Ӕ Gradient Following (Galápagos Albatross)

Introduction

Summary: Using proxy Elevated Ӕ fields (Solar + geomagnetic proxies), we demonstrate that albatross movement aligns with the gradient of Ӕ. Effects replicate across tests, individuals and controls. Rotation-null confirms specificity. These results justify Phase 3 with high-fidelity IGRF/WMM + space-weather.

Key Findings

• Uphill preference: steps uphill fraction ≈ n/a (>0.5).

• Angular clustering: Rayleigh p ≈ n/a (movement angles biased toward +∇Ӕ).

• Alpha mixing: n/a (mixed fields outperform solar-only).

• Per-bird meta: Fisher p(α=0.25) ≈ n/a, Fisher p(α=0.5) ≈ n/a.

• Rotation-null: alignment collapses under ±90° field rotation, confirming direction-specificity.

Methods (Brief)

Computed Ӕ_solar from solar geometry; proxy Ӕ_geomag from centered dipole intensity, inclination scaling, a gradient proxy and a daytime equatorial-electrojet proxy. Elevated Ӕ defined as Ӕ_α = α·Ӕ_solar + (1–α)·Ӕ_geomag. Spatial gradients estimated by finite differences; movement vectors from sequential fixes. Statistics: uphill fraction tests, Rayleigh angular clustering, α-tuning with Fisher combine across steps/birds, stratified analyses and a rotation-null control.

Figures

Evidence Table (Snapshot)

Per-Bird Meta (Downsampled)

Conclusion & Next Step

Phase 2.5 confirms a directional coherence signal: albatross steps align with +∇Ӕ under mixed solar–geomagnetic fields, and the signal disappears when the field is rotated. The next step is Phase 3, replicate the full suite with per-fix IGRF/WMM geomagnetics and space-weather stratification for decisive confirmation.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams