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Mimus macdonaldi
The video shows two "gangs" of Española Mockingbirds facing off against each other on Osborn Islet (near Española Island, Galápagos). This standoff was going on for many minutes, uninterrupted and undisturbed by people lying and standing around them.
This is a very impressive video and series of photos! Congratulations! But it does look to me like the Hood or Espanola Mockingbird, Mimus macdonaldi, endemic to the island of Espanola. You captured a very special behaviour of these birds: They form family groups or clans, defend territories jointly and feed young communally. Again: Fantastic spotting!