ANFIS-derived response surfaces reveal organ-specific optimal conditions for nutrient supply, light quality, plant developmental status, and culture configuration in Phalaenopsis amabilis in vitro propagation

Abstract

Background

Tissue culture optimization in orchids is constrained by the impracticality of experimentally testing all possible combinations of environmental and nutritional factors. In this study, the interactive effects of culture media composition, light quality, plant developmental status (rooted vs. rootless), and culture configuration (single-phase vs. two-phase) on organ-specific morpho-physiological traits of Phalaenopsis amabilis were investigated under in vitro condition. Growth variables, pigment composition, carbohydrate metabolism, and maximum quantum efficiency of photosystem II (F_v/F_m) were quantified separately in leaves and aerial roots. The primary objective was to predict trait-specific optimal treatment regions using fuzzy inference system (FIS) and adaptive neuro-fuzzy inference system (ANFIS) models trained on organ-resolved datasets derived from 60 treatment combinations across 16 traits.

Results

ANFIS exhibited superior capability compared with FIS in predicting nonlinear response surfaces and identifying trait-specific optimal regions. For leaf growth traits, ANFIS predicted optimal regions under orange-red light combined with moderate nitrogen (N) availability, whereas FIS produced narrower and more localized optima. For root biomass and carbohydrate accumulation traits, ANFIS predicted red light dominated optimal regions with elevated phosphorus (P) and reduced N, indicating stronger sensitivity of sink-related traits to light nutrient interactions. For leaf pigment accumulation traits, ANFIS identified broader optimal regions under blue light with lower N levels, while carbohydrate related traits showed distinct optima under red and green spectral conditions depending on nutrient balance. Overall, ANFIS generated more distinct and physiologically consistent response surfaces than FIS across all traits.

Conclusions

Machine learning assisted modeling effectively identified organ-specific optimal treatment regions and revealed complex nonlinear interactions among experimental factors that are not directly observable from mean treatment comparisons. The ANFIS framework provides a robust predictive tool for optimizing orchid tissue culture systems and for generating testable hypotheses for future in vitro propagation studies.

Background

The orchidaceae, one of the largest and most diverse plant families, includes Phalaenopsis orchids which dominate the global ornamental plant market due to their aesthetic value and long-lasting blooms [1]. Micropropagation through tissue culture has become the primary strategy for large-scale orchid production [2, 3]. Although substantial progress has been made in developing efficient culture protocols [4, 5], optimizing in vitro growth requires an integrative understanding of how light quality, nutrient composition, and culture systems interact to regulate organ-specific development. The organ-specific functions of leaves and roots, particularly their comparative morphology and photosynthesis activity and physiological coordination under varying culture conditions, are still poorly characterized [6]. A more comprehensive understanding of these interactions seems crucial for enhancing in vitro growth efficiency and achieving balanced organ development in Phalaenopsis and similar ornamental plants.

Leaves and roots exhibit distinct physiological functions during in vitro development [7, 8], yet their responses to environmental and nutritional conditions have rarely been evaluated systematically within a unified organ-resolved framework. Leaves are the principal photosynthetic organs in plants, characterized by well-developed mesophyll structures, high chloroplast densities, and adaptive pigment profiles that enable efficient light capture [7]. In contrast, the aerial roots of epiphytic orchids such as Phalaenopsis exhibit unique structural adaptations. These roots possess velamen tissues that aid in water absorption, as well as chlorophyll (Chl)-containing cortical cells that enable photosynthetic activity, albeit with lower efficiency than leaves [6, 8]. Also, roots can produce oxygen under illuminated conditions, recycle internal CO₂, and contribute to carbohydrate metabolism. Such findings indicate that roots may provide supplementary autotrophic capacity, especially under in vitro conditions where gas exchange and carbohydrate availability are restricted [6, 9]. Previous studies have demonstrated that light quality, nutrition composition, plant developmental stage and culture system architecture influence photosynthesis, pigment accumulation, biomass allocation, and carbohydrate metabolism in Phalaenopsis and other orchids [10, 11]. Nevertheless, it remains unclear which combinations and interaction of culture conditions preferentially optimize leaf performance versus root performance, and how these organ-specific responses can be integrated to achieve high plantlet development during micropropagation.

