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The emergence and evolution of a referential code in populations of bee-like agents

Grzegorz Chrupała

arXiv:2608.25779v1q-bio.PEcs.MA

TL;DR

Shared sender–receiver codes can break down during evolutionary change, as illustrated by the transition between honeybee waggle-dance variants. The paper models this transition with colony-level selection and finds that ecology enables direct pointing, while mutation, vertical-comb benefits, and sender–receiver coupling govern the later shift without communication collapse.

  • Problem

    The study asks how a population can evolve from direct pointing to gravity-referenced waggle dancing while maintaining coordination between senders and receivers.

  • Method

    The authors model evolving populations of bee-like agents, with heritable colony traits, individual worker behavior, colony-level selection, and explicit comb-geometry effects.

  • Results

    Direct pointing evolves under moderately difficult foraging, while the transition to gravity-referenced coding depends mainly on mutation rate and vertical-comb benefit, with sender–receiver coupling important at low mutation rates.

  • Takeaways & Limitations

    The gravity-referenced code can replace direct pointing reliably without communication breakdown when favorable ecological and evolutionary factors coincide.

  • Takeaways & Limitations

    The model represents only directional signaling and uses an exogenous vertical-comb benefit, so it does not establish how distance coding or the real advantage of vertical combs would affect the transition.

Abstract

from arXiv · show

Communication requires a shared code, and any change to it must be coordinated between senders and receivers to avoid a breakdown of communication. The honeybee waggle dance illustrates this problem: species with horizontal combs point directly at a food source, while species with vertical combs cannot point directly and instead reference the dance to gravity, decoded against the position of the sun. We model the emergence and evolutionary transition between these two codes in populations of bee-like agents, with selection acting at the level of colonies. In a horizontal-comb model, we find that direct pointing evolves readily when food is moderately hard to find by random search alone, whether because sites are few and large or many and small, and fails when food is too sparse to spark dances or so abundant that it is found without signaling. Adding an exogenous benefit for vertical combs, we then find that the transition to the gravity-referenced code is driven mainly by the mutation rate and the magnitude of this benefit, with the coupling between sender and receiver mutations playing a further role at low mutation rates. Given a favorable confluence of these factors, the transition proceeds reliably and without a breakdown of communication.

1 Introduction

The paper models how honeybee colonies can coordinate the emergence of direct-pointing and gravity-referenced waggle-dance codes despite the risk of communication breakdown. It finds that ecological conditions favor direct pointing, while mutation, vertical-comb benefits, and sender–receiver coupling shape the later transition.

  • Motivation: Shared communication codes require sender–receiver alignment, so code changes risk disrupting communication when only one role changes.The paper frames this coordination problem as central to explaining communicative-code evolution.
  • The waggle-dance codes: Horizontal-comb bees directly point toward food, whereas vertical-comb bees reference gravity and encode food azimuth relative to the sun.The direct code is iconic, while the gravity-referenced code uses an indirect spatial mapping.
  • Approach: The study uses a computational model of evolving bee-like populations with selection at the colony level to investigate code emergence and transition.Individual workers express colony traits, while heritable variation and mutation operate across colonies.
  • Direct-pointing code: Direct pointing evolves readily when food is moderately difficult to find, whether sites are few and large or many and small.It fails when food is too sparse to spark dances or so abundant that random search makes signaling unnecessary.
  • Code transition: The transition to gravity-referenced pointing is driven mainly by mutation rate and the exogenous benefit of vertical combs, with sender–receiver coupling especially relevant at low mutation rates.Under favorable conditions, the transition proceeds reliably without a breakdown of communication.

2 Related work

Related computational work studies communication emergence, ecological recruitment benefits, and learned waggle-dance representations. This study differs by modeling an evolutionary transition between specific directional codes with interpretable heritable traits and colony-level selection.

