The "pygarg" is a species of gazelle, and the "wild ox" and "chamois" are swift types of antelope.

The hart - איל aiyal, the deer, according to Dr. Shaw: see the note on Deuteronomy 12:15.
The roebuck - צבי tsebi, generally supposed to be the antelope, belonging to the fifth order Pecora, genus Mammalia, and species 38. It has round twisted spiral horns, hairy tufts on the knees, browses on tender shoots, lives in hilly countries, is fond of climbing rocks, and is remarkable for its beautiful black eyes. The flesh is good and well flavoured.
The fallow deer - יחמור yachmur, from חמר chamar, to be troubled, disturbed, disordered: this is supposed to mean, not the fallow deer, but the bubalus or buffalo, which is represented by Dr. Shaw, and other travelers and naturalists, as a sullen, malevolent, and spiteful animal, capricious, ferocious, and every way brutal. According to the Linnaean classification, the buffalo belongs to the fifth order Pecora, genus Mammalia, species bos. According to 1-Kings 4:23, this was one of the animals which was daily served up at the table of Solomon. Though the flesh of the buffalo is not considered very delicious, yet in the countries where it abounds it is eaten as frequently by all classes of persons as the ox is in England. The yachmur is not mentioned in the parallel place, Leviticus 11.
The wild goat - אקו akko. It is not easy to tell what creature is intended by the akko. Dr. Shaw supposed it to be a kind of very timorous goat, known in the East by the name fishtall and serwee, and bearing a resemblance both to the goat and the stag, whence the propriety of the name given it by the Septuagint and Vulgate, tragelaphus, the goat-stag; probably the rupicapra or rock-goat. The word is found nowhere else in the Hebrew Bible.
The pygarg - דישן dishon. As this word is nowhere else used, we cannot tell what animal is meant by it. The word pygarg πυγαργος, literally signifies white buttocks, and is applied to a kind of eagle with a white tail; but here it evidently means a quadruped. It was probably some kind of goat, common and well known in Judea.
The wild ox - תאו teo. This is supposed to be the oryx of the Greeks, which is a species of large stag. It may be the same with the bekker el wash, described by Dr. Shaw as "a species of the deer kind, whose horns are exactly in the fashion of our stag, but whose size is only between the red and fallow deer." In Isaiah 51:20 a creature of the name of תוא to is mentioned, which we translate wild bull; it may be the same creature intended above, with the interchange of the two last letters.
The chamois - זמר zemer. This was probably a species of goat or deer, but of what kind we know not: that it cannot mean the chamois is evident from this circumstance, "that the chamois inhabits only the regions of snow and ice, and cannot bear the heat." - Buffon. The Septuagint and Vulgate translate it the Camelopard, but this creature is only found in the torrid zone and probably was never seen in Judea; consequently could never be prescribed as a clean animal, to be used as ordinary food. I must once more be permitted to say, that to ascertain the natural history of the Bible is a hopeless case. Of a few of its animals and vegetables we are comparatively certain, but of the great majority we know almost nothing. Guessing and conjecture are endless, and they have on these subjects been already sufficiently employed. What learning, deep, solid, extensive learning, and judgment could do, has already been done by the incomparable Bochart in his Hierozoicon. The learned reader may consult this work, and, while he gains much general information, will have to regret that he can apply so little of it to the main and grand question. As I have consulted every authority within my reach, on the subject of the clean and unclean animals mentioned in the law, and have detailed all the information I could collect in my notes on Leviticus 11, I must refer my readers to what I have there laid down.