Machine learning (ML)-based models, particularly artificial neural networks (ANNs), have emerged as powerful approaches for modeling the experimental conditions in plant tissue culture [12]. Recent studies have demonstrated the effectiveness of such models in modeling the growth conditions for various crops, including Cannabis sativa [13] and Passiflora caerulea [14]. Recently, Mahdavi et al. (2025a) utilized ANNs to identify the optimal macro-nutrient levels necessary for enhancing the morphology and biochemistry of Phalaenopsis orchids. They showed that doubling the nitrate (NO₃⁻) content, a 2.5% increase in potassium (K), and a 5.0% increase in P, compared with the half-strength Murashige and Skoog (MS) medium, resulted in an over a 50% increase in morphological traits and a 200% increase in biochemical traits. They used the ability of ML models to provide response surfaces of the traits to find the optimal levels of the model inputs [15]. Despite their promising performance, challenges remain in using ANNs for the modeling approach, particularly regarding dataset size requirements and model complexity. Small datasets often necessitate the use of algorithms that can provide reliable prediction performance with a small number of training observations [16]. Among ML-based methods, fuzzy inference systems (FIS) and their combination with ANNs, called adaptive neuro-fuzzy inference system (ANFIS), have become popular algorithms to design robust prediction models because of their ability to transfer the human skills into linguistic rules [17]. Instead of being black-box, FIS provides membership functions for features and target along with logical fuzzy rules to properly relate the features to the model outputs. Moreover, ANFIS uses fuzzy rules in its learner layer, i.e., the hidden layer, to provide reliable predictions [18, 19]. In addition to reliable prediction from limited experimental observations, ANFIS models can generate continuous response surfaces that extend beyond the experimentally tested input combinations, thereby enabling quantitative optimization of culture conditions across multidimensional parameter spaces [20]. Although ML approaches have been applied previously in plant tissue culture [15], the use of organ-resolved FIS and ANFIS modeling for continuous optimization of leaf and root specific conditions in Phalaenopsis has not yet been systematically investigated.

Optimizing in vitro growth in Phalaenopsis represents a complex multi-variable problem in which culture media composition, light quality, plant developmental status, and culture configuration interact simultaneously to regulate plant performance. Because these interacting factors generate a large combinatorial experimental space, exhaustive empirical testing of all possible culture conditions is impractical. Consequently, ML-based approaches have emerged as promising tools for identifying optimal culture conditions and predicting plant responses across multidimensional experimental systems [12, 15]. Therefore, the aim of this study was to identify the optimal region within the combination of four factors: culture medium composition, light spectra, plantlet type, and culture configuration system, for each morphological and physiological trait of leaves and roots of Phalaenopsis plantlet (16 traits in total) using FIS and ANFIS models (Fig. 1). The review of previous studies shows that no in vitro orchid study has modeled such a wide range of treatments and traits so far. The ANFIS model, due to its ability to analyze highly nonlinear interactions, was particularly effective in predicting trait responses under treatment conditions that had not been experimentally tested.

Fig. 1.

Schematic overview of the experimental design illustrating the workflow from initial culture establishment to optimization based on fuzzy inference system (FIS) and adaptive neuro-fuzzy inference system (ANFIS) modeling in Phalaenopsis amabilis ‘Anthura Beijing’

Materials and methods

Plant material and growth conditions

Three-month-old in vitro plantlets of Phalaenopsis amabilis ‘Anthura Beijing’ were used as explants. The intact plantlets were selected for uniform size (with two- to three-leaf mean length of 2.5 ± 0.3 cm). Protocorm-like bodies (PLBs) used for plantlet production were obtained from the asexual propagation of leaf sections of keikis after node culture. Explants leaves were cultured in half-strength modified Murashige and Skoog culture medium (1/2 MMS, Merck Co., Darmstadt, Germany) [21] supplemented with 2 g/l peptone (Merck Co., Darmstadt, Germany), 30 g/l sucrose (Merck Co., Darmstadt, Germany), 4.8 g/l plant agar (Duchefa Biochemie Co., Haarlem, The Netherlands), and 3 g/l tidiazoron (TDZ, Sigma Co., Tokyo, Japan). The cultures were maintained in a controlled-environment growth chamber at 25 ± 1 °C, 70% relative humidity, and a 16:8 h light: dark photoperiod, with cool white fluorescent light at an intensity of 50 µmol/m² s.

