1. General principles.
TribeSim is an individual-based model designed to simulate genetic and cultural evolution in a population of a social species. Population consists of competing social groups. Maximum possible group size is specified by a parameter G ; after reaching this limit, the group splits in two halves. Group members engage in cooperative effort to acquire resources from the environment in competition with other groups (we dubbed it ‘collective hunting’, although other behaviours, e.g., collective defence of the group territory, can also be considered in this context).
The environment produces a fixed amount of resources per year (R ). R indirectly determines the maximum possible population size. Average number of groups is determined by the combination of R and G .
The resources acquired by the group are then distributed among the group members. Individuals compete with each other to increase their share. Thus there are two levels of competition: between groups and between individuals, similar to the ‘nested tug-of-war’ model which was previously used to show that between-group competition is a powerful driver of within-group cooperation (Reeve, Hölldobler, 2007).
The outcome of competition, and thus the amount of resources acquired by groups and individuals, depends on behavioural traits that can evolve genetically or culturally. In the current study, we focused primarily on two behavioural traits which we call ‘Hunting efficiency’ (HE) and ‘Machiavellian trick efficiency’ (TrE). Both traits depend on culturally transmitted skills (memes) which can be invented from scratch (with a fixed low probability) or acquired from other group members via social learning. Both traits can also evolve as genetically determined predispositions, but this option was not used in the current study. All individuals are born with genetically determined ‘starting’ values of HE and TrE (10 and 0, respectively).
Higher values of HE benefit the group (HE is a ‘cooperative trait’), because the amount of resources acquired by the group is proportional to the sum of individual HEs of all group memebers who go hunting (‘hunting effort’ of the group) realtive to other groups’ hunting efforts. For instance, if R =3000 and the population consists of two groups with hunting efforts 2000 and 4000, then the groups will get 1000 and 2000 resources, respectively. The higher the hunting effort of a group, the less is the share of other groups. If R exceeds the sum of the hunting efforts of all groups, then each group gets the amount of resources which is equal to its hunting effort. In this case, there is no between-group competition. However, such situation is not likely to last long because the population, under any reasonable parameters that ensure basic survival and reproduction, quickly grows up to the carrying capacity of the environment, after which between-group competition becomes inevitable.
Within groups, the resources are distributed according to the individual values of TrE. If all individuals have equal TrEs, the resources are divided equally. TrE is a ‘selfish trait’: high TrE benefits the individual but not the group. Importantly, the memory capacity of each individual is limited and costly (see below), so if one remembers many HE memes, less space is left for the TrE memes, and vice versa. This makes being a good hunter a somewhat altruistic strategy, while being a skillful trickster is ‘selfish’.
There are three levels of competition and selection.
1. Group selection . Between-group competition for resources and selective survival, growth and ‘reproduction’ (splitting) of the groups result in group selection which favours the development of ‘cooperative’ traits.
2. Individual selection . Within-group competition for a larger share of resources results in selective survival and reproduction of individuals. Individual selection favours the development of ‘selfish traits’ which benefit the individual and are either deleterious or neutral for the group (TrE is mostly neutral for the group because enhanced reproduction of individuals with higher TrE compensates for poor reproduction of individuals with lower TrE, see below).
3. Meme selection . Memes compete for dominance in individual memory and in the group’s meme pool (culture). With all other things being equal, meme selection favours memes that spread faster (those that are easier to learn or require less memory capacity to be remembered). The meme’s fate is also dependent on its influence on the individual phenotypes.
Individuals are diploid and reproduce sexually, with recombination. Genes are not linked (progeny receives one random copy of each gene from each parent). Phenotypic value of a genetically determined trait in a heterozygous individual is calculated as the mean of the ‘genotypic values’ of the two alleles. Pairs are formed at random within groups (between-group migration is a separate process); a pair produces one progeny if the parents have enough resources; both parents invest in progeny; pairs are formed anew each year.
Individuals perform the following types of actions:
1. Machiavellian tricks are performed by individuals with TrE > 0; tricks increase the share of the group resources received by the individual.
2. Learning : acquisition of a meme from another (randomly chosen) group member, initiated by the learner. The probability of success depends on the presence of a meme known by another individual but not by the learner, meme size, free memory capacity of the learner, and phenotypic trait ‘Learning efficiency’ (LE), which can evolve genetically and/or culturally. In the latter case, a special category of memes is added (LE memes).
3. Teaching: active transfer of knowledge from teacher to learner. The probability of success, apart from the factors listed in the previous paragraph, depends on ‘Teaching efficiency’ (TE) which also can evolve genetically and/or culturally (TE memes).
