Dear Ronny,

JTK-cycle, COSOPT and CircWave are all aimed at gene expression data with relatively low sampling rates (~ 1 sample per hour or so). CircWave is an F-tested forward harmonic regression procedure and similar to you Rscript, except that CircWave automatically detects how many harmonics can be added by F-test criterion (step forward regression style), your Rscript is fixed at 2 harmonics. CircWave has not been used in over 50 publications, and circadian biologists seem to like for its simple logic and ease of use.

We have tested COSOPT against CircWave and found that COSOPT more conservative (less powerful) and very obscure (Oster et al JBR 2006). The parameter settings and threshold for detecting a rhythm seems quite arbitrary and is not documented (the publication is not clarifying it either). On top of that, COSOPT is far too conservative in detecting rhythmicity when compared to CircWave.

JTK cycle is different from CircWave and COSOPT in that it uses a non-parametric approach and therefore likely less powerfull to detect rhythmicity in normal distributed data, but more reliable when data not normally distributed.

But you asked about activity data. Such data are usually not sine shaped, so you would need a lot of harmonics to be added (certainly more than 2!) in order to describe the profile of your activity pattern. JTK cycle mightwork better, but I cannot recall that anybody ever published JTK cycle with activity data.

For activity data, people like Bill Schwartz have advocated to use Wavelet analysis for onset & offset determination, but this analysis depends greatly on the choice of Wavelet shape, which depends again on the shape of the activity profile and the species etc.

In my view (and I have ample experience in a behavioural chronobiology lab), the best option for analysing activity data still is the periodogram analyses (either Sokolof & Bushell or Lomb-Scargle with missing data) to test for significance of circadian rhythmicity and to find the circadian period. The big advantage of this method is that periodogram analysis is independent of the shape of the 24-h activity profile. Onsets and Offsets of activity can be simply determined by 24-h running average vs. 3-h running average based threshold crossing, as published by Kamiel Spoelstra (Speolstra et al - journal of biological rhythms 2004). Kamiel also wrote a freely available software package to do this, called ChronoShop.

Both ChronoShop and CircWave are downloadable from the Hut-lab website. If the site does not download (it had some problems recently), please contact me directly by email.

greetings,

Roelof Hut.

There are a number of methods and freely available software available. Depending on the frequency of your sampling and the question(s) you want to ask will influence the choice. My lab uses JTK_CYCLE (Hughes et al., J Biol Rhytm) but has also used COSOPT. We are interested in testing circadian/oscillatory periodicity with interests in period length, amplitude and phase. JTK can provide these outputs if you have sufficient data sampling.

Cosine curve fitting is the best statistical approach

Hi, As Karyn said, JTK_Cycle works really well for circadian time series. My lab also use CIRCWAVE (by Roelof Hut, Groningen). I tend to compare the results from both algorithms and choose the ones that pass the criteria of both softwares, just to be more stringent.

Dear Ronny,

JTK-cycle, COSOPT and CircWave are all aimed at gene expression data with relatively low sampling rates (~ 1 sample per hour or so). CircWave is an F-tested forward harmonic regression procedure and similar to you Rscript, except that CircWave automatically detects how many harmonics can be added by F-test criterion (step forward regression style), your Rscript is fixed at 2 harmonics. CircWave has not been used in over 50 publications, and circadian biologists seem to like for its simple logic and ease of use.

We have tested COSOPT against CircWave and found that COSOPT more conservative (less powerful) and very obscure (Oster et al JBR 2006). The parameter settings and threshold for detecting a rhythm seems quite arbitrary and is not documented (the publication is not clarifying it either). On top of that, COSOPT is far too conservative in detecting rhythmicity when compared to CircWave.

JTK cycle is different from CircWave and COSOPT in that it uses a non-parametric approach and therefore likely less powerfull to detect rhythmicity in normal distributed data, but more reliable when data not normally distributed.

But you asked about activity data. Such data are usually not sine shaped, so you would need a lot of harmonics to be added (certainly more than 2!) in order to describe the profile of your activity pattern. JTK cycle mightwork better, but I cannot recall that anybody ever published JTK cycle with activity data.

For activity data, people like Bill Schwartz have advocated to use Wavelet analysis for onset & offset determination, but this analysis depends greatly on the choice of Wavelet shape, which depends again on the shape of the activity profile and the species etc.

