Volume estimation models for avocado fruit.

Avocado (Persea americana Mill.) is an important horticultural crop and proved to be a very profitable commercial crop for both local consumption and export. The physical characteristics of fruits are an important factor to determine the quality of fruit produced. On the other hand, estimation of fruit volume is time-consuming and impractical under field conditions. Thus, this study was conducted to devise cultivar-specific and generalized allometric models to analytically and non-destructively determine avocado fruit volume of five wildly distributed avocado cultivars. A significant relationship (P ≤ 0.01) was found between fruit diameter, length, and volume of each cultivar. Our best models (VM2 -for cultivar specific, and VM7-generalized model) has passed all the rigorous cross-validation and performance statistics tests and explained 94%, 92%, 87%, 93%, 94% and 93% of the variations in fruit volume of Ettinger, Fuerte, Hass, Nabal, Reed, and Multiple cultivars, respectively. Our finding revealed that in situations where measurements of volume would be inconvenient, or time-consuming, a reliable volume and yield estimation can be obtained using site- and cultivar-specific allometric equations. Allometric models could also play a significant role in improving data availability on avocado fruit physical appearance which is critical to assess the quality and taste of fresh products influencing the purchase decision of customers. Moreover, such information can also be used as a ripeness index to predict optimum harvest time important for planned marketing. More importantly, the models might assist horticulturists, agronomists, and physiologists to conduct further study on avocado production and productivity through agroforestry landuse system across Ethiopia.

Introduction

Avocado is a highly variable species and classified into three ecological races (i.e., the West Indian (WI), Guatemalan (G) and Mexican (M) "races") [1, 2]. It is an evergreen tree species and the most economically important species of the Lauraceae family. It is grown commercially in America, Africa, Europe, Asia and Oceania. In 2019, the estimated world’s total avocado production was about 7.2 million tonnes from 726, 660 hectares [3]. The major avocado-growing countries are Mexico, USA, Colombia, Indonesia, Chile, the Dominican Republic, Kenya and South Africa [3]. In Africa, Kenya and South Africa are leading in the production and export of avocado to the global market [4]. In Ethiopia, it was first introduced around 1938 in the eastern and southern parts of the country and it is now being widely distributed throughout the country, and mainly used for household consumption and local market [5-7]. Currently, Ethiopia is one of the top five avocado-producing countries in sub-Saharan Africa (SSA) and 20th in the world [3].

Avocado is recognized as a source of energy and vitamins. It also provides specific non-nutritive physiological benefits that may enhance health [8], thus, it can be considered as a "functional food" [9]. It is one of the top important commercial crops to be traded at a global scale [10, 11], and becoming one of the most promising fruit crops for both food and nutrition security and earning a considerable amount of financial return from export and domestic market [12-14]. Due to government initiatives in promoting investment in horticulture sector as well as combating climate change through land diversification and agroforestry practices, the plantation and the production of avocado is considerably increasing over the last few years across different parts of Ethiopia. Despite the expansion of avocado tree plantations, the physical characteristic of avocado fruits and productivity of small-scale avocado farming are not well studied in Ethiopia. On the other hand, information on fruit size is critical factor to determine the quality of the avocados and has been used to describe the fruit’s growth curve, predict yield, and conduct physiological studies [15]. More importantly, on-tree and non-destructive volume estimates can be used as a ripeness index to predict maturity and optimum harvest time, and can be used while deciding packing material (tray insert) purchasing and marketing arrangements [16]. For physiological studies, measurement of the size of individual fruit over time allows monitoring fruit expansion rate and its response to physiological disorders and agronomic conditions [16, 17]. Moreover, in the context of postharvest operations, fruit size determination is important for several reasons, such as to determine packing material, fruit classified into batches of uniform size, assign market and price differentials of large and small produce, to match consumer preferences [18]. Thus, the availability of reliable fruit size information is critical in horticultural crop processing and marketing. Fruit volume is also a good measure of size, but direct measurement of fruit volume using water displacement approach is time-consuming as well as impractical under field conditions. On the other hand, length and width measurements of avocado fruit are quick and easy in the field or indoors and can be used to numerically represent fruit volume and weight. Therefore, this study was conducted to: (a) determine fruit volume of five avocado cultivars, (b) determine which biometric parameter of the avocado fruit best correlates with volume; (c) derive various cultivar-specific and mixed-cultivar allometric equations to predict fruit volume and (d) to evaluate the predictive performances of the equations and to identify the best allometric equation for the study region.

Materials and methods

Study area and climate characteristics

The study was conducted in the Upper Gana (7° 34’ 24” N, 37° 46’ 4”E) and Jewe (7° 30’ 35” N, 37° 47’ 1”) Kebeles of Limu district, situated in Hadiya zone, in the Ethiopian Southern Nations, Nationalities, and Peoples’ Region (SNNPR) [19] (Fig 1). The study area is located at 223 km South of Addis Ababa. The altitudinal ranges of Jewe and upper-Gana Kebles were between 2000 and 2400m (Fig 1). Based on the data from the Central Statistical Agency of Ethiopia (CSA), the district has an estimated total population of 153,783 and 93% of the people are living in the rural areas and practicing subsistence farming depending on rainfed production system [20]. The average farm size per family head was estimated to be 0.5 ha [19].

Fig 1

The location of the study area in Hadiya zone, Ethiopia.

