While the Ottomans aren't a medieval state, I'll still take the time to talk a little about Ottoman menageries in the context of Islamic civilization.
The Ottoman menagerie of sixteenth-century Constantinople was perhaps the best-endowed such institution in all of Eurasia. Historian Thomas T. Allsen calls it outright "the best royal zoo in early modern times," and contemporary visitors were similarly impressed by its "many beasts and fowles of Affrica and India."
The Ottoman menagerie was the incarnation of a global tradition in which kings managed exotic, fantastic animals. In the Islamic context, the Abbasid caliphs were renowned for their great collections. In 917, Byzantine ambassadors to Baghdad were treated to a scene where
They [the Byzantines] came to a palace where there were one hundred lions, fifty to the right hand and fifty to the left, each lion being held in by the hand of its keeper, and about its head and neck were iron chains.
Three thousand years before these unnerved Byzantines even saw the light of day, the pharaohs of Old Kingdom Egypt had managed "gazelles, oryx, addax, ibis, falcons, cheetah, hyenas, and mongooses." And several centuries later and half the world away, the Spanish conquerors of Mexico were no less impressed than our Byzantines by the Aztec menagerie of Moctezuma.
Why this ancient and world-spanning fascination with exotic beasts? Certainly there were issues of individual personality, i.e., many monarchs had a personal interest in such strange and dreamlike creatures. But in the Ottoman-Islamic context (and I find it safe to generalize), menageries were also political statements.
Here's one. Zookeeping is an act of domination over nature, a state of control over the wild. For the Ottoman sovereign, the menagerie was a statement that the emperor's absolute writ extended even to the fiercest and noblest creatures of the natural world. Hence the emphasis on keeping large predators like lions. In one Ottoman miniature painting, a lion—the "king of animals" in both European and Islamic literature—cowers before the feet of Osman I (founder of the dynasty) and licks his shoes. This is exactly the message the Ottomans sought to reproduce through the menagerie.
In seventeenth-century Istanbul, the Ottoman government would occasionally host parades of uncaged beasts of prey ("ten lions, five leopards, twelve tigers, and a group of hyenas, foxes, wolves, and jackals" in one account) across the city. This makes another political statement. These animals could kill any of the thousands of onlookers if they so wished. But the Ottoman government could (with chains and staffs and opiates) control their beastly instincts and have them walk along peacefully, at harmony with the physically vulnerable people and creatures of the city. This was a visual guarantee of "the sultan’s power to provide a social and political sanctuary in which all creatures, weak and strong, meek and violent, could live together in serenity and security."
Another of the menagerie's political statement is that this is a universal ruler, a sovereign whose word is heeded across seas and climes. The Ottoman collection featured animals found nowhere near the imperial capital (discussed below), and to citizens, officials, and ambassadors alike, they were visual proofs of the far-spanning borders of the Empire.
The ideology of the menagerie having been sketched out, let's talk a bit about what animals actually lived there.
Now, the political significance of the menagerie makes it clearer what kinds of animals would be welcomed there. The most effective statements were made by animals both impressive and exotic. This meant megafauna and beasts of prey from outside the Mediterranean region were particularly welcome.
These included Indian elephants, which had become increasingly both common and prestigious in the Islamic world following the Turko-Muslim conquest of India. Elephants were valuable symbolic capital for a number of reasons. They're very visually impressive, being the largest megafauna on land; they're not native to the Ottoman heartland in Anatolia and the Balkans; they're very intelligent and can be trained fairly easily, demonstrating the absolute power of the sultan over even the natural world. This explains why the Habsburg ambassador to Istanbul in the 1550s was made to attend the following performance:
When this Elephant was bid to dance, he did so caper or quaver with his whole Body, and interchangeably move his Feet, that he seem’d to represent a kind of Jig; and as for playing at Ball, he very prettily took up the Ball in his Trunk, and sent it packing therewith, as we do with the Palm of the Hand.
Elephants were brought into the city during important festivals, such as the circumcisions of imperial princes, where they served as memorable reminders of both the wonders of God's creation and the sultan's power over them. While this account refers to an elephant in Ottoman Cairo, surely the same popular enthusiasm must have been found at Istanbul:
During this year [1776] came a group of Indians with a small elephant... The people [of Cairo] rushed to this spectacle. At the gates servants stood who took money from the sightseers. Likewise the Indian grooms of the elephant collected a great deal of money. The people would bring him pastries and sugar cane and they would amuse themselves observing him sucking the cane and eating it with his trunk. The Indians would address him in their language and he understood their words. Whenever they presented him to a grandee, they would say something to him and the elephant would go down on his knees and salute with his trunk.
Then there were the beasts of prey, including lions. For the reasons mentioned in the earlier section, lions were extremely important to the ideology of the menagerie. An imperial order of September 1574 authorizes that ninety-three sheep be provided daily for the Lion House (the Arslan Hane, established in a repurposed Byzantine cathedral), which is noted to house unknown numbers of lions, tigers, wolves, and civets.
Other exotic animals in the collection included
The admirablest and fairest beast that ever I saw was a jarraff, as tame as a domesticale deere and of a reddish deere colour, whitebrested and clovenfooted. He was of a very great hieth; his forelegs longer then the hinder; a very longe necke; and headed like a cambel, except two stumps of horne one his head. This fairest anymale was sent out of Ethiopia to this Great Turks [Great Turk: Ottoman sultan] father for a present.
Under the walls are stables for seahorses called Hippopotami, which is a monstrous beast taken in Nilus, Elephants, Tygres, and Dolphines: sometimes they have Crocadiles and Rhinoceros: within are Roebuckes, white Partridges, and Turtles, the bird of Arabia, and many beasts and fowles of Affrica and India.
The Animal in Ottoman Egypt (Alan Mikhail, 2014)
The Royal Hunt in Eurasian History (Thomas T. Allsen, 2006)
"The Sultan’s Beasts: Encountering Ottoman Fauna" (Gerald MacLean, 2007)