The hart, the roebuck, and the fallow deer,.... All of the deer kind, and very agreeable food; harts were very common in the land of Canaan and parts adjacent; Aelianus says (u) harts are bred in the great mountains in Syria, Amanus, Lebanon, and Carmel: the roebuck, or "dorcas", from whence a good woman had her name, Acts 9:36 is spoken of by Martial (w) as very delicious food, and so are fallow deer; the word "jachmur", here used, having the signification of redness in it, may be used for that sort which are called red deer: it is observed that in the Arabic language it is used for an animal with two horns, living in the woods, not unlike an hart, but swifter than that; and it is asked, is it not the "aloe" or "elch" (x)?
and the wild goat, and the pygarg, and the wild ox, and the chamois; the wild goat is reckoned by Pliny (y) among the half wild creatures in Africa; according to the philosopher (z) there are none but in Syria, on which Canaan bordered, and were very remarkable ones, having ears a span and nine inches long, and some reached to the ground. The Hebrew name for this creature is "akko"; and there is a fourfooted wild beast, by the Tartarians called "akkyk", and by the Turks "akoim", and which with the Scythians and Sarmatians are to be met with in flocks; it is between a hart and a ram, its body whitish, and the flesh exceeding sweet (a); it seems to be the same with the "tragelaphus", of which there were in Arabia, as Diodorus Siculus (b) says; the next is the "pygarg", which we so render from the Septuagint and Vulgate Latin versions, or white buttocks, so called from the hinder part of it being white; a species of the eagle with a white tail is called a "pygarg", but here a four footed animal is meant; and which is mentioned as such, along with hinds, does, and goats, by Herodotus (c), Aelian (d), and Pliny (e): it has its name "dishon", in Hebrew, from its ash colour, and the "tragelaphus", or goat deer, has part of its back ash coloured, and has ash coloured spots or streaks on its sides (f): some take it to be the "strepsiceros", a kind of buck or goat with writhed horns, which the Africans, as Pliny says (g), call "addaca", which is thought by some to be a corruption of "al-dashen", so Junius; the Targum of Jonathan takes it for the "unicorn" or "rhinoceros"; and the Talmudists say (h) that the unicorn, though it has but one horn, is free, i.e. lawful to be eaten: the "wild ox" was common in Arabia; Strabo (i) speaks of multitudes of wild oxen in some parts of Arabia, on the flesh of which and other animals the Arabians live; in the Septuagint version it is called the "oryx", which is a creature that has but one horn, and divides the hoof (k), and so might be eaten; See Gill on Isaiah 51:20, the last, the "chamois", has a French name, and is a creature of the goat kind, from whose skin the chamois leather is made; in the figure of its body it seems to approach very much to the stag kind (l); perhaps it is the same with the "cemas" of Aelian (m), mentioned by him along with roebucks. Some take it to be the "tarandus", of which Pliny says (n) it is of the size of an ox, has a head bigger than a hart, and not unlike it; its horns are branched, hoofs cloven, and is hairy like a bear. In the Targums of Onkelos and Jonathan this is the "pygarg"; these several sorts of beasts were allowed to be eaten; the three first there is no difficulty about them, but the other seven it is hard to determine what they are, at least some of them. Dr. Shaw (o) thinks that the deer, the antelope, the wild bear, the goat deer, the white buttocks, the buffalo, and jeraffa, may lay in the best claim to the "ailee", "tzebi", "yachmur", "akkub", "dishon", "thau", and "zomer", here.
(u) Hist. Animal. l. 5. c. 56. (w) "Delicium parvo", &c. Epigram. l. 13. 93. (x) Castel. Lex. Polyglott. Colossians. 1. 294. (y) Nat. Hist. l. 8. c. 53. (z) Aristot. Hist. Animal. l. 8. c. 28. (a) Scheuchzer. Physic. Sacr. vol. 3. p. 415. (b) Bibliothec. l. 2. p. 134. Vid. Plin. l. 8. c. 33. (c) Melpomene, sive, l. 4. c. 192. (d) Hist. Animal l. 7. c. 19. (e) Nat. Hist. l. 8. c. 53. (f) Calmet's Dictionary on the word "Pygarg". (g) Nat. Hist. l. 11. c. 39. (h) T. Bab. Cholin, fol. 59. 2. (i) Geograph. l. 16. p. 530. (k) Aristot. Hist. Animal, l. 2. c. 1. (l) Supplement to Chambers's Dictionary on the word "Rupricapra". (m) Hist. Animal. l. 14. c. 14. (n) Nat. Hist. l. 8. c. 34. 34. (o) Travels, p. 418.

OF BEASTS. (Deuteronomy 14:4-8)
The hart--(see on Deuteronomy 12:15).
fallow deer--The Hebrew word (Jachmur) so rendered, does not represent the fallow deer, which is unknown in Western Asia, but an antelope (Oryx leucoryx), called by the Arabs, jazmar. It is of a white color, black at the extremities, and a bright red on the thighs. It was used at Solomon's table.
wild goat--The word akko is different from that commonly used for a wild goat (1-Samuel 24:2; Psalm 104:18; Proverbs 5:19), and it is supposed to be a goat-deer, having the body of a stag, but the head, horns, and beard of a goat. An animal of this sort is found in the East, and called Lerwee [SHAW, Travels].
pygarg--a species of antelope (Oryx addax) with white buttocks, wreathed horns two feet in length, and standing about three feet seven inches high at the shoulders. It is common in the tracks which the Israelites had frequented [SHAW].
wild ox--supposed to be the Nubian Oryx, which differs from the Oryx leucoryx (formerly mentioned) by its black color; and it is, moreover, of larger stature and more slender frame, with longer and more curved horns. It is called Bekkar-El-Wash by the Arabs.
chamois--rendered by the Septuagint Cameleopard; but, by others who rightly judge it must have been an animal more familiar to the Hebrews, it is thought to be the Kebsch (Ovis tragelaphus), rather larger than a common sheep, covered not with wool, but with reddish hair--a Syrian sheep-goat.