Abstract
AbstractAccurate 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.
Highlights
Potato (Solanum tuberosum L.) production is a high input, high output operation driven by well-developed, technologically advanced markets which depend on a consistent supply of high-quality potatoes
The log relative likelihood analysis of the overall distribution showed that the maximum likelihood approaches generalized to the observed discrete proportions better than the percentiles approach and the Weibull distribution maximum likelihood approach was the best method for generalizing the shape and scale of the distribution
The shape parameter was 3.4 for tuber size distribution (TSD) modelled after proportional tuber numbers and 6.46 for TSD modelled after proportional weight
Summary
Potato (Solanum tuberosum L.) production is a high input, high output operation driven by well-developed, technologically advanced markets which depend on a consistent supply of high-quality potatoes. High output alone does not necessarily translate into high returns for growers due to the selectivity of processing factories for tuber size grades (Machakaire et al, 2016). This occurs especially in the pre-fried potato processing sector which accounts for 62% of the global processed potato market (Keijbets, 2008). Travis (1987) described TSD using the spread of tuber sizes around the modal grade assuming a Gaussian distribution, allowing the determination of a coefficient of variation (CV) as an index for TSD. The probability densities plotted by Struik et al (1991) revealed that the TSD by weight skews to the right and the Gaussian distribution may not necessarily capture the spread of the data
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