Food Income and the Evolution of Forager Mobility

Forager mobility tends to be high, although ethnographic studies indicate ecological factors such as resource abundance and reliability, population density and effective temperature influence the cost-to-benefit assessment of movement decisions. We investigate the evolution of mobility using an agent-based and spatially explicit cultural evolutionary model that considers the feedback between foragers and their environment. We introduce Outcomes Clustering, an approach to categorizing simulated system states arising from complex stochastic processes shaped by multiple interacting parameters. We find that decreased mobility evolves under conditions of high resource replenishment and low resource depletion, with a concomitant trend of increased population density and, counter-intuitively, decreased food incomes. Conversely, increased mobility co-occurs with lower population densities and higher food incomes. We replicate the well-known relationships between mobility, population density, and resource quality, while predicting reduced food income, and consequently the reduction in health status observed in early sedentary populations without the need to invoke factors such as reduced diet quality or increased pathogen loads.


S1. Ethnographic data
A large dataset of information about hunter-gatherers from all over the world is provided by Kelly (1). This data includes details of hunter-gatherer mobility behavior and the environments in which the groups live. A summary of how often people move, how far they move, how dense their groups are, their mortality, and fertility rates, from the Kelly (3) dataset is shown in Table S1. Table S1. Summaries of the cleaned data collected by Kelly (1) on the mobility, population density (Table 7- Kelly's dataset shows that the number of residential moves per year exponentially decays with increasing population density -this can be seen in Fig. S1. In a study by Mace (2) the relationship between wealth and fertility in the Gabbra nomadic pastoralists was investigated. The number of camels is used as a proxy for wealth and 848 households are included in the study. Mace   Based on the work by Mace (2), discussed in SI Appendix section 1, the relationship between wealth and fertility can be modelled as where the and are constants. We use this relationship between agent food income (which can be thought of as a measure of wealth) and fission probability (which should be proportional to fertility). Hence we take, The upper limit for the probability of fission, !"# , will be reached when agent food income is 1. Hence !"# = + (1), and thus = !"# . Since the probability of fission is 0 when food income is at its minimum, !"# , then we can find , .
Thus by substituting these we have The maximum number of agents that can survive at a site is We can find an estimated value for !"# by using data on hunter-gather fertility and mortality from Kelly (1). Using this data we found that the average fertility rate of the sample of hunter-gatherer groups is 5.7, with a minimum of 2.6 and a maximum of 8.5, and the average mortality for children < 15 years old is 35.3%.
Assuming that children under 15 are not reproductive, then using the average childhood mortality, the proportion of children who survive to reproductive age is And thus the number of children a woman will have that survive to a reproductive age is the proportion that survives to reproductive age multiplied by the total fertility rate.
From the ethnographic data this is a minimum of 0.647×2.6 = 1.68 children and a maximum of 0.647×8.5 = 5.5 children (using the minimum and maximum total fertility rates respectively).
For the family units in my model (the agents), we assume that two children need to stay in the family to replace the previous generation, but any other children can form new families. Therefore we find the family fission probability every year should be If we set the generation time to 25, then the lower fission probability is 0128 (in effect this is 0), and the upper fission probability, !"# , is The modelled relationship between food income and fission probability using !"# = 0.14 can be seen in Fig. S3. The number of years until there is a new family based on these fission probabilities is simply 1 .

S3. Modeling mutation
When strategy mutation happens the distribution the new strategy is picked from is dependent on both the family's food income and its previous strategy.
We use a Binomial distribution to pick the new mutated strategy value from, where the distribution is influenced by the family's original strategy value, ! , and food income, : This distribution means that if is high then the distribution is narrow and if is low then the distribution is wider and therefore the new strategy may be quite different from the original strategy. Values chosen from this distribution then need to be divided by 100× so that the family's new mobility strategy is between 0 and 1.
Using a Binomial distribution also makes sense as a model for cultural transmission, since the value for the number of components in the distribution can be thought of as the number of components that make up mobility. However, there is the problem that when the family's strategy is 0 or 1 then the variance is 0 (variance = * * (1 − * )).

S4. Calculating site attractiveness for movement
If a family moves site the site it moves to is determined by proximity and site quality.
All the site 'attractiveness' scores, , are calculated and the site the family moves to is then picked weighted by these values. The attractiveness of site to a family that was previously at site is calculated as where !,! is the distance between site and site , and !"# is the maximum distance possible in this region. ! * is the potential food income a family could have at site and is calculated as ! is the foraging quality of site and ! is the number of agents at site .
A visualization of calculating site attractiveness can be seen in Fig. S4.

S5. Site size and the maximum number of agents
We can estimate the size of the region we are modelling from the ethnographic data found in (1). We found that the maximum total distance moved each year by the hunter-gatherer groups in the dataset given in (1)  The maximum population density will occur when there are !"# agents at every site and the minimum will occur when there is one agent in the entire region. I will assume a family has four members, and therefore the number of people is 4 multiplied by the number of agents. Thus for the maximum population density 4 !"# = 2.665 persons/km ! and for the minimum population density where is the area of a hexagon, In a region of 10×10 hexagons then ! ! = 100 and by rearranging these equations = 10km 2 and !"# = 6.66. Since we must have a discrete value for !"# and we want the population density to fall in the observed range of [0.004, 2.665] persons/km 2 then we will use !"# = 6 as a default value.
Using these values we can rearrange these equations to find = 1.96km. Thus using a 10×10 region we are modelling a region of 1000 km 2 which can theoretically support a maximum of 600 agents (although practically this will be limited by other parameters).

S6. Model properties over time
The

S7. Food income oscillations
We ran the model 50 times with low mobility parameter values and 50 times with high mobility parameter values -shown in Table S2. With the exception of ! these parameter values were the mean values found in the most and least mobile simulations (Table 3, main text).  Fig. S7. and 25th percentiles), the mean food income value and the mean mobility strategy were calculated for each agent in each of the low and high mobility simulations. The distributions of these values can be seen in Fig. S8 and Fig. S9. From these we see that the IQR for food income is generally higher in the agents in the high mobility simulations than the agents in the low mobility simulations. The mean IQR of the food income values for each agent in the low mobility simulations is 0.14 and in the high mobility simulations is 0.20. A Welch two sample t-test reveals there is a statistically significant difference in these means (t-score = -22.7 and p-value < 2.2e-16).