[Paper Review] Quantum Probabilistic Structures in Competing Lizard Communities

Diederik Aerts, Marek Czachor+3 more|arXiv (Cornell University)|Dec 1, 2012

Quantum Mechanics and Applications45 references2 citations

TL;DR

This paper demonstrates that the mating competition dynamics among three morphs of side-blotched lizards exhibit quantum probabilistic structures, as evidenced by experimental data from 1990 to 2011 showing cyclic rock-paper-scissors dynamics. The authors prove that a classical Kolmogorovian probability space cannot model the data, and instead construct a faithful Hilbert space representation that captures the non-classical correlations observed in the system, extending quantum probabilistic modeling beyond human cognition to animal behavior.

ABSTRACT

Department of Biology and Evolutionary BiologyUniversity of California, Santa Cruz, California, USAEmail: [e-mail] two decades of research on the use of the mathematical formalism of quantum theoryas a modeling tool for entities and their dynamics in domains different from the micro-world has now firmly shown the systematic appearance of quantum structures in aspects ofhuman behavior and thought, such as in cognitive processes of decision-making, and in theway concepts are combined into sentences. In this paper, we extend this insight to animalbehavior showing that a quantum probabilistic structure models the mating competition ofthree side-blotched lizard morphs. We analyze a set of experimental data collected from1990 to 2011 on these morphs, whose territorial behavior follows a cyclic rock-paper-scissors(RPS) dynamics. Consequently we prove that a single classical Kolmogorovian space doesnot exist for the lizard’s dynamics, and elaborate an explicit quantum description in Hilbertspace faithfully modeling the gathered data. This result is relevant for population dynamicsas a whole, since many systems, e.g. the so called plankton paradox situation, are believedto contain elements of cyclic competition.

Motivation & Objective

• To investigate whether quantum probabilistic structures underlie the cyclic mating competition observed in three morphs of side-blotched lizards.
• To determine if classical probability theory can account for the observed behavioral dynamics in these lizard communities.
• To develop a quantum mechanical model in Hilbert space that faithfully represents the experimental data on territorial and mating behaviors.
• To extend the application of quantum probability beyond human cognition to animal behavioral systems, particularly in ecological contexts involving cyclic competition.

Proposed method

• Analysis of longitudinal experimental data collected between 1990 and 2011 on territorial and mating behaviors of three side-blotched lizard morphs.
• Application of quantum probability theory to model decision-making and state transitions in the system, using Hilbert space formalism.
• Construction of a quantum state vector to represent the joint probabilities of morph interactions, with observables corresponding to behavioral outcomes.
• Use of quantum interference terms to account for non-classical correlations that violate classical conditional probability rules.
• Mathematical proof that no single classical Kolmogorovian probability space can describe the observed data, indicating contextuality and incompatibility of events.
• Explicit derivation of a quantum model that reproduces the empirical frequencies of behavioral outcomes with high fidelity.

Experimental results

Research questions

• RQ1 Can quantum probabilistic structures explain the cyclic rock-paper-scissors dynamics observed in the mating competition of three side-blotched lizard morphs?
• RQ2 Is the observed behavioral data incompatible with any classical Kolmogorovian probability space, indicating non-classicality?
• RQ3 How can a quantum mechanical model in Hilbert space be constructed to faithfully represent the empirical data on lizard territorial and mating behaviors?
• RQ4 What does the presence of quantum structures in animal behavior imply for models of population dynamics involving cyclic competition?
• RQ5 To what extent do quantum-like interference effects emerge in ecological systems such as the plankton paradox or similar cyclic competition systems?

Key findings

• The experimental data on side-blotched lizard morphs cannot be modeled by any single classical Kolmogorovian probability space, indicating fundamental incompatibility with classical probability theory.
• A quantum probabilistic model in Hilbert space successfully reproduces the empirical frequencies of behavioral outcomes observed in the lizard communities.
• The model accounts for non-classical correlations through quantum interference effects, which are absent in classical models.
• The study provides the first empirical evidence of quantum probabilistic structures in animal behavior, extending their known application from human cognition to ecological systems.
• The findings suggest that quantum-like structures may be prevalent in systems with cyclic competition, such as the plankton paradox, offering new theoretical tools for population dynamics.