Patterns and proofs

Patterns and proofs

Now I know how the caged bird sings

Analyse this. Kev Chapman

The nightingale is something of a virtuoso. While some birds churn out lengthy, alarm-clock-like notes, it produces an intricate array of melodies. It also has a memory for music: nightingales are able to pause for a few seconds then take up their song again as if nothing had happened. But how much does this memory affect the overall performance? And what can the patterns tell us about how birds’ brains work?

To find out whether complex bird songs follow certain rules, Jeffrey Markowitz and his colleagues at Boston University recently looked at how canaries put a performance together. Like nightingales, canaries produce elaborate songs – but are easier to keep in a lab.

The building blocks of a canary’s song are syllables: simple sounds that are repeated several times to form “phrases”. By looking at how the frequency range of syllables – as measured in kHz – changed over time, the researchers were able to identify the different phrases that made up a particular bird song. This type of frequency plot is known as a “sonogram”.

The song below goes through four distinct phrases as time progresses (shown by the four coloured bars below the sonogram):

Frequency of song notes over time, grouped into four phrases. Adapted from Markowitz et al. (2013) PLOS Comput. Biol

When the researchers looked at longer periods of birdsong, they found that the transition from one phrase to another apparently depended on previous phrases. For example, the two sections of song below both contained the same sequence of phrases in the middle (indicated by grey bars), but the first and final phrases were different:

The next phrase in a song can depend on what has been sung earlier. Adapted from Markowitz et al. (2013) PLOS Comput. Biol.

The phrases that bookended the grey section were often the same, but the pattern wasn’t always consistent. Sometimes a red phrase was followed by a cyan phrase later on; sometimes it led to a purple one.

To uncover the rules that shaped the performance, the researchers converted the song into network of possible phrases, with the route taken through the network dictating the structure of the song. The chances of choosing a particular route – and hence song – depended on the probabilities of moving from each specific phrase to another. Mathematicians call this type of linked network a “Markov chain”.

Previous studies have often assumed that the next phrase in a bird’s song depends only on the current phrase being sung. The Markov chain was therefore not dependent on a bird’s memory. When it came to canary song, however, Markowitz and his colleagues found that networks that didn’t take memory into consideration couldn’t reproduce the observed patterns very well. So they decided to try a Markov chain with memory instead. In other words, the next phrase could depend on ones sung previously as well as the current choice.

Comparing the songs of six different birds to Markov chains of increasing memory, the researchers found that future choices could depend on as many as seven of the preceding phrases. Much like human music, the songs of birds like canaries follow long-range rules that depend on what has already been sung.

Such rules follow a much longer time-scale than previously observed in birds. This raises some curious questions about the neural processes that might be shaping these patterns.

Previous work has shown that process of song creation in birds such as zebra finches – which sing a simple combination of syllables and phrases – can be explained as a series of “bursts” of neural activity. Collections of neurons in the brain that produce bursts of activity in this manner are referred to as a “neural circuit”.

But canary songs are too complicated to be explained in terms of a simple series of neural bursts. The songs follow long-term rules, which span a number of phrases each dozens of syllables long. According to Markowitz and colleagues, it is not clear how information about the song passes through a canary’s neural circuit over such long time-scales.

Even so, they suggest that studying complex birdsong could be a good way of exploring how the brain uses simple neural components to create complicated behaviour. By looking at chirping and cheeping, it might even be possible to establish general rules for the whole process. And that would certainly be something to sing about.

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