Dozens of small birds called zebra finches have made their home in Erich Jarvis's lab at Duke University Medical Center in Durham, North Carolina. The birds are mostly grey and white, but they have striking black-and-white stripes around their beaks and eyes – hence the name.

Zebra finches are known for their complex, boisterous songs. But these finches cannot sing properly. They constantly get stuck on one note, which they repeat over and over again. In a word, they stutter.

These remarkable birds can help us understand how songbirds produce their amazing, intricate songs, and how their ability to sing first evolved. What's more, they could even offer insight into how human language evolved.

The sweet twittering of songbirds may seem far removed from the intricacies of human speech. In one sense, that is literally true: birds are separated from us by over 300 million years of evolution. Nevertheless, our feathered friends can teach us a thing or two about ourselves.

Both birdsong and human language are learned by listening to, and imitating, others

This idea has a long pedigree. Over 2,000 years ago, Aristotle argued that birdsong might serve as a useful model for studying human speech.

"In general the birds produce most voice, and with most variety, when they are concerned with mating," he wrote in Historia Animalium. He went on to note that "a mother nightingale has been observed to give lessons in singing to a young bird, from which spectacle we might obviously infer that the song was... capable of modification and of improvement."

However, by the end of the 19th Century a combination of evolutionary theory and religious doctrine had led scientists to assume that other animals had only the most limited brainpower.

And yet, research published over the past two decades shows that Aristotle was probably right.

For starters, both birdsong and human language are learned by listening to, and imitating, others.

Japanese tits use syntax to combine the notes in their vocal repertoire in different ways

Each human language contains a finite set of words. These can be combined to express infinitely many meanings.

Each language has a set of rules by which words can be combined into meaningful phrases and sentences. These rules – known as compositional syntax – were thought to be unique to our species.

However, a study published in March 2016 showed that Japanese tits use syntax to combine the notes in their vocal repertoire in different ways, creating different meanings. Birdsong really is remarkably similar to human language.

In humans, this delicate system sometimes goes wrong – and the result is impediments such as stutters.

They not only stutter but also lose their ability to learn new songs

People with a stutter involuntarily repeat syllables, prolong certain speech sounds, and often hesitate and pause. Stutters are most common between 3 and 6 years of age, when children are learning to speak.

"Most children who have a stutter will eventually recover, and around 80% will be fluent as adults," says neuroscientist Sophie Scott, who studies the neural basis of vocal communication at University College London, UK. "But the problem persists in the rest, and they will have a problem for life."

In the past two years, two research groups have independently created songbirds with stutters. They are the first of their kind.

In a study published in 2014, Jarvis and his colleagues used electrical currents and neurotoxins to selectively destroy neurons in one region of their zebra finches' brains. This region, known as Area X, is considered to be the bird equivalent of a part of the human brain called the striatum, which becomes active when people imitate the speech of others.

What we hear as stammering is actually the person trying to cope with their disfluency

The brain damage affected the tempo of the birds' songs and the sequencing of syllables within songs. The birds also repeated syllables much more often, and about a month after the damage was done they started making stuttering-like sounds.

"When you do this in young animals, you prevent their ability to imitate during their critical period of vocal learning," says Jarvis. "But when you do it in adults after imitation has been completed, they not only stutter but also lose their ability to learn new songs."

Not only do the birds stutter similarly to humans, Jarvis has found evidence that the underlying mechanism may be similar.

In humans, stuttering may be an unfortunate by-product of the person trying to correct an underlying speech deficit.

"Quite often, what we hear as stammering is actually the person trying to cope with their disfluency," says Scott. "Repetition can occur because people are trying different things to get past the problem and keep their speech going."

Humans with damage to the basal ganglia get a stutter

Something similar may be happening in the brain-damaged zebra finches. A chance discovery by Jarvis and his colleagues suggests that the birds' stuttering may actually be a result of their brains trying to repair themselves.

"We think it's due to the brain forming new neurons," he says. "When the new cells enter Area X they try to form new connections, but they don't do it properly at first, and this causes stuttering."

Jarvis thinks the same could be true of people with stutters.

Several areas of the human brain, including the striatum, produce small numbers of new brain cells throughout life. "Humans with damage to the basal ganglia get a stutter," says Jarvis. "I predict that this could be due to the production of new neurons in the striatum."

When these results are combined with those of the second research group, they reveal clues to how the vocal learning pathway works.

The second group, led by Wan-Chun Liu of the Rockefeller University in New York, made genetically-engineered zebra finches. The birds carried human mutations associated with Huntington's Disease: a neurodegenerative disorder marked by involuntary and repetitive dance-like movements, and by problems with speech and communication.

They found that the entire song-producing system had been thrown out of whack

The zebra finches carrying the Huntington's mutations grew up with profound vocal deficits. They stuttered, and struggled to imitate other birds' songs. What's more, over time both their syllables and their syntax deteriorated.

The team published their results in October 2015.

Liu's team was hoping to unravel why Huntington's affects people's speech in the way it does. We know that neurons die in a part of the brain called the striatum, but the question is how this affects the rest of the brain.

Liu's zebra finches had damage in their song-producing brain circuitry, in particular in Area X. This pattern is similar to that seen in the brains of people with Huntington's Disease.

When they took a closer look, they found that the entire song-producing system had been thrown out of whack.