  • General communication models: Signaling-game and agent-based traditions model how shared vocabularies, conventions, and compositional signals emerge among interacting agents.These approaches generally address coordination and communication structure at an abstract computational level.
  • Ecological foraging models: Agent-based bee-foraging models vary ecology and recruitment to measure colony performance, but they typically fix communication strategies and omit evolution or learning.They ask when an existing dance pays off rather than how the code itself emerges.
  • Evolutionary communication models: Evolutionary studies of displaced communication examine how signals bootstrap from behavior, often selecting individual sender–receiver pairs rather than colonies.These models abstract away the specific geometry of the honeybee dance.
  • Learned waggle-dance models: Within-lifetime learning studies find that direction is readily encoded, while compositionality depends strongly on representational overlap and distance is harder to encode directly.Their neural agents learn representations without population dynamics or selection.
  • Position of the present study: The present model treats the evolutionary transition between iconic direct pointing and abstract gravity referencing at the colony level using interpretable heritable traits.Costs, benefits, and comb geometry become explicit parameters for studying conditions driving the shift.

3 Method

The model uses simplified bee-like agents whose heritable traits evolve at the colony level, while workers express those traits with individual variation. It represents direct pointing through noisy directional signals interpreted as search directions.

  • Model organization: The model treats colonies as evolutionary units and individual bee-like agents as behavioral units.This simplification is motivated by the reproductive and social organization of real bee colonies.
  • Heritable traits: Four heritable traits govern workers’ behavior: directional bias b, receiver attention a, dance propensity p, and foray distance ℓ.The first three traits are bounded to [0, 1], while ℓ is bounded to [0, D].
  • Heritable traits: Workers express colony traits with non-heritable individual variation, making each colony a noisy ensemble sharing an underlying genotype.Foray-distance variation instead comes from per-foray draws rather than separate worker jitter.
  • Signal production: On horizontal combs, a successful worker produces a direct-pointing signal centered on the food azimuth α, with concentration κ = b_i κmax and added dance noise.The direct-pointing code is modeled as iconic because signal direction mirrors the food direction.
  • Signal production: Directional bias controls signal sharpness: low bias produces nearly uninformative directions, whereas high bias reliably indicates α.Followers interpret the recovered direction as a search direction, with additional interpretation noise.

3.3 Foraging environment

Each foraging episode samples a variable environment of circular food patches and a sun position that provides the external reference for the gravity-based code. Patch number, size, distance, and worker travel distance vary according to specified distributions.

  • Patch environment: Each episode draws a fresh environment with a Poisson-distributed number of food sites having mean n.Sites are placed at uniformly sampled azimuths and distances, with radii drawn independently from a lognormal distribution.
  • Patch environment: Food sites are physical circular disks whose patch capacity scales with area, so larger patches hold proportionally more food while per-visit value remains fixed.The model uses v = 1 and log-scale radius spread σr = 0.6; minimum distance is dmin = 0.75 km.
  • Worker movement: Each worker’s foray length is independently drawn from a Gamma distribution centered on the colony’s mean foray distance and capped at D.These draws create within-colony variation in short and long travel distances.
  • External reference: The sun’s azimuth is constant within an episode but varies between episodes, serving as the external reference for the gravity-based code.It is sampled uniformly from an arc of width Δsun centered on μsun.

3.4 Foraging and colony payoff

Colonies perform sequential foraging attempts in sampled environments, with workers choosing between following dances and searching randomly. Fitness combines foraging rewards and travel, dance, and attention costs, with colony payoff averaged across episodes.

  • Foraging behavior: After a dance exists, a worker follows a randomly chosen dance with probability equal to attention a_i; otherwise it searches in a uniformly random direction.The worker then travels a sampled foray distance along the selected direction.
  • Foraging behavior: A successful foraging attempt yields patch value v minus travel cost and may trigger recruitment through a dance.Dance probability is 1 − (1 − p_i)^C, where C is remaining patch capacity, so exhausted patches do not prompt dances.
  • Foraging environment: Figure 3 varies patch count, patch radius, azimuth, and distance around a central colony, while also displaying the sun used by the gravity-based code.Its representative examples use mean patch count 6, median radius 150 m, and maximum distance 6 km.
  • Payoff: Episode payoff aggregates successful and failed attempts, recruitment-related dance costs, travel costs, and attention costs before scaling and averaging into colony fitness.Fitness is the mean episode payoff and is floored at a small positive value.

