Innovation rate and population structure moderate the effect of population size on cumulative technological culture

The study investigates how demographic factors, particularly population size and innovation rate, interact with cognitive capacities to shape cumulative technological culture (CTC). Prior work often posited that larger populations enhance cultural complexity, but empirical findings and archaeological records show mixed support. The authors extend a micro-society computational model to simulate populations and ask: (1) How does population size influence CTC across generations? (2) How do innovation dynamics (frequency and type) moderate this relationship? (3) Do individuals rely more on asocial or socially acquired innovations across population scales and over time? The work is motivated by reconciling conflicting evidence about population size effects and highlighting the potentially stronger roles of innovation rate and population structure in explaining observed cultural trajectories.

Classical models (e.g., Henrich 2004) linked larger population size to increased cultural complexity, used to explain cases like Tasmanian cultural loss, while subsequent research investigated toolkit size, learning biases, and population structure. However, archaeological reanalyses and empirical studies often found weak or no correlation between population size and cultural complexity; climate and other factors may explain observed changes. Micro-society experiments sometimes show no benefit or even inhibition of CTC with larger demonstrator sets. Alternative demographic factors have gained prominence: partially connected or fragmented population structures can enhance CTC relative to fully connected networks; social learning strategies (success/prestige biases vs unbiased copying) modulate outcomes, with unbiased copying often weakening population-size effects; innovation rate can cap the benefits of larger populations; and effective population size (linking size and connectedness) better predicts cultural dynamics than raw size. On the cognitive side, both social-cognitive (e.g., theory of mind) and non-social technical reasoning capacities contribute to high-fidelity transmission and innovation, with debates about their relative roles.

Design: The study extends a prior micro-society computational model to run multiple transmission chains in parallel to approximate a population. Each chain holds a variant of a general technology. At each generation, a new cohort replaces predecessors, inherits chain-specific technology, socially learns from one randomly chosen individual in the prior generation (unbiased social learning), modifies their inherited technology, and may innovate asocially with a specified probability. Socially acquired innovations occur when learning from a teacher who possesses innovations absent in the learner’s chain. Population and flow: A population comprises Nc parallel chains (akin to population size). Each generation: (1) individuals inherit the chain’s technology; (2) each individual selects one teacher uniformly at random from the previous generation (global cross-learning); (3) they update their understanding via three components—reverse engineering (observing teacher’s technology), observation (seeing teacher’s modification), and teaching (direct instruction)—and then modify their own technology; (4) they may asocially innovate with probability Pinnovation if criteria are met. Simulations typically run 200 generations and are averaged over 200 runs per condition. Population sizes examined range up to 100 for main analyses; Nc also takes larger values when noted. Technology representation: A technology T consists of n independent traits, each with a quality (initially 1) and a limit (maximum potential quality, initially 2 unless otherwise stated). Technology quality is the sum of trait qualities; technology limit is the sum of trait limits. Innovations increase the number of traits (groundbreaking innovation) and raise limits of all traits (innovative combination), expanding the ceiling for future improvements. Individuals and cognition: Each individual has two cognitive skills: theory of mind (ToM) and technical reasoning (TR). ToM is drawn from a truncated Gaussian in [0,1]. TR is drawn from a truncated Gaussian in [0, TE], where TE represents the individual’s technological environment. TE is computed from the inherited chain technology’s quality plus a small noise term centered on that quality, assuming other environmental technologies are of similar quality. The model posits that richer technological environments yield higher TR. An individual’s knowledge is stored as cogs per trait, allocated heterogeneously up to a pool constrained by TR, allowing specialization. Social learning update: After selecting a teacher, the learner updates trait-specific knowledge using a sum of contributions: reverse engineering (difference between the teacher’s trait quality and learner’s knowledge), observation (improvement seen in the teacher’s technology during modification), and teaching (difference between teacher and learner knowledge), with negative values truncated to zero. Teaching efficacy scales with teacher ToM; learning efficacy scales with learner TR relative to TE. Modification: Post-learning, each trait’s quality is multiplied by a trait-specific factor βi that scales linearly between βdown and βup as a function of the learner’s knowledge for that trait. Default parameters in text set βup=1.2 and βdown=0.6; a parameter sweep indicates robustness. Innovation: Asocial innovation occurs with probability Pinnovation if at least one of two criteria is met: (a) TR criterion: the learner’s TR relative to TE exceeds 0.8; (b) optimization criterion: the current technology is near its limit (quality(T)/limit(T) > 0.8). If neither is met, the opportunity is missed. When innovation occurs, the technology gains a new trait and all trait limits increase. Socially acquired innovation occurs if the teacher’s technology contains innovations absent in the learner’s; the learner adopts the new trait(s) and increased limits, then learns across all traits. Newly added traits start at minimum quality and knowledge for the learner. Outcomes measured: Across generations and runs, the model tracks technology quality, counts of innovations (asocial and social), opportunities and missed opportunities, proportion of innovation types over time and population size, distributions of criteria met for asocial innovations, TR/TE (mastery) and optimization ratio quality(T)/limit(T) across generations and population sizes, innovation propagation speed (generations required for full population adoption), and the moderation of population-size effects by Pinnovation. Simulation settings: Unless stated otherwise, common settings include n=2 traits initially, βup=1.2, βdown=0.6, Pinnovation=0.01, with 200 simulations of 200 generations for each Nc tested (typically Nc from small values up to 100). Additional experiments vary Pinnovation (0.001, 0.01, 0.05, 0.10) to test moderation by innovation rate. Parameter sweeps and supplementary computational analyses (e.g., diffusion trade-off) support robustness.

