Political organization and gender predict violence in the Andean archaeological record

Significance

The extent to which “civilization” acts as an agitating or pacifying force for violent conflict over human history remains one of the longest-enduring questions in anthropological thought. Reconstructing the role gender may have played in the distribution of violent conflict in archaeological populations is crucial for understanding how violence may be structured today. We construct a multinomial logistic regression and use Bayesian Hamiltonian Monte Carlo methods to fit our model. We find that biological sex, rather than just sociopolitical organization, had an important impact on the experience of interpersonal conflict. This study has important implications for how future scholars engage with concepts of violence, gender, and sociopolitical change and serves as a case study for future meta-analyses of violence.

Abstract

The relationship between sociopolitical organization and violence remains an enduring question in anthropological research. Less studied is the articulation of gender with violence in societies of different sociopolitical organization. We investigate the frequency and type of violence experienced by adult males and females in pre-Hispanic Andean archaeological contexts, comparing exposure to antemortem (nonlethal) and perimortem (potentially lethal) violence across three categories of sociopolitical organization: autonomous communities, regional cultural formations, and states. Using a database of 8,607 adults from 169 publications and over 155 sites, we construct a multinomial logistic regression using Bayesian Hamiltonian Monte Carlo methods to fit our model. The odds of antemortem and perimortem trauma were low for both sexes. However, the odds of antemortem trauma were consistently higher for males than females in all categories of sociopolitical organization, suggesting that men were more frequently exposed to violence. Males display similar odds of cranial trauma across all forms of sociopolitical organization, while females display slightly reduced odds of cranial trauma in states compared to autonomous communities. Perimortem trauma is especially strongly patterned by sex. In autonomous communities, the odds of potentially lethal cranial trauma are equivalent between the sexes; in states, they are consistent for males, but depressed for females. In the pre-Hispanic Andes, living in states dramatically reduced the chances of encountering lethal violence for females, but not males. Our study complicates the notion that increasing sociopolitical complexity leads to decreasing interpersonal violence and highlights the importance of gender in understanding the human history of violence.

Most popularly formulated as the contrast between a Hobbesian “war of all against all” vs. Rousseau’s “noble savage”, the relationship between sociopolitical organization and violence has been at the center of debates on human nature and culture for centuries (1–3). While social scientists now situate questions about the driving forces of violence within cultural and ecological contexts (4–6), the relationship of violent intergroup conflict to sociopolitical organization remains one of active interest (7–10). A more recent topic centers how violence and sociopolitical context have intersected with gender (11–13). Ethnographic evidence demonstrates that small-scale and nonhierarchical societies engage in conflict in manners distinct from large centralized states and empires, with implications for gendered exposure to interpersonal violence. We conduct a quantitative investigation of the relationship between sociopolitical organization, sex, and violence using the Andean archaeological record as a rich source of information.

For this study, we define sex as the expression of biological organs and associated traits and gender as the expression and performance of social identities that is often but not always linked to biological sex (14–16). We follow other large-scale analyses and focus on the biological sex of the individuals studied, making the assumption that biological sex may have structured aspects of the lives of past peoples, such as their exposure to interpersonal violence (13).

While most commonly understood as the visible use of force to harm other persons, violence can often manifest in subtle and largely invisible ways, such as unequal access to necessary resources (17). We focus on direct interpersonal violence: the intentional use of physical force against another person with the intent to harm or kill. The most common osteological evidence for direct violence takes the form of antemortem or perimortem cranial fractures or ulnar parry fractures (18, 19). Direct violence has a wide breadth of potential causes (20, 21), including intergroup conflict as well as intragroup conflict within the community and the household. Consequently, violent trauma at the population scale is best viewed as a palimpsest of different forms of violence within and between groups.

Expectations from the Ethnographic Record

Research regarding the ways that intergroup conflict differs between small-scale, noncentralized societies and large, politically centralized societies has been developed in considerable depth by several scholars (22–25). The relationship of sociopolitical context to intragroup violence is less well theorized, although the literature allows some insights. These studies tend to focus on the two extreme ends of the sociopolitical spectrum, contrasting warfare and conflict in ethnographic accounts of small hunter-gatherer or horticultural societies, such as the Yanomamö, with the military campaigns of states and empires like ancient Rome (6, 9, 26, 27). One of the key advantages of archaeological research is the ability to examine patterns of warfare among multiple different cultural groups and systems of sociopolitical organization prior to the destructive and destabilizing impact of European colonization.