3.5 Evolutionary dynamics

Evolution occurs across non-overlapping generations in a fixed population of colonies, with parent selection proportional to fitness and offspring traits subject to mutation.

  • Population update: The model evolves a fixed-size population of colonies through non-overlapping generations without sexual reproduction.Each generation evaluates every colony before producing the next generation.
  • Selection and mutation: Parent colonies are selected repeatedly with probability proportional to fitness, and selected traits are copied to offspring colonies with mutation.Each trait receives an independent Gaussian perturbation and is then clipped to its permitted range.

3.6 Horizontal comb

The horizontal-comb model examines when direct pointing can emerge and stabilize, beginning with populations possessing weak communication.

  • The model fixes the comb flat and makes direct pointing the only available code.Initial populations have low directional bias and low attention, so early foragers signal weakly and rarely attend to dances.

3.7 Modeling code transition

The transition model imposes an external benefit for vertical combs and tests whether communication survives as combs tilt and codes change gradually.

  • The model does not explain why combs become vertical; it imposes a multiplicative vertical-building benefit, 1 + Bγ.The benefit rewards greater comb tilt independently, while coupling its value to colonies’ foraging performance.
  • Because tilt evolves through small mutational steps, populations pass through intermediate comb orientations rather than jumping directly from horizontal to vertical.Intermediate tilts create the central transition problem because direct pointing progressively loses information.
  • As tilt weakens direct pointing, the model allows colonies to switch gradually through a blend with the increasingly reliable gravity-referenced code.Two direct-code decoders are modeled because recovery depends on whether receivers correct for comb orientation.

3.8 Dancing on a tilted comb

The tilted-comb model represents evolving comb geometry, competing direct and gravity codes, alternative direct decoders, and sender–receiver code blending.

  • Comb geometry: Comb tilt γ ranges from 0 for horizontal to 1 for vertical, while orientation ϕ gives the compass heading faced by the comb.These heritable nest traits mutate independently and are shared by all workers in a colony.
  • The two codes: The direct code projects food direction onto the comb, whereas the gravity code measures food azimuth relative to the projected vertical reference.Direct-code strength decreases with tilt and can vanish for the food direction facing a fully vertical comb; gravity-code strength increases to 1.
  • Decoding: The unproject decoder inverts direct encoding exactly, while the flatten decoder makes a second projection and therefore produces systematic bias on tilted combs.The two decoders coincide on flat combs, where the encoding matrix is a rotation.
  • Transposition and blending: Sender and receiver transposition traits determine how much weight each worker gives the gravity-referenced code when producing and interpreting dances.Workers blend the two code directions using their respective transposition traits, with geometric strength also scaling each channel’s influence.
  • Coordination: Communication becomes less accurate as receiver and sender transpositions diverge, except on horizontal combs where zero gravity strength makes receiver transposition irrelevant.Sender–receiver mutation steps may be correlated through coefficient ρ because code changes pay off when matched across roles.

4 Experimental setup

Experiments first test direct-code emergence across food ecologies, then search for evolutionary transitions under vertical-comb benefits, mutation, and sender–receiver coupling.

  • Experimental stages: The two-stage design tests direct-code maintenance on horizontal combs and code migration under evolving tilt in the full model.The full transition requires both a vertical comb and a matched gravity code.
  • Horizontal-comb experiment: The horizontal-comb experiment crosses 9 Poisson mean patch counts with 6 median patch radii across 50 replicate seeds.Colonies evolve for 60 generations with mutation rate σm = 0.07, and direct-code performance is assessed using recruitment advantage and related outcomes.
  • Transition search: The transition search varies eight ecological and evolutionary parameters on a discrete grid, including B, σm, and ρ, over 120 generations.The search space contains about 2.3 billion settings, motivating optimization rather than exhaustive evaluation.
  • Scoring: A trial is stable when final comb tilt reaches γ∗ = 0.80 and both transposition traits reach t∗ = 0.50, while non-viability is defined by minimum foraging success m∗ = 0.02.The score prioritizes completed stable transitions and penalizes runs whose foraging success becomes inadequate.
  • Validation: Candidate settings are re-run on 40 confirmation seeds and then validated on 100 held-out seeds to distinguish robust transitions from lucky search outcomes.One-parameter sensitivity sweeps around the strongest validated candidate estimate the width of the viable region.

