The Simulation Model

Our simulation model follows the Overview, Design concepts, and Details (ODD) protocol (Grimm et al. 2010). This protocol is intended to address the criticism that agent-based models lack reproducibility.

10.3.1 Agent and State Variables

The agent in our model was defined as an ancient person with the following variables.

10.3.1.1 Identity (ID) Number and Spatial Placement

The following information was assigned to an agent: an ID number and a coor­dinate position (X: 50 cells, Y: 50 cells) within a two-dimensional space. This space represented only the Northern Kyushu region (a small portion of Japan) and not the entire chain of Japanese islands. The Northern Kyushu region is situated close to the Korean Peninsula and is the location where agriculture was first introduced and from where it rapidly diffused outward. In our simulation model, the simulation space is so abstract that the model space is not directly related to the real geo­graphical one. Our study intends to provide an alternative perspective regarding the conclusions offered by Nakahashi and lizuka (1998, 2008). Thus, we mainly focus on discussing the relative diffusion between agrarian culture and trait genes. Fur­ther, as described below, the diffusion speed of agriculture in our simulation model is determined by the probability of agricultural introduction and the range of dif­fusion. Therefore, considering the gene flow relative to the speed of agricultural diffusion, this abstract space is sufficient to discuss the issues at hand. The size of the space within our simulation is determined by the speed of diffusion of agrarian culture as described below.

10.3.1.2 Sex

The agent was Male or Female.

10.3.1.3 Life Expectancy and Age

Upon creation (birth), an agent was given a life expectancy based on the mortality table.

10.3.1.4 Food Production System

The food production system variables were hunting and gathering or agriculture. This system changed from hunting and gathering to agriculture through the dif­fusion of agriculture based on the assumption that the cold climate from the late Jomon to the early Yayoi period introduced an opportunity for this conversion process (Miyamoto 2009). However, we assumed that the opposite condition did not hold, because there is no evidence of the diffusion of hunting and gathering during this period in the literature.

10.3.1.5 Marriage Institution

The marriage institution variable for the male agent was monogamous or polyga­mous for the Yayoi period. Polygamous marriage was assumed to occur based on descriptions of this type of marriage contained in “Gishi-Wazin-Den,” an ancient Chinese text on Yayoi period customs. According to this text, some men of high status had four or five wives, and there were even some men of normal status who had two or three wives. To date, the type of marriage institution that prevailed during the Jomon period has not been ascertained. While both polygamy and polyandry may have existed during this period, the mathematical model formulated by Nakahashi and lizuka (1998, 2008) assumed that monogamy prevailed among the Jomon people. Therefore, to present a clear alternate perspective in our study, we also assumed that monogamy was the marriage institution of the Jomon people. Additionally, we postulated that sustaining more than one wife—polygamous marriage—requires a surplus of food. Therefore, in our simulation model, if the male agent included both of the following variables: polygamous and a high yielding food production system, namely agriculture, then the agent was assumed to be married to three female agents.

10.3.1.6 Pottery Style

The pottery style variable was either the Jomon style or the immigrant style. In our simulation model, for the sake of convenience, we restricted the pottery style to either the Jomon or immigrant styles. We assumed a continuous change in the characteristics of the pottery style and focused on the issue of which style was dominant. This did not mean that the distinction between these two styles was a discontinuous one.

The argument made by Tsude (1982) that females produced pottery during the Yayoi period is supported by an extensive ethnographic literature (Murdok and Provost 1973). Therefore, within the field of Japanese archaeology, it has generally been held that females produced pottery during ancient times. Additionally, Tanaka and Ozawa (2001) have discussed how cultural diffusion occurred through a ver­tical transmission process within society during the Yayoi period. Based on these descriptions in the literature, we assumed in our simulation model that the new agent (child) borne by a female inherited the mother agent's pottery style.

10.3.1.7 Trait Genes

Trait genes determine trait characteristics. Originally, it was thought that trait characteristics are determined through the involvement of many genes in a complex manner. However, to simplify this for the simulation, in our simulation model, following Nakahashi and Iizuka (1998, 2008), it is assumed to be composed of a major pair of alleles: the Jomon-type gene (J) and immigrant-type gene (T). When a new agent (child) is created (born), the agent inherits either of the father agent's and either of the mother agent's alleles. That is, the combination of alleles of an agent is JJ, TT, or JT. In accordance with these combinations, each agent is classified as one with Jomon or immigrant traits. Specifically, a JJ agent comprises traits of the Jomon people, a TT agent comprises immigrant traits, and a JT agent displays mixed traits (mixed people).

