Below I will use terms which have long been used in the Anabat world. Characteristic Frequency (Fc) is the frequency at the right hand end of the flattest (lowest slope) part of a call. As far as I can see, this corresponds well with your QCF value. I agree this is a much better parameter than Peak Frequency, as it is inherently tied to the shape of the call. Characteristic Slope (Sc) is the slope of the flattest part of a call. For Rhinolophus, this will generally be zero.
The Problem With Extremes
Extremes are rare. This is just the nature of biology. Therefore, the more you sample, the further out you will push the extreme values.(1)
We can illustrate the impact of this with a couple of examples (purely hypothetical!). Suppose we find a Nyctalus with Fc at 15 kHz in northern Norway. We have been recording bats there for 20 years and never encountered a noctula. Because 15 kHz is below the range we recognise for noctula, we conclude the bat must be lasiopterus (2). This is actually a pretty safe bet, because 15 kHz would be extreme for noctula, so it is extremely unlikely we would find our first Nyctalus in the region and it would also happen to have an unusually low frequency for its species. This logic has a flaw though, because there may be a hidden bias in operation. For example, maybe exceptionally low frequency noctula have a higher than normal propensity for vagrancy. (3)
Another case - suppose we find a 15 kHz Nyctalus in northern England. We have been recording noctula there for 20 years and never encountered one at such a low frequency. So we think this must be a lasiopterus. But now the equation has changed. Is this bat more likely to be a lasiopterus or an extreme case of noctula? Because we have a large sample of noctula from that area, the confidence with which we can assign this bat to lasiopterus has been greatly reduced! This may seem counter-intuitive, but the more noctula we detect, the more likely we are to encounter an extreme example beyond the known limits for the species.
The meaning of this event (discovery of a 15 kHz Nyctalus) depends critically on the context. An understanding of the frequency distribution of a parameter will be much more helpful than just a statement of the extreme values.
Response by Batecho: You are right, especially the last phrase hits the mark. This is actually what we tried to do, to provide, say, the value at the lowest or highest 98% point of the curve. In brackets is then the highest value ever recorded, this would be your 15 kHz noctule. We don't have the exact curves (of many individuals in extreme dense or open environments) yet. They may not all be normally distributed. The numbers in the table are an attempt to give the number that would be at the extreme end of a curve. I admit that this isn't very scientific and that all the numbers should be corrected in the future to follow exactly some kind of distribution-criterion as you suggested. Regarding your second point about extreme values being rare, this is mainly a problem when it comes to getting extreme narrowband recordings. In my experience it is not so hard to get a good recording of an approach phase (leading to a buzz) which will show the extreme clutter values. For the narrowband-case, this is different. Often, the observer will have to resort to using calls that are not completely narrowband and try to "extrapolate the trends" in call design to guess the narrowband limits.
The Advantage of a Bivariate Approach
Recording Noctules at Fc = 25 kHz isn't unusual, and this is well within the range of species such as Nyctalus leisleri and Eptesicus serotinus. So if you look at the extremes for noctula you might find 17 to 24, broadly overlapping the extremes for leisleri at 21 to 32 (these are your figures, I actually think the overlap is even broader). But if you take into account the slope of the flattest part of the call (Sc) you will find much increased discriminating power, because noctula calls at 24 kHz will all be steep calls. Low slope calls at 24 kHz will not be noctula. Likewise, steep calls at 22 kHz will not be leisleri. You've greatly increased your ability to distinguish these species just by taking into account one other variable, and you can now confidently identify many individuals within the zone of overlap.
Rather than showing a one-dimensional table, it would be far more powerful to show bivariate plots of Sc against Fc. I appreciate that measuring Sc is not easy in the full-spectrum world, but it really is time you started to make use of it as a standard parameter!
Response by Batecho: Absolutely! It already says so in all the texts and explanations surrounding the table. I hope the users are already clever enough to do all this in their mind when analysing calls: to look at all parameters at the same time and imagine how they change together. The table provides the extremes of the changes, now also providing the slopes of calls. Still, because the changes may be nonlinear it would be best to show multi-dimensional diagrams as you proposed. I already mention this on the website and I would love to do it, but I don't have an ideal database of calls yet and not so much time, but I agree that this is the true way forward.
A Surrogate for Clutter
We can all appreciate that calls of bats in clutter (ie getting echoes from something) converge towards a common design across a wide range of species. For this reason, high clutter calls tend to be harder to identify than calls in low clutter (ie in the open). (4). If we could tell the degree of clutter in which a bat is flying, we could greatly enhance our chances of identifying species. Unfortunately, we don't have any universal surrogate for clutter. Within a given species, there will usually be a close correlation between clutter and Sc, but the relationship between Sc and clutter differs between species.
As an example, in North America, Myotis volans, even when flying in completely open situations, never produces calls as long in duration or low in slope as Myotis lucifugus in slight or zero clutter. This is despite the fact that volans is a bat which generally flies more in the open than lucifugus. So while extreme calls of lucifugus are easy to distinguish, no calls of volans are so distinctive. Its calls when in the open, look like calls of lucifugus in more clutter. If we had a surrogate for clutter, we could identify many volans because they would be producing steeper calls in situations where lucifugus would be producing flatter calls. Unfortunately, we don't! But it's not impossible that closer examination of other features, such as curvature, might help.
Response by Batecho: Since it is impossible to measure the amount of clutter (and even if we could what means clutter to a noctule is extremely open to a long-eared) we use the calls themselves to assess how cluttered the environment must have been to the bat. You then see that the most clutter-adapted Myotis bats have higher starting frequencies and usually a broader bandwidth than more open-adapted Myotis bats. I explain in the FAQ about the table how to measure starting frequency reliably. Not many people like starting frequency, for instance Michel Barataud and Ecoobs (batcorder) don't like it very much. I use it because it reflects a difference in physiology between bat species and in the sensory adaptation (resolving ability) which has been measured in the lab, making it a biologically meaningful parameter.
