From ultrasonic bat chirps to eerie whale songs, the animal kingdom is a noisy place. While some sounds might have meaning — typically something like “I'm a male, aren't I great?” — no other creatures have a true language except for us. Or do they?

A new study on animal calls has found that the patterns of barks, whistles, and clicks from seven different species appear to be more complex than previously thought. The researchers used mathematical tests to see how well the sequences of sounds fit to models ranging in complexity.

In fact, five species including the killer whale and free-tailed bat had communication behaviors that were definitively more language-like than random. The study was published online Wednesday in the Proceedings of the Royal Society B.

“We're still a very, very long way from understanding this transition from animal communication to human language, and it's a huge mystery at the moment,” said study author and zoologist Arik Kershenbaum, who did the work at the National Institute for Mathematical and Biological Synthesis. “These types of mathematical analyses can give us some clues.”

While the most complicated mathematical models come closer to our own speech patterns, the simple models — called Markov processes — are more random and have been historically thought to fit animal calls.

“A Markov process is where you have a sequence of numbers or letters or notes, and the probability of any particular note depends only on the few notes that have come before,” said Kershenbaum.

So the next note could depend on the last two or 10 notes before it, but there is a defined window of history that can be used to predict what happens next.

“What makes human language special is that there's no finite limit as to what comes next,” he said.

Kershenbaum used recordings of the wild rock hyrax, a small and furry rabbit-like critter that grunts, wails, whistles, and barks, along with calls of free-tailed bats, Carolina chickadees, Bengalese finches, orangutans, pilot whales, and killer whales. For comparison, he also threw in the text of Shakespeare's "Hamlet" as a sample of human language.

Each animal recording was broken down into a series of sounds, with each distinct sound represented by a different letter. So a chickadee's low whistle would be an A, a higher whistle written as a B, etc. The final sequence would be a long string of letters, each corresponding to its own musical note or sound (ABCECBEAB and so on) which were then analyzed.

The researchers were surprised to find that none of the animal calls fits the Markovian model. In particular, the sequences from the chickadee, finch, bat, and both whales fit one of the more complex models much better. None of equations could explain the vocalizations of the hyrax or orangutan very well, for reasons not yet known.

When birds chirp or monkeys chatter, it's natural for us to interpret this as animals talking to one another. For instance, vervet monkeys have a distinct alarm call that goes with each type of predator they have. Scientists wondered whether the monkeys were calling out words for “eagle” or “leopard” as warnings to the rest of the group.

But then they noticed that after a leopard call, the group would respond by running up into a tree, staring at the predator, and making that same call over and over.

“If it was a word, that's just not what would happen,” said evolutionary biologist Tecumseh Fitch at the University of Vienna, who was not involved in the study. “I think it's more reasonable to say it's a reaction to seeing a leopard.”

That means, as far as we know, humans are still the only ones with language. But what separates language from communication? Why can't we assume that whales, with their elaborate songs, are simply speaking “whale-ese”?

To be considered a true language, there are a few elements that are usually considered to be essential, says Kershenbaum. For one, it must be learned rather than instinctive — both whales and birds have this piece covered. For instance, killer whale calves learn a repertoire of calls from their mothers, and the sounds gradually evolve from erratic screams to adult-like pulsed calls and whistles.

What holds whales and other animals back from language is that there is a limit to what they can express. There are only so many calls that each may convey different emotions, but only we have an unlimited ability to express abstract ideas.

The problem for scientists is that no one knows how language evolved. Oddly enough, there don't seem to be any transitional proto-languages between whale and bird songs — said to be the most sophisticated animal calls — and our own speech.

There are two conflicting theories of how language evolved in humans. The first is that human language evolved slowly and gradually, just as most traits evolved in the animal world. So perhaps it started with gestures, and then words and sentences. Or language may have started out more like bird song — with complex but meaningless sounds — and the last stage was attaching meaning to these sounds.

Fitch, who uses similar mathematical analysis methods for his own work, approves of the study's “big data” approach. But for the mathematical methods to truly work, he stresses the authors should have used many more recordings.

“The problem is they don't have big data,” said Fitch. “For most of the species they talk about, they have tiny data sets.”

He also doesn't believe that a lack of randomness means animal communication is any more complex or closer to language.

“Say there's four things that dogs do: bark, whine, growl, and howl — do you really think a dog randomly switches between barks and growls?” he said. “Most of the time, if they start barking, they keep on barking.”