01
Chi-square periodogram
Circadian period detection with a significance line.
Research Methods
Method
Periodogram analysis for circadian period detection
A periodogram decomposes an activity time series into its rhythmic components and reports the strength of each period, identifying the dominant circadian period and its power. The chi-square (Sokolove-Bushell), Lomb-Scargle, and FFT periodograms, plus cosinor fitting, are the standard tools.
4
protocol roles
4
control fields
4
reporting items
What this method is
A periodogram answers two numeric questions an actogram only shows visually: what is the dominant period, and how strong is it. The activity series is tested against a range of candidate periods, and the method returns a power value for each; the tallest peak near 24 h is the circadian component.
The chi-square periodogram of Sokolove and Bushell is the classic circadian tool and gives a significance threshold. The Lomb-Scargle periodogram is preferred when data are unevenly sampled or contain gaps, which is common in home-cage records. FFT is fast for evenly sampled data, and cosinor analysis fits a sinusoid to return mesor, amplitude, and acrophase.
Report the power at the circadian peak as the rhythm-strength endpoint and the peak period as the free-running period. Always inspect the matching actogram first, because a clean peak can still arise from artifacts in a short or gappy record.
- 01Endpoint
Start with the measured outcome
- 02Training role
Separate training from testing
- 03Workload
Define the exercise dose
- 04Apparatus
Match equipment to the protocol
- 05Reporting
Make replication fields visible
1
Endpoint
Start with the measured outcome
Decide whether the study is measuring adaptation, capacity, fatigue, metabolism, tissue response, recovery, or a downstream behavioral endpoint. The endpoint determines whether exercise is the intervention, the assessment, or both.
2
Training role
Separate training from testing
Training sessions deliver a repeated workload. Capacity, fatigue, exhaustion, or VO2peak sessions measure performance limits. Treating those roles as interchangeable makes the method harder to interpret.
3
Workload
Define the exercise dose
Record speed, incline, duration, frequency, progression rule, rest days, recovery timing, and total distance when relevant. The method name is not enough to reproduce the exposure.
4
Apparatus
Match equipment to the protocol
Treadmill lanes, belt calibration, incline range, cue method, metabolic integration, and tracking options all change what the method can support.
5
Reporting
Make replication fields visible
Report acclimation, animal factors, cue policy, completion rules, exclusions, stop criteria, and endpoint timing so another lab can reproduce the dose and judge interpretation limits.
How the protocol families differ
These are different method roles. Pick the row that matches the scientific question before setting speed, incline, duration, or endpoint timing.
| Protocol type | Purpose | Typical use | Watch for |
|---|---|---|---|
| Chi-square periodogram | Circadian period detection with a significance line. | Wheel-running and home-cage activity in DD. | Sensitive to record length and trends; detrend first. |
| Lomb-Scargle periodogram | Period detection for uneven or gappy sampling. | Home-cage records with missing intervals. | Interpret power relative to the false-alarm level. |
| FFT | Fast spectral decomposition of evenly sampled data. | Long, continuous, evenly binned records. | Requires even sampling and benefits from windowing. |
| Cosinor analysis | Fit a sinusoid for mesor, amplitude, and acrophase. | Parametric amplitude and phase with goodness of fit. | Assumes a roughly sinusoidal waveform. |
Chi-square periodogram
- Purpose
- Circadian period detection with a significance line.
- Typical use
- Wheel-running and home-cage activity in DD.
- Watch for
- Sensitive to record length and trends; detrend first.
Lomb-Scargle periodogram
- Purpose
- Period detection for uneven or gappy sampling.
- Typical use
- Home-cage records with missing intervals.
- Watch for
- Interpret power relative to the false-alarm level.
FFT
- Purpose
- Fast spectral decomposition of evenly sampled data.
- Typical use
- Long, continuous, evenly binned records.
- Watch for
- Requires even sampling and benefits from windowing.
Cosinor analysis
- Purpose
- Fit a sinusoid for mesor, amplitude, and acrophase.
- Typical use
- Parametric amplitude and phase with goodness of fit.
- Watch for
- Assumes a roughly sinusoidal waveform.
Apparatus and settings that change the method
The same method label can describe very different experimental exposures. These settings should be visible before protocol selection.
Activity series
Binned distance/min, wheel revolutions, or beam breaks.
Method
Chi-square, Lomb-Scargle, FFT, or cosinor.
Record length
One to three weeks for a stable circadian estimate.
Preprocessing
Detrending, gap handling, and windowing choices.
Decision summary
Use a periodogram to turn a continuous activity record into two numbers: the dominant period (free-running period under DD) and its spectral power (rhythm strength). Choose chi-square or Lomb-Scargle for circadian work in home-cage data, FFT for long even records, and cosinor when a parametric amplitude and phase are wanted. Validate every peak against the actogram.
| Output | Power vs candidate period, with the circadian peak highlighted. |
|---|---|
| Period | Period at the dominant peak (free-running period in DD). |
| Strength | Spectral power at the circadian peak. |
| Significance | Threshold or false-alarm level for the method used. |
Use when
- You need an objective period estimate or a rhythm-strength number for statistics.
- You are comparing rhythm robustness across genotypes or treatments.
- The record is unevenly sampled or has gaps (Lomb-Scargle).
Do not use when
- The record is only a few days long, which makes the spectrum unreliable.
- You only need a qualitative picture (use the actogram instead).
Reporting and interpretation checks
Use this section as the methods-record audit: caveats explain what can distort interpretation, and checklist fields make the workload reproducible.
Caveats
- Spectral power scales with activity level and record length; compare within a study.
- Detrending and windowing choices change the spectrum.
- Gaps and uneven sampling bias FFT; prefer Lomb-Scargle there.
- A significant peak in a short record can be an artifact.
Reporting checklist
- Method (chi-square, Lomb-Scargle, FFT, cosinor) and software.
- Record length, bin size, and detrending.
- Peak period and peak power, with the significance threshold.
- Lighting condition and activity measure.
References
Sokolove PG, Bushell WN. 1978. The chi square periodogram: its utility for analysis of circadian rhythms.
Original chi-square periodogram for circadian period detection.
https://doi.org/10.1016/0022-5193(78)90022-x
Refinetti R, Cornélissen G, Halberg F. 2007. Procedures for numerical analysis of circadian rhythms.
Comparative review of spectral and periodogram methods.
https://doi.org/10.1080/09291010600903692
Cornelissen G. 2014. Cosinor-based rhythmometry.
Cosinor fitting for mesor, amplitude, and acrophase.
https://doi.org/10.1186/1742-4682-11-16
Related surfaces
Use these related surfaces to move from the scientific method question to the relevant product page, endpoint definition, analysis tool, or adjacent guide.
ConductPhenotype
Runs periodogram and cosinor analysis on home-cage activity.
Actogram (method)
The visual companion to validate periodogram peaks.
Circadian spectral power (endpoint)
The rhythm-strength number the periodogram returns.
Free-running period (endpoint)
The period at the dominant periodogram peak.