Experimental design and statistical analysis

A factorial arrangement was conducted in a completely randomized design to evaluate the physiological traits of Phalaenopsis leaves and roots. The experiment incorporated four factors: culture media composition, light quality, plant developmental status, and culture phase system (60 treatment combinations) (Table 1) with four replications (culture vessels). Each culture vessel was considered independent experimental replicate that contained one mini-plantlets as explants. The 1/2 MMS semi-solid medium with a rooted plantlet under white fluorescent light served as a control. The treatment levels considered in this work are described in the following sections. Explants were sub-cultured every three weeks on fresh medium of the same composition (9 sub-culture cycles). No selection was applied during sub-culturing, as only one plantlet was maintained per replicate at each cycle. After seven months of cultivation, plantlets were removed from the vessels, and leaves and roots were collected for the assessments. Prior to using FIS and ANFIS individually to find their optimal levels for maximizing the traits, the data were analyzed in the MATLAB programming environment (R2018b, MathWorks, USA) using multi-factor analysis of variance (ANOVA) based on an interaction model to evaluate the effects of treatments and their interactions on the measured traits. The factorial completely randomized design (CRD) served as the data collection strategy, providing a structured sample of the input space for model training. The ML models then extended beyond the discrete experimental range via continuous response surface generation (Fig. 1). Heatmap visualization was used to explore multivariate patterns and correlation between treatments in selected physiological and morphological traits of leaves and roots, prior to FIS and ANFIS models and visualization. It was not applied to all measured variables, but rather to a subset of representative leaf and root traits to provide an integrated overview of key physiological responses. All selected traits were standardized using z-score normalization to ensure comparability across variables with different measurement scales. A blue–white–red color scale was applied for heatmap visualization, where blue represents values below the mean, white indicates mean values, and red represents values above the mean.

Table 1.

Experimental design and treatment combinations showing culture media composition, light spectra, plant developmental status (rooted vs. rootless), and culture system configuration (single-phase vs. two-phase) evaluated in this study

Culture media composition	Light spectra	Plantlet type	Culture system	Treatment code
1/2 MMS	White fluorescent	Rooted	Single-phase	T1
			Two-phase	T2
		Rootless	Single-phase	T3
			Two-phase	T4
	White	Rooted	Single-phase	T5
			Two-phase	T6
		Rootless	Single-phase	T7
			Two-phase	T8
	Red	Rooted	Single-phase	T9
			Two-phase	T10
		Rootless	Single-phase	T11
			Two-phase	T12
	Green	Rooted	Single-phase	T13
			Two-phase	T14
		Rootless	Single-phase	T15
			Two-phase	T16
	Blue	Rooted	Single-phase	T17
			Two-phase	T18
		Rootless	Single-phase	T19
			Two-phase	T20
MS+16P+1/10N	White fluorescent	Rooted	Single-phase	T21
			Two-phase	T22
		Rootless	Single-phase	T23
			Two-phase	T24
	White	Rooted	Single-phase	T25
			Two-phase	T26
		Rootless	Single-phase	T27
			Two-phase	T28
	Red	Rooted	Single-phase	T29
			Two-phase	T30
		Rootless	Single-phase	T31
			Two-phase	T32
	Green	Rooted	Single-phase	T33
			Two-phase	T34
		Rootless	Single-phase	T35
			Two-phase	T36
	Blue	Rooted	Single-phase	T37
			Two-phase	T38
		Rootless	Single-phase	T39
			Two-phase	T40
MS+16P+1/20N	White fluorescent	Rooted	Single-phase	T41
			Two-phase	T42
		Rootless	Single-phase	T43
			Two-phase	T44
	White	Rooted	Single-phase	T45
			Two-phase	T46
		Rootless	Single-phase	T47
			Two-phase	T48
	Red	Rooted	Single-phase	T49
			Two-phase	T50
		Rootless	Single-phase	T51
			Two-phase	T52
	Green	Rooted	Single-phase	T53
			Two-phase	T54
		Rootless	Single-phase	T55
			Two-phase	T56
	Blue	Rooted	Single-phase	T57
			Two-phase	T58
		Rootless	Single-phase	T59
			Two-phase	T60

