Background

The use of artifact class and stylistic richness as measures of behavioral and cultural diversity has a long history in archaeological thought, beginning with the theoretical paradigm of culture history (see Conkey and Hastorf Reference Conkey and Hastorf1990). Viewed through the lens of culture history, variation in material culture could not be readily explained by the same processes that dictate biological change (e.g., Currie Reference Currie2013). But brewing social and cultural changes in 1960s America drew archaeologists to a practice that could help analyze and explain the range of differences and similarities that constitute the human condition through an analytic and often Darwinian lens (Goodale Reference Goodale and Prentiss2019). Whereas Binford (Reference Binford1962:218) identified culture as an “extra-somatic means of adaptation for the human organism,” Dunnell (Reference Dunnell1980) and other early evolutionary archaeologists focused on the mechanisms driving cultural variation and the evolution of material culture. As applications of processual archaeology expanded, they broadly acknowledged the importance of environment, population density, social organization / risk sensitivity, and cultural transmission as means of driving material culture change (see Eerkens and Lipo Reference Eerkens and Lipo2007; Prentiss et al. Reference Prentiss, Walsh and Foor2021, Reference Prentiss, Walsh, Foor, Tehrani, Kendal and Kendal2023; Walsh et al. Reference Walsh, Riede, O'Neill and Prentiss2019).

During this time, researchers began using evolutionary-informed models to identify the learning strategies by which people acquire culture, defined as complex, accumulated, socially learned behaviors, skills, knowledge, values, and beliefs (Cavalli-Sforza et al. Reference Cavalli-Sforza, Feldman, Chen and Dornbusch1982). Because cultural information varies, can be inherited, and competes for behavioral representation, natural selection should produce cognitive structures to guide social learning toward better-choice outcomes. Accordingly, cultural evolutionists have identified several social learning mechanisms that can result in adaptive outcomes across a range of environmental and social conditions (Boyd and Richerson Reference Boyd and Richerson1985). They predict that accuracy of learning, availability and quality of demonstrators, and costs of learning will affect how an individual finds it most efficient to learn (Kameda and Nakanishi Reference Kameda and Nakanishi2002; Kendal et al. Reference Kendal, Rendell, Pike and Laland2009; McElreath Reference McElreath2004; Rogers Reference Rogers1988). Thus, the costs and benefits of different social learning strategies are affected by the same overarching drivers of technological changes: environmental conditions and population size.

General Simulation of Social-Ecological Conditions and Learning Strategies

Archaeological data, cultural evolutionary models, simulations, and experiments all show that population size, selective pressures, and environment affect the incubation and spread of new cultural ideas and technologies (Derex and Boyd Reference Derex and Boyd2016; Derex et al. Reference Derex, Perreault and Boyd2018; Kolodny et al. Reference Kolodny, Creanza and Feldman2015). Clearly, gaps exist in our ability to understand these dynamics. These gaps are sometimes the result of patchy archaeological and environmental records, but we also often lack the ability to measure and predict complex mechanisms such as the rate of drift and selective pressures. Models enable us to explore how tweaks in these variables affect the degree and types of innovation we may expect within any specific population. To explore our predictions of cultural evolution patterns and implications for the archaeological record, we first simulate a population living in an environment that varies over time. Although simulated environments must necessarily sacrifice reality for generality, they allow us to logically test our assumptions about how the world works and to further interrogate our hypotheses and their implications as being consistent with empirical observations. We provide an agent-based simulation to explore how a population's social learning mechanisms evolve based on a variety of parameters, including the rate of environmental variation and the number of individuals people can look to when choosing someone to imitate. We use the archaeological record and previous cultural evolution models to constrain the multidimensional parameter space to investigate patterns of interest. We structured the base model around Rogers' paradox so that we could test for validity with each additional parameter setting (Rogers Reference Rogers1988). Curious readers are welcome to visit the github site to run basic versions of the model with just unbiased imitation (random copying) and individual learning to explore proofs of concepts; for example, increasing rates of environmental variation are correlated with higher proportions of individual learners in a society (https://github.com/matthewclark1223/MindToMatter/tree/main). We explore more complex versions later and hope others may find the simulation a useful tool for testing their own hypotheses.

