Comparison of potato (Solanum tuberosum L.) tuber size distribution fitting methods and evaluation of the relationship between soil properties and estimated distribution parameters

Abstract

Abstract Accurate estimation of tuber size distribution (TSD) parameters in discretely categorized potato (Solanum tuberosum L) yield samples is desirable for estimating modal tuber sizes, which is fundamental to yield prediction. In the current work, systematic yield digs were conducted on five commercial fields (N = 119) to compare the Weibull, Gamma and Gaussian distribution functions for relative-likelihood-based goodness-of-fit to the observed discrete distributions. Parameters were estimated using maximum likelihood estimation (MLE) for the three distributions but were also derived using the percentiles approach for the Weibull distribution to compare accuracy against the MLE approaches. The relationship between TSD and soil nutrient variability was examined using the best-fitting model's parameters. The percentiles approach had lower overall relative likelihood than the MLE approaches across five locations, but had consistently lower Root Mean Square Error in the marketable tuber size range. Negative relationships were observed between the percentile-based shape parameter and the concentrations of Phosphorus and Nitrogen, with significant (non-zero-overlapping 95% confidence interval) regression coefficients for P (−0.74 ± 0.33 for distribution of proportional tuber numbers and −1.3 ± 0.62 for tuber weights). Stem density was negatively associated with the scale and mode of tuber number (regression coefficients −0.98 ± 0.63 and −1.08 ± 0.78 respectively) and tuber weight (regression coefficients −0.99 ± 0.78 and −1.04 ± 0.69 respectively) distributions. Phosphorus is negatively related to the scale of the tuber-number-based distribution while positively associating with the tuber weight distribution. The results suggest that excess P application was associated with the increase in small tubers that did not contribute significant weight to the final yield.