Culture media compositions

Three culture media were used in this study, consisting of 1/2 MMS as the control, and two modified MS formulations: MS medium containing 16-fold higher P and 1/10 (0.1)-fold lower N relative to standard MS (MS+16P+1/10N), as well as MS medium containing 16-fold higher P and 1/20 (0.05)-fold lower N relative to standard MS (MS+16P+1/20N) (Table 2; Fig. 2A and B), which were selected based on previous studies and literature review [10, 22]. The pH of the media was adjusted to 5.7 ± 0.1 prior to sterilization. Then, 4.8 g/l plant agar was added to all semi-solid media. Media were sterilized by autoclaving at 121 °C for 20 min. The liquid media had the same chemical composition as the corresponding semi-solid media, except that agar was omitted.

Table 2.

Composition of four culture media including macro- and micro-nutrient concentrations (mM) and supplementation details that half-strength modified Murashige and Skoog culture medium (1/2 MMS), MS medium containing 16-fold higher P and 1/10 (0.1)-fold lower N relative to standard MS (MS+16P+1/10N), and MS medium containing 16-fold higher P and 1/20 (0.05)-fold lower N relative to standard MS (MS+16P+1/20N) used across treatments

Ionic and chemical composition	Culture media
	MS	1/2 MMS	MS+16P+1/10N	MS+16P+1/20N
Macro-elements (mM)
NH4+	20.62	10.31	3	1.50
NO3−	39.42	19.71	3	1.50
N	60.04	30.02	6	3
H2PO4−	1.253	0.627	20.05	20.05
K+	20.06	10.03	20.06	20.06
Mg2+	1.5	0.75	1.5	1.5
Ca2+	3.96	1.98	3.96	3.96
SO42−	1.76	0.88	1.76	1.76
Micro-elements (mM)
Fe2+	0.082	0.082	0.082	0.082
Mn2+	0.1	0.1	0.1	0.1
Zn2+	0.03	0.03	0.03	0.03
Cu2+	0.0001	0.0001	0.0001	0.0001
BO33−	0.1	0.1	0.1	0.1
Na+	0.083	0.083	0.083	0.083
Cl−	0.2	0.2	0.2	0.2
MoO42−	0.001	0.001	0.001	0.001
Co2+	0.0001	0.0001	0.0001	0.0001
I−	0.005	0.005	0.005	0.005
Vitamins (mM)
Nicotinic acid	0.0041	0.0041	0.0041	0.0041
Pyridoxine-HCl	0.0024	0.0024	0.0024	0.0024
Thiamine-HCl	0.0015	0.0015	0.0015	0.0015
Glycine	0.027	0.027	0.027	0.027
Myo-inositol	0.56	0.56	0.56	0.56
Additive compounds (mM)
Peptone	0	8.2	8.2	8.2
Sugars (mM)
Sucrose	87.72	87.72	87.72	87.72

The pH of the media was adjusted to 5.7 ± 0.1. The liquid media maintained the same compositions as a semi-solid media, excluding the addition of 4.8 g/l agar

Fig. 2.

Heatmap of (A) Macro-elements and (B) Micro-elements concentrations in four culture media that half-strength modified Murashige and Skoog culture medium (1/2 MMS), MS medium containing 16-fold higher P and 1/10 (0.1)-fold lower N relative to standard MS (MS+16P+1/10N), and MS medium containing 16-fold higher P and 1/20 (0.05)-fold lower N relative to standard MS (MS+16P+1/20N) used across treatments. Color intensity corresponds to element concentration (mM), with light yellow indicating the lowest values and dark green indicating the highest values. Color scaling was applied independently for macro- and micro-elements to enhance visualization of relative differences

Light spectra

To investigate the effects of light spectra on in vitro explants of Phalaenopsis, plantlets were exposed for seven months to five light treatments: white fluorescent light (control, ranging at 400–700 nm), white LED light (ranging at 400–700 nm), red LED light (ranging at 660 nm), green LED light (ranging at 530 nm), and blue LED light (ranging at 460 nm). All LED lights (Guangzhou Grow Light Company Model IGL-158‐18R17B7‐DC; Input voltage: 220–240 V; 18 W; 0.09 A) provided a photosynthetic photon flux density (PPFD) of 80 µmol/m² s. Light intensity was measured using a PAR‐FluorPen device (FP 100‐MAX, Photon Systems Instruments, Drásov, Czech Republic), and the spectral distribution was verified using a SpectroMaster (SEKONIC C‐7000, Tokyo, Japan) over the 300–800 nm range. Plantlets were kept in a 16:8 h light: dark photoperiod. Phytotron supplemented with LED lights with a 20 cm vertical distance between the lights and culture vessels.