In our simulation, there is one adaptive behavior for the environmental state occurring per given time period, which changes between time periods with a given probability. After birth into our population, each individual has the chance to acquire the adaptive behavior for the current environmental state. If they acquire the correct behavior, they receive a corresponding fitness benefit. After learning, each individual will be given the chance to reproduce into the next generation with a probability weighted by their fitness. Over time, the learning strategy that produces the adaptive behavior more often will increase in frequency in the population. One caveat we discuss later is that we can also set the cost of using each learning strategy (proportional to the potential benefit gained); therefore, the fitness outcomes of a particular learning strategy will depend on the cost/benefit ratio and adaptiveness to the ecological context. We can also set the accuracy of learning strategies (the proportion of time the adaptive behavior is not only observed but is also copied correctly to the same effect), so there is still a chance that individuals will be unable to acquire the adaptive behavior even with the best-choice strategy.

Individuals inherit a learning strategy from a parent (this is a haploid sexual model) and will be one of several types: individual learners (learn on own), unbiased social learners (randomly copy), content-biased social learners (observe a sample and copy the best), kin-biased learners (learn from parent; not included in the analysis of this article), or success-biased social learners (choose to copy weighted by the model's fitness; cf. Henrich and McElreath Reference Henrich and McElreath2003). Before reproduction and death, individuals can act as cultural demonstrators for the population in the next generation (generations are nonoverlapping). We use roulette selection as a reliable model of inheritance because it works within the framework of Wright-Fisher analytical models (Zhang et al. Reference Zhang, Sakamoto and Furutani2008). We assume that the learning strategy phenotype is a polygenic trait in an organism with infinite loci; the phenotype depends on the inheritance of a combination of alleles at each of the loci for the learning genes.

We begin each simulation by setting up the population size and costs of learning, set any additional variables of interest (accuracy of learning, sample size of learning), and then simulate outcomes across a range of rates of environmental variation. We keep the selection pressure on learning at 20% following the average selection pressure of 16% on most quantitative traits in the wild (Kingsolver et al. Reference Kingsolver, Hoekstra, Hoekstra, Berrigan, Vignieri, Hill and Hoang2001) and genetic moderate mutation rates at 5/1,000 replications (we also demonstrate results at 1/1,000 and 1/100 replications for context). Initial simulation begins with the frequency of individual and social learning alleles surrounding a normal distribution with a mean of 0.5 and standard deviation of 0.1, with additional results varying the starting proportions of individual and social learners. We allow each population to complete 5,000 generations and report the average for the frequency of each learning strategy from the final 200 generations.

Finally, we provide some notes on the model structure for those analytically inclined. First, almost everything in the model is adjustable, from the mutation rate to the number of generations used to calculate fitness. Necessity requires us to choose parameter settings; we report on combinations of variables that we think are of interest to our readership, although you may want to explore other settings. In an effort to limit their complexity and increase the interpretability of our model results, we make several key simplifications: (1) we test scenarios of varying population size but do not impose spatial structure on this population (discussed later); 2) we do not allow cumulative learning to occur, justifying critiques along the lines of Rogers' paradox; and (3) populations evolve through a hierarchical structure of learning strategies, allowing each to mutate and come to fixation after asking whether a previous learning strategy was more or less adaptive. This introduces a structured interdependence of the evolution of learning mechanisms that may be of interest to some (and is also modifiable to those familiar with R). Finally, although the potential to also explore a kin-biased learning mechanism is included in the code, we do not have the space to provide the analysis here. Feasibility tests of the model show that setting the learning parameters to favor any learning strategy over another does indeed lead to that strategy's success. The figures show results from varying combinations of parameter settings including (1) population size of 10–10,000 individuals, (2) rate of environmental change from 1%–60% every generation, (3) mutation rate of 1/100–1/1,000, and (4) selection pressure of 20%–40%. Baseline conditions of simulations from which we vary the parameters are as follows.

General Simulation Results

Increasing Environmental Variation Leads to a Greater Reliance on Individual Learning

As a baseline and test of validity, we explore a dynamic where we allow our population to evolve learning strategies across a range of rates of environmental variation. We set the parameters so that each learning bias is equally penalized (50% of the benefit of learning the adaptive behavior is sacrificed during the learning process), none is favored in terms of accuracy, and 50% of the population employs individual (versus social) learning in the first generation. Under these conditions, we observe that, as the likelihood of the environment changing between generations increases from 1% to 60%, the proportion of individual learners in the population increases, and the proportion of individuals employing all social learning strategies decreases (Figure 1). We also observe a general trend of decreased overall population fitness as the rate of environmental change is increased.