While there are several dimensions of difference in warfare along this sociopolitical spectrum (28), the frequency, duration, and regional pervasiveness of conflicts—best represented through casualty rates—offer especially important insights and lie at the heart of longstanding debates (29). In small-scale societies, violent intergroup conflict takes the form of surprise raids on settlements, ambushes of people outside settlements, formal battles which broadcast group strength and alliances but typically result in few casualties, and opportunistic massacres when a settlement is inadequately defended (23, 30, 31). Although small-scale societies may experience few casualties in any one hostile encounter, wars can be very frequent, and cumulative injuries and deaths in ethnographic sources can be devastatingly high (23, 31, 32).

From the perspective of bioarchaeological evidence, nonstate violent conflict in the precolonial past appears highly variable in intensity, but in most cases, perimortem trauma is rare (19, 33, 34). Factors such as subsistence patterns and resource stress are likely to have played a major role in the intensity of violence and resultant casualty rates (e.g., ref. 35). By contrast, historical sources suggest that states (large regional polities with strongly centralized governments) waged large-scale wars that could be shockingly bloody in absolute terms but still resulted in lower exposure to war violence for the population as a whole (23, 36). Regional polities can use mobile military forces and border defenses to effectively protect a heartland, shielding interior populations from threat. Consequently, the violence of war is disproportionately experienced by smaller subsets of the much larger population: soldiers or warriors, the inhabitants of dangerous borderlands, and other particularly exposed populations. Meanwhile, within larger-scale societies, concentration of hegemonic power within a small societal elite structures the landscape of internal (intragroup) violence (36, 37). In principle, large centralized states exerted exclusive authority over certain forms of violence and the ability to conscript soldiers from the populace to engage in state-mandated warfare (23, 36, 37). They also sponsored and performed internal violence (sacrifice, punishment) as an integral part of order, sovereignty, and control. Alongside the increased monopoly over violence would likely come a decrease in intragroup conflict, as localized skirmishes and conflicts were violently discouraged by the state.

Gender intersects with these patterns in important ways. Soldiers and warriors are most frequently adolescent and young adult males, with warrior activity linked to conceptions of masculinity and prestige cross-culturally (11–13). In nonhierarchical societies, where warrior activity is typically considered the responsibility of all adult able-bodied males (38), achievement in war is an important source of prestige (7). In hierarchical societies, warrior activity may offer routes to social advancement for both commoner and elite males, albeit usually within their respective socioeconomic and political classes (39). Meanwhile, adult and adolescent males are usually considered the preferred targets for wounding, killing, and capture for sacrifice during periods of conflict (28, 40–43).

However, females are not always shielded from war-related violence. Women, girls, and preadolescent children of the enemy group might be killed, captured, or ignored, depending on the situation (41, 44). Massacres in particularly severe conflicts target females and preadolescent children as well as men, and this kind of genocidal violence may be more common in nonstate contexts (45). The violent capture of women in war is extremely common across cultures (26, 46, 47). Even when captives are nominally integrated into captor society as wives or adoptees, they almost always remain more socially vulnerable and marginal than home community members, and typically experience more and worse violent trauma throughout their lives (22, 44, 48, 49). Many ethnographic accounts note that captured women have a much higher fatality risk than their peers (22, 26). In addition, numerous studies demonstrate connections between the presence of warfare and an increase in domestic violence (50–52). Finally, females sometimes fight as combatants, although far less frequently than males (53, 54). Thus, even if males disproportionately experience war violence, increased intergroup conflict can be expected to result in more violence for females as well.

Bioarchaeological methods and theory are uniquely situated to empirically investigate these trends in the ethnographic record through a deep-time perspective. Additionally, they allow us to mitigate the potential influence of written historical records. Empires and states have a vested interest in maintaining and legitimizing their hegemony and thus largely paint themselves as pacifying forces bettering the lives of their subjects (55, 56). Taking a quantitative bioarchaeological approach through a deep time perspective allows us to investigate this question while minimizing the influence of historical bias.

Andean Archaeology as a Case Study

The archaeological record of the South American Andes presents an ideal case study for investigating the relationship between violence, sociopolitical organization, and gender for numerous reasons. Foremost among these is over a century of focused osteological research (57–59), originally pioneered by the famous Peruvian archaeologist Dr. Julio C. Tello (60, 61). Paired with the exceptional preservation found throughout the Andes, this long tradition of research creates an unparalleled published osteological record, allowing for the sample sizes required for robust statistical analyses (33, 35, 62, 63).

