Ornithologists among us all know that birds have specific wingbeat patterns. A woodpecker, for instance, one can already recognise as such just by hearing the typical fast flapping interspersed with silent periods. Bats have a wing morphology that is species specific: some species are suited to hover, whereas others have the perfect design to cross long distances while using very few joules per km. Some bats glide every now and then, some turn rapidly all the time. Since wingbeats and pulse emissions in bats are coupled to some degree (although seemingly less so in whispering bats or under high emission rates) it would be interesting to analyse a long series of pulse intervals on rhythmical patterns. This idea is certainly not new. When bat-detector research started off in Europe in the late 1980s, nearly everybody was using heterodyne detectors, listening for smacks, but also paying attention to rhythm. Herman Limpens from the Netherlands claims some species of bat can be recognised by emitting very regular series of pulse intervals, others are tap-dancers and so on. Surely, some Emballonurids can be as regular as a clock, but this was still unknown at the time. Studies, so far, have provided histograms of pulse intervals used by bats. This data you can also find back in the tables. Clearly, open space bats use longer pulse intervals than bats hunting in dense space. The length of the typical intervals used by a species can help to discriminate between some open space QCF bats. However, variation in Myotis bats seems to be very large. Judging from the tables, using this criterion is unlikely to help much in this group of bats.
Still, rhythm is not the same as the average length of pulse intervals used by a species. Nobody has really given a clear definition of what he means by rhythm, but the most general definition would be: a recurring temporal pattern. The word "recurring" implies that the pattern would occur more often than expected by pure chance. The strangest thing is that, to my knowledge, nobody has ever attempted an investigation into rhythmical patterns in series of pulse intervals. In this section I will make a first attempt to do so by using a long recording of Eptescus serotinus flying back and forth, so the recording is more or less continuous. I chose this species because people tend to describe it as having a typical rhythm.
Freek Cornelis from the Netherlands provided me with a long recording of one individual bat. Since the bat did produce some feeding buzzes every now and then, I did have to make some cuts in the recording, but I made sure that each fresh pulse after a buzz would be at the position of the last pulse I took. As a criterion for the position of the last pulse I took pulses where the intervals were decreasing to go below 60 ms. This is a pretty random criterion and it may be have to be done differently and more precisely in the future, however, afterwards, the recording still sounded rhythmical. We can therefore use this recording to do an analysis to find what parameters are responsible for the rhythm.
I wrote a script that measures all intervals from the series automatically. This is useful because the script can then be used for more species or other pulsed patterns in the future. I checked with Batsound whether the intervals my script measured were correct. As far as I can judge they are as correct as the results one would achieve by analysing the sequence manually. I then sorted the data in Matlab and made one of those old-fashioned histograms:
Things appear normal: 577 pulse intervals from the sequence showing a bimodal (2 peaked) distribution with peaks at 150 and 270 ms. This means that most intervals were about 150 ms and sometimes the bat skipped a pulse, so the interval became twice as long. This behaviour is normal in (half) open space bats. The peak around 270 ms would get higher (more observations) if the bat went up to more open space. To calculate an average and standard deviation I only analysed data around the first peak of 150 ms which appears to have a normal distribution (otherwise calculating the mean and SD make no sense). The results are: mean=140.5 ms and SD=28.8 ms. This has already been done a million times, the real question is of course if there is some method we could use to measure if the sequence also has a rhythm. As a well trained scientist I typed in some search terms in Google and came across the "correlogram". A correlogram shows whether consecutive numbers in a series are dependent on previous numbers, or whether they are random. A rope on a mast of a sailing boat doesn't really care how it has been banging (by force of wind) against the pole just before. It will keep on ticking against the mast around a certain average, but with random variations. The intervals between the bangs processed into a correlogram would therefore show randomness: A first value of 1 (always), but all subsequent values being very close to zero. However, if pace length was measured of a person walking through a landscape with flat terrain, hills, rivers, etc, there would be many recurrent intervals. The correlogram would therefore not drop to zero immediately and some cyclic behaviour might be observed.
Above you can see how random Freek's serotine was emitting its pulses. Not much of a pattern there! The right image is the first one, but then zoomed in to the first values. But maybe it's just the wrong method of analysing data. To test its sensitivity to rhythm I called on our late friend Michael Jackson and analysed his famous hit: Beat It. The intervals the script extracted are mainly between the beats (or handclap like sounds) and gaps and double handclaps show up nicely in the data. I am not going to put the song on this website as I don't want to be sued, but you are probably familiar with the song.
Michael, Michael, is your music as random as a rope clattering on a pole? Feeling desperate, I turned to a group sometimes hailed as Germany's most influential band ever, called Kraftwerk, known for their highly repetitious electronic music that sounded very modern at the time. I took the song "Boing Boom Tschak".
I think that the shortcoming of the correlogram-method is that it is quite insensitive to short-duration repeating elements. A bat or a piece of music really has to be very monotonous to show up as non-randomness in the correlogram. I am working on a different method, but decided to share the preliminary results with you to get some feedback and give you some new ideas. So, thank you for sharing your thoughts.