Co-occurrence analysis based on keywords

As per Fig. 3, the positioning of 652 keywords on the map was based on a clustering algorithm allocated by VOSviewer software 1.6.18. The similarity of any two keywords is inversely proportional to the distance between, with a smaller distance indicating a stronger similarity or relationship between the keywords (McAllister et al., Reference McAllister, Lennertz and Atencio Mojica2021). The frequency co-occurrence clearly shows the main keywords as well as how keywords link to each other within our field of study. We found that, the highest number of articles have been forcused on the mathematical modelling of banana fruit yield. The smallest occupancy is visualized by ‘natural-fibre’ within the context of our review title, signifying that a lower number of studies have been executed on this subject (Fig. 3).

Fig. 3. Colour online. The co-occurrence of keyword map based on the 75 selected full-text articles on mathematical models to estimate yield and growth of banana. Note. The occurrence of keywords was specified to the colour of a specific cluster algorithm.

The map identified six keyword clusters [(1) prediction/crop yield/growth rate, etc, (2) fruits, (3) natural fibre/tensile strength, (4) musa/banana (5) fruit production and (6) numerical model/ regression] based on probabilistic latent semantic analysis (McAllister et al., Reference McAllister, Lennertz and Atencio Mojica2021). Except for some noticeable overlap on the left side of the map where clusters of 5 and 6 terms are related and had tied together with clusters 1 and 4, most of the clusters (e.g., 1, 2, 3, 4) are distinguishable from one another. These overlapping map clusters indicate that the clusters are related but not similar enough to be grouped together (Fig. 3). Furthermore, it indicates a strong association between clusters and the connection to the same field of study, ensuring that banana modelling is more closely associated with fields such as fruit production, growth and yield, the later in the context of our systematic review. Natural fibre, tensile strength and related modelling aspects are further away and even have small clusters (Fig. 3), indicating that natural fibres and related modelling aspects relevant to the banana crop are scarce in publications.

Basic statistics of published papers related to banana crop modelling

The number of publications related to mathematical modelling on banana fruit production (a, b, c), growth and development (d, e, f), and fibre-related characteristics (g, h, i) by year, country, and mathematical approach is shown in Fig. 4. In 2020, the highest number of papers related to banana yield modelling attempts were reported (Fig. 4(a)), and India and Brazil, are the major countries where many scientists are interested in the topic (Fig. 4(b)). Multiple linear regression (MLR) approaches have been widely employed in the development of banana yield models, followed by machine learning techniques such as artificial neural networks (ANN) (Fig. 4(c)). The years 2009 and 2020, followed by 2008, had the largest number of publications among the efforts made in developing models to predict growth and development (Fig. 4(d)), and France being the top country that significantly contributed for developing growth-related models (Fig. 4(e)). As shown in Fig. 4(f), the majority of published models were built using MLR and CSM. Most articles on banana fibre were published in 2019, followed by 2017 (Fig. 4(g)), and India was the leading country for these publications (Fig. 4(h)). There were no particular fibre-related models generated using mathematical approaches (Fig. 4(i)), but the majority of articles in the literature indicated the use of mechanical measures to assess tensile strength, and several other characteristics were linked to banana fibre processing.

Fig. 4. Number of publications related to mathematical modelling on banana fruit yield (a, b, c), growth and development (d, e, f), and fibre-related characteristics (g, h, i) by year, country, and mathematical approach. Note. The country of the publication was chosen solely based on the first author.

Modelling of banana fruit production

Thirty four of the full-text articles were related to banana fruit production. The current review highlights how the fruit yield of banana has been estimated through mathematical modelling approaches in previous studies. In this context, several previous studies have shown evidence of how they used simulation, mechanistic, and/or statistical models to estimate the yield of bananas (Fig. 4 and Table S1).

MLR has been more prevalently used (38%) in modelling banana fruit/bunch yield according to the content analysis of previous studies (Fig. 4). Salvacion (Reference Salvacion2020) used time series analysis and a regression model to investigate the impact of climate (i.e., annual rainfall, frequency of wet days, precipitation seasonality, annual mean temperature and temperature seasonality) on banana yield at the provincial level in the Philippines. MLR analysis revealed that 10% of banana-producing areas in the country are affected by local weather conditions (Salvacion, Reference Salvacion2020). Sharath (Reference Sharath2016) used stepwise multiple regression and it showed that plant height at the fourth month, girth at the fifth month, the number of fruits per bunch, and fruit girth at the final stage were the most significant factors in predicting total banana yield, while sucker parameters and number of leaves had no significant impact on banana yield. Zucoloto et al. (Reference Zucoloto, Lima, Coelho and Xavier2013) found that morphological characteristics such as the third leaf's width, number of leaves per tree, the bunch's diameter, and the number of bananas per bunch estimated the bunch weight of banana cv. Prata Ana using MLR models with moderate accuracy (Coefficient of Determination (R ²) = 0.58).

Olivares et al. (Reference Olivares, Calero, Rey, Lobo, Landa and Gómez2022) converted soil morphological factors in banana plantations to numerical scale and created a multiple linear regression model between those parameters and the banana crop Productivity Index (PI), with R ² = 0.645 as the model accuracy. Robinson and Human (Reference Robinson and Human1988) used regression allometries to forecast banana harvest based on seasonal variations in bunch development rate and bunch mass. However, 15% coefficient of variation (CV) reflected a 100-day harvest time, limiting the prediction capacity of the derived model.

Wairegi et al. (Reference Wairegi, Van Asten, Tenywa and Bekunda2009) developed a mathematical model with high accuracy (R ² = 0.73) to estimate the bunch weights of bananas using parameters such as log-transformed girth of pseudostem at the base and 1 m height, a number of hands, and a number of fingers in the lower row of the second-lowest hand using an MLR method. The same authors employed a quadratic or linear regression model (R ² = 0.58) to quantify the substantial geographic variations in banana yield including biotic constraints (e.g. percentages of nematodes and weevil) in highland banana production in Uganda (Wairegi et al., Reference Wairegi, van Asten, Tenywa and Bekunda2010).

The statistical models developed by Venugopalan and Shamasundaran (Reference Venugopalan and Shamasundaran2005) showed that at 70 days after planting (DAP), the number of leaves and plant girth with optimum values as eight leaves and 15.1 cm were the best yield indicators for bananas. Further, MLR showed that at 250 DAP, plant height and plant girth with optimum values as 159.2 and 67.8 cm and at 315 DAP, leaf breadth and leaf length with optimum values as 67.2 and 164.1 cm were the significant yield predictors. Finally, during the harvest stage, i.e. at 375 DAP, fingers per bunch and number of hands per bunch with optimum values as 26 fingers hand-1 and 13 hands bunch-1 were the best crop yield indicators. All models were robust as the coefficient of determination ranged from 0.81 to 0.99. Kuneepong et al. (Reference Kuneepong, Silayoi, Apauthaipong and Chutchwanchaiphan2020) used a general linear model for predicting the growth of a new banana variety (Kasetsart 2) in Thailand with aid of data related to local weather, irrigation systems and soil types. However, model predictions of banana yields for some locations were under-estimated in their model.

Scientists have also used MLR in conjunction with multivariate analysis to develop mathematical models for banana crops. For example Villegas-Santa and Castañeda-Sánchez (Reference Villegas-Santa and Castañeda-Sánchez2020) identified the relationship between soil variables and crop performances of bananas using the multivariate statistical tool. Three clusters of sites were evaluated based on dry mean weight, pH, and Ca + Mg/K ratio of soils, and all these soil properties highly correlated with banana yield, however the principal component analysis (PCA) was unable to identify the production quartiles due to the lack of significant causal relationships.

Jaiswal et al. (Reference Jaiswal, Jha and Bharadwaj2012) used a non-destructive method using calibration models in the wavelength range of 299–1100 nm and partial least square (PLS) as well as MLR to predict dry matter (DM), total soluble solids, and acid-Brix ratio, pH for a banana at their maturity and/or ripening stage. The result indicated that DM of banana could be accurately estimated in the best range of wavelength of 106.2–1089.4 nm with a correlation coefficient (R) value of 0.83. Salazar-Díaz and Tixier (Reference Salazar-Díaz and Tixier2021) investigated the impact of the plant community around each cacao tree and banana plant on their growth and yield parameters. First, they used linear mixed models to identify the radius of a specific species' zone of influence that best explained the proportion of attainable yield (PAY), using the number of plants from each category (banana, cocoa, wood trees, fruit trees) as a predictor. The models were relatively accurate in predicting the average effect of all plant communities, accounting for almost 60% of the variance in PAY, which is a good result. The Bayesian technique was used by Yeasin et al. (Reference Yeasin, Singh, Lama and Gurung2021) to forecast banana yield. They compared traditional regression models with modified Bayesian regression model, and observed that Bayesian regression [root mean square error (RMSE) = 216.9] predicts banana yields more accurately than traditional regression (RMSE = 223.1).

Olivares et al. (Reference Olivares, Araya-Alman, Acevedo-Opazo, Rey, Cañete-Salinas, Kurina, Balzarini, Lobo, Navas-Cortés, Landa and Gómez2020) developed a model to predict the banana Productivity Index (PI) in two main cultivation areas in Venezuela using soil properties of Magnesium (Mg), penetration resistance (PR), total microbial respiration (TMRc), bulk density (BD), and free-living omnivorous nematodes (NVLomc). The soil variables were selected through the random forest and the final model was derived from MLR (stepwise) models. The following model performed well, with a coefficient of determination (R ²) of 0.55, the root mean squared error (RMSE) of 1.0 and the mean absolute error (MAE) of 0.8 indicating the capability of estimate banana production using soil properties:

(1)$${\rm PI} = 9.03 + 0.19\,( {\rm Mg}) -\;8.78\,( {\rm PR}) -\;0.40\,( {\rm TMRc}) -\;4.70\,( {\rm BD}) + 0.02\,( {\rm NVLomc}) $$

In certain models, simple linear regression has been used to estimate banana yield or biomass using only one independent variable. For instance, Alcudia-Aguilar et al. (Reference Alcudia-Aguilar, Martínez-Zurimendi, van der Wal, Castillo-Uzcanga and Suárez-Sánchez2019) demonstrated that above-ground banana biomass (AGB) was strongly correlated with the diameter of pseudostem at the height of 30 cm (DBH) and to a certain extent with height data. Considering cross-evaluation, the best-derived model was:

(2)$${\eqalign{{\rm AGB} = {-} 0 .0927 + 0 .0203\;{\rm DB}{\rm H}^ 2\;{\rm with}\;R^2 = 0.88\;{\rm and}\;{\rm MSE} = 1.9}}$$

In the context of modelling of growth and yield of banana, non-linear mathematical models were also used by many authors that take complicated non-linear relationships of predictor variables and banana yield into account. Laskar et al. (Reference Laskar, Sileshi, Nath and Das2020) used mathematical models to estimate biomass accumulation of wild Musa spp. The predictors of diameter, height and combination of diameter and height of pseudostem were used to estimate total biomass using a non-linear, seemingly unrelated regression analysis. Further, mathematical forecasting approaches such as regression and time series analysis were used for linear data, but most real-world data are non-linear. Rathod and Mishra (Reference Rathod and Mishra2018) have tackled this problem in their study by proposing a new hybrid model to forecast mango and banana crop yield in Karnataka, India which is consisted of both linear and non-linear components. They have used banana and mango yield as dependent variables and weather variables, socioeconomics, and some other agricultural variables as independent variables.

Bugaud et al. (Reference Bugaud, Belleil and Tixier2011) developed a model to estimate the effects of source/sink parameters by simulating the increase in pulp dry weight as the source/sink ratio changes. To simulate the cell filling rate in the bunch according to the source/sink ratio during cell filling, they used a Michaelis-Menten relationship, which is a popular non-linear equation. The exponential regression model proposed by Ortiz-Ulloa et al. (Reference Ortiz-Ulloa, Abril-González, Pelaez-Samaniego and Zalamea-Piedra2020) that employs circumference at breast height (CBH) has the best biomass prediction capacity for Ecuadorian banana, with a R² of 0.85 (Table S1). Negash et al. (Reference Negash, Starr and Kanninen2013) used allometric biomass models with linear and nonlinear regressions to estimate above and below-ground biomass of Enset's false banana plant, and found that the simple power model with trunk basal diameter at 10 cm (d10) and total plant height (H) performed well, explaining 90% of the total biomass:

(3)$${\rm Biomass}\,( Y) = 0.0007d10^{2.571}H^{0.101}$$

Weighted least square regression models were built by Stevens et al. (Reference Stevens, Diels, Brown, Bayo, Ndakidemi and Swennen2020) to estimate aboveground vegetative biomass over time and to forecast bunch potentials. Pseudostem volume as a predictor for bunch weight forecasting led to good model performance in both tested cultivars in their study [relative root mean squared error (RRMSE) 0.13–0.14].

Gaussian functions are commonly employed in statistics as a stochastic process to explain normal distributions using a set of random variables indexed by time or space. For example, de Deus et al. (Reference de Deus, Neves, Soares, de Lima Neto, de Albuquerque, dos Santos and Natale2020) developed models to estimate dry matter partitioning in banana mat (collection of fruit-bearing stems). Dry matter estimation models were generated for the different plant organs in mother and daughter plants of banana as a function (i.e., Gaussian) of the dry matter weight of the banana mat (Fig. 4 and Table S1).

Process-based crop simulation models were also found in our review. For instance, Tixier et al. (Reference Tixier, Malézieux and Dorel2004) made a tremendous effort to describe banana crop growth, development, and yield as a function of plant physiological parameters, weather conditions, soil properties and crop management-related variables. This model gives a reliable estimation of the harvesting time and the number of harvested bunches. The fruit development curve was used to estimate sink demand, which was calculated as the fruit's requirement multiplied by the number of fruits per bunch.

The ANN approach could handle non-linear relations among the biometrical characteristics in crop modelling research for a realistic representation of nonlinearity. An Autoregressive Integrated Moving Average (ARIMA) model was developed by Hossain et al. (Reference Hossain, Abdulla and Majumder2016) that analysed univariate time series data and estimated a value in a response time series to forecast the development of bananas in Bangladesh. Moreover, Hossain et al. (Reference Hossain, Abdulla and Majumder2016) mentioned that ARIMA (0, 2,1) could be considered the best model to forecast banana production in Bangladesh. Soares et al. (Reference Soares, Pasqual, Lacerda, Silva and Donato2013) estimated the bunch weight of banana using a Tropical (YB42-21) hybrid cultivar. The weight of the rachis, stalk length and diameter, weight of the second hand, the total number of hands per bunch, the weight of the fruit, number of fruits per bunch, length of the fruit, diameter of fruit, and number of fresh leaves at harvest were considered as input layers. They employed the ANNs method to predict banana yield with 10:10:1 architecture, and the model performed well with high accuracy (MPE = 1.40, MSD = 2.29 and R ² = 91%).

de Souza et al. (Reference de Souza, Neto, Piazentin, Junior, Gomes, Bonini and Putti2019) developed a model using ANN to find the relationship between climatic variables (average temperature, minimum temperature, maximum temperature, relative humidity, precipitation and photoperiod) and banana bunch gestation period to predict the harvesting time. Network training indicated reliable results (RMSE = 0.3% and R ² = 0.89). For a AAAB tetraploid banana hybrid, Soares et al. (Reference Soares, Pasqual, Lacerda, Silva and Donato2014) used ANN and MLR to determine bunch weights. Although the models were reliable (R ² > 0.71), the model consisted with the predictors that could only be measured destructively at harvest.

Guimarães et al. (Reference Guimarães, Donato, Aspiazú and Azevedo2021) used ANNs to assess the yield of ‘Prata-Ana’ and ‘BRS Platina’ banana plants. The model was built using data on growth-reproductive-traits. For ‘Prata-Ana’ (R ² = 0.99) and ‘BRS Platina’ (R ² = 0.97–1), the optimum adjustments were obtained with two and three intermediate layer neurones, respectively. Eyduran et al. (Reference Eyduran, Akın, Eyduran, Çelik, Ertürk and Ercişli2020) investigated various ANN methods, including ARIMA (0,1,1), ARIMA (1,1,0) and ARIMA (1,1,1), as well as Exponential Smoothing (Holt, Brown and Damped) models, and discovered that the Brown exponential smoothing model was the best for forecasting banana harvest area and production (R ² = 0.99 and mean absolute percentage error (MAPE) = 19). Khan et al. (Reference Khan, Qiu, Qureshi, Iqbal, Mehmood and Hussain2020) employed three potential deep ANN networks [Levenberg-Marquardt optimisation (LM), scale conjugate gradient back propagation (SCG) and Bayesian regularisation back propagation (BR)] to estimate future fruit production in Pakistan, including banana, from 1980 to 2025. Although the accuracy of these algorithms varies, the best accuracy is seen with BR, which has a 75% accuracy. To estimate banana harvest yields, a deep multilayered system that included a number of recurrent neural network-long term memory (RNN-LSTM) layers was also used. When compared to models that used multiple LSTM layers and models that used a single LSTM layer, the enhanced model performed better, with an RMSE of 34.8 and error rates of 45 and 43.5%, respectively (Rebortera and Fajardo, Reference Rebortera and Fajardo2019a, Reference Rebortera and Fajardo2019b).

Modelling of banana growth

A total of 20 studies presented mathematical modelling techniques to estimate plant growth and development. In particular, many attempts were executed to assess the leaf area of banana crops using regression analyses (n = 9) and crop simulation models (Fig 4. and Table S2).

MLR approaches (n = 7) are commonly used regression techniques in banana growth models, as shown in Fig. 4. A more realistic leaf area estimation model was developed by Donato et al. (Reference Donato, Donato, Brito, Fonseca, Gomes and Rodrigues Filho2020) for ‘Prata-Ana’ and ‘BRS Plantina' banana plants using the variables width (W), length (L) and width/length ratio (WLR). The following models gave precise results (R ² around 0.96, and R = 0.98, respectively):

(4)$${\eqalign{{\rm LA}\,{\rm ( Prata}\hbox{-}{\rm An\sim a\ ) } = {-}0.0133624 + 0.000489859L + 0.00183182W}}$$

(5)$$\eqalign{{\rm LA}\,( {\rm Platina}) = 0.00237026 + 0.00478116\;W-0.0968020WLR}$$

Vinson et al. (Reference Vinson, Coneva, Kemble, Woods, Sibley, Fonsah, Perkins-Veazie and Kessler2018) developed a regression model to determine flower emergence and to assess vegetative and reproductive growth of Cavendish and non-Cavendish banana using the circumference of pseudostem (CM), the height-to-circumference ratio (HCR), and the number of days from planting to inflorescence emergence (DPE). Separate models were developed to predict leaf area of medium and tall banana varieties using regression models.

In addition, Mekwatanakarn and Turner (Reference Mekwatanakarn and Turner1989) constructed a robust model (R ² = 0.96) to evaluate the leaf emergence rate in bananas in the subtropics by assessing the relation of leaf emergence rate to temperature and ontogeny. Allen et al. (Reference Allen, Dettmann, Johns and Turner1988) created a model for estimating the leaf initiation rate (LIR) of 17 banana cultivars based on average monthly air temperature, day length, age of planting, plant density and cultivar stature. The model was evaluated with an independent data set from South Africa and it gave a reliable prediction of LIR with R ² = 0.78. Arantes et al. (Reference Arantes, Donato, Siqueira, Amorim and Rodrigues Filho2016) used MLR equations to find a correlation between chlorophyll index and nutrient contents of leaves and estimate the nutritional status of ‘Prata’ banana. The selected models reliably predict the leaf nutrient content of Prata' banana (R ² = 0.84 to 0.97).

Nyombi et al. (Reference Nyombi, Van Asten, Leffelaar, Corbeels, Kaizzi and Giller2009) studied different phenological stages of highland bananas grown in East Africa and assessed growth and yield using simple regression as well as MLR algorithms. Individual area was estimated as:

(6)$$\eqalign{{\rm LA}\,( {\rm m}^ 2) & = {\rm length}\,{\rm ( m) } \times {\rm maximum}\;{\rm lamina}\;{\rm width}\;( {\rm m}) \cr& \quad\times 0.68\,( R^2 = 0.99)}$$

The product of the measured middle leaf area (MLA) and the number of active leaves was used to calculate the total plant leaf area (TLA) and estimated as:

(7)$$\eqalignno{{\rm MLA}\,( {\rm m}^ 2) & = {-} 0 .404 + 0 .381\;{\rm height}\,{\rm ( m) } + 0 .411\;{\rm girth}\,{\rm ( m) }\;\cr& \quad( R^2 = 0.67) & (7)}$$

The mathematical relationship between above-ground biomass (AGB in kg DM) and girth (cm) during the vegetative stage followed a power function, AGB = 0.0001 (girth) 2.35 (R ² = 0.99), but followed exponential functions at flowering, AGB = 0.325e^{0.036 (girth)} (R ² = 0.79) and at harvest, AGB  =  0.069e^0.068(girth)(R ² = 0.96). Demirsoy (Reference Demirsoy2009) constructed models for the leaf area of fruit trees, including two banana varieties using simple linear regression. Several subsets of the independent variables were used in their leaf area prediction model, such as leaf length (L), leaf width (W), L ², W ² and [L ²/W ²].

Potdar and Pawar (Reference Potdar and Pawar1991) applied multiple linear regression to predict leaf area (LA) in the banana cultivars ‘Ardhapuri’ and ‘Basrai’ using various combinations of leaf length (L) and width (W), and found that the models had a predictive power with R² of around 0.96. Taulya (Reference Taulya2013) used multiple linear regression to estimate the fresh mass (FW) of the plants from the growth parameters (plant height (H); number of functional leaves (L); and the mean pseudostem volume with R ² = 0.59 accuracy:

(8)$$\eqalign{{\rm PV}( {\rm FW}) = 0.03873H + 0.281L + 3.169\;\times 10^{{-}6}\,{\rm Pv}) -\;2.905}$$

Latif et al. (Reference Latif, Mushoddad and Azmai2020) investigated the use of a simple logistic growth model to predict banana vegetative growth in response to foliar fertiliser. To simulate pseudostem height, pseudostem girth, and leaf area at harvest (Y), variables of time (week) (t), carrying capacity (maximum growth (cm) (K), constant (A) and growth rate (r) were used:

(9)$$Y = Y = K/1 + Ae-rt$$

Mendes et al. (Reference Mendes, Filippi, Demetrio and Rodriguez1999) applied adjusted Poisson regression models to study multiplication rates (Y) of in vitro banana plants during successive subcultures using number of shoots (N) as:

(10)$$Y = \exp \,( 3.75 + 2843N-0.2312\;\times \;N^2) \,( R^2 = 0.98) $$

Stochastic models are also widely exploited as mathematical models where random variables are considered. For example, Lamour et al. (Reference Lamour, Le Moguedec, Naud, Lechaudel, Taylor and Tisseyre2020) used a novel stochastic model to estimate the average time gap between two flowering occurrences on the banana plant (CD) using population dynamics and banana phenological development stages. The results indicated differences in CD with a median of 209 days ± 24 days. There was a positive effect of elevation, cultivar and irrigation v. Julian days on model fitting and the CD estimation. Moreover, some other crop simulation models deal with plantain (Musa × paradisiaca) crop systems to simulate growth or plantain yield. In the given context, Chaves et al. (Reference Chaves, Cayón and Jones2009) introduced models to estimate the potential yield of plantains using the models already developed by Spitters and Schapendonk (Reference Spitters and Schapendonk1990) and Kooman and Haverkort (Reference Kooman, Haverkort, Haverkort and MacKerron1995), especially considering the involvement of dry matter partitioning, light interception and daily conversion of light in dry matter production. Mechanistic modelling and non-linear regression analysis were used to develop the above models. Chaves et al. (Reference Chaves, Cayón and Jones2009) observed that leaf, stem and corm dry matter increased in equal proportions during the vegetative stage. However, only the stem was observed to extend its dry-matter content during the reproductive period, while the leaves and corm were found to reduce dry weight. Tixier et al. (Reference Tixier, Malézieux, Dorel and Wery2008) developed a model called SIMBA with different sub modules, design for a sustainable banana-based cropping system that mimics several cropping cycles at the field level.

A modified version of the SIMBA-GROW module was developed by Tixier et al. (Reference Tixier, Malézieux, Dorel and Wery2008) to simulate growth of banana plant considering four growth stages (planting, sucker initiation, flower initiation and harvesting) while taking the bunch as the sink. The SIMBA-GROW model is constructed using radiation interception, biomass conversion and dry matter partitioning to leaves, suckers and bunches. The physiological development of banana is determined by thermal degree days taking base temperature as 14°C. SIMBA-GROW calculates the plant growth for every cohort defined in the SIMBA POP module (Tixier et al., Reference Tixier, Malézieux, Dorel and Wery2008). SIMBA-POP is the first crop model for long-term simulation in non-synchronized banana cropping systems (Tixier et al., Reference Tixier, Malézieux and Dorel2004). The SIMBA-POP sub-module was developed based on a cohort population concept (i.e., a group of individuals characterized by the same phonological stage) that simulates the banana plant population and its growth and development patterns. Further, this model considered the details about sucker selection which affects plant management (Tixier et al., Reference Tixier, Malézieux and Dorel2004). They used log-normal distribution for the sucker appearance and flowering patterns in the field as explained by Cottin et al. (Reference Cottin, Melin and Ganry1987).

Using a compaction score, the SIMBA-SOIL module simulates soil structure. This accounts for data on essential management practices in the banana field, including the use of fertilizers, harvest trailers and ploughing. The SIMBA-WAT, a water balance module that simulates the content of the soil, water, flow-off and nutrients leaching (Tixier et al., Reference Tixier, Malézieux, Dorel and Wery2008). Tixier et al. (Reference Tixier, Lavigne, Alvarez, Gauquier, Blanchard, Ripoche and Achard2011) developed the SIMBA-CC model to select cover crops for banana cover-cropping systems using 11 cover crop species, LAI, biomass, N content in the biomass, light interception traits, and values of optimal photosynthetically active radiation (PARopti). The SIMBA-COV sub-module simulates soil cover, including weed growth and the impact of herbicides, mulching, and crop residues on weed growth in banana cultivation. Weed growth is represented as a percentage of soil cover that calibrates using a logistic function and it has an inverse proportion to the leaf area index of banana. Damour et al. (Reference Damour, Ozier-Lafontaine and Dorel2012) used simplified indicators of soil water and nitrogen availability, as well as integrated plant characteristics, to estimate the growth of banana (Musa spp.) cultivated on cover-crop. Dorel et al. (Reference Dorel, Achard and Tixier2008) designed the SIMBA-Nitrogen (N) model to simulate N dynamics in the banana cropping system with reliable evaluated results that can use in N fertilizer management in banana cultivation.

The STICS (Standardized mulTIdisciplinary Crop Simulator) model was used by Brisson et al. (Reference Brisson, Ozier-Lafontaine and Dorel1997) to estimate the impact of soil and water management on banana growth between planting and flowering. Solar radiation, minimum and maximum temperatures, rainfall, and evaporation were taken into the model development. Soil parameters of carbon and nitrogen were also considered as input variables. The model simulates the carbon, nitrogen and water balance of the banana cropping system and calculates growth using environmental data. A comprehensive description of model calibration and evaluation was not given in their paper.

ANN models are widely applied in crop modelling studies and indicate their applicability to estimate banana plants' growth rate. Revathi et al. (Reference Revathi, Sivakumaran, Ramajayam, Saraswathi, Backiyarani and Uma2019) developed a non-destructive model for tissue-cultured banana plantlets during the acclimatization period using bootstrapped artificial neural network (BANN). Both non-destructive and destructive growth parameters, greenhouse temperature, radiation and carbon dioxide concentration were recorded on a regular basis as independent data. The projected growth statistics indicate the reliability of the model to predict the growth with satisfactory Nash and Sutcliffe efficiency (NSE) coefficient, RMSE and MAE.

Modelling of banana fibre

No previous studies have specifically (Jayasinghe and Kumar, Reference Jayasinghe and Kumar2021) addressed the modelling of fibre yield of the banana plant according to our review results. However, many efforts have been made to predict the tensile strength (n = 14) and other mechanical properties (n = 4) of banana fibre (Fig. 4 and Table S3). Two studies that use mathematical approaches to assess the fibre yield of false bananas (Ensete ventricosum) have been identified, and we have included them in our review. Researchers employed a range of statistics to investigate fibre properties and a diverse applications in the search (Fig. 4), demonstrating how predictive models are used to determine the orientation and, mechanical and chemical properties of banana fibre using different regressions, numerical measures (i.e., mean, median, mode, percentiles, range, variance and standard deviation), and ANN statistics.

For instance, Chokshi et al. (Reference Chokshi, Gohil, Lalakiya, Patel and Parmar2020) used mathematical models (e.g. exponential, linear, logarithmic, polynomial and power models) to predict the tensile strength at different strain rates of natural fibre. The polynomial model yielded higher accuracy (R ² = 0.96) to predict tensile strength at low and high strain rates. Mwesigwa and Mwasiagi (Reference Mwesigwa and Mwasiagi2019) used a MLR model with strong model performance (R ² = 0.9) to study the parameters influencing the tensile and compressive characteristics of banana bio-composites. Monzón et al. (Reference Monzón, Paz, Verdaguer, Suárez, Badalló, Ortega and Diaz2019) used a statistical approach to characterize the mechanical properties of newly developed technical textile with a composite of banana fibre and compare the results with numerical simulation. Madhusudan et al. (Reference Madhusudan, Bhargava and Madhukiran2018) used mathematical equations to predict hygric strain coefficients for natural hybrid composites of banana and pineapple.

The basic mathematical model was used by Mizera et al. (Reference Mizera, Herak and Hrabě2017) to describe the dying behaviour of false bananas and fibre strength. Venkateshwaran et al. (Reference Venkateshwaran, Elayaperumal and Sathiya2012) predicted tensile properties of hybrid-natural fibre composites. Besides, Venkateshwaran and ElayaPerumal (Reference Venkateshwaran and ElayaPerumal2011) assessed the tensile properties of banana fibre. de Oliveira et al. (Reference de Oliveira, do Nascimento, Costa, Santana, Costa and Ribeiro2020) developed nine mathematical models to study the drying behaviour, moisture diffusivity, activation energy and thermodynamic properties of banana pseudostem fibre using thermogravimetric, morphological and spectroscopic methods. Devireddy and Biswas (Reference Devireddy and Biswas2018) developed a mathematical model to calculate thermal conductivity and the predicted thermal conductivity was very close to actual values. Chokshi and Gohil (Reference Chokshi and Gohil2018) developed mathematical models to predict the tensile strength of the banana fibre. According to their study, linear relationships of exponential, linear, logarithmic, polynomial and power models were used to study the behaviour of tensile strength and they found that tensile strength increases with an increase in strain rate.

Patwari et al. (Reference Patwari, Bhuiyan, Ahsan, Khan and Khan2019) proposed a quadratic model to forecast the compressive load of moulded green composite materials (containing banana fibre):

(11)$$Y = aX^2 + bX + c$$

Bhaskar et al. (Reference Bhaskar, Srinivas and Devireddy2020) developed a novel mathematical model to predict the transverse thermal conductivity of hybrid composites based on microstructural characteristics. Mizera et al. (Reference Mizera, Herák, Hrabě, Müller and Kabutey2016) used general exponential models to describe the effect of gauge length of false banana fibre for tensile strength.

Natural fibres have many advantages over synthetic fibres, but the reduction of quality is a drawback of natural fibres due to climate and growing conditions (Rao et al., Reference Rao, Rao, Naidu and Bahubalendruni2017). When predicting the tensile strength of the fibre, the issue has arisen due to the variation of the cross-sectional area of the fibre with the length (Sia et al., Reference Sia, Fernando, Joseph and Chua2018). Sia et al. (Reference Sia, Fernando, Joseph and Chua2018) produced a Weibull distribution with modification to predict the tensile strength of the fibre by providing the solution to the issue of cross-sectional variation. As per their findings, the fibre tensile strength decreases when the gauge length of the fibre increases. We found some other statistical approaches related to fibre processing that was adopted by researchers. For example, Macedo et al. (Reference Macedo, Vimercati, da Silva Araújo, Saraiva and Teixeira2020) and Veeramanipriya et al. (Reference Veeramanipriya, Sundari and Asaithambi2019) developed simple mathematical models to identify the drying kinetics of banana fibre. Devireddy and Biswas (Reference Devireddy and Biswas2018) and developed a mathematical model to calculate thermal conductivity with minimum errors (>11%).

Pujari et al. (Reference Pujari, Ramakrishna and Padal2017a) compared the performances of ANN and regression analysis for predicting the water absorption behaviour of jute and banana fibre reinforced epoxy composites and indicated that ANN gives better results for physical properties of natural fibre composites of banana than the regression analysis. Moreover, Pujari et al. (Reference Pujari, Ramakrishna and Padal2017b) predicted the volume changes of jute and banana fibre composites by using ANN and regression analysis and they indicated that ANN performs better than regression analysis.

For the enset or false banana crop (Ensete ventricosum), a close relative of the banana crop, Haile (Reference Haile2014) attempted to estimate enset fibre content from aboveground plant traits using a linear regression model, but even when fibredata was log transformed, he was unable to produce significant regression equations (R ² = 0.01). For the first time, Yemataw et al. (Reference Yemataw, Said, Dejene, Ocimati, Amwonya and Blomme2021) developed an allometric model that can correctly estimate enset fibre yield. The PCA was selected using a biplot and the Kaiser–Meyer–Olkin (KMO) method of eigen values over one, and a backwards regression analysis was utilised to automatically establish the most significant model to explain fibre yield. Accordingly, fibre yields of enset can be estimated using leaf length, petiole length and plant height (adj. R ² = 0.35–0.57).