5 Results

The results first identify when direct pointing is favored on horizontal combs, then show that gravity-code transitions depend mainly on benefit and mutation parameters. Across validated candidates and sensitivity analyses, transitions are broadly feasible but vary in stability with ecological and evolutionary conditions.

  • Horizontal-comb ecology: Direct pointing is favored in a moderate foraging regime, with recruitment advantage highest for few, large patches and declining when food is too scarce or abundant.The evolved directional bias rises above baseline only along a diagonal band of patch counts and radii.
  • Parameter search: Stable vertical-gravity transitions are common under both decodes, with unproject slightly broader and strongly stable trials concentrated in abundant, large, reachable food with strong tilt incentives and high mutation.The searches identified similar stable regions across the two decoding variants.
  • Held-out validation: 80–91 of 100 flatten candidates and 82–92 of 100 unproject candidates produced stable transitions in held-out validation, with no non-viable seeds.The strongest candidates had similar held-out rates and overlapping favorable ecologies.
  • Sensitivity: 91/100 flatten transitions fell to 49/100 at σm = 0.05, while unproject fell to 16/100 at σm = 0.04; validated mutation scales remained on a stability plateau.Food-site count was the sharpest ecological boundary under flatten, whereas unproject was more robust to count.
  • Evolutionary-parameter interaction: Stable rates are robust near B ≈0.56–0.60 but become marginal by B = 0.30 and collapse at B = 0.10; higher mutation and correlation only partly compensate.Correlation matters most at low mutation scale, where increasing it from 0 to 0.9 roughly doubles stable rate.

6 Discussion and Conclusion

The study treats both code emergence and code replacement as feasibility questions rather than probability estimates. It finds that direct pointing requires moderate foraging difficulty, while gravity-code transition remains possible across most tested conditions and can preserve communication.

  • Direct-pointing emergence: Direct pointing is feasible only within a moderate band of foraging difficulty, because too little food fails to seed useful dances and too much makes independent search sufficient.The band’s edges are gradual rather than sharp.
  • Gravity-code transition: Only 3 of 64 parameter cells per decode failed to produce any stable transition, all at the lowest tested benefit and mutation scale.Elsewhere, some seeds completed the transition, although often only a minority.
  • Interpretation: The study presents transition feasibility rather than likelihood: evolutionary parameters rule the transition out across only a small part of the tested range.The high-benefit, high-mutation regime favored by search is not necessary for transition occurrence.
  • Broader implications: The results complement a mechanistic proposal by locating the remaining barrier in population-level coordination between senders and receivers rather than individual cognition.This interpretation is conditional on heading representations being indifferent to spatial reference frame.
  • Conclusion: A shared code can be revised without communication breakdown across most examined conditions, but historical likelihood would require independent evidence about ecology, comb benefit, and genetic architecture.The conclusion is explicitly about what is possible, not what was likely in Apis evolution.

7 Limitations

The model’s conclusions are bounded by simplified biological assumptions and experimental designs that limit how broadly the findings can be interpreted.

  • Only the dance’s directional component is modeled, so the results do not address how distance encoding affects code emergence or transition.The model omits the waggle dance’s distance component.
  • The exogenous vertical-comb benefit is fixed-form rather than mechanically or thermally derived, leaving its real-world magnitude and origin unspecified.The model therefore does not establish why vertical combs are advantageous in nature.
  • The mutation scale controls trait-space exploration over a fixed horizon, rather than representing a real per-generation mutation rate.
  • Sensitivity and interaction analyses hold ecology at one validated candidate, so their parameter effects are not shown to generalize elsewhere.
  • Because the two stages use different ecological grids and evolutionary horizons, their results should be read side by side rather than combined into one claim.
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