Cumulative technological culture (CTC), the generational improvement of tools and techniques, is a defining characteristic of humanity, enabling our global expansion. While cognitive abilities like high-fidelity information transmission and technical reasoning are crucial, demographic factors also play a significant role. The population-size hypothesis posits that larger populations foster greater CTC, supported by studies linking population size to cultural complexity. However, this hypothesis faces challenges: archeological evidence is not always consistent, empirical studies show limited correlations, and micro-society experiments have yielded mixed results, with some suggesting that population size only has a significant impact in small-scale populations. Therefore, alternative demographic factors such as population structure, social learning strategies, and innovation rate have gained attention. This study aims to integrate cognitive and demographic aspects of CTC by extending a computational model of micro-societies to simulate populations and investigate the impact of population size, innovation rate, and cross-learning dynamics on CTC. The primary research question is to determine the relative importance of population size compared to other factors in driving CTC.

Existing literature highlights the interplay between cognitive and demographic factors influencing CTC. The ratchet effect, enabled by high-fidelity information transmission, emphasizes the role of cognitive capacities like theory of mind. Conversely, the technical-reasoning hypothesis focuses on causal reasoning in understanding and improving tools. While the population-size hypothesis has been influential, linking larger populations to greater cultural complexity, challenges exist. Studies have revealed inconsistencies in archeological support and limited empirical correlations between population size and CTC. Micro-society paradigms have further complicated the picture, showing varying or even negative relationships between group size and CTC in some instances. The influence of population structure (connectivity), social learning biases (e.g., success bias, unbiased learning), and innovation rate have also been explored, with suggestions that these may offer viable alternative explanations for archeological patterns.

The study utilizes a computational model based on the micro-society paradigm, extending a previous model (Bluet et al., 2022) to simulate populations. The model incorporates multiple transmission chains representing individuals within a population, with each chain possessing a variant of a general technology (e.g., different types of bows). A cross-learning structure allows individuals to learn from any member of the previous generation (unbiased social learning). The model includes components for technology inheritance, social learning (incorporating reverse-engineering, observation, and teaching, with the teacher's theory of mind influencing teaching), technology modification, and innovation. Innovations can be asocial (originating from an individual's experience) or socially acquired (learned from others). Asocial innovations are triggered by either high technical reasoning skills relative to the technological environment or near-optimization of the current technology. The model simulates population dynamics over multiple generations, tracking technology quality, number of innovations, and other relevant metrics. The core parameters manipulated include population size (number of chains), and innovation probability (P_innovation). The study averages results over multiple simulation runs to account for stochastic elements.

The model reveals a non-linear relationship between population size and CTC, characterized by diminishing returns as population size increases. While larger populations exhibit more innovations (both asocial and socially acquired), the increase in technology quality follows a logarithmic-like function. The number of both asocial innovation opportunities and missed opportunities scales linearly with population size, implying that larger populations have more potential for innovation but don't necessarily convert it into higher technology quality. In smaller populations and earlier generations, asocial innovations are more prevalent than socially acquired innovations. Asocial innovations are driven primarily by the technical reasoning (TR) criterion in larger populations, while smaller populations rely more on the technology optimization criterion. The analysis of individual knowledge shows that larger populations have individuals with higher TR skills, particularly in early-to-middle generations, while optimization is lower in the same range. This pattern is less evident in very small populations. Innovation propagation speed increases logarithmically with population size, meaning that the increased time to learn from an innovator in a larger group is sufficient to explain the non-linear nature of CTC and group size. The study also reveals that the effect of population size on CTC is strongly moderated by the rate of asocial innovation (P_innovation). When the innovation rate is low, population size has a linear positive impact on CTC, but this effect diminishes as the innovation rate increases, reaching an asymptote when there is approximately one asocial innovation per generation.

The findings challenge the simple population-size hypothesis for CTC, demonstrating that other demographic factors significantly influence the process. The non-linear relationship between population size and CTC suggests that the benefits of increased population size are limited beyond a certain threshold. The crucial role of innovation rate aligns with previous research indicating that the frequency of innovation constrains the effect of population size. The model's results highlight the importance of considering the interplay between asocial and socially acquired innovations, along with the different mechanisms driving asocial innovations (TR vs. optimization). The study underscores the limitations of assuming unbiased social learning and the potential impact of integrating social learning biases on the results. The model's limitations, such as the assumption of a fully cross-learning population, also suggest avenues for future research.

This study demonstrates that the relationship between population size and CTC is complex and non-linear, significantly modulated by innovation rate and potentially by social learning biases. Population size exerts a stronger effect in smaller populations and earlier developmental stages. The results highlight the need to shift focus from population size to other demographic factors and the mechanisms of innovation and its transmission in order to improve understanding of CTC. Future research should explore the impact of population structure, social learning biases, and more nuanced models of innovation and knowledge transfer.

The model simplifies population structure by assuming a fully connected population (cross-learning), neglecting the potential influence of population structure and effective population size. The assumption of unbiased social learning also limits the exploration of the effect of social learning biases. The model's innovation mechanism, while based on existing literature, might not fully capture the complexity of real-world innovation processes. Finally, the assumption of costless social acquisition of innovation is a simplification that might bias results.