Cf. Victoria and Albert Museum, Indian Art, 1969, fig. 34 of an attendant leading a black buck signed by the artist Manohar for a very similar rendering of the tethered buck. Manohar and Mansur were two of the court painters in Jehangir's atelier who were renowned for their animal studies. When Shah Jahan ascended to the throne in 1627, the imperial workshops continued to document the exotic flora and fauna of the realm with painters striving for the delicate naturalism exemplified by these artisans coupled with a greater attention to detail and ornamentation.
For further discussion of the black buck paintings in the Mughal era, see L. Leach, Mughal & Other Indian Paintings from the Chester Beatty Library, 1995, vol. 1, no. 3.73.