Chaos from order: a network analysis of in-fighting before and after El Chapo’s arrest

To model changes in the decisions of cartels and militias of whether to engage in infighting between the five years before and after El Chapo’s capture I employ a before-and-after design. Effects are estimated via a stochastic actor oriented model (SAOM), although it would also be possible to utilize relational event modeling (REM) or a temporal exponential random graph model (TERGM). However, while REM models may be interpreted in an actor-oriented framework (Butts, 2017), they are fundamentally tie-oriented (Stadtfeld et al., 2017). Similarly, TERGMs treat ties as a function of previous ties rather than actor choices (Block et al., 2017; Snijders and Pickup, 2017). On the other hand, SAOMs explicitly model actors’ choices with a rate function and an objective function. The rate function determines the probability that an actor can change a tie. In this analysis, the rate function gives each actor an equal probability of being able to change its tie at a given time step. The optimization function is a linear combination of covariates that nodes try to maximize given by (1) f i ( x ( 0 ) , x ; β ) = ∑ k = 1 K β k s ki ( x ( 0 ) , x ) where s ki ( x ( 0 ) , x ) are network effects. SAOMs proceed in mini steps where nodes are randomly selected by the rate function to change a tie according to their objective function (Snijders and Pickup, 2017).

To understand how El Chapo’s arrest changed the way cartels and militias decide whether to attack each other, I employ SAOMs to estimate the differences in the mean relative importance in the five years before and after El Chapo was captured. The relative importance for a single network effect k on an actor i derived from an estimated coefficient θ ˆ , as proposed in (Indlekofer and Brandes, 2013), is given by (2) I k ( X , i ) : = ‖ π i ‒ π i ‒ k ‖ ∑ l = 1 K ‖ π i ‒ π i ‒ k ‖ l where π_i is the probability that actor i forms a tie with the actor it was observed forming a tie with. Stated differently, the relative importance of an effect k on an actor i represents the change in i’s probability of forming a tie with another actor j if effect k was excluded from the model. The mean relative importance of an effect k is the summation of the relative importance of k on all actors divided by the number of actors. In this analysis, the difference in the mean relative importance of an effect represents the change in how much it contributed to cartels’ and militias’ decisions to attack other organizations after El Chapo was arrested compared to before his arrest. It is important to note that this is not the same as the regression coefficients of a SOAM.

To create the network data, I collated event data from the Social Conflict Analysis Database (SCAD) (Salehyan et al., 2012), the Uppsala Conflict Data Program Georeferenced Events Dataset (Pettersson et al., 2021; Sundberg and Melander, 2013), and the Armed Conflict Location and Events Database (Raleigh et al., 2010) that occurred between 2012 and 2021. Each data source relies on news articles from a different set of media outlets, so combining them ensures a greater number of events are included in the final dataset and at least partially eliminates the reporting bias that might be present in any one dataset. Additionally, some events in each dataset were coded as having unknown actors but employing multiple datasets ensures that at least some of the gaps in each dataset will be filled in by the others. All datasets include events from around the world and events where the state was the perpetrator. In addition to lethal attacks, SCAD includes riots strikes, and protests.

To isolate violent interactions between Mexican cartels and militias, I excluded events that occurred outside of Mexico; included a government actor; were coded as a protest, riot, or strike; or occurred before 2012 or after 2021. The final dataset includes militias because they were formed to protect communities from cartel violence and may influence tie formation between cartels. One might make the case that transnational actors should also be included in my analysis because they operate in Mexico and are involved in the Mexican conflict. However, unlike Mexican cartels, these groups are not heavily involved in Mexican politics and do not attempt to gain material support and sympathy from Mexican citizens, so their role in Mexico’s drug war is tangential to the role of Mexican actors. Finally, I merged events that had the same attacker and victim and occurred on the same day in the same municipality.

Ties between actors are directed and represent at least one violent interaction from the sender to the receiver. I created one network for interactions that occurred between 2012 and 2016 and another for 2017 to 2021. To ensure an equal comparison, the network in the pre-arrest period only contains ties that were observed before El Chapo’s arrest and the post-arrest network only contains ties that were observed in the post-arrest period. Many militias and sub-factions of larger cartels were not observed in the pre-arrest network, so I code them as “joiners” as per Ripley et al. (2021). The network in the pre-arrest period only contains 29 nodes and 19 edges while the post-arrest network contains 132 nodes and 124 edges, due to the formation of new sub-factions and militias after El Chapo’s arrest. This does not mean that edges only observed in one period were not present in the other, but that they were not observed in the other period. Figure 1 shows the two networks and Figure 2 displays their degree distributions. Nodes in Figure 1 are colored according to their structurally defined role. The majority of nodes are small cartels and militias that control small swaths of territory. The cartels in this role tend to specialize in a small number of subtasks of drug trafficking and align themselves with larger cartels. Unsurprisingly, the most powerful cartels—the Gulf, Jalisco Nueva Generacion, Los Zetas, and Sinaloa cartels—occupy a unique role. Rising Challengers—Nueva Plaza, Santa Rosa de Lima, Los Caballeros Templarios, and La Nueva Familia cartels—are relatively new cartels that are rapidly growing while the White Dwarfs—Juarez and Beltran Leyva cartels—represent cartels that are on the decline.

