Quantum structure in competing lizard communities

Maciej Kuna,Diederik Aerts,Sandro Sozzo,Marek Czachor,Barry Sinervo,Jan Broekaert

doi:10.1016/j.ecolmodel.2014.02.009

Abstract

Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing that an analysis of an interactive situation involving a mating competition between certain lizard morphs allows to identify a quantum theoretic structure. More in particular, we show that when this lizard competition is analyzed structurally in the light of a compound entity consisting of subentities, the contextuality provided by the presence of an underlying rock-paper-scissors cyclic dynamics leads to a violation of Bell's inequality, which means it is of a non-classical type. We work out an explicit quantum-mechanical representation in Hilbert space for the lizard situation and show that it faithfully models a set of experimental data collected on three throat-colored morphs of a specific lizard species. Furthermore, we investigate the Hilbert space modeling, and show that the states describing the lizard competitions contain entanglement for each one of the considered confrontations of lizards with different competing strategies, which renders it no longer possible to interpret these states of the competing lizards as compositions of states of the individual lizards.

Highlights

This article looks into the challenging question of whether quantum structures are present in aspects of animal behavior
The presence of contextuality in a situation of a compound entity consisting of two subentities essentially means that what happens with one of the subentities affects the behavior of the other subentity, which as a general situation is quite common
If we regard two competing lizard morphs as a compound entity of two individual lizard morphs, we can recognize the same type of contextuality that we identified for the ideal RPS game; whether one of the lizards in competition will impregnate a female depends essentially on the color of the other lizard

Summary

Introduction

This article looks into the challenging question of whether quantum structures are present in aspects of animal behavior. The compound entity entails a new type of difficulty when attempted to be interpreted as two subentities, which is the fingerprint of the presence of quantum structure for any situation of compoundness This is why finding Bell’s inequality to be violated by the ideal RPS game to us was a straightforward reason to investigate whether a quantum structure was involved in this RPS dynamics. The general result obtained supports intuitions that dynamical systems based on non-Kolmogorovian probability may provide a fruitful conceptual framework for reallife interactions of populations (Aerts et al, 2013)

The RPS-type nature of the lizard dynamics

Calculating the RPS-type outcome probabilities

The construction of a Hilbert space model

First modeling rule

Non-Kolmogorovity in the RPS game

Conclusions