Design for an Individual: Connectionist Approaches to the Evolutionary Transitions in Individuality

What to take away

1. 1. Monotonic non-linear fitness interactions between particles, though non-aggregative, leave the collective explanatorily redundant with respect to the direction of selection on particles, because an increase in a particle character still reliably increases particle fitness regardless of context (Eq. 4 in the paper).
2. 2. Only non-linearly separable functions — where the sign of a particle character's effect on collective fitness reverses depending on the values of other particles, as in XOR or IFF — produce a collective that is non-decomposable in the strong sense required for a genuine new evolutionary unit (Eq. 5).
3. 3. The 'heterogeneous functions with homogeneous fitness' (HFHF) problem states that division-of-labour solutions require phenotypically different particles, yet reproduction through any propagule larger than size one drives particle-level selection on those differences, creating transmission bias that opposes collective-level heritability.
4. 4. Particle plasticity — either phenotypic plasticity (same genotype, different phenotype, as in fraternal transitions) or reproductive plasticity (synchronised reproduction equalising fitness, as in egalitarian transitions) — is identified as the necessary individuating mechanism that decouples particle function from particle fitness.
5. 5. Tudge et al.'s (2016) two-player division-of-labour model showed that natural selection can evolve phenotypic sensitivity enabling complementary differentiation in homogeneous-genotype collectives, but this result has not yet been extended to networks with more than two players or to bottom-up selection without presupposing genetic relatedness.
6. 6. Power's (2019) ecological model demonstrated that individual-level selection acting on inter-specific interaction strengths caused Lotka-Volterra community dynamics to find solutions to Sudoku-equivalent combinatorial optimisation problems — adaptive organisation at network scale without any system-level selection — constituting an existence proof for bottom-up associative learning in evolutionary systems.
7. 7. Single-layer (shallow) interaction architectures, equivalent to single-layer Perceptrons, are provably insufficient to represent non-linearly separable functions, so ETI-capable interaction structures must have at least one hidden-variable layer, making topological depth a necessary (not merely sufficient) architectural condition.
8. 8. Hypothesis H2 predicts that deep model induction in connectionist systems and ETIs share the same four necessary conditions: heritable variation in relational traits, a model space permitting asymmetric feed-forward interactions, repeated perturbation of system state providing a distribution of training samples, and a parsimony pressure favouring simpler network structures.
9. 9. An open question the paper raises is whether the two categorically different non-linearly separable functions — XOR (favouring complementary differentiation, corresponding to fraternal transitions) and IFF (favouring sameness, potentially corresponding to egalitarian transitions) — map onto the two known ETI types in a principled way that could be tested empirically or in simulation.
10. 10. A researcher wishing to test H1 and H2 could replicate the methodological approach of Nash et al. (2021) — evolving asymmetric interaction structures under short-term individual selection with a strong parsimony pressure in a multi-player network — but extend it to include reproductive control as the output of the network's computed function, thereby closing the loop between developmental computation and Darwinisation of the collective.

Peer brief — for seminar discussion

Watson, Levin, and Buckley propose that evolutionary transitions in individuality (ETIs) are the evolutionary equivalent of deep model induction in connectionist learning systems — and that this is a functional equivalence, not a metaphor. Working within the framework they call evolutionary connectionism, they build on a formal equivalence between natural selection acting on heritable variation in inter-unit relationships and unsupervised Hebbian associative learning, previously established for shallow (single-layer, symmetric) networks in evo-devo and evo-eco models (Watson et al., 2016; Power et al., 2015). The key move in this paper is identifying the specific class of interaction structure that a new level of individuality requires: non-linearly separable functions, in which the sign of the effect of one particle's character on collective fitness reverses depending on context (e.g., XOR, or division-of-labour games). This is a strictly stronger condition than the non-aggregative but monotonic interactions discussed by Bourrat (2021), which, as the paper shows through Equations 1–4, leave the collective explanatorily redundant with respect to the direction of selection on particles. The paper introduces the heterogeneous functions with homogeneous fitness (HFHF) problem as the central structural obstacle: division-of-labour solutions need phenotypically diverse particles, but diversity creates particle-level selection that undermines collective heritability. Particle plasticity — either phenotypic or reproductive — is the proposed individuating mechanism that decouples function from fitness. Two hypotheses follow. H1 states that individuality requires a developmental process computing a non-linearly separable function of embryonic particle characters whose output coordinates particle reproduction. H2 states that the conditions for deep model induction — specifically: heritable relational variation, asymmetric feed-forward interaction structures capable of computing non-linearly separable functions (impossible in single-layer Perceptrons per Box 3), repeated perturbational sampling of the selective environment, and parsimony pressure — are jointly predictive of the conditions for a bottom-up ETI. Partial empirical support comes from Tudge et al.'s (2016) two-player phenotypic plasticity result and Power's (2019) Sudoku-based ecological associative memory, but the authors explicitly acknowledge that no unified evolutionary model yet instantiates deep asymmetric interaction structures driving an ETI without system-level selection. An alternative theoretical apparatus the paper does not pursue would be major-transition models using multilevel Price equation decompositions (Bourrat, 2021; Czégel et al., 2019), which could in principle quantify the non-aggregative response-to-selection component the paper needs, but which the authors argue cannot identify causal mechanisms or explain why bottom-up selection would construct the required structures. The most contestable claim is the assertion that non-decomposability (non-linear separability) is not merely necessary but constitutively definitive of a genuine ETI — critics could argue that real transitions like the origin of eukaryotes or chromosomes may be explainable through ecological scaffolding and monotonic synergies without requiring sign-reversal epistasis across evolutionary units, and that the formal criterion of non-linear separability may be too demanding or difficult to operationalise empirically. The prediction that evolving non-linearly separable functions will exhibit the same non-guaranteed convergence and symmetry-breaking difficulties known from backpropagation in deep networks is potentially testable in agent-based evolutionary simulations and constitutes the paper's most specific empirical handle.