In my view (and I have ample experience in a behavioural chronobiology lab), the best option for analysing activity data still is the periodogram analyses (either Sokolof & Bushell or Lomb-Scargle with missing data) to test for significance of circadian rhythmicity and to find the circadian period. The big advantage of this method is that periodogram analysis is independent of the shape of the 24-h activity profile. Onsets and Offsets of activity can be simply determined by 24-h running average vs. 3-h running average based threshold crossing, as published by Kamiel Spoelstra (Speolstra et al - journal of biological rhythms 2004). Kamiel also wrote a freely available software package to do this, called ChronoShop.

Both ChronoShop and CircWave are downloadable from the Hut-lab website. If the site does not download (it had some problems recently), please contact me directly by email.

greetings,

Roelof Hut.

Hi,

maybe this is interesting for you:

The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series

DOI: 10.1076/brhm.30.2.178.1422

T. Ruf, pages 178-201 (Biological Rhythm Research, Volume 30, Issue 2, 1999)

It's an alternative method for the chi-square periodogram analysis. The author has also written a small program...

Cheers,

Frank

In a recent field study we performed in Barcelona we used the cosinor analysis to describe rhythms of urinary 6-sulfamelatonin (aMT6s) and other steroid hormone metabolites in day and night workers based on 24 hour repeated measurements but we also compared cosinor curves with GAM splines. For metabolites such as aMT6s that show a marked rhythm cosinor analysis works best asuming 24 h periodicity and symmetrical incrrease and decrease of levels over the 24 hours. We were more concerned with other metabolites with not such a well decribed rhythm or metabolites such as cortisol for example that has spike-like peaks and thus cosinor analysis would not describe well enough theses rhythms. However GAM analysis (with more degrees of freedom) showed that the cosinor curves describe the rhythms as good as GAM splines. We decided to use cosinor analysis and its derived parameters for the purposes of our comparisons.

Hi all,

following up on the previous exhanges, is there an acceptable way to determine the presence of 24h-oscillations from behavioral data with only 1 time point every 4h over 1 cycle ? (but at least 3 independent repeats of the whole curve)

Thanks for your attention.

André

The Fourier transfer/periodogram/autocorrelation approaches to frequency analysis. are all related. If you go back into the literature of the early 1960s, you will see this same curiosity applied to determining the best approach to assessing the frequency content of the spontaneous scalp EEG. Each approach has its strengths, weaknesses and proponents. All of these approaches use the assumption that biological rhythmic processes are sinusoidal, which they often are not.

I have fiddled with different methods over the years. The EEG world pretty much settled on the FFT with certain sampling and re-sampling and averaging approaches that reduce, to the degree possible, the noise introduced into data by the sampling and analysis processes. One surprise there, for me, is that commercial methods have ignored the Blackman and Tukey sampling window (10% taper at each end of the time sample) even though B&T demonstrated its mathematical superiority over the Hanning window, Hamming window and others for minimizing noise introduction. I mention this detail to point out that, even though the EEG industry has settled pretty much on one approach, it’s probably not optimal.

I also find that generalized frequency analysis packages can be a bit limiting. The idea that these approaches are focused on the circadian rhythm is encouraging, but I’d have to play around with them to see how useful they might be. The approach that I finally settled on was to write my own discrete Fourier transform and do my own windowing and re-sampling and averaging. The FFT was useful in the old days, when mainframe computers were slow, because it emphasized the use of binary arithmetic. You could play games with bit registers and the like to speed computation. Nowadays, computers are so fast that you can just take Fourier’s original equations, write them in C, and execute them as quickly as needed for circadian rhythm data. All Fourier did was repetitive least-squares fits of cosine curves to the data as he varied frequency, amplitude and phase systematically. You can do that easily with do loops in code. Additionally, I have used the optimization function in MS Excel to create a spreadsheet template that tells me the best fit of a cosine function to a set of data.

The available software approaches are a bit of overkill for the first step in data reduction. If you understand least-squares curve fitting, you can write, manipulate and understand a simple data reduction to a cosine estimate. You can even add a circasemidian harmonic. The question you are asking here is, "How much of the variance in my data is explained by a 24-hour cosine curve?" After you answer that question, you can look at the residuals of the cosine fit to see if further analysis is warranted. Are there one or more obvious sinusoidal oscillations, warranting more sophisticated frequency analysis? Are the residuals just distributed randomly? Is there an obvious wavelet approach?

Thanks for all the replies. I will read them thoroughly. Before I do that I just want to add some more information. My activity data is nest attendance in breeding birds. I have repeated measurements of several breeding pairs. And I look at nest visits per hour block (activity index). From this I would like to model the circadian activity throughout the day, and try to see if there are some peaks.

check out sigmoidally transformed cosine curves:

M. R. Marler, P. Gehrman, J. E. Martin, S. Ancoli-Israel, The Sigmoidally-transformed Cosine Curve: A Simple Mathematical Model for Circadian Rhythms with Symmetric Non-sinusoidal Shapes. Statistics in Medicine, 25:3893-3904, 2006, presented at the poster session at the Joint Statistical Meetings, Aug 2005.

There may not be a singe "best" method.

The method is easily generalizable to multiple peaks per day, as long as the fundamental period is 24 hours and the other peaks have consistent phase relations. I have an unpublished poster to share if you are interested.

I'm going to refer you to the expert Dr. Martin Teicher. Please feel free to contact him at [email protected]

Reply to Andre Klarsfeld's question: I would try CircWave in your case because your data have a relatively low sampling rate.

Reply to Ronny: Nest attendance maybe is a bit more difficult because it comes in long blocks without much variation in behaviour over time. This only works well with periodogram analysis if you have many days (>10, btu rather >20). How many days of nest attendance do you have? If you have only a few days and if the behaviour was recorded under a light-dark cycle, I would simply compare dark vs. light activity in a T-test, or perhaps make 6-12 blocks of average nest attendance over the average day and than run CircWave. CircWave can handle a minimum of 4 points per 24h cycle. I hope this helps!

Thanks again for replies.

To Roelof: my observations varies a bit between the species I have studied. In general I have filmed 5-10 breeding pairs for about 5-14 days (24h) each, hence I have repeated measurements on each breeding pair. The issue with repeated measurements have been dealt with by specifying 'breeding pair' as a random effect in the mixed effect model. I downloaded CircWave and used it for one of my data-sets, it works well. Do CircWave allow for the random effect term?

More information about my data: For each breeding pair I have summed the number of prey deliveries at nest per hour block for the days filmed (activity index). The number of prey deliveries per day varies between 5-20 per breeding pair. Some of my study species are diurnal, nocturnal or both, when looking at the raw data some have a bimodal or monomodal pattern in their activity, e.g. peak in the morning and afternoon or peak in the mid-day or mid-night. Their activity is most likely driven by prey availability.

Some time ago I had to answer this same question, and I found a paper (it was really a letter to an editor) written by Dr. Enright who explained very well the problem behind the data analysis in biological time series analysis. It all depends in the hypothesis you try to prove. In that letter he explained that the periodogram he was ussing to analyze circadian rhythms was very useful to him because the algorithm is very good to seek very conservative phases. A circadian rhythm, by definition is always phase conservative. In my opinion, and based in my work with circadian rhythmicities in crustaceans and other invertebrates, the sokolove and bushnell's periodogram has always been very useful in the analysis of our data sets. We are ussing the Lomb Scargle's periodogram now too. I agree with Dr. Hut arguments and I think all the answers are very useful for me too! Anyway I always try to use the Dr. Enright's approach first: I try to use the best analysis that help me answer the original hypothesis.

Good luck! and have fun with your data! (it is always fascinating to me, the discovery of the hidden rhythms in the biological data!)

@Ronny,

What I would do in your case is to try and calculate % of time nest attendance in hourly or 2hourly blocks for each breeding pair on a continuous time axis. Than run CircWave on each breeding pair and put the parameters that CircWave calculates in a table with one case per breeding pair. Now you can calculate amplitude [=sqrt(a^2+b^2)] and phase [=arctan(a/b), taking into account the quadrants) in a standard way for each breeding pair. Once you have those numbers, you can run any kind of mixed model anova on the parameters you found. I hope this helps!

Dear Ronny, Cosine fitting is well tried and gives the necessary output variables. See our paper: Coffee in the cornflakes: time-of-day as a modulator of executive response control. Neuropsychologia. 2002;40(1):1-6. At the time we wrote our own software and used SPSS, however now CircWave and CoSOPT are available. Hope this helps. Best wishes

I suggest you use periodogram (Lomb-Scargle) to analyze the data. There is a MATHEMATICA version available.

Cheers.