Citation: Amaral, M.H.; Walsh, K.B. In-Orchard Sizing of Mango Fruit: 2. Forward Estimation of Size at Harvest. Horticulturae 2023, 9, 54. https://doi.org/10.3390/ horticulturae9010054 Academic Editors: Alessio Scalisi, Mark Glenn O’Connell and Ian Goodwin Received: 2 November 2022 Revised: 29 December 2022 Accepted: 30 December 2022 Published: 3 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). horticulturae Article In-Orchard Sizing of Mango Fruit: 2. Forward Estimation of Size at Harvest Marcelo H. Amaral and Kerry B. Walsh * Institute of Future Farming Systems, Central Queensland University, Rockhampton 4701, Australia * Correspondence: k.walsh@cqu.edu.au Abstract: Forecast of tree fruit yield requires prediction of harvest time fruit size as well as fruit number. Mango (Mangifera indica L.) fruit mass can be estimated from correlation to measurements of fruit length (L), width (W) and thickness (T). On-tree measurements of individually tagged fruit were undertaken using callipers at weekly intervals until the fruit were past commercial maturity, as judged using growing degree days (GDD), for mango cultivars ‘Honey Gold’, ‘Calypso’ and ‘Keitt’ at four locations in Australia and Brazil during the 2020/21 and 21/22 production seasons. Across all cultivars, the linear correlation of fruit mass to LWT was characterized by a R 2 of 0.99, RMSE of 29.9 g and slope of 0.5472 g/cm 3 , while the linear correlation of fruit mass to L( (W+T) 2 ) 2 , mimicking what can be measured by machine vision of fruit on tree, was characterized by a R 2 of 0.97, RMSE of 25.0 g and slope of 0.5439 g/cm 3 . A procedure was established for the prediction of fruit size at harvest based on measurements made five and four or four and three weeks prior to harvest (approx. 514 and 422 GDD, before harvest, respectively). Linear regression models on weekly increase in fruit mass estimated from lineal measurements were characterized by an R 2 > 0.88 for all populations, with an average slope (rate of increase) of 19.6 ± 7.1 g/week, depending on cultivar, season and site. The mean absolute percentage error for predicted mass compared to harvested fruit weight for estimates based on measurements of the earlier and later intervals was 16.3 ± 1.3% and 4.5 ± 2.4%, respectively. Measurement at the later interval allowed better accuracy on prediction of fruit tray size distribution. A recommendation was made for forecast of fruit mass at harvest based on in-field measurements at approximately 400 to 450 GDD units before harvest GDD and one week later. Keywords: yield estimation; machine vision; sizing 1. Introduction Yield forecasts of tree fruits are essential to harvest resource planning and marketing. A range of technologies can be employed in these forecasts, as reviewed by Anderson et al. [1]. One approach relies on manual- or machine-vision-based estimates of both fruit number and mass. Manual estimation of fruit number involves counting fruit on a sample of trees in each orchard, while the estimation of fruit mass distribution requires estimation of mass of a sample of fruit in each orchard. As manual procedures, both are tedious given the number of samples required for a statistically valid estimation. To alleviate the manual workload, machine vision has been applied to orchard fruit counting, e.g., Anderson et al. [2] used a camera system mounted to a vehicle to assess number of fruit in mango (Mangifera indica L.) orchards, reporting an absolute percentage error of less than 10% in 15 of 20 orchards. An in-orchard estimation of fruit mass can be achieved non-destructively through correlation of mass to fruit lineal dimensions, based on fruit allometry, and a forward prediction of mass at harvest can be made based on an assumed growth rate. Mango fruit mass (M) can be estimated from measurements of fruit length (L), width (W) and thickness (T) (Equation (1), Figure 1), as described by Spreer and Muller [3] and confirmed by Wang et al. [4] and Anderson et al. [5]. Horticulturae 2023, 9, 54. https://doi.org/10.3390/horticulturae9010054 https://www.mdpi.com/journal/horticulturae