- Population size effect is nonlinear: Technology quality increases with population size but follows a logarithmic-like function with diminishing returns. Gains are substantial in small populations and limited in large populations; the effect becomes notably constrained around Nc ≈ 100 when Pinnovation = 0.01. - Innovation counts scale linearly: Total number of innovations (asocial + socially acquired) increases linearly with population size. Both innovation opportunities and missed opportunities increase linearly, but the fraction of missed opportunities declines and asymptotes by populations of roughly 20 individuals. - Innovation type shifts over time and size: Early generations and small populations rely more on asocial innovation because social transmission of novel traits is initially unavailable or rarer. The proportion of asocial innovations rapidly drops to about 10% of total innovations as socially acquired innovations dominate with time and size. - Criteria for asocial innovation differ by context: Small populations more often meet the optimization criterion (near-optimized technology) to innovate, whereas large populations innovate primarily via the TR criterion (high technical reasoning relative to environment). In later generations, optimization-based asocial innovations re-emerge even in large populations as technologies become too advanced for individuals to fully master. - Cognitive mastery and optimization dynamics: Individuals’ TR/TE (mastery) peaks in early-to-mid generations, especially in larger populations, while technology optimization (quality/limit) is lowest at those times due to expanding limits from innovations. Small populations, despite lower absolute quality, tend to re-optimize faster after innovations. - Diffusion speed not limiting: The average number of generations for an innovation to spread to all individuals increases only logarithmically with population size, indicating diffusion does not explain the weak size–CTC link in large populations. - Innovation rate moderates size effects: With low Pinnovation (e.g., 0.001), technology quality increases roughly linearly with population size. As Pinnovation increases (0.01, 0.05, 0.10), the marginal benefit of larger populations declines sharply, plateauing around the threshold where the expected number of asocial innovations is about one per generation (approximately Nc ≈ 100 for 0.01, ≈ 20 for 0.05, ≈ 10 for 0.10).

The findings address the central question by showing that population size alone does not linearly drive cumulative technological culture; rather, innovation dynamics and cognitive–demographic interactions control the relationship. Larger populations generate more innovations, yet technology quality does not scale accordingly due to diminishing returns and rapid reliance on socially acquired innovations. The prevalence of unbiased social learning in the model can produce a form of free-riding, where many learners benefit from the few innovators, consistent with Rogers’ paradox, thus weakening size effects without learning biases. The model further clarifies that the mechanism for asocial innovation depends on whether individuals surpass their environment in technical reasoning or whether technologies are near-optimized; this balance shifts with population size and over generations. Diffusion dynamics are sufficiently fast (logarithmic in size), ruling out slow spread as the bottleneck. Crucially, the asocial innovation rate determines when additional population size ceases to matter—once the system reliably produces approximately one asocial innovation per generation, further increases in size yield minimal CTC gains. These insights align with empirical and archaeological reports of weak or context-dependent size effects and point to innovation rate and population structure (effective population size, connectivity) as more decisive determinants.

This work extends a micro-society model to a population-level framework to reconcile debates about demographic drivers of cumulative technological culture. It demonstrates that: (1) population size exhibits diminishing returns, strongly influencing CTC only in small populations; (2) total innovations scale with size, but technology quality does not, due to social learning dynamics; and (3) the innovation rate constrains the benefit of adding more individuals, with a plateau near one asocial innovation per generation. The study highlights innovation processes (frequency, type, transmission) and population structure as key levers beyond raw population size. Future research should incorporate structured and partially connected populations, effective population size, social learning biases (e.g., success/prestige), and realistic costs or criteria for socially acquired innovations to test how these factors might restore or further limit size effects. Empirical validation via laboratory micro-societies and archaeological calibrations of innovation rates and connectivity would strengthen and refine the model’s predictions.

- Fully cross-learning population: Everyone can learn from anyone in the previous generation; real populations are structured, and effective population size may differ from census size. This assumption likely overestimates connectivity and may mask structure-driven effects. - Unbiased social learning: Teachers are chosen uniformly at random; the model omits social learning biases (e.g., success/prestige), which could alter innovation uptake and size effects. - Innovation modeling and transfer: Asocial innovation criteria and the assumption that socially acquired innovations incur no costs may oversimplify real learning constraints. Results depend on how innovations increase trait numbers and limits. Alternative cost structures or criteria for socially acquired innovations could change dynamics. - Parameter choices and simplifications: Selected β parameters, initial trait limits, and distributions for ToM and TR are simplified and, while robustness checks are reported, may not capture all real-world variability. Genetic inheritance, reproduction, and multi-domain technologies are not modeled.