Consistent synchronization and circaseptennian (about-7-yearly) modulation of circannual gonadal index rhythm of three marine invertebrates.  A circannual rhythm in mean gonadal weight, expressed as percentage of overall body weight, is quantified by cosinor and linear-nonlinear least-squares rhythmometry in three marine invertebrates. Data series from the purple sea urchin (Strongylocentrotus purpuratus), a mollusk, the black chiton (Katharina tunicata), and the ochre sea star (Pisaster ochraceus), exhibiting circannual periods of 368, 361, and 365 days, have relatively tight 95% limits of 356-387, 356-367, and 359-371 days, respectively, when scrutinized by nonlinear least-squares rhythmometry. These limits overlap a precise year (365.25 days). This findings supports the occurrence of a 1 year-synchronized circannual rhythm in these marine invertebrates. For the ochre sea star, the about-yearly timing of greatest gonadal weight in relation to body mass, analyzed for a circannual rhythm by the fitting of a 1-year cosine to the data, remains virtually identical within 30 years. The 95% confidence intervals of the acrophase for mean gonadal weight (as percentage of body weight), range from March 3 to April 12 in the 1950s and from March 8 to April 12 in the 1980s. A MESOR (midline-estimating statistic of rhythm) difference may relate to geographic factors (Pacific Grove, California, from January 1954 to December 1958 vs. Terrace Point near Santa Cruz, California, from December 1978 to June 1985) that in turn may reflect a different food supply and/or temporal factors, e.g., it may result from changes in the ecology of the sea. A possible circaseptennian rhythm is only suspected in the data from the ochre star (P = 0.14); it is rigorously described for the purple sea urchin (P less than 0.001) and also detected in the black chiton (P = 0.029) in time series covering 9.5 years, from September 1953 to April 1963 for the purple sea urchin and from January 1957 to September 1966 for the black chiton. Least-squares rhythmometry (with trial periods between 1 and 15 years in 6-month increments) resolves the two (circannual and circaseptennian) components concomitantly below the 3% level of statistical significance. Nonlinear least-squares rhythmometry validates a period of 7.01 years for the purple sea urchin, although within broad 95% limits (ranging from 5.58 to 10.41 years). The life span of these marine invertebrates is not determined. One deals with a population rhythm sampled with serial independence.(ABSTRACT TRUNCATED AT 400 WORDS)