Additionally, the weapons used in interpersonal conflict in the Andes remained relatively consistent over time. The vast majority of violent trauma on Andean skeletal remains, from early hunter-gatherers to the Inka Empire, is cranial blunt force trauma consistent with the widespread use of maces and slings (64–66). This continuity over time allows for the comparison of violence and interpersonal conflict between different sociopolitical systems.

The Andes have also been host to a wide diversity of archaeological cultures with varying types of sociopolitical organization (67–70). The Andean sequence includes large, centralized states encompassing large and diverse populations and interstitial periods of smaller, politically autonomous communities expressing cultural heterogeneity. It also includes some cases of relatively large-scale regional religious and cultural formations that were not politically centralized, most famously the Early Horizon Chavín-Cupisnique religious phenomenon. Hypothetically, Andean regional cultural formations may have provided mechanisms of friendly interaction and conflict resolution that could have reduced violence within their spheres of influence. The periods of greatest interpersonal violence within the Andean archaeological chronology are widely accepted to be the Final Formative (400 BCE to 100 CE), the beginning of the Middle Horizon (600 to 1000 CE), and the Late Intermediate Period (1000 to 1400 CE) (13, 29, 33). Although a temporal analysis of violence over time within the Andes is not the primary purpose of this paper, a cursory qualitative assessment of the data in this study supports this interpretation (Fig. 1).

Fig. 1.

Odds of trauma over time. Circle size is proportional to skeletal assemblage sample size. Red line represents spline of trauma over time, with a 95% uncertainty band.

Bioarchaeological Implications

We summarize our expectations as follows:

• 1)Higher cumulative cranial trauma rates are expected for both sex categories in autonomous communities. Higher rates of perimortem trauma from war should be expected in autonomous communities as well.
• 2)Sex differences in exposure to violence should be present across the spectrum of sociopolitical organization. Warriors are usually male, and male enemies are usually preferred as targets; thus, the contexts in which men and women experience violence should differ. We expect males to present more perimortem and antemortem trauma than females across all types of sociopolitical organization.
• 3)We expect that this difference (increased trauma for males) will be more pronounced in state societies as intergroup conflict increasingly becomes the domain of specialized male warriors and soldiers.
• 4)More frequent warfare probably generates more frequent nonwar violence. Consequently, we expect increased perimortem and antemortem trauma among males to correlate with increased antemortem trauma among females.

Results

Our models returned $\widehat{R}$ values of 1, likely indicating successful model convergence. The results of our models are presented in Fig. 2, and we present these results as probabilities in Fig. 3. The probabilities are summarized numerically in Table 1. The area underneath the curves in Fig. 2 represents the odds of trauma compared to no trauma for any given sociopolitical category (log scale). These posterior density distributions indicate that the log odds of both perimortem and antemortem are low compared to no-trauma for across all subpopulations. Similarly, the log odds of perimortem trauma are lower than antemortem trauma across both sexes and all forms of sociopolitical organization, sharing overlapping regions of high posterior support.

Fig. 2.

Posterior density estimates of odds of antemortem and perimortem trauma generated by our model, across both sexes and all three categories of sociopolitical organization. Gold represents female and blue male. Note log scaling.

Fig. 3.

Posterior density estimates of odds of antemortem and perimortem trauma generated by our model, converted into probabilities.

Table 1.

Model estimates for the probability of different forms of cranial trauma by sex and sociopolitical organization

Sociopolitical Org.	Sex	None	Antemortem	Perimortem
Auto	Male	0.835	0.138	0.027
	Female	0.859	0.116	0.025
Regional	Male	0.848	0.123	0.029
	Female	0.912	0.073	0.015
States	Male	0.849	0.126	0.025
	Female	0.911	0.081	0.008

Note that these are point estimates and that the variability of model estimates is portrayed in Figs. 2 and 3.

