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).