The shape files were accessed from open data sources of the open AFRICA https://open.africa/dataset/africa-shapefiles), http://geoportal.icpac.net/layers/geonode%3Aafr_g2014_2013_0 (Open access).

In the study area, the annual rainfall ranges between 1300 and 1400 mm with a bi-modal rainfall seasonality, occurring from February to April and from June to September [19]. The average annual minimum and maximum temperatures were 18°C and 23°C [19]. The typical land use system of the district is characterized by Agroforestry (i.e., mixed crop-tree-livestock production) [21]. The district has a favourable climate and agroecological condition for multi-strata agroforestry and home garden intensive farming system.

Tree selection for sample fruit collection

In this study, five different avocado cultivars including Ettinger (race—Guatemalan (G) X Mexican (M) hybrid), Fuerte (race–G X M), Hass (race—G X M), Nabal (race—G), and Reed (race—G) were considered (Fig 2, S1 File) [22, 23]. From each cultivar, 30 avocado trees, representing 30 small-scale farmlands, were selected for fruit sample collection. Fruit samples were collected considering each radii of the crown [24-27]. A total of 360 fruit samples were randomly harvested from each cultivar (i.e., three fruits from each radius or 12 sample fruits per tree = 12 fruit X 30 trees = 360 fruits). Then, fruit length (FL in mm), diameter (FD in mm) and weight (FW in g) were measured using digital calliper and weighing scale, respectively. For fruit volume measurement, the collected sample fruits were first classified into three sizes (small, medium, and large). Then, 15 fruits were randomly selected from each size class (total = 45 fruits from each cultivar). For each fruit, actual fruit volume (AFV) was measured using water displacement method [15, 28], in the Biotechnology Laboratory of Wachemo University (WCU), Hossana, Ethiopia.

Fig 2

Photographic documentation of the studied avocado cultivars during fruit sample collection.

Model development, performance evaluation and cross-validation test

Cultivar-specific and mixed-cultivar generalized avocado fruit volume (FV) estimation models were developed using linear and non-linear regression equations based on either fruit diameter, fruit length alone or both fruit length and diameter at the same time as independent variables. Moreover, using two predictors (i.e., length and diameter) may introduce potential problems of co-linearity, resulting in poor precision in the estimates of the corresponding regression coefficients [29]. Thus, we conducted a multicollinearity analysis using Variance Inflation Factors (VIF = 1/(1-r2) and the Tolerance Values (T = 1/VIF) [30]; where r is the correlation coefficient between length and diameter of fruit. VIF value exceeding 10 or if T value was smaller than 0.10 then co-linearity may have a considerable impact on the prediction of the parameters, and consequently, one of those should be excluded from the model [31, 32].

Model performance was checked using various goodness-of-fit statistics, such as the Coefficient of Determination (R2), Standard Error of Estimate (SEE), Index of Agreement (D), Mean Absolute Bias (MAB), Percent Bias (PBIAS), Root Mean Square Error (RMSE), Prediction Residuals Sum of Squares (PRESS), Reduction of Error (RE), and Coefficient Efficiency (CE), [33-35]. The estimation models with higher R2 may sometimes also have unstable parameters estimates. Thus, we further calculated Percent Relative Standard Error (PRSE) of the coefficients and Weighted Akaike information criterion (AICiw) to check the stability of model parameter estimates [29]. Outlier and influential diagnostic test statistics, including Cook’s distance, Leverage point, Studentized Residuals and DFFITS were analysed to examine the accuracy of model fit [29, 36]. Finally, models were evaluated and ranked based on all goodness-of-fit statistics, outlier, and influential diagnostic statistics [35].

To validate the best fitting equation for volume estimation, model cross-validation was conducted following a split-sample approach in which 45 measured fruit sample were partitioned into two sets, 33 for ‘‘training” (i.e., to develop the equations) and the remaining 12 fruit samples for ‘‘testing” the equations. The partitioning was performed according to the following procedure. From each size class (small, medium, and large) of the samples, four samples were randomly selected to perform the ‘‘test” dataset and the remaining sample fruits were used to form the ‘‘training” dataset. The goodness-of-fit statistics and equation coefficients of the ‘‘training” equations were compared with those derived using the full dataset, and the estimated and measured volume of ‘‘test” sample fruit was compared [35, 37, 38]. Finally, the full dataset was used to build fruit volume estimation models.

Statistical analysis

Pearson correlation tests were conducted between actual AFV-FD and FL to be able to identify which fruit biometric variables were most strongly correlated with FV. A correlation analysis was also conducted between independent variables (i.e., FL vs FD). The differences among avocado cultivars in AFV was assessed using one-way analysis of variance and the significance of differences were tested using the least significant difference test (LSD) with P < 0.05 [35].

Results and discussion

The relationship of physical characteristics of avocado fruits

The physical characteristics of sample avocado fruits and their statistical attributes are presented in Table 1. The AFV ranged from 125–480 cm3, FW ranged from 129 – 595g, FL ranged from 64.5–129.9 mm, and FD ranged from 53.8–99.8 mm (Table 1). These findings are in line with other reports [2, 39, 40]. Information on fruit physical appearance is important for the customer who is used to assess the quality and taste of fresh product influencing the purchase decision [16].

Table 1

Summary of volume, and fruit size characteristics of five avocado cultivars.

