A description and sensitivity analysis of the ArchMatNet agent-based model

Model environment

Our model contains three types of agents: people, camps (comprising multiple people), and bands (comprising multiple camps). There are two types of camps: Hunter-gatherer residential camps where individuals live (Binford, 1980; Kelly, 1983); and sites where seasonal aggregations take place (a common practice among hunter-gatherers; Rorabaugh, 2019; Lieberman et al., 1993). Because the camps are stationary, they can also represent villages in small-scale horticultural societies. The model world is a square grid divided into band territories, as well as environmental zones (analogous to different ecosystems). Alternatively, we also include a possibility for the environment to be spatially homogeneous yet changing with a specified probability. Each time step represents a month.

People meet one another through hunting, visiting and engaging in seasonal aggregations. Hunting is done exclusively with people from one’s own band, but visiting is done between allies, which can be of other bands. In the ethnographic literature, it is well-documented that hunter-gatherers tend to travel further distances to visit acquaintances and family members than to carry out subsistence activities (Wiessner, 1977; Hewlett, Van de Koppel & Cavalli-Sforza, 1982; Hill et al., 2014). Similarly, individuals also aggregate with members of their own band (Bahuchet, 1991; Lieberman et al., 1993; Lewis, 2015).

In addition to temporary moves, we also include migration. Migration implies that an individual changes their residence camp permanently. In the literature, one of the key events that marks the permanent migration of people from small-scale societies to a different residential location is the post-marital change of residence (Kelly, 2013; Dyble et al., 2015; Moravec et al., 2018). Given that societies differ with regards to whether only members of one gender or both tend to change residence after marriage, in our model we include also the possibility of gendered migration. That is, of only allowing members of one sex to change their residence camp. This corresponds to patrilocality/matrilocality.

People have cultural inventories of up to 10 pots and 10 points. These two types of objects represent cultural domains that have been hypothesized to be subject to different cultural evolutionary pressures (and therefore respond differently to changes in ecological or social dynamics). This is because they serve different functions. Points, and other subsistence tools must be adaptive for the extraction of available resources in specific environments, which may potentially promote high-fidelity copying to prevent “maladaptive errors” and bias the transmission of certain functional (i.e., more efficient) variants (Arthur, 2009; Rogers, Feldman & Ehrlich, 2009). On the other hand, pots, and other stylistic traits are not necessarily subject to ecological pressures, and instead, their transmission might be affected by other factors such as aesthetics, the desire to converge with others or convey membership to a particular group (Da Silva & Tehrani, 2016). Precisely because of that, we have also implemented two types of cultural transmission: prestige-based and conformist-based. During prestige-based cultural transmission, people identify within their camp location the most prestigious individual, and copies one of their point or pot traits. For points, people acquire prestige depending on the number of successful hunts they have achieved. For pots, prestige can either be deactivated or assigned in a random fashion at the start of the model. When deactivated, a person is chosen at random to be have the highest prestige. We include this option, to include the possibility of popular people’s behaviour to be copied even when the behaviour itself does not have a selective advantage. This is analogous to people copying fashion trends of important individuals. During prestige-based cultural transmission, people identify within their current location the most prestigious individual, and copy one of their point or pot traits. During conformist-based cultural transmission, people identify within their current location the most common trait for a particular tool type, and adopt it.

Objects from those inventories are created based on traits in the agent’s repertoire. Main trait types are represented as integers. People can invent either a new trait type or new variants of a type they know (see Kolodny, Creanza & Feldman, 2015; Creanza, Kolodny & Feldman, 2017 for a similar approach). Variants are represented as discrete letters (a to o only). Each point trait is adaptive in the environment where it was innovated. For example, a point trait created by an agent in one environment will be adapted to that environment and not necessarily in another environment.

The model has an option to include trait visibility. Visibility is essential for understanding material styles and the underlying social behaviors generating them (Wobst, 1977; Carr, 1995a). Some traits, like the size of a pot or large designs, are easy to see. These traits are high-visibility traits. Other traits, like the temper used in pottery, are difficult to see. These are low-visibility traits. Low-visibility traits generally spread through observation of production or active teaching, whereas high-visibility traits can easily be observed in the finished product. When visibility is switched on in the model, high-visibility traits are preferentially learned over low-visibility traits. Traits are given an even chance of being high-visibility or low-visibility, but learning procedures select high-visibility traits most of the time in accordance with relevant literature (e.g., Carr, 1995b; Carr, 1995a; Clark, 2001).

Overview of model dynamics

At each time-step, the dynamics of the model proceed as follows:

1. ENVIRONMENTAL CHANGE: First, if the probabilistic environmental change is specified, the model will randomly throw a die to see if the environment will change. If it does, a new environment will be set. People remove any alliances they have made that exceed the maximum parameter (agents only visit people they have an alliance with and the number of alliances is controlled).