Frameworks (2)

• Evolutionary Connectionism
  Proposed framework translating connectionist learning principles into natural selection domain to explain ETIs.
• Evolutionary Transitions in Individuality (ETI)
  Theory explaining how new levels of biological organization and individuality emerge through transitions in collective intelligence and problem-solving rescaling.

Findings (7)

• Planaria reproduce by fissioning without a cellular population bottleneck and accumulate somatic diversity, yet maintain holistic morphology and behaviour (Lobo et al. 2012)

  Finding showing genetic heterogeneity is not necessary for organismic individuality

• Cancerous growth can be induced by disruption of electrical coordination signals and reversed by re-establishing them, without genetic changes (Levin 2021a)

  Empirical finding in developmental biology that supports organismic individuality independent of genetics

• Gene regulatory networks can evolve associative memory, storing and recalling multiple phenotypes from partial selective cues (Watson et al. 2010)

  Demonstrates information integration in evolutionary systems with system-level selection

• Natural selection can evolve phenotypic plasticity that solves division of labour games in two-player collectives (Tudge et al. 2016)

  Shows plasticity as solution to HFHF in minimal models with homogeneous genotypes

• Power's ecosystem model with individual-level selection on interaction traits evolves to solve Sudoku puzzles (Power 2019)

  Demonstrates that ecological networks can learn complex problem-solving without system-level selection

• Ecological community networks can evolve associative memory under individual-level selection (Power et al. 2015)

  Shows that systems can learn without presupposing system-level unit of selection

• Artificial multicellular genetic chimeras can exhibit holistic behaviours and functions (Blackiston et al. 2021)

  Experimental demonstration that chimeric organisms can act as integrated individuals despite genetic differences

Claims (20)

• Organised structure of relationships between parts, sufficient to exhibit information integration and collective action, can be produced via fully-distributed unsupervised learning.

  Central claim from connectionist models: complex coordination emerges without centralized control or external teacher.

• For a new level of individuality to have causal role as evolutionary unit, heritable fitness differences must be non-aggregative (not decomposable into lower-level differences).

  Core claim: monotonic non-linearities are insufficient; evolutionary outcomes must change depending on context.

• A connectionist approach resolves the chicken-and-egg problem of ETIs by focusing on the changing organisation of relationships between lower-level units, not unit frequencies

  The paper's proposed solution

• When direction of selection on particle character depends on context (other particles), particle character does not determine its own fitness; the collective is not redundant

  Formal condition for meaningful higher-level individual

• The conditions necessary to evolve a new level of individuality are described by the conditions necessary to learn non-decomposable functions (deep model induction)

  Core interpretive claim of the paper connecting ETIs to connectionist learning

• Developmental interactions required for evolutionary individuality must be able to coordinate solutions to non-decomposable functions (division of labour games)

  Developmental process is identified as computing non-linearly separable collective phenotypes

• Conventional evolutionary framework cannot explain adaptations in systems that are not already evolutionary units, creating a chicken-and-egg problem for ETIs

  Central critique of existing theory, motivating the connectionist alternative

• Organismic individuality is appropriately ascribed to systems capable of information integration and collective action at some spatiotemporal scale

  Claim that organismic self is a cognitive notion not dependent on neurons; endorsed by the authors

• Non-decomposability (non-linearly separable function) is a refinement of non-aggregative interactions, necessary for collective to be non-redundant

  Sharpens previous concepts of emergence in ETIs

• Shallow interaction structures cannot compute non-linearly separable functions; depth (hidden layers) is necessary for ETI-relevant individuality

  Assertion that deep organization is mandatory, based on connectionist theory

Hypotheses (6)

• H1: Individuality requires a dynamical process (development), mediating the plastic expression of components in the context of one another, with the specific form of computing a collective character that is a non-linearly separable function of (embryonic) particle characters, with the effect of coordinating reproduction based on this collective character.

  Main hypothesis about the architecture of individuality

• ETIs are the evolutionary equivalent of deep learning: (i) required functional relationships encode non-decomposable functions, (ii) these are enacted by basal cognition mechanisms, and (iii) conditions for deep model induction predict ETI occurrence.

  Overarching three-part hypothesis stated in introduction

• H2: The conditions necessary for the induction of deep models, familiar in connectionist models of learning and cognition, are predictive of the conditions necessary for an ETI to occur.

  Second hypothesis linking learning theory directly to evolutionary transitions

• Functional relationships required for new individuality level encode non-linearly separable functions and are enacted via information integration and collective action
• Conditions necessary to evolve new individuality level are described by conditions for learning non-decomposable functions (deep model induction)
• ETIs are described by conditions necessary for deep learning / non-decomposable function learning

Questions (6)

• How do multiple short-sighted, self-interested entities organise their relationships with one another to create a new level of individuality?

  Central puzzle of ETIs: how cooperation at higher level evolves when lower-level selection favors individual reproduction.

• Why would lower-level selection favor traits that reduce particles' independent response to selection and increase dependence on collective?

  Unresolved tension: individuation mechanisms seemingly oppose particle-level fitness, yet must evolve through bottom-up selection.

• How can selection explain adaptations at system level before the higher-level unit exists as an evolutionary unit?

  Fundamental challenge: conventional evolutionary theory cannot explain system-level features required for ETI without presupposing the higher-level unit.

• Heterogeneous Functions Homogeneous Fitness (HFHF) Problem
• How do they come to work together in this way?

  Earlier framing question

• Chicken-and-Egg Problem of ETIs

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