Figure 1. One run of the agent-based simulation. Colored lines show the proportion of the population employing each learning bias in the final 200 generations of 5,000 total. Mean population fitness across all types of learners is included along with the proportions of individual learners. The simulation parameter settings for Figure 1 are as follows: Population size = 1,000; Mutation rate = 0.005; Success rate of individual learning = 50%; Cost of evaluating content = 50%; Cost of success biased learning = 50%; Cost of random copying = 50%; Cost of kin-biased learning = 50%; Probability that success-biased learning leads to the appropriate cultural variant = 50%; Sample size of observable individuals for content-biased learning = 3; and the starting proportion of individual learners in the first generation is 0.5. (Color online)

Figure 1 shows results for conditions that favor a content-biased social learning strategy when we allow learners to sample several cultural models and choose the most effective behavior, with a sample size of three. Using a smaller sample size than three cultural models made the content-biased learning strategy too ineffective to evolve, and a sample size larger than three did not increase the fitness of content-biased social learners. However, this bias can continue to outperform individual learners, even at higher rates of environmental change, if it starts in the majority. Yet, there are many conditions produced in these simulations that result in no clear winner for learning strategies. Any learning bias that is set to be cheaper (and more accurate) evolved to fixation because the costs of the learning bias affect an individual's likelihood of reproduction. These costs may vary by the thing to be learned or the social situation of the learner, further producing variability to be explored in the future.

Increasing Population Size Decreases Variability in the Mixes of Social Learners

Across populations of 10, 100, 1,000, and 10,000 we can observe decreasing variability in the proportions of individual learners and unbiased imitators (Figure 2). As population size increases, clear trends in selection for learning types emerge at different rates of environmental change. Smaller archaeological populations may have more randomness in the types of social learning that people use (not just the traits they have available to copy), with drift-like processes affecting how people may learn new technology; these processes then affect the nature of technological evolution. We ran the simulation 10 times at each population size.

Figure 2. Ten runs of the simulation at each rate of environmental variation across a range of population sizes from 10 to 1,000 individuals. Simulation parameters are the same as for Figure 1, with the exception of population size. Dashed lines show median trends in proportion of different learning strategies. (Color online)

Increasing the Mutation Rate Has a Similar Effect to Increasing Population Size

We allowed for more extreme mutation rates of 1/1,000 and 1/100 compared to our baseline of 5/1,000. Under the reduced mutation rate (1/1,000), we see reduced variation in learning strategies that emerge at lower levels of environmental variation, indicating that there is not enough variation in the population for selection to find the optimal strategy. Additionally, compared to when the mutation rate is very high (1/100), we observe a more marked shift from biased social learning to individual learning as the rate of environmental change increases, using the intermediate, baseline mutation rate. Instead, under the high mutation rate, we observe that intermediate rates of environmental change drive the evolution of an unbiased imitation learning strategy (Figure 3). Again, we ran the simulation 10 times at each level of environmental variation.

Figure 3. Ten runs of the agent-based simulation for each of three mutation rates. Colored lines show the proportion of the population employing each learning bias in the final 200 generations of 5,000 total for each of the 10 runs. Dashed lines show the median proportion of the population employing each learning bias across the 10 runs. The simulation parameter settings are identical to those shown in Figure 1, with the exception of the mutation rate. (Color online)

Case Study: Adoption of the Bow and Arrow in the American West

Given archaeologists’ interest in leveraging agent-based models to explore past phenomena, we return to the bow and arrow case study and use our model to test the underlying assumptions of the Bettinger and Eerkins (Reference Bettinger and Eerkens1999) scenario. To restate, Bettinger and Eerkins hypothesize that the variability in arrow form observed between eastern California and central Nevada is the result of two different forms of knowledge transmission—a direct or content bias learning involving trial and error, and an indirect bias to copy successful individuals, instead of traits—each driven by underlying population dynamics. We extrapolate values for eastern California and central Nevada (Figure 4) prehistoric population density and environmental variability, as described later, to set the starting parameters for our model and to explore how environmental and population differences lead to forms of cultural transmission that could manifest differences in tool form observed in the archaeological record.

Figure 4. Locations of source assemblages examined in Bettinger and Eerkens (Reference Bettinger and Eerkens1999); central Nevada including Monitor Valley and eastern California including Owens Valley, California.