There will always be situations in which one bat produces a call that would be typical for another species in a limit-situation. This is why the observer has to record many calls, preferably with a buzz and also in the open, if possible to cover as much as possible the extremes.
Bias and its Effect on Quantitative Methods
Methods such as DFA and ANN are only meaningful if we train them using unbiased samples. What this means may not be obvious.
Suppose we train a DFA on a large set of calls obtained from bats released after capture. We train it on half the sample we have, then validate it on the other half. We find we can identify 90% of all the calls we test it on. Unfortunately, this validation tells us nothing about our ability to identify wild bats, unless we assume that our released bats represent an unbiased sample of wild bats. But this is very unlikely to be the case.
Ultimately, what we want from our DFA is to identify wild bats, not captured bats. Any action we take which reveals the species of a bat must necessarily apply a bias to which calls we will record from it. Even if we identify a species visually, we are still limited to recording the types of calls it will produce when close enough to see (and be illuminated, which may be a bigger problem).
Taking a random 50% of our sample to test the DFA doesn't help, because that 50% is still subject to the same biases as the 50% we used to train the DFA. In effect, we have tested the DFA on the same data we used to train it.
The Importance of Inference
In Australia, Chalinolobus gouldii is a common, widespread species which can nearly always be identified by its characteristic J-shaped calls alternating in frequency around 30 kHz. If you release gouldii after capture, you may be lucky and see these calls if you get a good release and the bat stays around long enough to settle down.
Chalinolobus gouldii has another side to its acoustic behaviour. When in very open situations (zero clutter) it can produce very flat calls which look very similar to calls produced by Mormopterus species. You will never see such calls produced by a bat released after capture. Even worse, you will probably never see a gouldii producing such calls, because they only do so when flying high enough to be hard to identify visually.
The fact that Chalinolobus gouldii produces such calls is important, not so much for identification of gouldii, which is usually easy, but because of the confusion it can create with Mormopterus. Yet no quantitative method currently used could have discovered this behaviour. Instead, we know about it because we have inferred its existence from countless observations of gouldii under many different conditions. We may even be wrong! But by drawing inferences in this way, we progress, even if at times it draws us to wrong conclusions..
My feeling is that we are still at a very early stage in understanding acoustic identification. It is too early to be thinking about using DFA and ANN, because we don't yet have the basic knowledge we need to know what questions to ask of such methods. We are still in a descriptive stage, refining our basic understanding.
In such a phase, we need to exploit various methods, many of which are not quantitative, and will be hard to reproduce. We need to make leaps of faith based on our experience, using our intuitive skills to see patterns hidden in our data. In doing so, we will make mistakes. But this doesn't matter, so long as we are aware of the risk and can be realistic about it. If an identification has important consequences, we should try to confirm it in other ways, because the risk of being wrong will always be there.
Being wrong is an essential part of learning. If we don't make mistakes, we aren't trying hard enough! But mistakes are only useful if we discover them, so a great deal of effort must be put into trying to find our mistakes. That means constantly challenging our own assertions (and those of others), trying to find exceptions which prove us wrong. Trust nothing, question everything, and be prepared to put our egos aside when we are wrong!
Despite all the problems with acoustic identification of bats, the technique has enormous potential which will only increase. Many problems which seem intractable today will seem easy in the future. I find it very satisfying that I can identify most of my local bats, just by watching them and looking at the display on my bat detector. Only recently has this become possible, so we shouldn't be concerned if it still seems difficult.
Response by Batecho: I agree on the fact that ANNs have been used far too quickly and I fear that lots if their identification power relied on the dataset-typical distribution of, say, pulse duration, rather than on the relationship between parameters. This relationship is what we both believe to be a very important criterion to discriminate species when many are potentially present. As you can see with the table I am not always that scientific in my approach. I think a good guideline is to take the (vocal-) physiology and its sensory performance of the bat and compare this between species. One of the parameters that seems to be emerging from this is the parameter that I call QCF. Ecoobs uses it, the Anabat community uses it and you find it in my table. Within Myotis, there seems to be a correlation in size and this QCF frequency, so I really think there is a physiological cause for it. I believe that if we keep considering the physiological and sonar-processing (performance) background of a certain parameter we can't go wrong.
1) By the way, I have recordings (using Anabat) of presumed Nyctalus noctula in both Southwaite, northern England, and Marburg, Germany with Fc at or slightly below 16 kHz.
2) In fact, it might more likely be a Lasiurus cinereus! But for this exercise, let's assume we can magically tell that it really is a Nyctalus.
3) This may seem a bit far-fetched, but birders will tell you how often a vagrant bird is also unusual in other respects. An example is the Varied Thrush which turned up in the UK. This is a bird which is normally found only along the pacific rim of North America, so its occurrence in the wrong ocean was extremely unexpected. But even more bizarre, this bird had white instead of rufous in the plumage. Such birds are very rare in the normal range of the species. So not only was this bird in the wrong place, but also a freak in other ways. This is such an improbable combination of events, that we have to consider the possibility that for some reason, white-plumaged Varied Thrushes are more likely to wander than normal-coloured birds.
4) There are exceptions to this. In North America, it can be very difficult to distinguish Lasiurus cinereus from Nyctinomops femorosaccus when both are in zero clutter, but differences become obvious when they go into clutter. These bats are in different families, and their confusing similarities are just co-incidence, while the distinctive differences reflect fundamental differences between the families. Although they can be hard to distinguish, they are fundamentally very different in acoustic behaviour.