4. Collective hunting to obtain resources from the environment (see above).
5. Useless actions (e.g., ineffective and costly rituals); this behaviour is guided by a special category of memes (‘Useless memes’). This option is used to explore the effect of different factors on the spread of maladaptive cultural traits (Enquist, Ghirlanda, 2007).
Actions 4 and 5 are costly (resources are spent to perform them).
TribeSim can be used to simulate genetic and cultural evolution of several other traits, e.g., ingenuity (chances to invent a new meme), propensity to learn, to teach, to particpate in hunting (those who do not participate are ‘free riders’), to apply costly punishment to free-riders, etc. Here we describe only the options explored in the current study. Other parameters were set to constants, mutation rates of the corresponding genes were set to zero.
The ‘evolvable’ part of the genotype (genes that can mutate and evolve) in most of our experiments included only one gene which determines memory capacity (MC gene). In some experiments we also made genes for LE and TE evolvable. We acknowledge that such traits are usually very polygenic; the simulated ‘genes’ thus can be regarded as large linked sets of genes. However, the genetic details are not likely to significantly affect the main results dicussed here.
Each copy of a gene has a ‘value’ which is directly translated into phenotype (e.g., the starting value of MC gene is 0; thus all individuals in the population initially have zero memory capacity; a heterozygous individual with two copies of MC gene with values 0 and 0.2 has MC=0.1). MC can vary from 0 to infinity, LE and TE vary from 0 (zero chance to transfer a meme) to 1 (100% success rate). Mutations can be positive and negative: they either increase or decrease the value of the gene.
Genotypic values of MC, LE, TE are linked to brain volume: increasing them results in larger brains. Brain volume is a costly trait because the amount of resources needed to produce a child is proportional to the child’s brain volume. This agrees with the idea that parental investment increased greatly in the course of hominin evolution along with the energetic and cognitive demands of the rapidly growing juvenile brain (Leigh, 2012; Hublin et al., 2015).
Memes are stored in memory and affect behavioural phenotypic traits (HE, TrE, LE, TE, and probability of performing a useless action). Memes are rarely invented, can be transferred via social learning and forgotten. Each meme is unique; only one copy of each meme can be stored in individual memory. Each meme is characterized by its category (HE, TrE, etc.), size (or comlexity; the amount of MC needed to store the meme) and efficiency (the increase in the phenotypic trait of an individual who knows the meme). Size and efficiency are positively correlated, but the correlation is weak (like in [Gavrilets, Vose, 2006]). Large memes can only be learned by individuals with sufficient free MC; thus, meme size is limiting its propagation, and MC limits the learning potential of an individual. LE affects the probability of successful meme transfer regardless of the meme size (the reasons for this are discussed below). The chance to forget a meme is fixed (2% per year for all memes and all individuals).
The individual phenotype includes the following variable traits:
1. Propensity to perform useless actions. The trait is calculated as the sum of probabilities defined by the efficiencies of Useless memes. E.g., if an individual knows two Useless memes with efficiencies 0.2 and 0.3, then the propensity to perform useless actions is 0.2 + (1-0.2)*0.3 = 0.44. This means that the individual will perform useless actions with probability 0.44 per year. The cost of useless actions is fixed (1 resource is spent for each action).
2. Hunting efficiency (HE) is calculated as the sum of a fixed genetic value (HE gene was set to 10, mutation rate to zero, in all experiments) and the efficiencies of all HE memes known by the individual. E.g., if an individual knows two HE memes with efficiencies 0.9 and 3.4, then HE = 10 + 0.9 + 3.4 = 14.3.
3. Machiavellian trick efficiency (TrE) is the sum of the efficiencies of TrE memes (TrE gene was set to zero and did not mutate). Like HE, it may vary from 0 to infinity.
4. Learning efficiency (LE) is the probability of succesfully learning a meme. It may vary from 0 to 1. It is calculated as the sum of probabilities defined by LE gene and LE memes. LE gene mutation rate (if not set to zero) is 0.04 per gamete, mutation effect (change in genetically defined LE value) is normally distributed around zero with standard deviation 0.4. If the resulting value of the gene is negative or exceeds 1, mutation is cancelled, and attempt is repeated.
5. Teaching efficiency (TE) is the probability of successfully teaching a meme to a group mate. It is calculated in the same way as LE. In most experiments, TE gene was set to 0, its mutation rate was 0, and TE memes were not allowed. Alternatively, TE gene mutated in the same way as LE gene (see above).