2. INNOVATION: People then have the opportunity to invent new tool types and new variants and create one pot and point each. A person may create a new pot and/or point each time step. Each new object is created based on a randomly selected trait from the person’s trait list. Each object also records the time step when it was created for use in subsequent analyses (as this is analogous to an archaeological date).

3. ACTIVITIES: The model then checks if it is time to aggregate based on a user-specified probability. If it is, people move to their respective aggregation camps. People aggregate for a specified duration, and then go back to their own camp. Whilst aggregating, people are recorded as “visiting” those who they are aggregated with. During aggregations, people can also go hunting with a certain probability.

When people are not aggregating, they can take part in several activities with user-specified probabilities: They can create a new alliance with members of other camps, they can go visit their alliances, or they can go hunting. When hunting, people gather other people from their band and go to a different location together. When the hunt occurs during an aggregation, the hunting site is near the patches of the aggregation sites. When the hunt occurs at other times, the hunting site is simply within the band territory. On a hunt, the hunters have different probabilities to drop a point, trade points with one another, and transmit trait knowledge to one another. Hunters keep track of how many times they hunted together. When the hunt is over, everyone returns to their own camp.

When visiting, one person chooses one ally to go visit at random. They move to that ally’s camp and visit with all the allies present there. The people who are involved in the visit keep track of how many times they visited one another. The people who participate in the visit have different probabilities to drop one pot, drop one point, trade objects with one another, and transmit trait knowledge to one another. When those activities are done, the visitor returns to their own camp.

1. CULTURAL LOSS: All people have a certain probability to forget one pot or point trait.

2. CULTURAL TRANSMISSION: All people have the possibility to exchange the knowledge of traits, and to trade objects from their inventories with one another.

3. GENERATING THE ARCHAEOLOGICAL RECORD: People may drop a pot of a point depending on a set probability. This is what generates the archaeological record in the model.

4. MIGRATION: After the first 1000 time steps, people may migrate every time step based on a probability set by the user. When migration occurs, the person who is migrating chooses another person to switch residential camps. There is also the possibility for gendered migration, whereby only people belonging to one gender can switch camps.

Model outputs

The model has a number of outputs and several ways to access them. The primary output is the raw data. The saveResults option produces four CSV files. These files include the virtual artifact assemblages for each camp, the number of interactions between each person, the metadata for each person (which camp and band they belong to), and a list of all the variables used to run the experiment. There is one drawback for this raw data, as the interaction links can provide inaccurate results when summarized by camp or band due to migration. An aggregating function can be used to produce adjacency tables that include accurate interaction counts between bands and camps. A HighResolutionData option can be used to export these adjacency tables, as well as adjacency tables for the pots and points that show the weighted Jaccard distance between each pair of assemblages at every 1000 ticks. The weighted Jaccard distance provides a value between zero (most similar) and one (most distant) and is calculated as follows: ${\displaystyle J_w\left(x,y\right)=\frac{{\Sigma }_{i}min\left(x_i,y_i\right)}{{\Sigma }_{i}max\left(x_i,y_i\right)}}$

These adjacency tables can also be returned when running behavioral experiments in NetLogo. One additional CSV file can be generated, although it is primarily for debugging purposes. The recordPerson option selects one agent and records each activity and the tick the activity occurred. It outputs this information in a CSV, which can be useful for closely tracking the frequency and timing of activities.

Besides the raw output, there are several other metrics the model can calculate. The showMetrics option produces a number of statistics, shown in Table 1. There are also functions available that can be called from the NetLogo Command Center or Behavior Space. The Jaccard distance for the number of traits held between camps and bands can be computed. Two additional network comparison methods are included: One is an absolute matrix comparison that binarizes the adjacency matrices using the median value and determines the proportion of edges that are shared between the networks. The other metric requires the sr extension enabled in NetLogo, as it relies on the “multinet” (Magnani, Rossi & Vega, 2020) package in R (R Core Team, 2022) to calculate the Pearson correlation coefficient between the network edges. These outputs provide several ways to evaluate the output with or without further analysis.

Environmental factors

The environmental factors relate to the duration of the model and the ways in which we modeled the environment. These parameters are:

• nTicks

• pEnvChange

As expected, the longer we ran our model, the greater the number of pots and points produced (as they are produced at regular frequencies), and the greater number of interactions between agents (as these also occur at regular frequencies). However, running our model for longer did not affect the overall cultural differentiation between assemblages, meaning that the dynamics of the model, and model outputs did not seem to be altered by running our model for more than 2,000 time steps.

Surprisingly, all other things being equal, the frequency of environmental change, pEnvChange, did not significantly affect any of the model outputs. That is, it did not alter the overall cultural differentiation between assemblages, or the frequency of interactions between model agents for any of the activities recorded.

