Chapter 11 ------- Wave Theory of Evolution

Quantum Wave Theory of Evolutionary Dynamics (QWTED)

Introduction :

We propose a novel theoretical framework — the Quantum Wave Theory of Evolutionary Dynamics (QWTED) — which conceptualizes evolutionary processes in terms of wave mechanics. Specifically, we draw analogies between:

• Divergence patterns in evolution and the diffraction of waves, and

• Adaptive radiation and the dispersion of waves.

 Foundational Analogies

                     Divergence Pattern

                                      

                      Diffraction

		The splitting and spreading of evolutionary lineages due to environmental barriers or constraints, like wavefronts diffracting through a slit.
		Adaptive Radiation Dispersion The rapid diversification of species into new forms driven by ecological opportunity, analogous to wave dispersion where different wavelengths separate in a medium.

• Hypotheses :

• H1: Evolutionary Wave Function

  The evolutionary potential of a population or species can be described by a wavefunction $\Psi(x, t)$, where:

  • $x$ represents genetic or phenotypic configurations,

  • $t$ is evolutionary time,

  • $|\Psi(x,t)|^2$ represents the probability density of expressing a certain phenotype or genotype under selective pressures.

  H2: Diffraction as Divergence

  Environmental constraints (e.g., geographic barriers, climate) act as apertures that diffract the evolutionary wavefunction, resulting in branching or divergent evolution — the spreading of lineages into new directions without immediate ecological separation.

  H3: Dispersion as Adaptive Radiation

• In adaptive radiation, an ancestral species enters a novel, unoccupied ecological landscape. This scenario is analogous to a dispersive medium, where the evolutionary wavefunction separates into multiple trajectories (niches), each evolving at different "rates" or selective velocities — akin to how different wavelengths travel at different speeds in a prism.

  Mathematical Formulation (Simplified)

  Let evolution be governed by a generalized wave equation:

•                    d2Ψ  / dt2 = c2∇2Ψ +  V(x)Ψ

•    Wave function of Evolution  =  catalyst (Shuffling of genetic traits) + Potential function of Trait land  
  
  

• Where:

• • $\Psi(x,t)$ is the evolutionary wavefunction,

  • $c$ is a constant proportional to the evolutionary rate (mutation × selection strength),

  • $\nabla^2 \Psi$ reflects variation in trait or gene space,

  • $V(x)$ is an environmental potential landscape (fitness function).

  This structure allows:

  • Diffraction-like effects when $V(x)$ includes sharp barriers,

  • Dispersion-like effects when $\mathrm{<br>}<span\; class="katex"><span\; aria-hidden="true"\; class="katex-html"><span\; class="base"><span\; class="mord\; mathnormal">V</span><span\; class="mopen">(</span><span\; class="mord\; mathnormal">x\; ) </span></span></span>varies\; smoothly\; and\; differently\; across\; the\; landscape.</span>$

Mechanistic Interpretation

• Mutations introduce perturbations in the wavefunction.

• Selection acts as a filter (slit or medium) that shapes wave behavior.

• Speciation occurs when wavefronts become orthogonal or localized in non-overlapping regions of the evolutionary landscape — analogous to decoherence.

Implications

• Evolution is not strictly linear but behaves as a complex, probabilistic wavefield over ecological time.

• Speciation can be treated as wave interference and collapse events.

• This model aligns with known phenomena like:

  • Punctuated equilibrium (rapid shifts = sudden wavefunction collapses),

  • Convergent evolution (constructive interference in trait space),

  • Genetic drift (random fluctuations in wave amplitude).