Abstract
Abstract Key message The power-law equation provides marginally better accuracy than the Montgomery–Koyama–Smith equation for estimating total tepal area, with flexible definitions of maximum tepal length maintaining prediction reliability. Abstract Montgomery–Koyama–Smith equation (MKSE) and power law equation (PLE) were evaluated for estimating the total tepal area ( A T ) of Magnolia × soulangeana flowers using 3231 tepals from 359 flowers. MKSE assumes an isometric relationship between the A T and the product of summed tepal widths ( L KS ) and maximum tepal length ( W KS ), while PLE incorporates an allometric scaling exponent (α). Results showed α = 0.9561 (95% CI 0.9481–0.9641), confirming allometry. PLE exhibited slightly lower root-mean-square error (RMSE: 0.0149 vs. 0.0172) and mean absolute percentage error (MAPE: 1.18% vs. 1.35%) than MKSE. Redefining W KS as a random selection from the largest 9, 6, or 3 tepal lengths per flower minimally affected model performance, with MAPE consistently below 5% even when sampling the entire length range. This flexibility simplifies field measurements without compromising accuracy. Variability in geometric series common ratios across flowers likely drives the observed allometric scaling. This study validates that A T can be reliably estimated using summed widths and a flexibly defined maximum length, emphasizing PLE’s marginally superior fit. These findings advance methods for non-destructive floral trait quantification in species with fixed organ counts.
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Claims 5
Claim · model-written summary
The fitted tepal-area scaling exponent was 0.9561, supporting allometry.
MagnoliaOrganisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“Results showed α = 0.9561 (95% CI 0.9481–0.9641), confirming allometry.”
t0“a Magnolia species”
Claim · model-written summary
The power law equation had lower RMSE than the Montgomery–Koyama–Smith equation.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“PLE exhibited slightly lower root-mean-square error (RMSE: 0.0149 vs. 0.0172) and mean absolute percentage error (MAPE: 1.18% vs. 1.35%) than MKSE.”
t0“a Magnolia species”
Claim · model-written summary
The power law equation had lower MAPE than MKSE.
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“PLE exhibited slightly lower root-mean-square error (RMSE: 0.0149 vs. 0.0172) and mean absolute percentage error (MAPE: 1.18% vs. 1.35%) than MKSE.”
t0“a Magnolia species”
Claim · model-written summary
Sampling maximum tepal length from the largest nine, six or three tepals minimally affected performance.
- Treatment
- random selection from the largest 9, 6, or 3 tepal lengths per flowere0
- Outcome
- model performancee0
- Value
- below 5%e0
- Comparator
- the entire length rangee0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“Redefining W KS as a random selection from the largest 9, 6, or 3 tepal lengths per flower minimally affected model performance, with MAPE consistently below 5% even when sampling the entire length range.”
t0“a Magnolia species”
Claim · model-written summary
Variation in geometric-series common ratios likely drives tepal-area allometry.
- Outcome
- observed allometric scalinge0
- Qualifier
- Variability in geometric series common ratios across flowerse0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“Variability in geometric series common ratios across flowers likely drives the observed allometric scaling.”
t0“a Magnolia species”