There is no generally accepted procedure for identifying ultradian pulsations in hormonal time series. We suggest an approach based on removing long-term trends, such as diurnal rhythms, from the series of observations; identifying peaks in the residual series; and resolving each peak, if appropriate, into overlapping secretory episodes. The first step uses a robust smoothing technique to generate a smoothed series that omits peaks or trends with time constants less than 6--12 h. The smoothed series is subtracted from the original, and in the second step their difference, the residual series, is examined for the presence of peaks. The standard deviation of the assay is calculated at each point, and the residuals are rescaled in terms of this unit. Peaks are identified as individual subseries elevated above the base line of duration n, all the points in which have magnitude at least G(n), where the values of G are cut-off criteria based on the width of the peak. Thus the algorithm selects both narrow high peaks and broader peaks that may be lower. The user selects the G(n) for each hormone based on theoretical considerations or a set of calibration data series. Points that meet these criteria are identified as belonging to peaks and flagged. To assure that the smoothing process is not influenced by runs of closely spaced peaks, these flagged points are then assigned a reduced weight, and the smoothing is repeated; the revised residuals are then reexamined. After these two steps are iterated until there are no further changes, each peak is examined once more to determine whether it can be resolved into more than one overlapping peak. Finally, the process collects statistics on the average frequency and amplitude of the peaks. We have developed computer programs to carry out these algorithms.

Theories about biological limits to life span and evolutionary shaping of human longevity depend on facts about mortality at extreme ages, but these facts have remained a matter of debate. Do hazard curves typically level out into high plateaus eventually, as seen in other species, or do exponential increases persist? In this study, we estimated hazard rates from data on all inhabitants of Italy aged 105 and older between 2009 and 2015 (born 1896-1910), a total of 3836 documented cases. We observed level hazard curves, which were essentially constant beyond age 105. Our estimates are free from artifacts of aggregation that limited earlier studies and provide the best evidence to date for the existence of extreme-age mortality plateaus in humans.

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SummaryThe main purpose of this study was to test the hypotheses that major changes in age structure occur in wild populations of the Mediterranean fruit fly (medfly) and that a substantial fraction of individuals survive to middle age and beyond (> 3-4 weeks). We thus brought reference life tables and deconvolution models to bear on medfly mortality data gathered from a 3-year study of field-captured individuals that were monitored in the laboratory. The average timeto-death of captured females differed between sampling dates by 23.9, 22.7, and 37.0 days in the 2003, 2004, and 2005 field seasons, respectively. These shifts in average times-to-death provided evidence of changes in population age structure. Estimates indicated that middle-aged medflies (> 30 days) were common in the population. A surprise in the study was the extraordinary longevity observed in field-captured medflies. For example, 19 captured females but no reference females survived in the laboratory for 140 days or more, and 6 captured but no reference males survived in the laboratory for 170 days or more. This paper advances the study of aging in the wild by introducing a new method for estimating age structure in insect populations, demonstrating that major changes in age structure occur in field populations of insects, showing that middle-aged individuals are common in the wild, and revealing the extraordinary lifespans of wild-caught individuals due to their early life experience in the field.