6. Memory capacity (MC) is geneticaly defined and can vary from 0 to infinity. Initial value of MC gene is 0, mutation rate 0.04 per gamete, mutation effect (change in MC value) is normally distributed around zero with standard deviation 0.4. Free memory capacity is MC minus the sum of the sizes of all memes kept in memory.
7. Brain volume is equal to 20 + k1MC + k2LEg + k3TEg , where LEg and TEg are genotypic values of LE and TE. By default, the parameters k1, k2, k3are 1, 0 and 0.
The default set of parameters is described in more detail in Supplementary Table 1.
2. Succession of events during one step of the simulation .
The life of the simulated population consists of steps (years). The following events take place every year.
1. Spending resources on life support: 3 resources per year are taken from each individual.
2. Spontaneous invention of new memes. An individual invents a meme of a given category with probability 0.000133 per year, regardless of the number of meme categories allowed.
3. Spontaneous forgetting of memes. Each individual can forget any meme with probability 0.02 per year.
4. Teaching. Each individual randomly selects a group mate and tries to teach him or her one meme. The meme is selected at random from those known by the teacher but not by the student. If there are no such memes, the attempt fails. If the selected meme is larger than the student’s free MC, the attempt fails. Otherwise, the probability of success is the sum of probabilities defined by the teacher’s TE and the student’s LE.
5. Collective hunting. All individuals who possess enough resources go hunting; the cost of the action is 2 resources. For each group, its hunting effort is calculated as the sum of hunting efficiencies (HEs) of the hunters. If the sum of the hunting efforts of all groups is less than 3000 (R , the amount of resources supplied by the environment per year), then each group receives the amount of resources which is equal to its hunting effort. Otherwise, each group receives its share of 3000 resources which is proportional to the group’s hunting effort.
7. Sharing the resources. By default, the resources obtained by the group are shared equally among all group members (such egalitarianism is reminiscent of the traditional behaviour of some hunter-gatherers [e.g., Hawkes et al., 2001], and even chimpansees often share meat after successful hunting [e.g., Gilby, 2006]). However, if there are individuals with TrE > 0, they perform ‘Machiavellian tricks’ to claim larger share. The resources are then distributed according to the individual values of TrE. Consequently, for a naive (e.g., young) individual it is difficult to survive among skillful tricksters, unless she quickly learns those memes herself.
8. Useless actions. If an individual knows Useless memes, he performs a useless action with probability calculated as the sum of efficiencies of these memes. The cost of a useless action is 1 resource.
9. Learning . Each individual randomly selects a group mate and tries to learn a meme from her. The meme is selected randomly from the memes known by the potential teacher but not by the student. If there are no such memes, ot if the size of the selected meme exceeds the free MC of the student, the attempt fails. Otherwise, the probability of success equals to the student’s LE.
10. Death. The probability of death depends on the individual’s age. By default, it is equal to age multiplied by 0.002. This results in average life span of about 27 years. Additionaly, an individual can die of hunger if he or she does not have enough resources for life support for two years in a row (one hungry year often follows the birth of a child and is not lethal, see below). If an individual does not have enough resources to perform a costly action (e.g., hunting or a useless action), then the action is not performed. If there is only one individual left in the group, he dies.
11. Reproduction. Each individual older than 6 years attempts to form a pair with a group mate and produce a child. Pairs are formed for one year only (serial monogamy). If there are no unpaired individuals in the group, the attempt fails. After the pair is formed, the possibility of producing a child is tested. To produce a child, the parents have to spend the amount of resources which is equal to the proposed child’s brain volume multiplied by 2. 40% of these resources are transfered to the child. If both parents together do not have enough resources, the attempt to produce a child fails. After the child is produced, and if the parents have some resources left, 40% of them are also transfered to the child, and the remainder is distributed equally among the parents. The equality of parents in TribeSim is reminiscent of the supposedely increased paternal care and decreased sexual dimorphism in hominins (Lovejoy, 2009; Stanyon, Bigoni, 2014). For simplicity, the simulated individuals in TribeSim do not have a fixed gender; any two individuals can form a pair and produce offspring.
The child inherits one randomly chosen copy of each gene from each parent. Genes for MC (and sometimes also LE and TE) can mutate and therefore evolve (see above). Mutations occur when the genes are passed from parent to child. The child’s memory is initially empty.
12. Splitting of the groups. If the group exceeds its upper limit G , it splits in two equal groups.
13. Between-group migration. An individual can leave her group and join another (randomly selected) group with a specified probability (0.001 per year by default).