The posterior density distributions for both antemortem and perimortem trauma are more loosely distributed for Regional Cultural Frameworks than for Autonomous Communities and States, indicating a higher degree of uncertainty in our model estimates for these populations. When Autonomous Communities are compared with States, females in State societies had slightly lower log odds of cranial trauma than in Autonomous Communities, while males did not, only partially fitting our first expectation. Our results show consistently lower odds of antemortem trauma among females than males for all forms of sociopolitical organization. Antemortem trauma rates among females also correlate across samples with antemortem trauma rates for males, as proposed in our fourth expectation. For both sexes, odds of antemortem violence are marginally reduced in States, but the effect is slightly stronger for females. Trends in perimortem trauma for the different sexes are particularly interesting. The odds of male perimortem trauma differ little between different sociopolitical categories. The posterior density estimates for perimortem trauma among males in Autonomous Communities, Regional Cultural Frameworks, and States approximately share a mode near 1:40.

By contrast, females had dramatically reduced odds of lethal injury in States. The log of the odds of perimortem violence among females is highest among Autonomous Communities by far—almost entirely overlapping with the male posterior density estimate with the mode of the distribution centered slightly under 1:40. Conversely, the posterior density estimate for perimortem trauma among females in States is lowered in comparison to the male’s posterior density estimate, with a mode centered on 1:110 for females in comparison to 1:40 in males.

While our first expectation that smaller scale societies would have higher cumulative trauma rates than State societies is partially supported, this statement is complicated by the influence of biological sex. We cautiously support our second expectation that males are generally exposed to interpersonal violence more frequently than females. The exception to this finding is in exposure to perimortem trauma among males and females in Autonomous Communities, where the posterior density estimates overlap almost entirely. The difference between males and females is most pronounced in State societies, a pattern we discuss below. Finally, we partially support our third expectation that trauma for females is correlated with antemortem and perimortem trauma for males. Specifically, we find support that antemortem—but not perimortem—trauma in females is correlated with trauma in males.

Discussion

One of the most striking finds of our model is the low odds of perimortem trauma among females in State societies when compared to males in the same context. This result corresponds with our expectation that within these societies, warrior males are most frequently victims of lethal violence and conflict (11, 13, 71). State societies have an increased ability to regulate violence within their spheres of influence, with violence occurring primarily within frontier areas and relatively formalized contexts—conducted by male warriors and soldiers (23, 36, 41). Furthermore, the hegemonic influence of the state may act to reduce the frequency of events where females fight with or are attacked by external enemies in lethal encounters by reducing the prevalence of violence within its borders (53, 54).

The odds of antemortem trauma are very slightly reduced in females in State societies, but the effect is much smaller for perimortem trauma, indicating that while the social and cultural structures of state societies may protect females from lethal violence, they are still exposed to nonlethal violence at similar frequencies in other forms of sociopolitical organization. Notably, the odds of both antemortem and perimortem trauma among males do not substantially change between Autonomous Communities, Regional Cultural Formations, or States. Rather than indicating that the frequency of conflict does not fluctuate with changes in sociopolitical organization, a more likely explanation is that males in state military forces may fight in more dangerous ways (23, 72), leading to a similar proportion of males experiencing violence, including lethal violence.

In our analysis, Regional Cultural Formations emerge as a particularly unusual category, with highly dispersed posterior density estimates for both sex and trauma categories. This high dispersal may be partly a result of the relatively low sample size for this category. Alternatively, looser integration in a broader cultural framework and regional practices may allow for a greater diversity and flexibility of the social and cultural norms leading to interpersonal violence than in more rigid hierarchical States and Autonomous Communities. Additionally, the mode of the posterior density estimates for the odds of trauma in Regional Cultural Formations exists close to the mid-point between States and Autonomous Communities. The high dispersal exhibited by this category may be indicative of a broad category of potential influences on violence—such as resource scarcity and sociopolitical needs for war (73, 74).

Modern ethnographic evidence supports the idea that Autonomous Communities engage in conflict through quick and intensely violent raids, largely perpetuated by males against other males as the predominant victims of lethal violence (12, 22, 31, 75). At a cursory glance, our analysis runs counter to this evidence and instead indicates the risk of lethal violence for females was similar to males. We offer the following explanations for these conflicting results: first, females may have been exposed to lethal violence as domestic abuse after capture by male raiding parties. Instances of bride kidnapping leading to fatal injury have been documented in the ethnographic record and may have occurred in the past as well; perhaps as a result of a lack of centralized policing or prevention of homicide within egalitarian societies (26, 46, 76). Second, females might have been targeted in raids and massacres more often than has generally been assumed (77). Third, women may have participated in combat more than is commonly assumed, especially in defense of the community. This hypothesis may be bolstered by evidence that in Andean hunter-gatherer communities, there is evidence that females engaged in hunting practices as well as men (78). By contrast, states generally protect the civilian component of their population from lethal violence, exerting hegemonic control over violence within their sphere of influence.