	Fruit Length (mm)		Fruit Diameter (mm)		Fruit wight (g)		Fruit Volume (cm3)
SPP name	Mean [SE]	Range	Mean [SE]	Range	Mean [SE]	Range	Mean [SE]	Range
Ettinger	108.9 [±1.5]	91.9–129.9	69.1 [±0.9]	57.1–84.2	253 [±8.8]	162–375	274.1 [±10.1]	145–410
Fuerte	106.2 [±1.4]	87.7–124.6	68.4 [±0.8]	57.4–79.6	248.8 [±8.2]	146–348	252.0 [±7.4]	150–350
Hass	90.3 [±1.4]	72.8–113.9	64.7 [±0.8]	53.8–76	192.6 [±7.0]	116–310	181.6 [±5.8]	110–300
Nabal	92.6 [±1.5]	70.1–118.7	82.6 [±1.2]	65.8–99.8	331.9 [±13.8]	160–595	324.7 [±11.3]	180–480
Reed	81.3 [±1.3]	64.5–98.1	74.1 [±1.1]	60.8–89.2	242.3 [±10.3]	129–426	247.1 [±10.4]	125–420

The relationship between FV and other pomological traits (i.e., FL, FD,) were significant (P < 0.01) (Fig 3) and that is in agreement with other studies that have shown strong relationships between different pomological traits of avocado fruit [2]. Moreover, the correlation between FD and FV were consistently stronger compared to the relationship between FL and FV (Fig 3), indicating the FD is a very good predictor of fruit volume and highlighting those changes in diameter, therefore, affects the fruit volume more than does a change in fruit length. More importantly, knowing the relationship between fruit physical characteristics is critical in the horticultural sector because these pomological traits are sometime used as fruit maturity index [2, 41, 42]. Several indices have been used to determine avocado fruit maturity, hence there is no single factor can be considered the most important; however, it can be stated that from a postharvest standpoint, quality begins at harvest with physiological maturity. This indicates that understanding the stage of physiological maturity is critical for the development of a successful avocado fresh fruit industry while assuring the quality to the consumer [43].

Fig 3

Fruit volume as a function of fruit length, diameter, and regression of fruit diameter as a function of fruit length.

On Fig 3, the letter E, F, H, N, R and M refers Ettinger, Fuerte, Hass, Nabal, Reed and Mixed cultivar data.

Allometric equations and model cross-validation

As a preliminary step to model calibration, the degree of collinearity among fruit length and diameter was analysed. The VIF was ranged from 1.1 to 4.6 and T values ranged from 0.21 to 0.95, depending on cultivar type, respectively (S1 Table). Hence, for all selected genotypes, VIF was < 10 and T was > 0.10, showing that the co-linearity between predictors (fruit length and diameter) is negligible, thus both predictors (FL, FD) were considered during model formation [31, 32] (S1 Table).

Cultivar-specific and mixed cultivar generalized volume model was developed to approximate the shape of avocado fruits using either fruit length (FL) or width (FD) separately and using both predictors at a time. We found that the predictive performance of tested model form were varied within cultivar (Table 2, S1 Table). This might be attributed to differences in the equation forms and predictors included in the models [35]. Allometric model performance analysis and cross-validation test results showed that the Linear Regression Model (MV2) which includes only FD as predictor was ranked the best model given the set of nine (9) candidate model forms for all cultivar-specific models, while the Multiple Linear Regression Model (VM7) was the best for generalized mixed cultivar model (Table 2), and detailed model performance statistics for all tested model forms are presented in S1 Table).

Table 2

Equations and goodness-of-fit performance statistics for estimating avocado fruit volume of five different cultivars and multiple cultivars grown in Limo district, Hadiya, zone.

