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Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in stochastic growth rates has been shown to be the critical driver of wealth inequality over long time scales. However, we still lack a general statistical theory that systematically explains the origins of these heterogeneities resulting from the dynamical adaptation of agents to their environment. In this paper, we derive population growth parameters resulting from the general interaction between agents and their environment, conditional on subjective signals each agent perceives. We show that average wealth growth rates converge, under specific conditions, to their maximal value as the mutual information between the agent’s signal and the environment, and that sequential Bayesian inference is the optimal strategy for reaching this maximum. It follows that when all agents access the same statistical environment, the learning process attenuates growth rate disparities, reducing the long-term effects of heterogeneity on inequality. Our approach shows how the formal properties of information underlie general growth dynamics across social and biological phenomena, including cooperation and the effects of education and learning on life history choices.

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In much of the developed world, the direction and patterns of urban growth have been the subject of public debate. Some scholars and practitioners believe that the current urban development pattern are too outward-oriented and are concerned about its possible negative consequences. Others defend outward expansion, arguing that it fulfils consumer preferences and promotes economic growth. Despite a sizeable literature on the topic, the discussion has been hampered by a lack of knowledge about how growth is perceived by key "agents of change", those individuals whose decisions and activities affect the direction and patterns of urban growth. Additionally, the news media often represents the urban growth debate in simplistic, oppositional terms (e.g. "pro-growth" versus "anti-growth", "pro-business" versus "anti-environment") with little or no regard for local factors that affect development patterns in specific situations. As described in this article, we used a multi-method case study approach to address these limitations and to better understand recent urban growth issues. The primary goal of this study is to assess multiple perceptions of urban growth and management debate in London, Ontario. As elsewhere, the issue of urban growth patterns is intensely debated in this case study. However, we argue that discussion on this topic should change from simplistic generalisations to consideration of locale-specific factors that influence urban growth patterns.