Population estimates for eastern California are derived from Steward (Reference Steward1933, Reference Steward1938) and recent deep-time population constructions for the Owens Valley, the western Sierra, and Deep Springs areas (Eerkens Reference Eerkens2003; Polson Reference Polson2009). These sources place population densities at 0.17–0.34 persons per km² during ethnographic times, and 0.08–0.16 persons per km² at approximately 1500 BP. The total population at 1500 BP was likely somewhere between 1,000 and 1,500 individuals. Annual precipitation for the Owens Valley, the western Sierra, and Deep Springs as reported by Eerkens (Reference Eerkens2003) averaged 25.9 cm. Broader precipitation trends for Inyo and Mono Counties, California, from 1900 to the present record annual rainfall at 15.5 cm for Inyo County and 39 cm for Mono County (National Centers for Environmental Information, https://www.ncei.noaa.gov/pub/data/cirs/climdiv/). Together, modern annual precipitation calculations across the areas of interest amount to an average of 26.8 cm annually. Deep-time environmental reconstructions for the Owens Valley and Mono Lake areas show peaks in aridity and low lake stands from 2500–1800 cal BP (Mensing et al. Reference Mensing, Sharpe, Tunno, Sada, Thomas, Starratt and Smith2013, Reference Mensing, Wang, Rhode, Kennett, Csank, Thomas and Briem2023; Stine Reference Stine1990) preceding the uptake of bow and arrow technology. Termed the Late Holocene Dry period (LHDP), this megadrought appears to have been more pronounced in central and southern Nevada than in northern Nevada and outside the Great Basin generally. We cannot know with certainty the pace of climate change after the LHDP; however, a wetter period did follow, although the overall trend toward increasing aridity persisted through about 500 cal BP. Thus, we expect precipitation in eastern California to have been lower during the period of bow and arrow adoption, though how much lower is difficult to infer.

Population density for central Nevada, again derived from Steward (Reference Steward1938), ranged from 0.12 to 0.11 persons per km² in ethnographic times. Population reconstructions, as have been done for Owens Valley, are not available for this region. However, for the purpose of our model, we need not calculate exact population numbers but rather note that the population in central Nevada was likely significantly smaller, perhaps by as much as half, than that in eastern California. Under this assumption we estimate a low value of between 500 and 750 individuals, though that number may have been even smaller. The Monitor Valley and surrounding areas also experienced the LHDP megadrought described earlier, and possibly to a greater extent than did the Owens Valley (Mensing et al. Reference Mensing, Wang, Rhode, Kennett, Csank, Thomas and Briem2023). Recent climate reconstructions for the alpine villages of Alta Toquima and nearby Dakabah, which are adjacent to Monitor Valley, demonstrate past variability. Inferred projections for past millennial fluctuations suggest warmest/cold intervals ranging from +2°C to −2°C relative to mid-twentieth-century means (Millar et al. Reference Millar, Charlet, Delany, King and Westfall2019; Thomas Reference Thomas, Bean, Burns, Canaday, Charlet, Colwell and Culleton2020). Modern precipitation trends for Nye County, Nevada (1900 to present), average 20 cm total precipitation annually (https://www.ncei.noaa.gov/pub/data/cirs/climdiv/). Given the severity of the LHDP, we expect that there was likely less precipitation in this area during the period of bow and arrow adoption.

We use these data to derive parameter settings for the model. First, we begin with a low-number population estimate of 500, which is representative of the central Nevada population. We run the model across populations up to 2,500 people in size (an estimate higher than any projected for precontact populations). We then run the model across a range of environmental conditions with the likelihood of environmental change between generations ranging from 1% to 50%. We assume a moderate mutation rate at 5/1,000 replications in each sweep. We model selection pressure at 20% and 60%.

Results

Lower Rates of Environmental Change Promote Social Learning, and Higher Rates Push Individual Learning

When we simulate across a range of conditions of increasing environmental variation and population (averaging across 10 runs of the simulation), we observe that environmental variation has a much stronger effect on the percentage of individuals who use individual learning (Figure 5). At low rates of environmental change, almost everyone in the population, regardless of size, uses social learning; at high rates of change, they use individual learning. We calculate the proportion of social learners to include all types of social learning.

Figure 5. Heat maps of 10 runs of the simulation across different combinations of rates of environmental variation and population sizes, for three selection pressures: (A) 20% selection pressure, as was used for previous results; (B) 40% selection pressure; and (C) 60% selection pressure. Darker cells indicate a higher proportion of all types of social learners; lighter cells indicate higher proportions of individual learners. (Color online)

Increasing Selection Pressure Increases the Proportion of Social Learners in the Population

When we run the same set of simulations while increasing the selection pressure of learning the adaptive behavior for the environment from 20% to 60%, we see an increase in the proportion of social learners in the population (Figure 5). Only at very low and very high rates of environmental variation, and for smaller population sizes, do we see the dichotomy produced in populations with the more moderate rate of selection pressure.