{"doi":"10.1371/journal.pcbi.1008567","title":"The risks of using the chi-square periodogram to estimate the period of biological rhythms","abstract":"The chi-square periodogram (CSP), developed over 40 years ago, continues to be one of the most popular methods to estimate the period of circadian (circa 24-h) rhythms. Previous work has indicated the CSP is sometimes less accurate than other methods, but understanding of why and under what conditions remains incomplete. Using simulated rhythmic time-courses, we found that the CSP is prone to underestimating the period in a manner that depends on the true period and the length of the time-course. This underestimation bias is most severe in short time-courses (e.g., 3 days), but is also visible in longer simulated time-courses (e.g., 12 days) and in experimental time-courses of mouse wheel-running and ex vivo bioluminescence. We traced the source of the bias to discontinuities in the periodogram that are related to the number of time-points the CSP uses to calculate the observed variance for a given test period. By revising the calculation to avoid discontinuities, we developed a new version, the greedy CSP, that shows reduced bias and improved accuracy. Nonetheless, even the greedy CSP tended to be less accurate on our simulated time-courses than an alternative method, namely the Lomb-Scargle periodogram. Thus, although our study describes a major improvement to a classic method, it also suggests that users should generally avoid the CSP when estimating the period of biological rhythms.","journal":"PLoS Computational Biology","year":2021,"id":171351,"datarank":1.0051917452720454,"base_score":3.295836866004329,"endowment":3.295836866004329,"self_citation_contribution":0.4943755299006494,"citation_network_contribution":0.510816215371396,"self_endowment_contribution":0.4943755299006494,"citer_contribution":0.510816215371396,"corpus_percentile":null,"corpus_rank":null,"citation_count":26,"citer_count":24,"citers_with_citation_signal":18,"citers_with_endowment":18,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9502,"is_data_producer":true,"deposit_databanks":{"figshare":["10.6084/m9.figshare.12805082"]},"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":19205,"name":"Jacob J. Hughey","orcid":"0000-0002-1558-6089","position":1,"is_corresponding":false},{"id":299234,"name":"Michael C. Tackenberg","orcid":"0000-0003-0220-865X","position":0,"is_corresponding":true}],"reference_count":22,"raw_metadata":null,"created_at":"2026-07-18T23:46:28.747384Z","pmid":"33406069","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}