Continuous Compositional Analysis Reveals Training Intensity Distribution Shifts in Swimmers

Recorded heart-rate zone compositions among competitive swimmers migrated across competition-preparation cycles even while the most frequent discrete training classification remained identical, according to a longitudinal study published in Frontiers in Physiology by Ziyu Liu, Yupeng Shen, Chijun Mu, and Zhao Gao of South China Normal University in Guangzhou, China. Training intensity distribution is conventionally summarized using discrete categories, such as pyramidal, polarized, threshold, or low-intensity training. Although proportions across three training intensity zones form a mathematical composition, discrete labels fail to capture shifts in relative zone allocation occurring within continuous compositional space. To overcome this limitation, the authors mapped weekly heart-rate zone compositions as points in a continuous space to track their migration across successive training cycles.

The investigation tracked 25 competitive swimmers across four distinct competition-preparation cycles, designated as P1, P2, P3, and P4. Over the course of the multi-cycle observation period, researchers gathered 1,202 athlete-weeks of heart-rate records, which accounted for 84.4 percent of all potential training weeks. Training time was divided across three intensity zones established by fixed percentages of estimated maximum heart rate. After excluding weeks in which athletes accumulated training time exclusively within the lowest intensity zone, 1,173 athlete-weeks were retained for coordinate-based evaluation.

To examine how athletes allocated their time across the three intensity zones without distorting compositional properties, weekly zone durations were converted into isometric log-ratio coordinates. The authors then conducted athlete-level comparisons across the four preparation cycles, deriving a single representative centroid for each athlete during each cycle. Differences between cycles were statistically evaluated using paired sign-flip permutation tests, applying Bonferroni correction to adjust for multiple comparisons.

When categorized under conventional discrete labels, pyramidal training emerged as the dominant type across all four cycles, representing between 80.3 percent and 85.7 percent of monitored weeks. However, continuous compositional analysis revealed significant relocations of training distributions across cycles that discrete classification obscured. Specifically, the cohort centroid for the third preparation cycle (P3) shifted toward higher proportions of Zone 2 and Zone 3 compared to the first cycle (P1), yielding an Aitchison distance of 0.717, a standardized effect of 0.82, and a statistically significant p-value of 0.0002. Similarly, the P3 cohort centroid differed significantly from that of the second cycle (P2), with an Aitchison distance of 0.495, a standardized effect of 0.60, and a p-value of 0.0019. None of the other pairwise cycle comparisons reached statistical significance.

Both the P1–P3 and P2–P3 compositional differences remained statistically robust across multiple sensitivity analyses, maintaining significance under alternative zero-replacement treatments, varying zone definitions, and different interpolation limits. When filtering by a minimum required number of recorded sessions per week, the difference between P2 and P3 ceased to be significant at the strictest minimum threshold. Additionally, the overall magnitude of the observed migration varied depending on how data processing handled weeks lacking recorded Zone 3 time. When restricting analysis strictly to weeks classified as pyramidal training, the P1-to-P3 migration moved in the same direction for 22 out of the 25 swimmers, although the statistical evidence for this subset was weaker.

The authors concluded that continuous compositional coordinates provide an objective measure of the position and displacement of an individual athlete’s training week or cycle, successfully complementing discrete training intensity distribution classifications during longitudinal monitoring. Because the recorded heart-rate zone compositions migrated across cycles while discrete classification labels remained static, continuous compositional tracking captures training dynamics that discrete classifications miss. However, the researchers emphasized that the direct relationship between these compositional migrations and prescribed training, physiological adaptation, or competition performance remains to be examined in future research.

Subject of Research: Continuous compositional analysis of training intensity distribution in competitive swimmers

Article Title: From discrete classification to continuous space: compositional analysis reveals training intensity distribution migration across competition cycles in competitive swimmers

Article References: Liu, Z., Mu, C., Gao, Z., & Shen, Y. (2026). From discrete classification to continuous space: compositional analysis reveals training intensity distribution migration across competition cycles in competitive swimmers. Frontiers in Physiology, 17, Article 1991485. https://doi.org/10.3389/fphys.2026.1991485

Image Credits: AI Generated

DOI: 10.3389/fphys.2026.1991485

Keywords: training intensity distribution, compositional data analysis, competitive swimming, heart rate monitoring, isometric log-ratio, longitudinal monitoring, exercise physiology, pyramidal training, discrete, classification, continuous, space