Model forms	Model forms	Coefficient			Performance statistics												PRSE			Rank
		a	b	c	R2	SEE	PRESS	RMSE	PBIAS	MAB	Di	RE	CE	AICi	Δi(AIC)	Wi(AIC)	a	b	c
Ettinger
VM2	a*FD + b	10.4484***	-447.701***		0.94	17.53	13210.88	17.13	0.00	12.20	0.98	1.00	0.94	259.70	11.31	0.00	4.0	-6.5		1
VM4	a*FD^2	0.0575***			0.88	24.19	25752.29	23.92	-0.94	18.94	0.96	0.99	0.88	287.73	39.34	0.00	1.2			2
VM9	a*(FL*FD)^2	4.53E-06***			0.74	35.17	54412.87	34.77	2.71	28.37	0.95	0.98	0.74	321.40	73.01	0.00	1.9			3
Fuerte
VM2	a*FD + b	8.369***	-320.756***		0.92	14.81	9425.88	14.47	0.00	10.93	0.98	1.00	0.92	244.50	0.22	0.46	4.6	-8.3		1
VM4	a*FD^2	0.0536***			0.89	16.33	11733.34	16.15	-0.31	12.71	0.97	1.00	0.89	252.36	8.07	0.01	0.9			2
VM7	a+ b*FL + c*FD	-333.124***	0.5107	7.757***	0.92	14.62	8973.05	14.12	0.00	10.62	0.98	1.00	0.92	244.29	0.00	0.52	-8.3	68.5	7.3	3
Hass
VM2	a*FD + b	6.5239***	-240.661***		0.87	14.33	8832.76	14.01	0.00	9.00	0.96	0.99	0.87	306.82	69.78	0.00	5.8	-10.3		1
VM4	a*FD^2	0.0432***			0.86	14.65	9438.43	14.48	-0.41	10.30	0.96	0.99	0.86	237.04	0.00	0.71	1.2			2
VM7	a+ b*FL + c*FD	-252.658***	0.5479	5.945***	0.88	13.93	8149.19	13.46	0.00	9.03	0.97	0.99	0.88	239.96	2.91	0.17	-9.9	53.3	8.1	3
Nabal
VM2	a*FD + b	9.314***	-444.277***		0.93	20.20	17549.35	19.75	0.00	14.44	0.98	1.00	0.93	272.47	7.34	0.02	5.57	-7.13		1
VM4	a*FD^2	0.0475***			0.90	24.42	26241.01	24.15	-0.63	20.08	0.97	0.99	0.90	288.58	23.45	0.00	1.05			2
VM1	a*FL + b	6.8725***	-311.718***		0.80	34.55	51343.88	33.78	0.00	27.55	0.94	0.99	0.80	320.78	55.65	0.00	7.55	-15.51		3
Reed
VM2	a*FD + b	9.3255***	-443.701***		0.94	17.99	13912.04	17.58	0.00	13.52	0.98	1.00	0.94	262.02	9.72	0.01	4.0	-6.2		1
VM4	a*FD^2	0.0453***			0.86	25.95	29637.53	25.66	-1.56	21.66	0.95	0.99	0.86	294.06	41.76	0.00	1.5			2
VM1	a*FL + b	7.0449***	-325.924***		0.83	29.02	36221.43	28.37	0.00	22.30	0.95	0.99	0.83	305.08	52.79	0.00	6.8	-12.0		3
Mixed
VM7	a+ b*FL + c*FD	-435.118***	1.8844***	7.110***	0.93	20.23	90851.70	18.84	0.00	15.44	0.98	0.99	0.93	1327.16	0.00	1.00	-3.0	5.2	2.2	1
VM2	a*FD + b	7.7671***	-301.595***		0.82	32.86	240785.37	29.00	0.00	27.08	0.95	0.99	0.82	1519.21	192.04	0.00	3.1	-5.8		2
VM4	a*FD^2	0.0491***			0.81	33.77	255523.93	30.18	-0.41	27.80	0.94	0.98	0.81	1535.16	208.00	0.00	0.8			3

*** is significant at P<0.001. Bold PRSE values indicates unreliable parameter estimates.

Our best model explained 94%, 92%, 87%, 93%, 94% and 93% of variation in fruit volume in Ettinger, Fuerte, Hass, Nabal, Reed and mixed-avocado cultivar model, respectively (Fig 4, Table 2, in S1 Table for more details). The three best-performing models for each avocado cultivar and mixed-cultivar are shown in Table 2, where the influence of coefficients was significant (P < 0.01) (Table 2). Our best model (VM2 for cultivar specific) and VM7 –for mixed cultivar models have passed all the rigorous verification and cross-validation statistical test and produced the lowest average relative error (PBIAS%), implying that fruit diameter is reliable predictors of cultivar specific fruit volume, while using both FL and FD might increase the predictive performances of generalized allometric models (S1 Table). Moreover, the performance of our best models (VM2, and VM7) to make an accurate prediction is not an artifact of overfitting, because the parameter values were stable across the subset of the cross-validations “training data set” and full data set (S1 Table). Moreover, the volume of the twelve ‘‘test” fruit volume estimated with the cross-validation equations (i.e., training dataset) differed little from the values estimated with equations produced with the full dataset (Fig 5, S1 Table). The deviations (PBIAS%) in the volume estimates between the two sets of equations were less than 1% for all and mixed cultivar equations (Fig 5). Moreover, the PRSE value of < 20% and outliers and influential points of less than 10% of the total observation as well as higher positive value of CE, and RE provides evidence that the parameter estimates were reliable in the selected best models [29, 44–46] (S1 Table). Thus, VM2 (i.e., cultivar-specific model) and VM7 (i.e., generalized model) are reliable to determine the fruit volume based on their easily measurable fruit pomological traits (i.e., FL or/and FD). Furthermore, measuring fruit length and diameter are easy in the field, thus site-and cultivar-specific allometric model would enable researchers to make non-destructive or repeated measurements on the same fruits. Our allometric models could provide accurate estimate of avocado fruit volume and may reduce required time and financial resources while using common method of volume measurements like water displacement, gas displacement and expensive instruments, e.g., image processing software or machine vision techniques. In line with this, review literature showed that there are different non-destructive volume estimation models developed from easily measurable parameters for different type of fruits such as pepper [15, 17], Babassu (Attalea speciosa) fruit [47], Karanda (Carissa carandas) fruit [31], and Apple fruit [48]. Our findings confirmed that non-destructive allometric models based on easily measurable morphometric dimensions can be more accurate and practical in field conditions than destructive methods used in traditional growth curves [18].

Fig 4

Relationships between FV and FD (left panel) and corresponding residual plots (right). Figs A-F refers Ettinger (A), Fuerte (B), Hass (C), Nabal (D), Reed (E) and Mixed species (F).

Fig 5

Relationship between estimated and measured fruit volume of the 12 cross-validation test fruits.

Circles are the volume estimates calculated using the full data set equations and the crosses are the estimates calculated using the cross-validation training dataset equations. On Fig 5, the letter E, F, H, N, R and M refers Ettinger, Fuerte, Hass, Nabal, Reed and Mixed cultivar data.

