Hey, long time, no see. This is a major issue that I don't feel has been addressed well in any literature. (Most likely, some of this lack of consideration is due to the reliance of Altman's 1974 paper on behavioral sampling.) I would argue that most people working in animal behavior have ignored this issue completely. The issue, in my opinion is this:

Much like detecting and reproducing a frequency in acoustic analysis, quantification of behavioral patterns is directly dependent on sampling at a high enough frequency in order to detect the most rapidly cycling/occurring behavior in your data. At the very least, to fully quantify behaviors with the accelerometer or any other type of remote sensing tool, your optimal sampling interval for detecting every event should be no longer than the shortest behavior. For detecting periodicity, you would need to sample at twice the rate of the behavior. So, there's a distinct difference between sampling intervals for simple detection and for determining patterns.

Your problems may be more easily solved since you are only interested in active versus resting states. But, I would say there's no general rule for sampling, as it's dependent on the rate of behaviors for any given species. MacArthur got awesome data for his seminal warbler paper by taking second-by-second data...with a total of about 8.5 hours of field data. So, this sampling rate worked for birds that transitioned between behaviors rapidly. For larger animals like elephants, I would expect 15-minutes sampling intervals to work well. I think that justification for sampling interval needs to be minimally based on knowledge about the duration of individual behavior. In the absence of some rapid sampling paradigm, these behavioral durations can be used in a simulation approach to get an idea of probability of detected active and resting states (and likewise help you estimate bias).

I've always been interested in fine-scale quantification and would be very interested in talking to you about this more in-depth. (I've been pecking at a manuscript for the use of Nyquist in behavioral analysis for several years now, and this intrigues me.) A lot can be done with this, and your data will certainly make headway on this front.

Patrick raises some good general points, but if you are using ACC you shouldn't have to worry too much about sample frequency. The only ACC data I've worked with was not instantaneous, and it was possible to set the exact number of seconds (or fraction thereof), that will be recorded during each ACC sample. Depending on the settings, this data can add up quickly (causing storage problems), but the parameters you state above seem unusually limiting (compared to ACC sensors I've used)! Are you studying a super-small animal, or something that is impossible to contact/observe in the wild? What brand of collar/sensor are you planning to use?

Good points, Ben. I think even with a scan/instantaneous sampling routine (x seconds every y minutes), sampling rate is still a potential issue. Certainly, the bias is reduced as one moves towards continuous sampling, but, at minimum, not controlling for sampling routine in some way could dramatically impact the detection probability of short events and therefore influence both the point estimate and errors for the occurrence of those events. And I still think it's worth emphasizing that detection of events is a separate issue from quantification of the characteristics of those events. How have these issues been treated in the literature, Ben? Just curious...

We plan on using a Hobo G-logger, made by Onset. They will be affixed to GPS collars. The collars that we have do not have built-in accelerometers, and the Hobo was the only stand alone accelerometer that we were able to find. Are there other brands that we should consider?

We aren't really too interested in events of short duration. Rather, we would like to capture bouts of resting versus non-resting. We would like the accelerometer to record data for ~year, but perhaps we would be better off if we used a more frequent interval and a shorter total amount of sampling time.

Patrick... yeah, there will be noise/error with any sampling method. I think that is why it's ideal to already have a good idea about the general activity patterns of the animals before you decide on the ACC settings. We have used e-obs GPS/ACC collars for several species on BCI (tamanduas, ocelots, capuchins, coatis, agoutis) and have had good experiences. One of the e-obs features is that it is possible to remotely download the data, which basically frees one from any serious storage problems. I think the current cost is around $1200-1700 per GPS/ACC combination collar, so if that is in your price range, I'd look into it.

I can't really figure out how useful the Hobo G-logger might work from the website. My suspicion is that if the controller program is not very flexible (i.e. you can only specify the time interval between readings) this will not work well. ACC data is only going to be useful if you have continuous bursts of data (see below), or you are able to take 4-10 instantaneous measurements in quick succession. If the software is really flexible you might be able to rig something useful up, but otherwise, I think this product might not work very well. It might be useful to try to find someone who has used the Hobo-G before, and ask them about how they used it. I suspect that the "instantaneous samples," might actually be short duration continuous samples, in which case you'll be fine.

