For a lion, a hyena won’t actually be much of a well-earned meal or a snack craved for, even if the cat was starving at the height of the dry season – as a matter of fact, hyena flesh isn’t really that nutritious; so if a lion did kill a hyena, it wouldn’t gain much from eating it, for hyena flesh is indeed unlikely to provide the promise of food.
But still, lions – especially males – regularly kill hyenas without necessarily eating them, mainly because of dietary overlap. Sure enough, lions see hyenas, as well as other predators in the African savanna, as huge competitors for food, territory and life, and therefore seek to eliminate them whenever possible, since the cats, being Africa’s top predators, have no tolerance for competition.
hyenas are extreme scavengers in their scavenging habit, i.e they scavenge a carcass down to the last bone which has got slightest of the meat stuck to it. Even the stinkiest meat is consumed by hyenas and vultures. Hyenas have been documented to store some of the meat in water graves as a future store for consumption. This extreme level of scavenging results in the hyena's meat not being good in taste, which becomes the primary reason why lions don't consume hyenas in maximum cases.
Now, lions primarily see hyenas as pests and treat them like one, the reasons being:
Hyenas actively look out for lion cubs to kill them and eliminate competition. They bully lionesses when lionesses are in small numbers and steal their kills or a significant part of it many a times. So killing hyenas is like a welfare act for the whole pride, it eliminates some competition and increases chances of survival of cubs. Any other victim of this welfare scheme like leopard, Cheetah or Wild dogs aren't consumed either.
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The extreme scavenging habit is seen more in male hyenas who are lowest in the hierarchy of a hyena society. Even the highest ranked male is below the lowest ranked females. So they don't get much opportunities to eat in a kill when the whole clan is feeding and hence have to resort to these type of habits. So, if the male lions haven't had anything in days and they are able to take down a healthy female hyena, they will reluctantly but out of necessity eat the soft underbelly region of hyena to replenish its energy levels.
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