AL-SHEEHANIYA, Qatar — Cobalt-plumed and flapping, Jewel, a young Spix’s macaw, hops into a plastic bowl. She’s well trained in the routine. Her handler, Ryan Watson, sets the bowl on a scale. He’s pleased. The 4-month-old parrot is growing. If Jewel continues to thrive, Watson will soon move her and a companion — a second young macaw shrieking at the far end of the pair’s long enclosure — to a larger aviary, where they will flock with others of their kind. Though the distance of the move will be short, it has far-reaching implications: It will foster fledgling hope that this rarest of parrots can be saved.