We find that differences in the frequency of violence between forms of sociopolitical organization are closely linked to gendered roles and behaviors. In other words, an individual’s sex was as important or more important than the kind of society they inhabited in affecting the risk of trauma. Gender, rather than just sociopolitical organization, has a critically important impact on the experience of interpersonal conflict.

Materials and Methods

Data Collection.

The data used in our analysis were collected from numerous published articles, unpublished reports, and gray literature by the second author. This dataset adds newly published reports and atypical contexts (massacres, sacrifice victims) to a recently published earlier version (79). At the time of analysis, the database has a total sample size of 8,607 adults from over 169 publications and over 155 sites. Data are scrubbed from the analysis if the original data source did not provide information regarding the likely sex in the individuals from a given site or if the original data source failed to include information regarding the type of bioarchaeological trauma (perimortem vs. antemortem). Juveniles are not included in our analysis due to the difficulty of establishing osteological sex estimates from this subset of the population (80, 81). Finally, in this analysis, we treat the presence of a given type of trauma as binary—with presence denoted as a 1 and absence denoted as a 0. While injury recidivism is an important factor worthy of investigation, it exceeds the bounds of this study. Individuals with both antemortem and perimortem wounds were counted only once (as perimortem) in Dataset S1.

Bioarchaeologists typically rely on primary and secondary sex characteristics of the skeletal, such as the ventral arc of the os coxa and the mastoid process of the cranium (80–85). These traits are then scored on a scale of 1 to 5 and a composite score is generated; with 1 as most likely female and 5 as most likely male. Although interobserver bias can influence sex estimation (86), we necessarily rely on the sex estimates of the original analysts in our data, The distinctions between perimortem, antemortem, and postmortem traumas can also be influenced by interobserver bias (87), but bioarchaeologists have developed systematic methods for distinguishing between these forms of trauma (18, 19, 80). These can include signs of healing, the patterns of fracture lines, and discoloration, among other factors (19, 80). Again, we rely on the trauma analysis provided by the original analysts for the purposes of this study.

There is a large degree of temporal and spatial variability in the archaeological sites and skeletal populations used in this analysis. The full temporal range of the data is from 8350 BCE to 1550 CE, with archaeological sites from Ecuador, Peru, Bolivia, and Chile included in the analysis. While skeletal data exist from archaeological sites in the Andes that postdate Spanish contact, we exclude these from our dataset due to the intense sociopolitical transformation that occurred as a result of European colonialization and often brutal exploitation of indigenous peoples (82–84).

Sociopolitical Organization.

Mapping sociopolitical complexity onto archaeological sites and cultures is a notoriously difficult and controversial task (88–90). We categorize archaeological cultures and sites as belonging to one of three broad types of sociopolitical organization: Autonomous Communities, Regional Cultural Formations, and States. We sort the Andean archaeological cultures represented in our database into these three categories as follows:

-Autonomous Communities:

Autonomous Communities are classified as those which do not clearly belong to a larger Regional Cultural Framework or State, including hunter-gatherers, isolated fishing communities, and isolated agriculturalists. Autonomous Communities are those for which there is archaeological evidence that people largely managed their own affairs without belonging to widespread hegemonic power structures or regionally dominant cultural-religious networks, as in the wake of state dissolution or prior to the formation of widespread Regional Cultural Frameworks. We classify hunter-gather societies, early agricultural sites, and the balkanized sociopolitical entities of the Late Intermediate Period—especially the pukaras of the Altiplano—under this category (91, 92).

It is important to note that classifying a site in this category does not require the site in question to share no cultural traits with other sites—just strong evidence that sociopolitical decisions were largely managed from within. The archaeological sites of Soro Mik’aya Patjxa and Ayawiri offer good examples of this form of sociopolitical organization in the Andean context in disparate time periods (91, 93).