For visual examples of ACC data, and analysis basics, these look pretty good:

http://horizon.science.uva.nl/public/SCGE2010/AMA/course_excercises/Day5_Friday/Presentations/Day5_accel_Kato.pdf

http://cs.swan.ac.uk/~csbob/research/biologySensor/grundy09visualisation.pdf

I think the real issue you'll have is that you want to get one year of data on one logger. That is a lot of data! If you can remotely download data, that should solve the problem. Depending on your study questions and the flexibility of the computer program, you might consider setting the logger to take detailed data only 1-2 days per week, but for an entire year.

Also, you might want to reach out to people with a lot of experience analyzing ACC data. I know that Roland Kays, Danielle Brown, and Scott LaPoint all have more experience/knowledge than I do.

100% agree with Ben about first having some understanding of the behavioral patterns. Again, the similarities to acoustic sampling rate are evident here...you must know the maximum frequency of the sound in order to set the sampling rate. On this note...

@ Kim. If you're just interested in active/rest states, then I too think the 15min sampling rate will work fine. You're probably already doing this, but it might be good to differentiate between active behaviors, even if this is only to define a threshold for distinguish locomotion from grazing. The same for resting behaviors too. In my experience, resting-type behaviors are longer in duration than active behaviors for birds and mammals (though this is likely a terrible generalization).

The links for visualization were great, Ben. Crazy!

when I measure anything from people to compressor shafts in a gas turbine I use an experiential rule of thumb...2 In fact:

#1 if your in frequency domain use 2x maximum frequency of interest ( nyquist frequency)

#2 if you are in time domain use about 30 points per cycle of the highest frequency. That is if ambulating they have a cadence of 2steps per second, use a minimum of 60 samples per second.

Whenever I have used the above the data had always been useful. However you do need to analyse the data in analogue first to get the Fmax values.

Hope this helps

@ Peter. Could you clarify a bit? In point #2, you mention time domain, but use steps/second, a frequency measurement. In this case, in order to detect a single step, Nyquist would demand that you minimally sample at 1 sample/0.5 sec (or 4 samples/sec).

For other readers, remember that the Nyquist frequency is the minimum sampling frequency that allows for accurate reproduction of the maximum frequency of interest. As I think Peter alluded to, in a natural system (that may exhibit a bit of variation), it's advisable that you sample at a rate slightly higher than Nyquist, given any data storage limitations.

In order to simple detect an event (without estimating/measuring the frequency of multiple events), you simple need to sample at a rate equal to the duration of the event.

One instantaneous sample every 15 minutes on a 2-axis accelerometer! The literature suggests recording behaviour data (e.g. acceleration, Hall effect) at high frequency e.g. 100 Hz and then line deleting data until you find the recording frequency that defines each behaviour with at least 10 data points. For scallops Pecten maximus a recording frequency of 40 Hz is recommended. You can buy a cheap 1.7 g tri-axial accelerometer that records at 100 Hz.

I think the following paper will provide you with many answers and insights.

http://www.phys.ocean.dal.ca/~taggart/Publications/Broell_etal_2013.pdf

Also - check this if you want HF units at small costs (my PhD student) and her colleague, a PhD student in Biomedical Engineering

http://maritimebiologgers.com/

Does anyone know of smaller accelerometers than the one used in the paper given by Christopher? The ones used in this study have ca. 10g (as a tag) and are 4.5cm long.

Melanie, are the accelerometers to be used in aquatic applications and require a pressure case? For (terrestrial) applications that do not require a pressure case, the Weelog mini (Maritime bioLoggers) is 34mm long, starting at 4.6g (heavier with multiple battery packs).

Thanks Franziska! I will have a look at the Weelog mini. It is for terrestrial systems to be mounted in a collar.