Eric's death seems to be a misunderstanding on Snorri's part due to an influence from the succeeding kings (see also the other sources below): Ynglingatal then gives Yngvi and Alf as Alrek's and Eirík's successors.
The Historia Norwegiæ presents a Latin summary of Ynglingatal, older than Snorri's quotation: This man [Dag] engendered Alrek, who was beaten to death with a bridle by his brother, Eirik.
[7] Gautreks saga also makes Alrek and Eirík sons of Agni by Skjálf and co-kings and it was to them that the warrior Starkad fled after his slaying of King Vikar.
This second saga introduces Thornbjörg, the daughter of King Eirík and Queen Ingigerd, who was a skillful shieldmaiden and ruled over part of the kingdom.
But eventually she fell in love with Hrólf son of Gautrek and agreed to marry him, at which point she gave up her weapons to her father King Eirík and took up embroidery.
Saxo Grammaticus in Book 5 of his Gesta Danorum introduces Ericus Desertus, that is Erik the Eloquent, son of a champion named Regnerus (Ragnar), both Norwegians in the service of King Gøtarus (Götar) of Norway, a monarch otherwise unknown.
This Erik is likely to be the Eirík the Eloquent or Eiríkr the Wise in Speech mentioned by Snorri Sturluson in the Skáldskaparmál as being of Ylfing lineage.
He relates how Erik outwitted all foes with clever tricks and became the counselor of Fróði son of Fridleif, king of Denmark.
Saxo then brings in a king of the Swedes named Alricus (Alrik) who corresponds to Alrek of the Norse tradition.
Erik and Skalk the Scanian pursued the war and slew Alrik's son Gunthiovus (Old Norse Gunnþjófr) leader of the men of Vermland and Solongs.
That the duel occurred at the end of a "secret interview" suggests that Alrik and Erik were alone when they fought just as were their counterparts in the Norse accounts.
That Erik was believed to have died suggests knowledge of the Ynglinga saga version in which both fighters met their death.
Name spellings are derived from Oliver Elton's 1905 translation, The First Nine Books of the Danish History of Saxo Grammaticus, via Wikisource.