ANNALS OF HUMAN BIOLOGY, 1998, VOL. 25, NO. 3, 203 219 An example of variation and pattern in saltation and stasis growth dynamics M. LAMPL'~, K. ASHIZAWA~, M. KAWABATA~ and M. L. JOHNSON§ t Emory University,Atlanta, GA, USA Otsuma Women's University,Tokyo, Japan §University of Virginia Health SciencesCenter, Charlottesville,VA, USA Received 4 August 1996; revised 9 July 1997 Summary. The serial data from two siblings, aged 6.6 and 7.5 years of age at the initiation of the study, measured each evening for total standing height during 365 days, are analysed by two methods to investigate the nature of the underlying growth pattern. The saltation and stasis model, designed to identify the presence of statistically significant pulses in sequential data, is compared for goodness-of-fitto first to sixth degree polynomial functions, used to investigate the presence of a slowly varying smooth continuous function in the data, and high order polynomials of the same degree of flexibility as the individual's saltation and stasis results. The saltation and stasis model is found to better-fit the experimental data than the slowly varying smooth continuous functions (p < 0.01 to 0.001). The timing character- istics of the saltation and stasis patterns are investigated and the temporal patterns are suggestive of a non-random, aperiodical deterministic system. 1. Introduction A pattern of saltatory growth characterized by variable amplitude pulsatile daily growth events, or saltations, followed by refractory intervals of stasis during which no significant growth takes place has been previously described for a sample of infants (Lampl, Veldhuis and Johnson 1992, Lampl 1993) and an adolescent (Lampl and Johnson 1993). The saltation and stasis model was based on time-inten- sive empirical observations that were statistically analysed and subsequently for- mally modelled to provide the possibility for statistical comparison between alternative mathematical algorithms. The saltation and stasis algorithm is a statisti- cally better descriptor of these growth data than a number of continuous mathemat- ical models (Johnson and Lampl 1995). The saltation and stasis algorithm is designed to investigate the presence of pulse/ stasis sequences and, thus, models an underlying two-phase growth mechanism: an on/off switch that is permissive for a growth event to take place. When growth occurs and how much growth can occur are not a part of the saltation and stasis model: There are no assumptions about the frequency or amplitude of saltations or the duration of stasis intervals. The model assumes only that saltations and stasis are sequential and the process is saltatory in nature. This is an important point to clarify because the process of saltation and stasis as originally published has been mis- represented in recent literature. The presence of saltation and stasis in the growth patterns of other samples has been questioned from short daily data series of five human infants (Heinrichs, Munson, Counts, Cutler and Baron 1995), seven rabbits (Oerter Klein, Munson, Bacher, Cutler and Baron 1994) and a sample of weekly and semi-weekly height measurements from a mixed-age sample of children (Hermanussen and Geiger-Benoit 1995). These studies all employ an analytic method that is methodologically unsound because it is a poor discriminator between growth patterns (Johnson and Lampl 1995, Lampl, Cameron, Veldhuis and Johnson 0301-4460/98 $12"00 © 1998 Taylor & Francis Ltd. Ann Hum Biol Downloaded from informahealthcare.com by Emory University on 04/26/12 For personal use only.