Question: The Red Queen is the story of the paternal grandmother of which king?

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Prince Hermann Friedrich of Leiningen: Prince Hermann Friedrich of Leiningen (born 16 April 1963) is the younger son of Prince Karl of Leiningen and his wife Princess Marie Louise of Bulgaria.  Hermann was born in Toronto, Ontario, as Hermann Friedrich Fernando Roland.  Through his mother, Hermann is a grandson of King Boris III of Bulgaria, a great-grandson of King Victor Emmanuel III of Italy and -great-great-grandson of King Nicholas of Montenegro.  Through his father, he is a great-great-great grandson of Queen Victoria (thus in the line of succession to the British throne), as well as Tsar Alexander II of Russia.  According to Marlene Eilers, Hermann of Leiningen belongs to the Eastern Orthodox Church.  His paternal grandmother was Grand Duchess Maria Kirillovna Romanova of Russia and his maternal grandmother was Princess Giovanna of Savoia, daughter of King Victor Emmanuel III of Italy.

Red Queen hypothesis: The Red Queen hypothesis, also referred to as Red Queen's, Red Queen's race or the Red Queen effect, is an evolutionary hypothesis which proposes that organisms must constantly adapt, evolve, and proliferate not merely to gain reproductive advantage, but also simply to survive while pitted against ever-evolving opposing organisms in an ever-changing environment.  The hypothesis intends to explain two different phenomena: the constant extinction rates as observed in the paleontological record caused by co-evolution between competing species, and the advantage of sexual reproduction (as opposed to asexual reproduction) at the level of individuals.

Margaret Beaufort, Countess of Richmond and Derby: Lady Margaret Beaufort (usually pronounced: , ; or , ), later Countess of Richmond and Derby (31 May 1441/1443 – 29 June 1509), was the mother of King Henry VII and paternal grandmother of King Henry VIII of England.

Antonia Minor: Antonia Minor ("PIR" A 885), also known as Julia Antonia Minor, Antonia the Younger or simply Antonia (31 January 36 BC - September/October AD 37) was the younger of two daughters of Mark Antony and Octavia Minor.  She was a niece of the Emperor Augustus, sister-in-law of the Emperor Tiberius, paternal grandmother of the Emperor Caligula and Empress Agrippina the Younger, mother of the Emperor Claudius, and both maternal great-grandmother and paternal great-aunt of the Emperor Nero.  She was additionally the maternal great-aunt of the Empress Valeria Messalina and Faustus Cornelius Sulla Felix, the paternal grandmother of Claudia Antonia, Claudia Octavia, and Britannicus and the maternal grandmother of Julia Livia and Tiberius Gemellus.

Jehoash of Judah: Jehoash (; Greek: Ιωας ; Latin: "Joas" ), also known as Joash (in King James Version), Joas (in Douay–Rheims) or Joás (), was a king of Judah, and the sole surviving son of Ahaziah after the massacre of the royal family ordered by his grandmother, Athaliah.  He was also the first Judahite king to be descended from both the House of David and the House of Omri, through his paternal grandmother and predecessor, Athaliah.  His mother was Zibiah of Beersheba.  Jehoash was 7 years old when his reign began, and he reigned for 40 years.  ( , ) He was succeeded by his son, Amaziah of Judah.  He is said to have been righteous "all the days of Jehoiada the priest" (2 Chronicles 24:2).

Claudia Capitolina: Claudia Capitolina (Greek: η Κλαuδία Καπιτωλίνα ) was an Egyptian Greek woman who lived in the Roman Empire, in the 1st century and possibly in the 2nd century.  Capitolina came from a distinguished family of Equestrian rank.  She was born and raised in Alexandria, Egypt.  Capitolina was the daughter and only child of Tiberius Claudius Balbilus by his unnamed wife.  The cognomen "Capitolina", is probably from her maternal side.  Her father was one of the highest magistrates of Equestrian rank that served in Rome.  Balbilus was an astrologer and a learned scholar, who was later Prefect of Egypt.  Capitolina’s paternal grandfather, was an Egyptian Greek Grammarian and Astrologer called Thrasyllus of Mendes or Tiberius Claudius Thrasyllus, who was a friend of the Roman Emperor Tiberius, while her paternal grandmother was Greek Princess Aka II of Commagene, who was a great, granddaughter of King Antiochus I Theos of Commagene.  Her paternal cousin was Ennia Thrasylla who married the Praetorian prefect of the Praetorian Guard, Naevius Sutorius Macro.

Shin Hpa of Pagan: Shin Hpa (Burmese: ရှင်ဘား , ] ) was a queen consort of King Narathihapate of the Pagan Dynasty of Burma (Myanmar).  She was the mother of King Kyawswa of Pagan; the paternal grandmother of King Uzana I of Pinya and Queen Saw Hnaung of Sagaing; and a great grandmother of King Swa Saw Ke of Ava.  Through Uzana, she was an ancestor of Toungoo kings Mingyi Nyo, Tabinshwehti and Nanda.  Through Saw Hnaung, she was an ancestor of Sagaing kings from Kyaswa to Tarabya II as well as King Thado Minbya of Ava.  Through Swa Saw Ke, she was an ancestor of Ava kings from Swa to Thihathu, as well as Toungoo kings from Bayinnaung to Mahadhammaraza Dipadi.

The Red Queen's Race: The Red Queen's Race is a science fiction short story by American writer Isaac Asimov; it uses the Red Queen's race from Lewis Carroll's "Through the Looking-Glass" as a metaphor for the final plot twist.  The story also makes reference to Asimov's psychohistory.  "The Red Queen's Race" was first published in the January 1949 issue of "Astounding Science Fiction" and reprinted in the 1972 collection "The Early Asimov".

Usaukpan (Sawlu): Usaukpan (Burmese: ဦးဆောက်ပန်း , ] ) was the chief queen consort of King Saw Lu of Pagan (Bagan).  She was the paternal grandmother of King Sithu I.  The queen died soon after Lu's accession to the Pagan throne, and was succeeded by Manisanda as the chief queen ("usaukpan").

The Red Queen (novel): The Red Queen is a 2010 historical novel by Philippa Gregory, the second of her series "The Cousins' War".  It is the story of Margaret Beaufort, mother of Henry VII of England.  The 2013 BBC One television series "The White Queen" is a 10-part adaptation of Gregory's novels "The White Queen" (2009), "The Red Queen" and "The Kingmaker's Daughter" (2012), and features Amanda Hale as Margaret Beaufort.

Supporting paragraphs: The Red Queen (novel) Margaret Beaufort, Countess of Richmond and Derby
Answer: King Henry VIII