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?
Western Horse Watchers Association 
Well great now what can be done to stop this criminal activity against our WILD HORSES and the Slaughtered that is going on every single day?
In Mt. States v Hodel, the court determined that “In structure and purpose, the Wild Free-Roaming Horses and Burros Act is nothing more than a land-use regulation enacted by Congress to ENSURE the survival of a particular species of wildlife.” How many ways does AML manipulation violate that structure and purpose? Is the capture and warehousing of non-excess wild equids an illegal CONVERSION of Gov property when one out of every 10 acres of US wildlife habitat ( approximately 245 million acres equal to 380,000 square miles) is managed by the BLM National System of Public Lands?
The criminal CONVERSION of wild horses as government property is specifically defined in the 1980 wild horse case: the United States v. Hughes. https://case-law.vlex.com/vid/626-f-2d-619-596454482.
Does the gov extraction policy of capture, sale, adoption, and warehousing constitute conversion of Wild horses and burros as well as an abuse of taxpayer funds? Shouldn’t jurisdiction have been changed to US Fish and wildlife for a “federally protected species” when the 1976 Supreme Court (Kleppe v New Mexico) decision confirmed the horse/burro WILDLIFE status? Moreover.. The Court ordered the RETURN of wild burros to the range as Chief Justice Thurgood Marshall stated the importance of the government’s interest in preserving herds IN THEIR NATURAL HABITAT.
Most succinctly on the issue of management in her MEMORANDUM OPINION ROSEMARY M. COLLYER, District Judge stated:
“BLM’s authority to “manage” wild free-roaming horses and burros is expressly made subject to “the provisions of this chapter[,]” 16 U.S.C. § 1333(a), including the provision that “[i]t is the policy of Congress that wild free-roaming horses and burros shall be protected from capture….” Id.§ 1331. It would be anomalous to infer that by authorizing the custodian of the wild free-roaming horses and burros to “manage” them, Congress intended to permit the animals’ custodian to SUBVERT the primary policy of the statute by capturing and removing from the wild the very animals that Congress sought to protect from being captured and removed from the wild. It is difficult to think of a “management activity” that is farther from a “minimal feasible level” than removal.”
Yet forty-five years following the Kleppe wildlife decision, et al, the Agencies continually neglect to implement Congressional mandates by amending Resource Management Plan (RMP)by NEPA protocols for compliance to restore and re-wild heritage herd INVENTORIES. Does the cumulative effect render RMPs fatally flawed?
This is why we need the evidence of mismanagement intent to result in a CONGRESSIONAL HEARING to put into proper language what has languished in interpretation for too long.