-Regional Cultural Formations:

Archaeological sites are classified as belonging to a Regional Cultural Formations if there is considerable evidence of shared ideological, religious, and other cultural practices between disparate communities without strong evidence of politically centralized decision-making, the use of violence as a coercive force by political elites, or other hallmarks of the state (37). Within the Andean context, good examples include Chavín de Huantar and Early Nasca (with the regional pilgrimage center of Cahuachi) (94, 95)

-States:

Our final category of sociopolitical organization is the state. In our conception, states are political bodies spanning a large geographic area with a centralized urban core (36, 37). In these societies, there is often evidence for longstanding rigid social classes, dense populations, and centralized political power centralized in ruling lineages. Within Andean contexts, the Inka and Wari Empires, as well as the states of Moche and Chimú, offer prime examples (70, 96, 97). Sites were coded as belonging to this category if they were clearly affected by state influence, even when it is not known whether they were directly controlled. For instance, we coded sites that would have been under the hegemonic control and/or influence of the Inka Empire as "state" to capture potential effects of Inka presence.

After sorting our data, we had a sample of 2,387 individuals from Autonomous Communities, 446 individuals from Regional Cultural Formations, and 2,699 individuals from States. Some burial contexts or skeletal assemblages lack the archaeological evidence required to a determination on the type of sociopolitical organization—these contexts were dropped from our data prior to analysis (flagged as “excluded” in Dataset S1). Where sociopolitical coding was potentially tentative, samples were included but a note was added in Dataset S1 to allow greater flexibility in data reuse. Across all categories of sociopolitical organization, we have a final sample size of 2,832 males and 2,655 females (Fig. 4 and Table 2).

Fig. 4.

Map of the study map. Red dots indicate skeletal assemblages represented in the data.

Table 2.

Sample sizes for sex and sociopolitical organization included in the final analysis

Sociopolitical Org.	Male	Female	Total
Auto.	1,258	1,129	2,387
Regional	244	202	446
State	1,330	1,324	2,699
Total	2,832	2,655	5,487

Statistical Analysis.

To analyze our data, we construct a multinomial logit model in the R statistical computing environment (98). We incorporate unique intercepts for different archaeological sites and skeletal assemblages into our model, accounting for cultural practices, context, and issues of variable sample sizes that could provide sources of assemblage to assemblage variability that should be broadly adjusted for. Our null models for antemortem and perimortem trauma are

$$\begin{array}{c}\text{log}\left(\frac{{\pi }_{ante,asb}}{{\pi }_{none,asb}}\right)={\mu }_{\mathit{ante}}+z_{ante,asb}+{\phi }_{\mathit{sex}}+{\theta }_{\mathit{org}}+{\psi }_{sex\ast org},\hfill \\ \text{log}\left(\frac{{\pi }_{peri,asb}}{{\pi }_{prri,asb}}\right)={\mu }_{\mathit{peri}}+z_{peri,asb}+{\phi }_{\mathit{sex}}+{\theta }_{\mathit{org}}+{\psi }_{sex\ast org},\hfill \end{array}$$

where ${\pi }_{ante,asb}$, ${\pi }_{peri,asb}$, and ${\pi }_{none,asb}$ represent the parameter space for antemortem trauma perimortem trauma, and no trauma per skeletal assemblage respectively, and ${\mu }_{\mathit{ante}}$ and ${\mu }_{\mathit{peri}}$ represent the population wide intercepts for antemortem and perimortem trauma. Finally, $z_{ante,asb}$ and $z_{peri,asb}$ represent skeletal assemblage-specific intercepts for antemortem and perimortem trauma. Our covariates are represented by $\varphi$ for sex, $\theta$ for sociopolitical organization, and $\psi$ which represents the interactive effect of sex and sociopolitical organization. $\varphi$ represents eight covariates, as sociopolitical organization is mathematically modeled as a 1 for the given category and a 0 for all other categories.

We use the Stan modeling language and the BRMS package in the R statistical computing environment to perform our computations using Hamiltonian Markov Cain Monte Carlo methods (99, 100). We choose ~ N (0,2) as a regularizing prior for our models given the relative infrequency of traumatic lesions in the bioarchaeological record and run 2 chains in tandem for a total of 1,000 iterations of the model (750 warm-up, 250 actual). This statistical approach is based on computer-generated stochastic samples from the joint density of the model parameters given the observations (101). The graphical output of these models is posterior densities, which display the sign, magnitude, and uncertainty of model estimates. All scripts and data used in this analysis are available as Dataset S1, Software S1, and Software S2.

Supplementary Material

Appendix 01 (PDF)

Dataset S01 (CSV)

Code S01 (TXT)

Code S02 (TXT)

Data, Materials, and Software Availability

All study data are included in the article and/or supporting information.