Conclusions and recommendation

This study provided the first avocado cultivar-specific and mixed-cultivar generalized allometric equations to estimate avocado fruit volume non-destructively. Among tested model forms, VM2 (for cultivar-specific model), and VM7 (generalized model) have passed all rigorous verification and cross-validation statistical tests, confirming that the models have sufficient skill to estimate fruit volume from easily measurable parameters. Our best allometric models (VM2 and VM7) explained > 87% of the variation in measured fruit volumes of each cultivar. A high degree of correlation (R2 > 0.93) between measured and estimated fruit volume provided quantitative evidence of the validity of the selected volume estimation models. The allometric equation developed in this research could be practical in the estimation of avocado fruit volume and applicable under field conditions. Besides, the generalized mixed-cultivar model can reliably be used to estimate avocado fruit volume when cultivar type is unknown. Our finding revealed that in the situations where fruit length and diameter measurements are possible and/or where measurements of volume would be inconvenient, or time-consuming, site- and cultivar-specific allometric equations can be used to estimate fruit volume while it is on the tree. Therefore, the allometric equations generated in this study could play a considerable role in improving data availability on avocado fruit physical appearance which is critical to assess the quality and taste of fresh products, which in turn, influences the purchase decision of customers. It can also potentially assist horticulturists, agronomists, and physiologists to estimate fruit volume of avocado accurately and to carry out yield estimation before harvesting. Finally, we also recommend conducting a similar study using a large dataset collected from different agro-ecological regions, which would help to have a robust generalized and species-specific avocado volume estimation model that can be used across regions.

Colored photograph of five Avocado cultivars.

(PDF)

Click here for additional data file.

Model performance statistics.

(XLSX)

Click here for additional data file.

10 Dec 2021

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Sajid Ali

Academic Editor

PLOS ONE

Journal requirements:

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. We suggest you thoroughly copyedit your manuscript for language usage, spelling, and grammar. If you do not know anyone who can help you do this, you may wish to consider employing a professional scientific editing service.

Whilst you may use any professional scientific editing service of your choice, PLOS has partnered with both American Journal Experts (AJE) and Editage to provide discounted services to PLOS authors. Both organizations have experience helping authors meet PLOS guidelines and can provide language editing, translation, manuscript formatting, and figure formatting to ensure your manuscript meets our submission guidelines. To take advantage of our partnership with AJE, visit the AJE website (http://learn.aje.com/plos/) for a 15% discount off AJE services. To take advantage of our partnership with Editage, visit the Editage website (www.editage.com) and enter referral code PLOSEDIT for a 15% discount off Editage services.  If the PLOS editorial team finds any language issues in text that either AJE or Editage has edited, the service provider will re-edit the text for free.

Upon resubmission, please provide the following:

The name of the colleague or the details of the professional service that edited your manuscript

A copy of your manuscript showing your changes by either highlighting them or using track changes (uploaded as a *supporting information* file)

A clean copy of the edited manuscript (uploaded as the new *manuscript* file)”

3. Please ensure that you refer to Figure 4 in your text as, if accepted, production will need this reference to link the reader to the figure.

4. We note that Figure 1 in your submission contain [map/satellite] images which may be copyrighted. All PLOS content is published under the Creative Commons Attribution License (CC BY 4.0), which means that the manuscript, images, and Supporting Information files will be freely available online, and any third party is permitted to access, download, copy, distribute, and use these materials in any way, even commercially, with proper attribution. For these reasons, we cannot publish previously copyrighted maps or satellite images created using proprietary data, such as Google software (Google Maps, Street View, and Earth). For more information, see our copyright guidelines: http://journals.plos.org/plosone/s/licenses-and-copyright.

We require you to either (1) present written permission from the copyright holder to publish these figures specifically under the CC BY 4.0 license, or (2) remove the figures from your submission:

a. You may seek permission from the original copyright holder of Figure 1 to publish the content specifically under the CC BY 4.0 license.

We recommend that you contact the original copyright holder with the Content Permission Form (http://journals.plos.org/plosone/s/file?id=7c09/content-permission-form.pdf) and the following text:

“I request permission for the open-access journal PLOS ONE to publish XXX under the Creative Commons Attribution License (CCAL) CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). Please be aware that this license allows unrestricted use and distribution, even commercially, by third parties. Please reply and provide explicit written permission to publish XXX under a CC BY license and complete the attached form.”

Please upload the completed Content Permission Form or other proof of granted permissions as an "Other" file with your submission.

In the figure caption of the copyrighted figure, please include the following text: “Reprinted from [ref] under a CC BY license, with permission from [name of publisher], original copyright [original copyright year].”

b. If you are unable to obtain permission from the original copyright holder to publish these figures under the CC BY 4.0 license or if the copyright holder’s requirements are incompatible with the CC BY 4.0 license, please either i) remove the figure or ii) supply a replacement figure that complies with the CC BY 4.0 license. Please check copyright information on all replacement figures and update the figure caption with source information. If applicable, please specify in the figure caption text when a figure is similar but not identical to the original image and is therefore for illustrative purposes only.

The following resources for replacing copyrighted map figures may be helpful:

USGS National Map Viewer (public domain): http://viewer.nationalmap.gov/viewer/

The Gateway to Astronaut Photography of Earth (public domain): http://eol.jsc.nasa.gov/sseop/clickmap/

Maps at the CIA (public domain): https://www.cia.gov/library/publications/the-world-factbook/index.html and https://www.cia.gov/library/publications/cia-maps-publications/index.html

NASA Earth Observatory (public domain): http://earthobservatory.nasa.gov/

Landsat: http://landsat.visibleearth.nasa.gov/

USGS EROS (Earth Resources Observatory and Science (EROS) Center) (public domain): http://eros.usgs.gov/#

Natural Earth (public domain): http://www.naturalearthdata.com/

Reviewers' comments:

Reviewer #1: Dear,

This study provided the first avocado cultivar-specific and mixed-cultivar generalized allometric equations to estimate avocado fruit volume non-destructively.

Major comments:

1. The title of the article does not provide a clear picture of the subject under consideration. The title implies that a general allometric model for all tropical crops is provided, but this model was only used for non-destructive measurement of avocado fruit volume. As a result, it is suggested that the article be given a more accurate title.

2. Avocado is a highly variable species and three botanical subspecies or ecological races of P. americana Mill. were recognized: Mexican (M) (var. drymifolia), Guatemalan (G) (var. guatemalensis), and West Indian (WI) (Antillean) (var. americana). Cultivars derived from Guatemalan and Mexican races and their hybrids are grown primarily in subtropical climates and have physiological adaptations to cooler temperatures, as opposed to cultivars derived from West Indian race or WI­hybrids, which are adapted to tropical climates.

Regarding this horticultural fact, there must be consistency throughout the manuscript's text as well as title. Now, none of the cultivars studied in this study are of tropical origin.

Using the words 'tropical' in the title and line 17 and 'subtropical' in line 40 made inconsistencies that must be addressed.

3. According to line 117: “model performance was checked using various goodness-of-fit statistics, such as the Coefficient of Determination (R2), Standard Error of Estimate (SEE), Index of Agreement (D), Mean Absolute Bias (MAB), Percent Bias (PBIAS), Root Mean Square Error (RMSE), Prediction Residuals Sum of Squares (PRESS), Reduction of error (RE), and Coefficient efficiency (CE)”.

As is obvious, the regression was run separately for the actual fruit volume and each of the independent variables, such as fruit length, fruit weight, and fruit diameter. In other words, a single factor regression has been investigated (Length with volume, diameter with volume and weight with volume). As you are aware, mathematical relationships such as regression between the sum of length and diameter with volume, regression between the multiplication of length and diameter by volume, or regression between the square of length + diameter by volume are preferable. It is strongly advised to provide better estimation by providing more mathematical relationships between fruit length and diameter and regressing them with fruit volume so that a better choice between them can be made.

4. According to section 2.3: “Cultivar-specific and mixed-cultivar generalized avocado fruit volume (FV) estimation models were developed using linear and non-linear regression equations based on either fruit diameter, fruit length alone or both fruit length and diameter at the same time as ndependent variables”.

Please include both linear and non-linear regression equations in the table, as well as the Goodness of Fit for the linear equation. If a non-linear equation is used, please explain it using terms such as logarithm, polynomial, and so on. Non-linear regression can provide more accurate predictions and is especially valuable for biological data. The value and strength of the proposed model are increased by including these items.

5. According to line 128: “To validate the best fitting equation for volume estimation, model cross-validation was conducted following a split-sample approach in which 45 measured fruit sample were partitioned into two sets, 33 for ‘‘training’’ (i. e., to develop the equations) and the remaining 12 fruit samples for ‘‘testing’’ the equations”.

Twelve fruits from each cultivar were used for testing (validation), which appears insufficient and represents a small statistical population. Moreover, validation requires sampling from other gardens or areas in the same climate. In other words, performing large-scale sampling will result in strong validation with a high correlation coefficient.

6. After obtaining the model and estimating the data, regression validation should be performed to determine whether a suitable correlation coefficient exists. Please include graphs of validation-related correlations.

Minor comments:

1. Line 17: Mill -> Mill (non-italicized)

2. Line 17: remove "genus Persea" at the end.

3. Line 19: The physical characteristic -> The physical characteristics

4. Line 23: "five wildly distributed avocado verities" -> Q: five varieties or cultivars? As mentioned in the materials and methods section, they are 5 avocado cultivars.

5. Line 23: "five wildly distributed avocado verities" -> … varieties

6. Line 24: found between Fruit diameter -> fruit

7. Line 58: small scall avocado farming -> scale

8. Line 59: information of fruit size are critical factors -> is critical

9. Line 73: five avocado verities -> … varieties (Q: five varieties or cultivars?)

10. Line 77: Materials and methods -> Materials and Methods

11. Line 78: 2.1 -> 2.1.

12. Line 101: classified in to three size -> into

13. Line 130: i. e. -> i.e.

14. Line 139: Fruit volume -> fruit volume

15. Line 145: Result and discussion -> Results and Discussion

16. Line 234: (VM2 and VM2) -> ?

17. Line 312: reference # 18: ?

Other comments:

1. The main body and reference section must be adjusted in accordance with the author's guidelines.

2. The manuscript must be significantly improved and rewritten as a result of comments and suggestions. All of the issues raised should be addressed. The manuscript must then be reassessed for quality and suitability for publication in PLOS ONE.

Reviewer #2:

Manuscript presents allometric models to non-destructively predict avocado fruit volume under both cultivar-specific and mixed-cultivar production systems. Introduction, Materials and Methods, and Results and Discussion sections are adequately written and justify the claims made in the manuscript. Data collection method, and statistical tests sufficiently verify the models. I suggest to maturity level of fruit at the time of harvest and add a colored photograph showing morphological differences among avocado fruits from studied cultivars. Since, all models have some limitations, it would be appropriate to add limitations for these models, too. Some English language improvements are suggested in the reviewed version of the manuscript.

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Submitted filename: PONE-D-21-36255_reviewer.pdf

Click here for additional data file.

18 Dec 2021

Response to reviewers comment

ID: PONE-D-21-36255

Title: Volume estimation models for tropical fruit

Dear Editor

First, we would like to express our sincere appreciation to you and the anonymous reviewers for their very insightful and constructive comments and suggestions to our manuscript. Kindly find the response to each of the comments below. We believe we were able to address all suggestions and comments adequately, otherwise please contact us.

Response to the editor: We are very great full for your comment and suggestion. We amended the structure/style of the revised manuscript as the journal guideline. Regarding, fig 1, we reproduced the map by taking the shapefiles from openAFRICA ( open sources Africa Shapefiles, please see: -https://open.africa/dataset/africa-shapefiles); http://geoportal.icpac.net/layers/geonode%3Aafr_g2014_2013_0.

On behalf of all co-authors,

Sincerely,

Mulugeta Mokria

Response to reviewer #1

This study provided the first avocado cultivar-specific and mixed-cultivar generalized allometric equations to estimate avocado fruit volume non-destructively.

Major comments:

Comment #1. The title of the article does not provide a clear picture of the subject under consideration. The title implies that a general allometric model for all tropical crops is provided, but this model was only used for non-destructive measurement of avocado fruit volume. As a result, it is suggested that the article be given a more accurate title.

Response #1: We thank the reviewer for making a very important point and we revised the title to “Volume estimation models for avocado fruit” please see line 1 in the revised manuscript.

Comment #2. Avocado is a highly variable species and three botanical subspecies or ecological races of P. americana Mill. were recognized: Mexican (M) (var. drymifolia), Guatemalan (G) (var. guatemalensis), and West Indian (WI) (Antillean) (var. americana). Cultivars derived from Guatemalan and Mexican races and their hybrids are grown primarily in subtropical climates and have physiological adaptations to cooler temperatures, as opposed to cultivars derived from West Indian race or WI-hybrids, which are adapted to tropical climates.

Regarding this horticultural fact, there must be consistency throughout the manuscript's text as well as title. Now, none of the cultivars studied in this study are of tropical origin.

Using the words 'tropical' in the title and line 17 and 'subtropical' in line 40 made inconsistencies that must be addressed.

Response #2: The reviewer makes a very important point, and we are grateful for that. Thus, we amended the titles and avoided the inconsistency in using the term “Tropical” through the manuscripts. Please see lines 1, 17, 38 in the revised manuscript.

Comment #3. According to line 117: “model performance was checked using various goodness-of-fit statistics, such as the Coefficient of Determination (R2), Standard Error of Estimate (SEE), Index of Agreement (D), Mean Absolute Bias (MAB), Percent Bias (PBIAS), Root Mean Square Error (RMSE), Prediction Residuals Sum of Squares (PRESS), Reduction of error (RE), and Coefficient efficiency (CE)”.

As is obvious, the regression was run separately for the actual fruit volume and each of the independent variables, such as fruit length, fruit weight, and fruit diameter. In other words, a single factor regression has been investigated (Length with volume, diameter with volume and weight with volume). As you are aware, mathematical relationships such as regression between the sum of length and diameter with volume, regression between the multiplication of length and diameter by volume, or regression between the square of length + diameter by volume are preferable. It is strongly advised to provide better estimation by providing more mathematical relationships between fruit length and diameter and regressing them with fruit volume so that a better choice between them can be made.

Response #3: The reviewer makes a very important point, and we are grateful for that. As hinted by the reviewer, we have tested about 9 model forms (see the supplementary information - S2_Model Performance statistics.xls) and we selected the three most potential models and their estimation efficiency also depends on the varieties. Please see the revised manuscript.

Comment #4. According to section 2.3: “Cultivar-specific and mixed-cultivar generalized avocado fruit volume (FV) estimation models were developed using linear and non-linear regression equations based on either fruit diameter, fruit length alone or both fruit length and diameter at the same time as independent variables”.

Please include both linear and non-linear regression equations in the table, as well as the Goodness of Fit for the linear equation. If a non-linear equation is used, please explain it using terms such as logarithm, polynomial, and so on. Non-linear regression can provide more accurate predictions and is especially valuable for biological data. The value and strength of the proposed model are increased by including these items.

Response #4: We thank for the suggestions. We provided both linear and non-linear regression equations and with their goodness of fit statistics (Please see the Supplementary information- S2_Model Performance statistics.xls). However, for simplicity, we provided only the three most performed equations in the main text and supplied the statistical performances of all tested models in the supplementary information document with more explanation (S2_Model Performance statistics.xls).

Comment #5. According to line 128: “To validate the best fitting equation for volume estimation, model cross-validation was conducted following a split-sample approach in which 45 measured fruit sample were partitioned into two sets, 33 for ‘‘training’’ (i. e., to develop the equations) and the remaining 12 fruit samples for ‘‘testing’’ the equations”.

Twelve fruits from each cultivar were used for testing (validation), which appears insufficient and represents a small statistical population. Moreover, validation requires sampling from other gardens or areas in the same climate. In other words, performing large-scale sampling will result in strong validation with a high correlation coefficient.

Response #5: The reviewer makes a very important point. We share the concern of the reviewers’ and agree on model validation using large and independent data will result greater confidence on model selection and use. However, we could not find such independent data in Ethiopia, and we also collected only 45 sample fruit from each variety. There for, we indicated as the limitation of the manuscript and suggested the need for further study using large database (if available). Please see lines 250 -252, in the revised manuscript.

Comment #6. After obtaining the model and estimating the data, regression validation should be performed to determine whether a suitable correlation coefficient exists. Please include graphs of validation-related correlations.

Response #6: We thanks the review for pointing out this and we have provided a cross-validation graph. please see line 225, Fig 5, in the revised manuscript.

Minor comments:

Comment #1. Line 17: Mill -> Mill (non-italicized)

Response #1: We revised the text accordingly, please see line 17 in the revised manuscript.

Comment #2. Line 17: remove "genus Persea" at the end.

Response #2: We removed the word “genus Persea, please see line 17”in the revised manuscript.

Comment #3. Line 19: The physical characteristic -> The physical characteristics

Response #3: Thanks, we revised the text accordingly, please see line 18 in the revised manuscript.

Comment #4. Line 23: "five wildly distributed avocado verities" -> Q: five varieties or cultivars? As mentioned in the materials and methods section, they are 5 avocado cultivars.

Response #4: We thanks the review for pointing out this and changed the text to “cultivars” through the manuscript, please see line 23 in the revised manuscript.

Comment #5. Line 23: "five wildly distributed avocado verities" -> … varieties

Response #5: Thanks, corrected accordingly, please see line 23 in the revised manuscript

Comment #6. Line 24: found between Fruit diameter -> fruit

Response #6: We revised the text accordingly, please see line 23 in the revised manuscript.

Comment #7. Line 58: small scall avocado farming -> scale

Response #7: Thanks, corrected accordingly, please see line 55 in the revised manuscript.

Comment #8. Line 59: information of fruit size are critical factors -> is critical

Response #8: Corrected, please line 56 in the revised manuscript

Comment #9. Line 73: five avocado verities -> … varieties (Q: five varieties or cultivars?)

Response #9: Thanks, changed to cultivars through the manuscript, please see line 70 in the revised manuscript.

Comment #10. Line 77: Materials and methods -> Materials and Methods

Response #10: We revised the text accordingly, please see line 74 in the revised manuscript.

Comment #11. Line 78: 2.1 -> 2.1.

Response #11: Thanks, revised accordingly, please see line 75 in the revised manuscript.

Comment #12. Line 101: classified in to three size -> into

Response #12: We revised the text accordingly, please see line 101 in the revised manuscript

Comment #13. Line 130: i. e. -> i.e.

Response #13: Thanks, corrected accordingly, please see line 133 in the revised manuscript

Comment #14. Line 139: Fruit volume -> fruit volume

Response #14: We revised the text accordingly, please see line 140 in the revised manuscript

Comment #15. Line 145: Result and discussion -> Results and Discussion

Response #15: We revised the text accordingly, please see line 147 in the revised manuscript

Comment #16. Line 234: (VM2 and VM2) -> ?

Response #16: Corrected and VM2 is changed to VM7, please see line 235 in the revised manuscript.

Comment #17. Line 312: reference # 18: ?

Response #17: We thank the reviewer for pointing out this, and corrected it accordingly, please lines 314-15, in the revised manuscript.

Other comments:

Comment #1. The main body and reference section must be adjusted in accordance with the author's guidelines.

Response #1: We thank the reviewer for pointing out this. We corrected the main body and the reference style as per the journal user guide.

Comment #2. The manuscript must be significantly improved and rewritten as a result of comments and suggestions. All of the issues raised should be addressed. The manuscript must then be reassessed for quality and suitability for publication in PLOS ONE.

Response #2: We thank the review for constructive comments and suggestions to our manuscript. We believe we were able to include all suggestions and comments in an adequate way, otherwise please contact us.

Response to reviewer #2

Reviewer #2:

Manuscript presents allometric models to non-destructively predict avocado fruit volume under both cultivar-specific and mixed-cultivar production systems. Introduction, Materials and Methods, and Results and Discussion sections are adequately written and justify the claims made in the manuscript. Data collection method, and statistical tests sufficiently verify the models. I suggest to maturity level of fruit at the time of harvest and add a colored photograph showing morphological differences among avocado fruits from studied cultivars. Since, all models have some limitations, it would be appropriate to add limitations for these models, too. Some English language improvements are suggested in the reviewed version of the manuscript.

Response #: We thank the review for constructive comments and suggestions to our manuscript. We added a colored photograph showing morphological differences of each avocado cultivars (Please see Fig 1 lines 106-107, and S1_Colored photograph of five Avocado cultivars.pdf, line 394 in the revised manuscript. In addition, we have added a recommendation to conduct a similar study using a large dataset to improve model performances and that can be used across regions (Please lines 249- 252, in the revised manuscript). We believe we were able to include all suggestions and comments including some language aspects in an adequate way.

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

10 Jan 2022