Social factors

Social factors are parameters that control social behaviors relating to population size and the frequencies of various activities. These parameters are:

• aggregationDuration

• aggregationFreq

• campPopulation

• genderedMigration

• huntingGroupSize

• maximumAlliesN

• pHunting

• pMigration

• pNewAlliance

• pTrading

• pVisiting

Similarly to what we observed when running the model for longer, increasing the number of agents in the model through increasing camp populations, or increasing the number of allies people were allowed to have led to more pots and points being produced (see Fig. 4), and a greater number of interactions between agents. However, having smaller camp populations, led to a greater cultural differentiation between assemblages for both pots and points (see Fig. 5).

Increasing the frequency and duration of seasonal aggregations did not affect any of the model outcomes with the exception of the frequency of visit interactions, given that whilst aggregated, the counter for visits between all agents aggregated at the same site increases.

The probability of migration events negatively affected the assemblage size of pots and points (see Fig. 6), as well as the interaction frequency of visiting and trading. Moreover, reduced migration resulted in assemblages being more culturally distinct from one another (i.e., increased the Jaccard distances between assemblages for both pots and points). Interestingly, having only one gender allowed to migrate resulted in a similar effect, even at similar migration rates (see Fig. 7).

The probability of visiting other agents had an effect on the assemblage size of pots, but not of points. At very high visiting probabilities, we also observed reduced Jaccard distances between the pot assemblages of camps. This was not the case when considering differences between the pot assemblages of bands or any of the point assemblages. The probability of visits also affected the frequency of learning and trading interactions.

The hunting probability and hunting group size also affected the frequency of hunts as well as the frequency of trading and learning events. However, more frequent hunts also reduced the cultural differentiation between the pot assemblages of camps. The probability of creating new alliances did not affect any of the model outputs.

Cultural/Material factors

The cultural/material factors relate to the innovation and transmission of traits, as well as traits inherent to the material objects. These parameters are:

• learningMethod

• pLuckyLeap

• pNewVariant

• pNewObject

• potteryPrestige

• transmissionRate

• uniqueTraits

• visibility

• pLoss

Out of these parameters, the one that had the greatest effect on the model dynamics was whether each camp started with unique traits. Figure 8 demonstrates how the Jaccard distance between bands correlates with starting with unique traits. None of the other parameters discussed in this section had a stronger correlation (0.87) with the Jaccard distance between band, but this metric also had no correlation with any other metric.

Another important parameter was the probability of losing a trait (i.e., forgetting a learned or innovated trait). As Fig. 9 shows, the correlation is not straightforward. What is clear is that this parameter is an important part of creating cultural distance as runs of the model with zero loss consistently resulted in small Jaccard distances between bands.

The lucky leap (i.e., invention of a new trait) only had a major affect on one metric: more innovation led to greater Jaccard distances between bands (see Fig. 10). A related parameter, the probability of creating a new trait (pNewVariant), primarily affected the number of traits found in the model but also had a significant effect on the Jaccard distance between bands with more traits resulting in a greater distance between bands.

The probability of creating a new object led to larger assemblages and slowed down the model. It also increased the frequency of trading, as agents create a new object when they learn a new trait. We consider this a natural part of learning. This increases the number of objects available to trade. Sometimes trading does not happen because there are no objects in a person’s inventory.

The learning method significantly affected one metric: the frequency of learning. Conformism involves more people, thus there are more learning interactions. The Jaccard distance between bands was moderately affected by the learning method. Prestige learning increased the distance between bands, and the effect was stronger for pots than points.

Closely related to the learning method is the transmission rate, but this parameter had some of the more interesting results. Increased learning decreased the Jaccard distance between bands when measured by pot traits, but increased the Jaccard distance between band when measured by point traits. Figure 11 shows that the Jaccard distance for pots with low transmission is greater than that for no transmission, but decreases as the transmission rate increases. This is expected as more learning allows traits to diffuse among bands. However, the functional value of points allows the Jaccard distance to continue to increase as the transmission rate increases. More learning was also strongly correlated with the size of the assemblages (as new objects are created when learned). More objects available also increased the frequency of trading. The number of traits was also correlated with learning, as the trait is less likely to be lost, although pot traits were more strongly correlated than point traits.

The parameter most directly related to the object itself is visibility. Once again, pots and points differed in their Jaccard difference for this parameter, but in this case points were negatively correlated. When visibility was on, point traits were more similar between. Whereas pot traits were more distinct between bands when visibility was on. High visibility traits are expected to spread more easily, thus decreasing distance between bands. The fact this did not happen with pots appears to be caused by the lack of any selective pressure. Visibility had a strong, negative correlation with the frequency of learning. There are fewer low-visibility traits, which means that if a low-visibility trait is chosen for transmission then occasionally nothing is transmitted.

Pottery prestige is either assigned randomly at the start of the model or one person is chosen at random as the prestigious individual. Neither method produced any meaningful correlations.