Jack displays animal-like behavior in his insatiable demand for meat. Instead of helping to build huts like he's supposed to, he's spending all his time figuring out the best way to kill pigs. He stalks one through the jungle, sharpened stick in hand, but is unsuccessful; the pig gets away. The way he creeps through the jungle is very animal-like indeed, but it's ultimately all to no avail. Jack and the other boys will be deprived of meat for a little while longer.

It's perfectly clear from this chapter that Jack has no real concern for the welfare of the group as a whole. He might say that the other boys want meat, but really this is all about himself and what he wants. Many animals can only really exist in larger groups, but Jack clearly isn't one of them; he's more of a lone wolf. At each and every turn, he only uses the group to serve his own ends. He'll take what he wants from the others, but beyond that he has no concern for their survival. In that sense, Jack is most definitely animal-like, showing a sense of self-preservation that will only become more and more pronounced as the story develops.

In the chapter's opening line, Jack is hunkered down, sniffing the earth like an animal. Golding refers to him as "dog-like." Jack ignores his own discomfort as he proceeds on all fours to track pigs that have passed through the underbrush. Except for "a pair of tattered shorts," he is naked.

Moments later, Golding describes Jack as "ape-like." When he is suddenly startled by a forest cry, he shrinks "with a hiss of indrawn breath," suggesting that he is guided by instinct rather than reason.

When Jack later meets up with Ralph, he has trouble conveying (in words) to him "the compulsion to track down and kill," a primitive, unreasoned, and animalistic behavior. Later in their conversation, Jack tells Ralph that sometimes when he is in the jungle he senses that he is being hunted. Since there are no predators of man on the island, it is as if Jack is slipping into animalistic, instinctive thoughts and behaviors, as opposed to the higher thinking of Ralph, Piggy, and Simon.

At the beginning of Chapter 3, Jack acts like an animal as he attempts to track pigs. Jack gets down on all fours like a sprinter and looks closely at the forest floor in order to spot any signs that indicate pigs are nearby. Golding describes Jack's mannerisms as being "dog-like" as he crawls on the ground looking for evidence of pigs. Jack even closes his eyes and breathes in the air to pick up a scent, which is something a dog would do. As Jack enters the forest, he travels in silence and examines pig droppings, which indicate the pigs are somewhere nearby. Overall, Jack's appearance and actions at the beginning of Chapter 3 resemble that of an animal, particularly a bloodhound. Unfortunately, Jack is unable to successfully kill a pig in Chapter 3 and begins arguing with Ralph about the importance of obtaining meat for the boys. 

At the start of the chapter Jack is on the hunt and most of the descriptions regarding his actions equate him to an animal on the prowl - a predator seeking its prey. In the first paragraph we read:

Jack was bent double. He was down like a sprinter, his nose only a few inches from the humid earth...
...Then dog-like, uncomfortably on all fours yet unheeding his discomfort, he stole forward five yards and stopped.

The highlighted words indicate that he has assumed the position of an animal. In paragraph two it is suggested that even his body seemed like that of some creature:

...his bare back was a mass of dark freckles and peeling sunburn.

He is described as naked (except for his shorts) and that his nostrils were flared - a description usually used to describe an animal.

To further emphasize Jack's animal-like behavior, we read in paragraph three that:

...he stole forward and cast this way and that over the ground.

And, in paragraph four:

Jack himself shrank at this cry with a hiss of indrawn breath, and for a minute became less a hunter than a furtive thing, ape-like among the tangle of trees...

The terminology makes it clear that Jack had become like an animal. In the first instance, he was casting his eyes around, as a predator would when seeking its prey. The highlighted words in paragraph four are self-explanatory.

Even after he has completed his unsuccessful hunt, Jack does not lose his bestiality, as illustrated by the following extract:  

Jack took up a coconut shell that brimmed with fresh water from among a group that was arranged in the shade, and drank. The water splashed over his chin and neck and chest. He breathed noisily when he had finished.

He drinks as an animal would.

He later declares that he has an instinctual sense which he shares with the animals: 

“There’s nothing in it of course. Just a feeling. But you can feel as if you’re not hunting, but—being hunted, as if something’s behind you all the time in the jungle.”

“Only I know how they feel. See? That’s all.”

His actions in this chapter foreshadow Jack's actions later when he rebels against rules and order, abandons civilized behaviour and adopts savagery. He and his hunters become savages and form a tribe. They are later primarily responsible for Simon's death and kill Piggy. They also capture others, such as Sam and Eric and hold them captive. Eventually, they hunt Ralph and plan to kill him.