```html Haplodiploid Bee Lineage & Fibonacci Paradox Simulator
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Bee Haplodiploidy & Fibonacci Paradox

Apis mellifera lineage simulator & genetic coefficient analyzer

👑 The Maternal Bridge (Ancestry)

A male drone has no biological father because he hatches from an unfertilized egg (1 parent: Mother). However, his mother had a father and a mother, giving him an immediate maternal grandfather.

🧬 The Female Bridge (Descendants)

A drone can only have daughters because all fertilized eggs develop into females (0 sons). Those daughters then lay unfertilized eggs that develop into male drones, giving him grandsons.

♂ Focal Drone Lineage Tree Haploid (n=16)
Fibonacci Lineage Progression Golden Ratio φ ≈ 1.618

Because males have 1 parent (♀) and females have 2 (♀ + ♂), each ancestral generation sums the previous two, forming the exact Fibonacci sequence.

Gen (g) Relationship ♀ Queens ♂ Drones Total (Fₙ) Ratio
Haplodiploid Relatedness (r) Hamilton's Rule

Because drones are haploid, all sperm carries 100% identical genes. Full sisters share 100% paternal DNA + 50% maternal DNA, yielding an extraordinary r = 0.75 relatedness.

Full Sisters
0.75
3/4 shared genome
Mother → Daughter
0.50
Standard diploid
Drone → Daughter
1.00
100% of his genome
Brothers (Drones)
0.50
Maternal haploid mix
Chromosome Inheritance Model (Worker Female)
Paternal (100%)
Maternal (50%)
High sister-sister relatedness (0.75 vs 0.50 to offspring) drives the evolution of eusocial altruism in honeybees.