10.3.1.8 mtDNA Macrohaplogroup

The mtDNA macrohaplogroup variable for an agent was macrohaplogroup N or macrohaplogroup M. The mtDNA, which is the cell organelle DNA of mito­chondria, is inherited maternally and is relatively easy to extract from human bone remains. Therefore, mtDNA analysis is a useful way of investigating the origin of the maternal line of ancient peoples. The mtDNA of East Asian populations has been broadly classified into two groups: macrohaplogroup N and macrohaplogroup M (Kivisild et al. 2002; Kong et al. 2003). Results of mtDNA analyses of human bone remains have recently been compiled in Japan. The frequency of mtDNA macrohaplogroups N and M indicates major differences between people of the Jomon and Yayoi periods (Shinoda 2006). Specifically, for populations during the Jomon period, the frequency of mtDNA macrohaplogroups N and M were each about 50 %. In contrast, for populations during the Yayoi period, the frequency of mtDNA macrohaplogroups N and M were about 20 % and 80 %, respectively. In our simulation model, when a new agent (child) was created (born), the agent inherited the mother agent's mtDNA macrohaplogroup as described below.

10.3.2 Process Overview and Scheduling

Our simulation model proceeded according to annual time steps. Thus, the annual time step was a year. Each year, the three submodels of each agent were executed in turn as follows: diffusion of the agrarian culture rule, the marriage rule, and the moving rule. Additionally, agents were processed in a random order during each year.

10.3.3 Design Concepts

Our simulation model corresponded to seven out of the eleven design concepts contained in the ODD protocol (Table 10.1). The model was simple, and we considered that the description of the model and design concepts were sufficient to indicate reproducibility.

10.3.4 Submodels

10.3.4.1 Diffusion of the Agrarian Culture Rule

The diffusion of agrarian culture occurred through neighboring agents and inheri­tance from a parent agent.

In the case of diffusion from a neighboring agent, if the agent's food production system was hunting and gathering, while that of all the other neighboring agents was agriculture within a given cell radius (the extent of diffusion occurring within a cell range was: one cell [narrow], three cells [moderate], and five cells [wide]), the agent's food production system would then be transformed into agriculture. This transformation was based on a given probability (introduction rate: impossible [0 %], difficult [0.1 %], middle [0.5 %], and easy [1.0 %]). Conversely, in the case of inheritance from a parent agent, and according to the marriage rule described below, when a new agent (child) was created (born), the agent inherited the food production system from either the father or mother agent. In this study, inheritance from the father or mother agent was simulated.

10.3.4.2 Marriage Rule

A new agent (child) was created (born) as a result of the marriage of a male and a female agent. The male agent was married to a female agent randomly selected

Table 10.1 Design concepts

• Recognizing whether an agent is near the female agent

from all of the female agents within three surrounding cells.

10.3.4.3 Moving Rule

Within each step, an agent moved one cell in random directions within the simu­lated space.

10.3.5 Initialization

10.3.5.1 Time Span of the Simulation

The time span of our simulation was 300 years (300 steps), extending from the early to the middle Yayoi period. This value was the same as that of the calculated representative example in Nakahashi and Iizuka (1998, 2008). While a new hypothesis, based on Accelerator Mass Spectrometry radiocarbon dating, postulates the start of the Yayoi period to be 500 years earlier than the date suggested by conventional hypotheses, no clear conclusions have been reached. Therefore, in this study, the time span was 300 years which is a more stringent condition for a demographic transition in which the small size of the immigrant population could account for the large majority a few hundred years later.

10.3.5.2 Population Growth Rate Based on the Food Production

System

The population growth rate of agriculturalists was higher than that of hunters and gatherers. We simulated two cases relating to the growth rate of each of the above populations as follows. The growth rate of each population for the first (high rate) case had the same value as that of the example of a representative calculation provided by Nakahashi and Iizuka (1998). The growth rate for each population in the second (low rate) case exhibited the lowest value shown in Nakahashi and Iizuka (1998).

• First (high rate) case: the growth rate of the hunting and gathering population was 0.1 % per year, while that of the agriculturalist population was 1.3 % per year.

• Second (low rate) case: the growth rate of the hunting and gathering population was 0.1 % per year, while that of the agriculturalist population was 0.5 % per year.

10.3.5.3 Speed of the Diffusion of Agrarian Culture

The speed of diffusion of agrarian culture in our simulation model comprised the range of cells associated with the diffusion and introduction rate. The range of diffusion cells corresponded to the distance within which cultural exchange would occur while they were in contact with each other. We assumed three degrees: narrow (one cell), moderate (three cells), and wide (five cells). The introduction rate corresponded to the difficulty associated with the introduction of an agrarian cul­ture. Here, we assumed four degrees: impossible (0 %), difficult (0.1 %), medium (0.5 %), and easy (1 %). The level of difficulty did not relate to agricultural tech­niques, but rather to the adequacy of the environment and culture required for the acceptance of the new agrarian culture. These values were set assuming that even when the range of cells was narrow and the introduction rate was difficult, approximately 300 years were required for the majority of agents to have agriculture.

10.3.5.4 Inheritance of the Food Production System from a Parent

The inheritance of a food production system from a parent was unknown. There­fore, to investigate the extent to which the simulation result was impacted by inheritance from either the father or the mother, we simulated two cases as follows.

• First case (father): a new agent (child) inherited the food production system from the father agent.

• Second case (mother): a new agent inherited the food production system from the mother agent.

10.3.5.5 State Variables of the Initial Jomon People and Immigrants

The simulation run commenced with the initial Jomon people and immigrants whose state variables are described below.

Initial Jomon People

• Trait gene: JJ

• Food production system: hunting and gathering

• Marriage Institution: monogamous

• Pottery style: Jomon style

• MtDNA macrohaplogroup: with reference to Shinoda (2006), 50 % had macrohaplogroup N and 50 % had macrohaplogroup M.

Initial Immigrants

• Trait gene: TT

• Food production system: agriculture

• Marriage institution: monogamous or polygamous in each simulation case

• Pottery style: immigrant style

• MtDNA macrohaplogroup: In total, 62.5 % had macrohaplogroup M and

37.5 % had macrohaplogroup N. The haplogroup frequency of the immigrants’ mtDNA is unknown. However, because immigrants are believed to have arrived via the Korean Peninsula, in this study, the frequency of macrohaplogroups within the current population of the Korean Peninsula (Shinoda 2006) was considered to be the same as that of the immigrants.

10.3.5.6 Spatial Placement of the Initial Jomon People and Immigrants

It is assumed that the immigrants initially arrived from northern coastal areas at the earliest stage. Therefore, in this study, the first immigrants were densely positioned in one area at the start of the simulation run. To investigate the extent to which the simulation result was influenced by this assumption, we simulated two cases per­taining to the spatial placement of the initial Jomon people and immigrants as follows.

• First (dense distribution) case: the initial Jomon people were uniformly ran­domly placed, while the initial immigrants were placed in the center of the upper side of the simulated space (X: 25, Y: 50), assuming that they came from the northern coastal area.

• Second (dispersed distribution) case: Both the initial Jomon people and immi­grants were uniformly randomly placed.

10.3.5.7 Initial Numbers of Jomon People and Immigrants

The initial number of Jomon people was 200 agents and that of immigrants was 1,800 agents referring to the ratio of 9:1 of initial Jomon people and immigrants shown by Nakahashi and lizuka (1998) in their example of a representative cal­culation. We set these absolute numbers of agents as the minimum numbers that were sufficient for matching the results of the numerical calculation provided by Nakahashi and lizuka (1998) with those of our simulation runs. We used the same population growth rates but did not include the gene flow and agricultural diffusion between the two populations.

10.3.5.8 Sex Ratio of Initial Jomon People and Immigrants

A leading hypothesis states that the immigrants were primarily male (Kenasaki 1976). Therefore, to examine the sex ratio of the initial immigrants, we simulated three cases for the initial immigrants’ sex ratio as follows. By contrast, the ratio of Jomon males and females was equal.

• First case (same): the number of males among the initial immigrants was 100 agents and the number of females was also 100 agents.

• Second case (more): 150 male agents and 50 female agents among the initial immigrants.

• Third case (majority): 175 male agents and 25 female agents among the initial immigrants.

10.3.5.9 Ratio Determining Mixed JT Individuals as Those with Immigrant Traits

If agents were genetically mixed, possessing the JT trait gene, then they displayed immigrant traits according to the given ratio. We simulated two cases for this ratio as follows.

• First case (100 %): individuals with immigrant traits at 100 %.

• Second case (50 %): individuals with immigration traits at 50 %.

In the first case, the individuals were determined to be immigrants based on the assumption that a person with even a small amount of immigrant traits is an immigrant.

10.3.6 The Number of Simulation Cases and the Evaluation Index

The total number of simulation cases was 441. This figure refers to cases combining each of the above parameters (Table 10.2) added to the representative example of a simple increase of calculation shown in Nakahashi and lizuka (1998). The simple increase of calculation is a model based on the assumption that numbers of Jomon people and immigrants increased separately without random mating and cultural exchange occurring between them.

For the number of simulation runs, cases that combined a 1.3 % agriculturalist population growth rate with a dispersed spatial distribution of the initial Jomon people and immigrants were run once, considering computational costs. The other cases were run ten times. The random seed value of these ten runs was the same across cases.

Table 10.2 Values of parameters

The main evaluation index in our simulation results was the ratio of people with immigrant traits across all agents. Regarding the demographic transition that occurred during the middle Yayoi period, Nakahashi and lizuka (1998) reported that 80 % or more people had immigrant traits. Therefore, determining whether this figure was close to 80 % or more after 300 years (steps) provided a measure of demographic transition in our simulation. In this study, we referred to the ratio of people with immigrant traits for each run of each case. Additionally, in simulation cases entailing demographic transition, to assess which group played a formative role in Yayoi agrarian culture, we depicted a time series of the diffusion ratio of agrarian culture and the composition ratio of each descendant of the agrarian culture holders.

The diffusion ratio of immigrant-style pottery and the frequency of the mtDNA macrohaplogroup M among the cases were also compared. We assumed that at the onset of the Yayoi period most pottery retained the characteristics of the Jomon style, with the immigrant-style pottery achieving predominance during the middle Yayoi period. Thus, starting with a situation in which immigrant-style pottery was less prevalent compared with Jomon-style pottery, we investigated whether the diffusion ratio of the immigrant-style pottery was higher 300 years later. Further­more, considering that the frequency of macrohaplogroup M within the population during the Yayoi period was about 80 %, we determine whether the frequency of mtDNA macrohaplogroup M was higher 300 years later.

10.4