowded bar on successive days, making decisions about whether to act (i.e. attend the bar) or not based on common limited knowledge about the past (see Ref. [33]2 for details).

netlogo program of El Farol

The El Farol bar problem is a problem in game theory. Based on a bar in Santa Fe, New Mexico, it was created in 1994 by W. Brian Arthur. 3 The problem was formulated and solved dynamically six years earlier by B. A. Huberman and T. Hogg in “The Ecology of Computation”, Studies in Computer Science and Artificial Intelligence, North Holland publisher, page 99. 1988. The problem is as follows: There is a particular, finite population of people. Every Thursday night, all of these people want to go to the El Farol Bar. However, the El Farol is quite small, and it’s no fun to go there if it’s too crowded.

So much so, in fact, that the preferences of the population can be described as follows:

  • If less than 60% of the population go to the bar, they’ll all have a better time than if they stayed at home.
  • If more than 60% of the population go to the bar, they’ll all have a worse time than if they stayed at home.

Unfortunately, it is necessary for everyone to decide at the same time whether they will go to the bar or not. They cannot wait and see how many others go on a particular Thursday before deciding to go themselves on that Thursday.



可以在不同的近似水平上写出来模型演化的动力学方程。某一次反叛军队的攻击情况可以分割表达为{$l_1, l_2, .., l_N$}。其中,$l_N$是攻击强度为s的攻击单位的数量(the number of attack units of attack strength s)。如果所有的叛军一起发动了攻击,那么可以表达为{0,0,..,1},即所有的N个人一起参与了攻击,其他攻击规模的数量都为0。显然,存在:



  1. APAR. D’HULST, & G. J. RODGERS. (2011). Exact solution of a model for crowding and information transmission in financial markets. International Journal of Theoretical & Applied Finance, 03(4), 303-320. 

  2. Financial market complexity / Neil F. Johnson, Paul Jefferies, Pak Ming Hui. Oxford University Press, 2003.  2

  3. Arthur, W. Brian (1994). “Inductive Reasoning and Bounded Rationality” (PDF). American Economic Review. 84: 406–411. 

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