Abstract At root, perception converts external information from an environment to signals of use in downstream cognition. We explore a population of interacting perceptual agents whose adaptive internal structure transforms input information to outputs. We show that autocatalytic networks of structural transformations—represented by <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42113_2025_241_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>-transducers—spontaneously emerge. Moreover, their population dynamics—who flourishes and with whom they interact—differ substantially between spatial (geographically distributed) and nonspatial (panmixia) populations. Generally, regions of spacetime-invariant autocatalytic networks—or domains—emerge in geographically distributed populations. These are separated by functional membranes of complementary <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42113_2025_241_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\epsilon $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation>-transducers that actively translate between the domains and are responsible for their growth and stability. We analyze both spatial and nonspatial populations, determining the algebraic properties of the autocatalytic networks that allow for space to affect the dynamics and so generate autocatalytic domains and membranes. In addition, we analyze populations of intermediate spatial architecture, delineating the thresholds at which spatial memory (information storage) begins to determine the character of the emergent autocatalytic organization. Author Summary How did perception emerge in early evolution? The first biological replicators are believed to have been autocatalytic networks of functional molecules that collectively were capable of self-reproduction. In a purely replicative system, though, how could a mechanism spontaneously arise that selects for individuals with different structural properties and transformational capabilities? We answer this question by demonstrating how selection emerges and how the spatial dimension of a population directly affects the nature of successful individuals and their autocatalytic networks. We provide a detailed mathematical model that includes both the spatial population dynamics and measures of structural organization for populations, delineating the algebraic characteristics required for cooperative survival. The results indicate how evolutionary processes can harness the dimension of space to support varying kinds of structural perception and functional collective organization.

Population Dynamics of Perception and Emergence of Translational Membranes

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2025年4月7日

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James P. Crutchfield,
Steve T. Piantadosi

摘要

Abstract

At root, perception converts external information from an environment to signals of use in downstream cognition. We explore a population of interacting perceptual agents whose adaptive internal structure transforms input information to outputs. We show that autocatalytic networks of structural transformations—represented by $\epsilon $ $ϵ$ -transducers—spontaneously emerge. Moreover, their population dynamics—who flourishes and with whom they interact—differ substantially between spatial (geographically distributed) and nonspatial (panmixia) populations. Generally, regions of spacetime-invariant autocatalytic networks—or domains—emerge in geographically distributed populations. These are separated by functional membranes of complementary $\epsilon $ $ϵ$ -transducers that actively translate between the domains and are responsible for their growth and stability. We analyze both spatial and nonspatial populations, determining the algebraic properties of the autocatalytic networks that allow for space to affect the dynamics and so generate autocatalytic domains and membranes. In addition, we analyze populations of intermediate spatial architecture, delineating the thresholds at which spatial memory (information storage) begins to determine the character of the emergent autocatalytic organization.

Author Summary

How did perception emerge in early evolution? The first biological replicators are believed to have been autocatalytic networks of functional molecules that collectively were capable of self-reproduction. In a purely replicative system, though, how could a mechanism spontaneously arise that selects for individuals with different structural properties and transformational capabilities? We answer this question by demonstrating how selection emerges and how the spatial dimension of a population directly affects the nature of successful individuals and their autocatalytic networks. We provide a detailed mathematical model that includes both the spatial population dynamics and measures of structural organization for populations, delineating the algebraic characteristics required for cooperative survival. The results indicate how evolutionary processes can harness the dimension of space to support varying kinds of structural perception and functional collective organization.