Computational protocol: Settlement Dynamics and Hierarchy from Agent Decision-Making: a Method Derived from Entropy Maximization

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[…] In the method applied, agents are assumed to be households of varying sizes (e.g., single-person, extended, and multi-family households). Key variables that define the model are given here, including those that are static, calculated, and given as user input. These are defined as: S ij = calculated volume of flow (i.e., movement of people and goods) between agent i and settlement j Z ij = calculated social-environmental attractiveness of settlement j to agent i; this represents all factors (e.g., presence of important temples, other kinship groups, etc.) that make a site attractive to settle at a given time c = operational costs, which includes bringing goods and food (e.g., via land transport) to a settlement to enable its continuity d ij = calculated distance between two sites (i and j) based on the natural log of the cost surface b i = weight for the endogenous or exogenous social benefits (e.g., trade with kinsmen), or benefit multiplier, an agent i has with those of similar social, cultural, or kinship backgrounds, enabling agents to be attracted to other like agents t j  = multiplier for endogenous or exogenous benefits (e.g., a distant state providing more goods to a settlement because of an important temple) provided for settlement j m i = the probability that an agent i will move based on negative or relatively low flow (S ij) α j = return of attractiveness for site j (i.e., this scales attractiveness of sites) based on social-environmental benefits (Z ij) β = measure of difficulty for movement (e.g., conflict limiting movement or settlement policy promoting easy movement); low to high β indicates decreasing to increasing impedance in movement between sites, respectively u j = population of settlement j S ij = calculated volume of flow (i.e., movement of people and goods) between agent i and settlement j Z ij = calculated social-environmental attractiveness of settlement j to agent i; this represents all factors (e.g., presence of important temples, other kinship groups, etc.) that make a site attractive to settle at a given time c = operational costs, which includes bringing goods and food (e.g., via land transport) to a settlement to enable its continuity d ij = calculated distance between two sites (i and j) based on the natural log of the cost surface b i = weight for the endogenous or exogenous social benefits (e.g., trade with kinsmen), or benefit multiplier, an agent i has with those of similar social, cultural, or kinship backgrounds, enabling agents to be attracted to other like agents t j  = multiplier for endogenous or exogenous benefits (e.g., a distant state providing more goods to a settlement because of an important temple) provided for settlement j m i = the probability that an agent i will move based on negative or relatively low flow (S ij) α j = return of attractiveness for site j (i.e., this scales attractiveness of sites) based on social-environmental benefits (Z ij) β = measure of difficulty for movement (e.g., conflict limiting movement or settlement policy promoting easy movement); low to high β indicates decreasing to increasing impedance in movement between sites, respectively u j = population of settlement j Of these variables, five of these are user-defined inputs that are tested in scenarios, which are α, β, m, c, and b. The variable u is generally left static as the proxy used mostly as the output to compare to settlement size from surveys. In addition, t is generally left static (i.e., as 1.0 and all settlements are assumed to have equal benefits) and used only in scenarios where specific settlements have advantages or disadvantages that can affect agent choice. In all scenarios, distance (d) is determined using a cost surface analysis as defined by Fontenari et al. (), which accounts for elevation. This variable is calculated using ASTER () terrain elevation data and measures relatively which sites are more or less costly to travel to from a given site. The variable b is an agent factor that could have many values, and a normal random number generator using a standard deviation to create greater variability allows for varied agent types and benefits; however, a single value is used for scenarios as this allows for an averaged value to be tested. The other variables are calculated within the simulation and discussed below.For the following scenarios, model operations are given below in notation and described qualitatively, provided as a downloadable code (see ), and demonstrated in a model flowchart (Fig. ). The download also has additional explanations regarding how to use the model in Repast Simphony 2.1 (), which was used to execute the simulation, and the scenario data are also provided. The notation numbers used here are indicated in the model flowchart, while the flowchart also indicates the names of the model methods (i.e., names used in code provided) that apply the algorithms below. To begin, after the model has been initialized, the first step in the model is called calculateSocioEnvironment:Fig. 3 1nij<→Zij=ujtjnij>=1→Zij=uj+nijtjbij with Z ij representing attractiveness of location j for agent i based on the population (u) of settlement j, benefits of j (t), and, if there are other agents from the same social group (i.e., (n ij ≥ 1)), benefits ( b ) these type i agents provide to a settlement j. This step is indicated as (1) in Fig. . This step calculates settlement attractiveness, or the reason why people want to settle in a given site, for agents based on endogenous and exogenous links the settlement has as well as those brought by agents with similar status, cultural, or kin backgrounds, with b controlling the relevance of this factor. This essentially allows settlements to be viewed for their sociocultural or environmental benefits, with the specifics of these purposely ignored so as to not make the model too rigid regarding a given case. The next method in the model, flowFromTowns, calls (2–4) below. Starting after the first time step, the following is calculated:2Sij=Zijaje−βlndij with S ij representing proportion of flow, that is movement of goods and people benefiting agent i from settlement j, using Z ij to the power of α with e measuring the effects of cost surface d, taking its natural log, and applying β to regulate how easy it is to move. Alpha, in essence, scales the effects of Z, while β regulates the effects of distance on movement flow. What the step does is enable distance, site attractiveness, and β to affect flow or goods an agent can obtain from settlements. The flow value also has a cost based on distance, which is determined below:3Sij′=Sij−c*lndij This calculation, in effect, can limit site flow benefits to an agent based on distance and other costs. While β relates to the ease of movement, cost is intended to reflect production or unit costs for items or people relative to moving in a given landscape. Cost reflects ideas such as land-based transport (e.g., donkeys carrying grain to and from settlements) that have a given energy or production cost affecting flow. The aggregate of (3) for all settlements affecting agent i creates a net flow for i:4Di=∑Sij′SDj=∑Di with (D i) being net flow for an agent and aggregate flow of all agents in a given settlement is SD. This provides a measure to evaluate total goods and flow an agent is getting and what the total flow is for a given settlement based on all agents in that settlement.The next step involves the key agent-based decision-making focused on in the model, with an agent determining to find a new settlement if needed based on negative or low flow relative to other agents. This conditional, or decision made by the agent, is applied in determineRelocate in the model with the relocate method being applied if the conditional is true; if it is false the simulation returns to (1) here. For the two model methods, including the conditional, they are stated as:5Di<0∨DiR⇒npj=1+nij/ujSDj>0→gj=dij/SDj*npj*bijSDj<0→gj=SDj*dij/npj*bijsj=MINgj∈g which determines, in the first part of this method, if negative flow or flow less than the mean flow for all agents and a probability (R), based on a uniform pseudorandom number generator, being less than m to another settlement for agent i results in the agent making a choice to resettle. This, essentially, allows agents to move if they are not benefiting from their current settlement or they may see their economic/social state is less desirable compared with others. The m factor regulates how important this is to the model. In the next part of this method, the choice of which specific settlement to move to, if the decision to move has been made, is based on the number of people (np) at settlement j that belong to the same social/kin group (n) as i relative to the settlement’s population (u). Then another step in this method is calculated based on if total settlement flow (SD) for j is positive or not and what the relative agent benefits (b) are. This calculation determines estimated benefits (g) for an agent based on distance and presence of social groups (np), including the weight of benefits  an agent has (b). In other words, towns, and thus other individuals in these towns, that have a higher benefit and social connection to an agent are preferred, but this could be mitigated by distance or lack of interest (i.e., low b) in moving to locations with similar social/kin groups. In the final step, the smallest g value, which in this case implies the settlement (s) with the greatest benefit, is selected. While using the minimal value of g (i.e., settlement of greatest benefit) may seem too deterministic, the variable t, as will be demonstrated, can allow greater variability in results.In effect, this last step allows agents not happy with their state in their given location to migrate. If they leave, they decide where to go based on kinship/social connectivity, distance, and social-ecological factors affecting settlements’ total flow (i.e., benefits to a settlement), with these factors’ influence affected by the five user-defined inputs discussed earlier. The last and earlier methods, in fact, are all regulated by the input parameters that the simulation will test, allowing for very different circumstances to be studied for their influence on simulation results. After this step, the model returns to (1) until the end of the simulation. […]

Pipeline specifications

Software tools kinship, Repast Simphony
Application Population genetic analysis
Organisms Homo sapiens