Figure 1:

Figure 2:

I include four independent variables that allow for the testing of the hypotheses above. Out-degree Jaccard similarity is the Jaccard similarity of out-degree ties between a node and every other node in the network. A high Jaccard similarity between the out-degree of two actors means that they both fight similar other actors, which would indicate an alliance. To account for preferential attachment, I include the in-degree popularity metric. If preferential attachment exists, this metric will be higher, indicating that attacks against a cartel or militia beget future attacks against the same cartel or militia. The out-in-degree assortativity effect is similar, but it quantifies the propensity for actors with high in-degrees to attract ties from actors with high out-degrees. Put differently, it indicates stronger cartels and militias preying on weaker groups. The final effect, transitive closure, is an approximate measure of clustering, which suggests increased competition among cartels due to uncertainty about the balance of power after El Chapo’s arrest.

In addition to these variables, I include five control variables. Reciprocity accounts for the proportion of a group’s outgoing ties that correspond to incoming ties from the same node that the outgoing ties are sent to. I also control for homophily related to four node-level attributes. Aggression is the log of the number of attacks conducted by each actor during both periods. The subfaction attribute codes whether an organization is a subfaction of a larger group or independent. Militia is a dummy variable that takes the value 1 if an organization is a militia and 0 if an organization is a cartel. The role variable assigns each organization to one of seven previously described roles as determined by each group’s structural equivalence with other organizations. More details on how structural equivalence groups were created is available in Appendix A.

Figure 3 shows the results of the first model. Out-degree Jaccard similarity is marginally positive (estimates are rounded to two decimal places) but does not achieve statistical significance. This somewhat contradicts Hypothesis 1, which predicts that actors would be less likely to refrain from attacking their allies after El Chapo’s arrest. If that were the case, we would see a statistically significant change in the positive direction for the effect of Jaccard similarity on tie formation. To the contrary, one might argue that cartels and militias have strong incentives to form alliances. With the power vacuum left by El Chapo’s arrest, cartels have more to gain from forming alliances because doing so increases their ability to wrestle control of drug smuggling routes from rivals. Militias also have an incentive to form alliances because they can pool personnel, resources, and intelligence to combat increasing cartel violence. In this case, we would see a statistically significant negative change in the effect of Jaccard similarity on tie formation probability. However, the lack of a positive or negative statistically significant effect implies that the decision-making of cartels does not adhere to either of these logics. Instead, they may have neither greatly expanded or backed out of their alliances because, as Christia (2012) has shown to be the case with insurgent groups, organizations aim to create alliances large enough to achieve their objectives while maximizing individual payoffs. Another possible explanation is that alliances between cartels formed more informally around the sharing of knowledge and resources among lower-level leaders. If this is the case, it would also explain why changes to upper echelon leadership seemed to have little effect on alliance formation or maintenance.

Figure 3:

Figure 4 presents the results for general preferential attachment and the preferential attachment of aggressive organizations to form conflict ties with those already under attack. In the first of these models, in-degree popularity has a large effect but is not statistically significant. In the second model, the effect of out-in-degree assortativity is large and statistically significant. This means more aggressive cartels preferentially attack cartels and militias that have already been under attack, probably to consolidate their power. With a power vacuum left after El Chapo’s arrest, more aggressive cartels probably view cartels that are frequently attacked as easy competition to eliminate. Yet some of the increase in the mean relative importance of out-in-degree assortativity might also be attributable to the growing number of militias after El Chapo’s detention, which more aggressive cartels might direct violence against. Conversely, cartels and militias with lower in-degree centralities were less likely to be attacked after El Chapo’s arrest than before, suggesting those organizations are more bellicose and would not be perceived as easy targets.

Figure 4:

Another interpretation is that very aggressive organizations are more involved in in-fighting as both initiators and victims of attacks. Put differently, cartels that are heavily involved in in-fighting and initiate many attacks against their rivals are probably on the receiving end of more attacks due to their involvement in in-fighting. Then, they probably reciprocate violence against the initiators so they are not viewed as easy targets. Accordingly, the large and statistically significant effect of reciprocity implies that retaliation against organizations highly involved as both initiators and victims of attacks is more likely to be carried out by the victims of those organizations than by a different cartel or militia. As in the previous interpretation, this suggests that cartels and militias on the receiving end of attacks are quick to reciprocate violence to prove that they are not easy targets.

Figure 5 shows the results for transitive closure. A negative change in the mean relative importance of this effect would indicate an avoidance of cartels to engage in in-fighting. For example, if a cartel attacked a second cartel and the second cartel attacked a third cartel, the third cartel would not attack the first. On the other hand, increased transitive closure would suggest that in-fighting ties are more likely to form around common social foci, as predicted by Feld (1981). Though Feld’s theory predicts that ties in a friendship or similar context will form around a social focus such as club membership, increased transitive closure in Mexico’s drug trade would imply that conflict ties are more likely to form around the shared focus of drug trafficking in contested areas. If that were the case, it would indicate that cartels are uncertain about the balance of power in a given area, which fighting would reveal. However, the effect of transitive closure is not statistically significant and only marginally contributes to the decisions of cartels and militias. This indicates that El Chapo’s arrest did not lead to uncertainty, or at least not enough to significantly increase transitive closure, around contested territories. Moreover, the lack of a statistically significant increase for transitive closure means the Sinaloa Cartel’s rivals did not greatly change the perceived balance of power. Finally, it is worth mentioning that the lack of uncertainty about the balance of power is likely due in part to the reputational mechanism described above. Cartels with higher in-degrees would be perceived as weak and those with low in-degrees would be perceived as strong, so there would be no need for them to form transitive closure around contested areas to reveal the balance of power.

Figure 5: