Banana Trees: Agronomy, Mechanics & Graph Theory

• Banana trees are a diverse subject combining crop physiology, biomechanics, disease management, and graph theory, with applications from smallholder production to combinatorial analysis.
• Advanced techniques like thermal imaging, machine vision, and deep learning enhance water-deficit phenotyping and foliar disease diagnostics in fast-evolving research.
• Field studies and mathematical models reveal the interplay of leaf mechanics, pathogen spread, and nematode control, shaping both yield outcomes and economic viability.

Banana trees designate a major Musa crop complex studied across crop physiology, biomechanics, epidemiology, pest management, machine vision, and, in a separate technical usage, graph theory. In the agricultural literature surveyed here, bananas and plantains are modeled as perennial production systems whose performance depends on leaf self-support, water status, pathogen and nematode pressure, and post-harvest surface quality; in combinatorics, “banana tree” denotes a structured family of graphs used in labeling theory and chip-firing analysis (Tadrist et al., 2016, Levanon et al., 2020, Sanga et al., 2020, Varghese et al., 2019, Kemayou et al., 17 Nov 2025, Knott et al., 2024, Wijaya et al., 2016, Beougher et al., 3 Oct 2025).

1. Agronomic identity and research scope

Banana and plantain (Musa spp.) are treated in the cited literature as staple food and cash crops in tropical production systems. Bananas are described as a staple food for about 70 million people in Africa, mainly produced by smallholder farmers, and Tanzania is identified as a major production zone in East Africa, with particular importance in Arusha, Mbeya, and Kilimanjaro. In Central Africa, Cameroon alone is reported to produce over 5.4 million tonnes per year, with government targets of 7.5 million tonnes by 2025 and 10 million by 2030 (Sanga et al., 2020, Kemayou et al., 17 Nov 2025).

In agronomic modeling, banana is treated as a perennial, non-seasonal herb rather than as a woody tree. That distinction matters because the literature repeatedly analyzes organs and time scales rather than an abstract whole plant: one line of work isolates a single leaf as a self-supporting mechanical structure; another follows one-month-old Musa acuminata plantlets under controlled water and fertilizer deficits; disease studies focus on symptomatic leaves or subsection-level infection states within plantations; and post-harvest studies operate on harvested bunches in sorting and packing facilities rather than on standing plants (Chedjou et al., 2020, Tadrist et al., 2016, Levanon et al., 2020, Knott et al., 2024).

This partitioning of scales is not merely methodological. It reflects the fact that banana performance is simultaneously constrained by organ-level mechanics, canopy thermodynamics, root age structure, vector-mediated disease spread, and handling-induced defects. A recurring theme across the literature is that visible morphology alone is often insufficient: thermal signals, longitudinal monitoring, or mechanistic models are required to detect processes before major yield losses or quality downgrading occur (Levanon et al., 2020, Varghese et al., 2019, Kemayou et al., 17 Nov 2025).

2. Leaf architecture and self-support mechanics

A mechanical treatment of giant monocot leaves includes one explicit banana sample and asks whether leaves are optimally designed for horizontal light interception under self-weight. The modeled organ is a simple beam-like system comprising a short petiole transitioning into a midvein supporting a long lamina. For the banana leaf sampled at Eguilles in the south of France, the reported measurements were $l = 49\ \text{cm}$, $2w = 12.2\ \text{cm}$, $d = 5.5\ \text{mm}$, $t = 210\ \mu\text{m}$, $V = 21\ \text{cm}^3$, $M = 13\ \text{g}$, $\rho = 0.62\ \text{g cm}^{-3}$, and $E = 8.3 \times 10^{6}\ \text{Pa}$. The study explicitly restricted itself to leaf mechanics; the banana pseudostem was not considered (Tadrist et al., 2016).

Variable	Banana leaf value
$l$	$49\ \text{cm}$
$2w = 12.2\ \text{cm}$0	$2w = 12.2\ \text{cm}$1
$2w = 12.2\ \text{cm}$2	$2w = 12.2\ \text{cm}$3
$2w = 12.2\ \text{cm}$4	$2w = 12.2\ \text{cm}$5
$2w = 12.2\ \text{cm}$6	$2w = 12.2\ \text{cm}$7
$2w = 12.2\ \text{cm}$8	$2w = 12.2\ \text{cm}$9
$d = 5.5\ \text{mm}$0	$d = 5.5\ \text{mm}$1
$d = 5.5\ \text{mm}$2	$d = 5.5\ \text{mm}$3

The governing mechanical relation is the classical beam formula

$d = 5.5\ \text{mm}$4

applied in two bending directions. Along the midvein, the lamina load is modeled with $d = 5.5\ \text{mm}$5 and $d = 5.5\ \text{mm}$6; across the lamina, the blade is modeled as a rectangular strip with $d = 5.5\ \text{mm}$7 and $d = 5.5\ \text{mm}$8. Biomass volume is written

$d = 5.5\ \text{mm}$9

and one-sided leaf surface is

$t = 210\ \mu\text{m}$0

The optimization problem is to maximize $t = 210\ \mu\text{m}$1 at fixed $t = 210\ \mu\text{m}$2 under both self-support constraints, with $t = 210\ \mu\text{m}$3 in the data comparison (Tadrist et al., 2016).

The banana point is reported to lie on or close to the same scaling trends as the larger palm leaves. The authors state that the model predicts actual values within an order of magnitude, that the data are consistent with the scaling laws, and that the model prefactors give estimates close to the absolute values. They also identify a minimal regime of applicability: with $t = 210\ \mu\text{m}$4, $t = 210\ \mu\text{m}$5, $t = 210\ \mu\text{m}$6, and $t = 210\ \mu\text{m}$7, the critical scale is about $t = 210\ \mu\text{m}$8 in length and $t = 210\ \mu\text{m}$9 in width. The sampled banana leaf, at $V = 21\ \text{cm}^3$0 and $V = 21\ \text{cm}^3$1, lies above that threshold. The broader conclusion is that the longer palms are optimally designed for self-support, whereas shorter leaves are shaped predominantly by other parameters of selection; the banana sample occupies an intermediate regime in which self-support is significant but not exclusive (Tadrist et al., 2016).

3. Water-deficit phenotyping and abiotic stress sensing

A controlled phenotyping study examined tissue-culture Musa acuminata plantlets as a drought-sensing system. The experimental material consisted of one-month-old clones grown in 1-L pots in a commercial greenhouse in northern Israel and subjected to four irrigation/fertilizer treatments: 100%, 80%, 60%, and 40% of normal commercial irrigation and fertilization. All plants received the same treatment for the first three days, treatment differentiation began on day 4, and on day 17 all plants were returned to full irrigation to allow recovery. The study emphasizes that reduced soil moisture in banana leads to diminished stomatal conductance and reduced leaf size, with growth slowdown and possible death under severe stress (Levanon et al., 2020).

The phenotypic signal was weak in RGB appearance but clearer thermally. Over the 17-day period, the rate of appearance of new leaves slowed as water was reduced, and the total number of new leaves per plant decreased in more stressed treatments. At the same time, experts and non-experts could hardly notice any difference between treatments in single RGB photographs, whereas average canopy temperature differed by about $V = 21\ \text{cm}^3$2 between the best-watered and most stressed plants, with drier plants warmer because of reduced transpiration cooling (Levanon et al., 2020).

The sensing pipeline used daily top-down RGB images from a Samsung SM-G930F camera at $V = 21\ \text{cm}^3$3 resolution and thermal images from an Opgal ThermApp at $V = 21\ \text{cm}^3$4 resolution in the 7.5–14 $V = 21\ \text{cm}^3$5 range. RGB and thermal images were manually annotated to isolate the plant, thermal masks were morphologically eroded to remove residual background, and RGB images were downscaled to thermal resolution. Baseline classification from temperature statistics alone yielded about 50% accuracy using average plant temperature, about 60% using plant-minus-contour temperature, and about 70% when three consecutive days were used. Shallow CNNs trained from scratch outperformed transfer learning from ResNet-50, GoogLeNet, MobileNet, and VGG16, which transferred poorly from generic objects to near-identical banana plantlets (Levanon et al., 2020).

The best-performing system fused single RGB predictions with thermal triplets by a weighted rolling majority vote across modalities and days. Per-image accuracies were 72% for RGB without augmentation, 82% for RGB with augmentation, 84% for RGB triplets with augmentation, 40% for thermal without augmentation, 62.5% for thermal with augmentation, and 72% for thermal triplets with augmentation. The fused single-RGB plus triplet-thermal configuration reached about 89–92% accuracy with 1–9 days of observations, 94.6–94.7% at 10–11 days, and 100% from day 12 onward. For the binary distinction between well-watered plants and any stressed treatment, rolling RGB-plus-thermal classification yielded 97–100% accuracy for all sequence lengths $V = 21\ \text{cm}^3$6–17. The study therefore places banana water-status monitoring within a multimodal RGB-T and temporal-learning framework rather than within purely visual scouting (Levanon et al., 2020).

4. Foliar disease diagnostics and within-field viral epidemiology

Two complementary literatures address banana disease at different scales. One concerns direct diagnosis from leaf images. A mobile deep-learning study targeted Fusarium wilt race 1 and black Sigatoka using 3,000 original banana leaf images and a final augmented dataset of 18,000 images balanced across black Sigatoka, Fusarium wilt race 1, and healthy leaves. ResNet152 achieved validation accuracy 0.992 and test accuracy 0.998 with loss 0.0539 after 50 epochs at about 515 seconds per epoch; InceptionV3 achieved validation accuracy 0.954 and test accuracy 0.955 with loss 0.1351 after 150 epochs at about 159 seconds per epoch. Although ResNet152 was more accurate, InceptionV3 was deployed on Android because of lower memory requirements. The resulting application, “FUSI Scanner,” used a 70% minimum confidence threshold and, in real-environment tests, detected the two diseases with a confidence level of 99% of the captured leaf area (Sanga et al., 2020).

The agronomic backdrop for that work is strong. The cited study notes that disease detection is difficult for smallholder farmers, including settings where one extension officer serves about 1,700 farmers in Arumeru district. It describes Fusarium wilt race 1 as a soil-borne fungal disease caused by Fusarium oxysporum f. sp. cubense and black Sigatoka as a fungal leaf disease caused by Pseudocercospora fijiensis. Both compromise leaf function and photosynthesis and are treated as major sources of yield loss under tropical production (Sanga et al., 2020).

A second line of work models banana bunchy top virus (BBTV) within a plantation as a stochastic network-based SIS process over subsections rather than individual plants. On a 12-ha plantation in Newrybar, NSW, monthly GPS observations from December 2014 to January 2018 were aggregated to subsection-level infection states and fitted by ABC-MCMC with separate summer and winter recovery, neighboring infectivity, and distant infectivity parameters. Posterior means were $V = 21\ \text{cm}^3$7 and $V = 21\ \text{cm}^3$8 for summer and winter recovery, $V = 21\ \text{cm}^3$9 and $M = 13\ \text{g}$0 for neighboring infection, and $M = 13\ \text{g}$1 and $M = 13\ \text{g}$2 for distant infection. Under actual seasonality the predicted infected fraction tended toward about 45%; using summer parameters year-round raised this to about 57%, whereas winter parameters year-round reduced it to about 40%. The AUC of about 0.64 indicates fair but nontrivial predictive discrimination. This framework formalizes the role of aphid-mediated local spread, occasional long-distance jumps, inspection accuracy, and seasonality in plantation surveillance (Varghese et al., 2019).

5. Soilborne nematodes, root age structure, and multi-season control

Root health is treated as a primary determinant of banana productivity under nematode pressure. An age-structured model for Radopholus similis distinguishes healthy root biomass $M = 13\ \text{g}$3, infected biomass $M = 13\ \text{g}$4, free nematodes in soil $M = 13\ \text{g}$5, and infesting nematodes within roots $M = 13\ \text{g}$6, with infection rate $M = 13\ \text{g}$7, natural mortality $M = 13\ \text{g}$8, and root consumption rate $M = 13\ \text{g}$9 all depending on root age. The threshold parameter $\rho = 0.62\ \text{g cm}^{-3}$0 governs invasion: if $\rho = 0.62\ \text{g cm}^{-3}$1, the pest-free equilibrium is stable; if $\rho = 0.62\ \text{g cm}^{-3}$2, it is unstable and infestation persists. This age dependence is biologically motivated by the preference of R. similis for young, tender roots, and the model is aimed at the 20–60% yield losses attributed to the pest in Cameroon (Kemayou et al., 17 Nov 2025).

The numerical consequences are large. For $\rho = 0.62\ \text{g cm}^{-3}$3, the model gives $\rho = 0.62\ \text{g cm}^{-3}$4 and the nematode populations decay to zero. For $\rho = 0.62\ \text{g cm}^{-3}$5, it gives $\rho = 0.62\ \text{g cm}^{-3}$6, with persistent infestation and strong yield loss. On a representative 600 m$\rho = 0.62\ \text{g cm}^{-3}$7 plot with 100 plants initially, cumulative production fell from $\rho = 0.62\ \text{g cm}^{-3}$8 kg without nematodes to $\rho = 0.62\ \text{g cm}^{-3}$9 kg without control, a 40.91% loss. An impulsive control schedule applying nematicide every 16 days for 1 day raised cumulative production to $E = 8.3 \times 10^{6}\ \text{Pa}$0 kg, reducing loss to 7.52% and yielding a 56.51% improvement relative to the uncontrolled infested case (Kemayou et al., 17 Nov 2025).

A separate multi-season optimization study replaces ratooning by a sanitary regime in which each crop begins with a healthy, nematode-free vitro-plant after uprooting the previous plant. Within a season, roots grow until flowering for $E = 8.3 \times 10^{6}\ \text{Pa}$1 days and harvest occurs at $E = 8.3 \times 10^{6}\ \text{Pa}$2 days; between seasons, a fallow period $E = 8.3 \times 10^{6}\ \text{Pa}$3 allows the soil nematode population to decay exponentially. Over a fixed horizon $E = 8.3 \times 10^{6}\ \text{Pa}$4 days, the optimization shows that deploying one season less than the maximum possible number of cropping seasons can increase total profit because it permits longer fallows and better nematode suppression. One reported optimum used 11 cropping seasons with 10 fallows totaling 370 days and fallow vector $E = 8.3 \times 10^{6}\ \text{Pa}$5, for total profit about 54,530 XAF and final soil infestation about 251 nematodes (Chedjou et al., 2020).

The same study also identified a simpler constant-fallow strategy. A fixed fallow of 37 days between crops gave total profit about 52,000 XAF, about 54% higher than no fallow, with final soil infestation about 82 nematodes. The profit was lower than the irregular optimum but the final infestation was also substantially lower. This establishes a sharp distinction between maximizing finite-horizon profit and minimizing terminal soil infestation, and it situates fallow as an eco-friendly control alternative to chemical methods rather than merely as idle land (Chedjou et al., 2020).

6. Post-harvest quality assessment and defect quantification

Post-harvest banana research increasingly treats surface defects as a segmentation problem. A weakly supervised panoptic-segmentation study used 476 smartphone images of single banana bunches collected in three commercial sorting and packing facilities in India between harvesting and packing. The dataset comprised 1,440 annotated defects and focused on bruises and scars, each subdivided into old and new categories. Sparse supervision consisted of one bounding box per defect plus point prompts for foreground and background banana regions; the Segment Anything Model, especially SAM2, generated dense pseudo-masks that were then used to train Maskformer with five-fold cross-validation, input size $E = 8.3 \times 10^{6}\ \text{Pa}$6, Adam at learning rate $E = 8.3 \times 10^{6}\ \text{Pa}$7, batch size 2, and 100 epochs (Knott et al., 2024).

The principal operational result is that dense annotation effort can be reduced sharply with limited performance loss. Full pixel annotation was estimated at 3–5 minutes per image, compared with about 15 seconds per image for defect bounding boxes, implying at least a factor-of-10 reduction in labeling time. SAM2 masks achieved IoU $E = 8.3 \times 10^{6}\ \text{Pa}$8 against human masks for 90.5% of defect instances. When all defects were merged into a single class, training on SAM2-generated masks and validating on human masks yielded $E = 8.3 \times 10^{6}\ \text{Pa}$9, compared with 77.5% for the fully hand-annotated baseline; defect IoU was $l$0, foreground banana IoU $l$1, background banana IoU $l$2, overall mIoU $l$3, and $l$4 (Knott et al., 2024).

These masks support two grading primitives: defect count and relative defect area. Exact defect count matched human annotation in 36.5% of images, and predicted count was within $l$5 defect in 78.3% of images. Relative defect size,

$l$6

showed Pearson correlation $l$7 with human annotation for $l$8 matched defects, although the regression slope was slightly below 1, indicating slight underestimation of area. The study also delineates a present limit: multi-class discrimination among old bruise, new bruise, old scar, and new scar reduced PQ to about 44–47%, reflecting class imbalance, small defects, and ambiguity in the label space (Knott et al., 2024).

7. Banana trees as graph-theoretic objects

In graph labeling theory, a banana tree is not a plant but a structured graph family. One formulation defines $l$9 by taking $49\ \text{cm}$0 copies of a graph obtained from a star with $49\ \text{cm}$1 vertices by connecting an additional vertex $49\ \text{cm}$2 to exactly one leaf, then amalgamating the $49\ \text{cm}$3 copies at that extra vertex. Within the framework of $49\ \text{cm}$4-coverings and $49\ \text{cm}$5-supermagic labelings, a graph $49\ \text{cm}$6 is $49\ \text{cm}$7-supermagic if there is a bijection $49\ \text{cm}$8 with $49\ \text{cm}$9 such that every subgraph isomorphic to $2w = 12.2\ \text{cm}$00 has the same total label sum over vertices and edges. For any integers $2w = 12.2\ \text{cm}$01 and $2w = 12.2\ \text{cm}$02, $2w = 12.2\ \text{cm}$03 is $2w = 12.2\ \text{cm}$04-supermagic, and more generally for any integers $2w = 12.2\ \text{cm}$05 and any $2w = 12.2\ \text{cm}$06, $2w = 12.2\ \text{cm}$07 is $2w = 12.2\ \text{cm}$08-supermagic (Wijaya et al., 2016).

A more recent chip-firing literature uses a broader multigraph definition: a banana tree is a loopless connected multigraph whose underlying simple graph is a tree, and it is called ripe if every edge bunch has size at least 2. On such graphs, legal adjacency moves transfer exactly $2w = 12.2\ \text{cm}$09 chips across an edge bunch, and effective divisors are equivalent if and only if they are connected by sequences of legal adjacency moves. For banana paths, the divisorial gonality can be computed in $2w = 12.2\ \text{cm}$10 time. For any banana tree, the scramble number and screewidth both equal the largest integer $2w = 12.2\ \text{cm}$11 such that the graph has a connected subgraph with at least $2w = 12.2\ \text{cm}$12 vertices and at least $2w = 12.2\ \text{cm}$13 parallel edges between each adjacent pair. The same paper proves that the gonality conjecture holds for all banana trees: $2w = 12.2\ \text{cm}$14 with equality possible only if all edge bunches have size at most 4, and only finitely many ripe banana trees attain equality. It also shows that deleting a single edge can increase or decrease gonality by an arbitrary amount while keeping the graph connected (Beougher et al., 3 Oct 2025).