In both songbirds and humans, sounds are produced by part of the brainstem. Neurons there coordinate the muscle activity of the vocal organ – the larynx in humans, the syrinx in songbirds – as well as the breathing patterns required to produce sounds.

These brainstem neurons are in turn controlled by a circuit that loops through two other parts of the brain: the cerebral cortex and the basal ganglia. These higher-level regions control motor skills, and motor learning, in general.

It turns out that similar circuits can also be found in far less vocal species

When Liu's team examined their zebra finches' brains in more detail, they realised that they were missing the connections that run from the cortex to the basal ganglia. This apparently disrupted the timing of signals entering the basal ganglia, leading to disorganised sound production.

An independent study published in March 2016 found that temporarily inactivating neurons in the cortex restores the signalling and restores the mutant birds' disorganised songs. This suggests that damage to the basal ganglia disrupts the timing of signals between it and the cortex, and that inactivating cells in the cortex restores the correct sequence.

These studies reveal how the song-producing regions of birds' brains work, and imply that the speech-producing bits of our own brains operate in a similar way.

Perhaps this similarity should not have come as a surprise; after all, songbirds were always impressive vocalisers. But it turns out that similar circuits can also be found in far less vocal species.

The ability to learn new vocalisations is rare. "Very few lineages have it – in particular humans, songbirds, and parrots," says Jarvis. "For many years, we thought of it as an all-or-none function: either you have it or you don't."

However, that changed in 2005 when a study showed that mice produce ultrasonic "songs" that share many characteristics of birdsong.

I came to believe that mice have a rudimentary form of vocal learning

Their high-pitched squeaks – which are inaudible to us – are much more complex than previously thought. They consist of several types of syllables, the arrangement of which varies according to the context in which the mice produce them.

In line with that, Jarvis and his colleagues found in 2012 that the mice's brains contain a simple version of the circuit found in songbirds.

"The dogma for 70 years was that non-vocal-learning species have [the] brainstem circuits, and only humans, songbirds and parrots have the [higher] circuits," says Jarvis. "We've found that this is not true, and that mice also have neurons in the cortex which project down to the brainstem."

The two are by no means identical. "In humans and songbirds this connection is really robust, with hundreds if not thousands of nerve fibres, but in mice it's very weak, with only a few," says Jarvis. Nevertheless, the overall circuit is the same.

Before these studies, scientists had assumed that mice are incapable of vocal learning by imitation, so the findings started a debate. "I came to believe that mice have a rudimentary form of vocal learning, but others said they have none," says Jarvis.

In a study published in 2015, Jarvis's team found that mice "display low levels of plasticity in their vocalisations. They use simple syllables when chasing a female, and then switch to more complex ones when they're trying to attract her."

We argue that the brain pathways involved have been duplicated

Jarvis now thinks vocal learning is not an all-or-nothing function. Instead there is a continuum of skill – just as you would expect from something produced by evolution, and which therefore was assembled slowly, piece by piece.

It also turns out that the vocal pathways of mice can be disrupted in much the same way as those in songbirds and people.

In April 2016, researchers at Washington University School of Medicine in St. Louis reported that they had created genetically-engineered mice that carried a mutation associated with human stuttering. The mice carrying the mutation produced fewer high-pitched squeaks than mice without it, with longer pauses between them. The mice's calls were similar to the stuttering speech of people with the mutation.

Together, these findings have led Jarvis and his colleagues to propose an explanation for how vocal learning first evolved.

Jarvis set out his ideas in December 2015. The notion is that animals first evolved the neural circuit for motor learning, and that some species then built a second copy of the entire circuit just for vocal learning.

It should be possible to jump-start the abilities of less skilled species

"We argue that the brain pathways involved have been duplicated from the surrounding motor learning circuit," says Jarvis.

"In mice, the neurons involved are embedded inside the motor pathway, and the connections are weak. In humans and songbirds, they're separated from it. The pathway has become a robust system, with lots more connections that go down to the brainstem and cantake over the circuit involved in innate vocalizations."

In a few highly vocal species, including humans, Jarvis thinks the circuit was duplicated again. "The pathway is also bigger in species that imitate human speech, and so we see this double duplication in parrots, too," he says.

Thus, the sound-producing brain structures of mammals are analogous to those of songbirds, but their complexity in any given species is directly related to the complexity of the sounds produced, and the extent to which they can be modified.

If Jarvis is right that vocal learning ability increases as the connections between the cortex and brainstem get strengthened, it should be possible to jump-start the abilities of less skilled species simply by boosting those connections.

The sound-producing brain structures of mammals are analogous to those of songbirds

"We want to take species that do not have vocal learning abilities and hook their motor learning pathway to the brainstem motor learning neurons, to see if we can create a vocal learner from a non-vocal learning species," says Jarvis.

These experiments are now underway in his lab. "We're trying to induce stronger brain pathways in mice, to see if we can get them to imitate songs."

If they succeed, they will effectively have re-run one of the most important steps in the evolution of the brain. The ability to learn new songs – or sentences – is crucial not just for birdsong, but for human language. Jarvis's stuttering songbirds and squeaking mice may be telling us how we first learned to speak.

Join over five million BBC Earth fans by liking us on Facebook, or follow us on Twitter and Instagram.

If you liked this story, sign up for the weekly bbc.com features newsletter called "If You Only Read 6 Things This Week". A handpicked selection of stories from BBC Future, Earth, Culture, Capital, Travel and Autos, delivered to your inbox every Friday.