The term does not appear in the original statute.
It can be found in the current statute, 16 USC 30, not in the definitions, but beginning in §1333(b)(1).
Footnotes to that section refer to amendments by Public Law 95–514, the Public Rangelands Improvement Act of 1978, a product of the 95th Congress.
The alteration, found in Section 14 of the original Act, authorized the government to get rid of excess animals on an arbitrary and capricious basis.
Appropriate Management Levels, the number of horses or burros allowed by plan, would be achieved by removing or destroying excess animals (bottom of page 6 in the pdf), not by allowing them to fill their niche. They were to be small, relative to the available resources.
Who benefits from that?