Plantlet types

Two developmental types of Phalaenopsis plantlets were considered in this work: rooted plantlets, characterized by the presence of visible, intact roots at least 5 cm in length (Fig. 3A and C); and rootless plantlets, in which all roots were completely excised, leaving only the shoot portion consisting of leaves and stem (Fig. 3B). To obtain rootless plantlets, individuals were carefully removed from the culture vessels and rinsed with sterile distilled water. The entire root system of each plantlet was carefully excised using a sterile scalpel, leaving only the aerial portion consisting of leaves and stem. Then, the rootless plantlets were transferred to the respective culture media.

Fig. 3.

Representative images of two types of three-month-old Phalaenopsis amabilis ‘Anthura Beijing’ plantlets cultured in vitro under different media systems: (A) Rooted plantlet cultured on single-phase semisolid medium (30 ml agar-semi-solidified medium) under white fluorescent light, (B) Rootless plantlet cultured on single-phase semi-solid medium under white fluorescent light, (C) Rooted plantlet cultured on two-phase semi-solid-liquid medium 30 ml agar-semi-solidified medium overlaid with 4 ml liquid medium under white fluorescent light: the liquid medium indicated by an arrow

Culture system configuration

Plantlets were cultured using two types of culture system configurations: single-phase semi-solid medium, consisting of 30 ml agar-semi-solidified medium dispensed into 250 ml culture vessels (Fig. 3A and B); and two-phase semi-solid-liquid medium, consisting of 30 ml agar-semi-solidified basal medium overlaid with 4 ml liquid medium (Fig. 3C).

Plant trait assessment

Growth and morphological traits were evaluated in all plantlets, seven months after culture. The assessments included fresh and dry weight, as well as volume of leaves and roots. For measuring dry weight, samples were placed in a forced-air drying oven for 48 h at 75 °C. For measuring volumes, following separating leaves and roots from the plantlets and removing culture media from the leaves and roots via gentle washing, volume was measured by employing a volume‐displacement technique [23]. Samples were suspended in a cylinder filled with water. Volume was then determined by measuring the volume of water displaced by the leaves and roots.

The Chl and carotenoid contents in leaves and roots were determined according to Arnon (1967). The samples (50 mg) from fresh leaves and roots were extracted in 2 ml of acetone (80%), and the extract was separated by centrifugation (SIGMA-3K30) at 4000× g for 10 min. Then, the absorbance of the supernatant was spectrophotometrically (Lambda 25-UV/VIS spectrometer) measured at 663, 645, and 480 nm [24].

Anthocyanin content was measured based on the Wagner (1979) method. For this purpose, 100 mg of fresh leaves and roots powder were mixed with 2 ml of acidified methanol and hydrochloric acid (1%) and then incubated in an incubator shaker at 4 °C for 24 h in dark conditions. After centrifugation (10 min at 4000 × g), the absorbance of the supernatant was measured at 550 nm [25].

Carbohydrates in leaves and roots were determined by the anthrone method using glucose as the standard [26]. Fresh leaves and roots (100 mg) were extracted in 13 ml of 80% ethanol. Then, 3 ml of anthrone solution (150 mg of anthrone powder per 100 ml of 72% sulfuric acid) was added to 0.1 ml of alcoholic extract. This mixture was placed in a water bath at 100 °C for 10 min and then cooled in an ice bath, and the absorbance was spectrophotometrically recorded at 625 nm. The remaining solid part after extraction of soluble sugars was used to extract starch in 52% perchloric acid. Starch concentrations were determined by anthrone and were spectrophotometrically recorded at 630 nm as described by McCready [27].

As a sensitive indicator of plant photosynthetic performance, the Chl fluorescence values were recorded in leaves and roots. Measurements were conducted using Handy FluorCam FC 1000-H (Photon Systems Instruments, PSI, Czech Republic). Plantlets were dark-adapted for 20 min prior to evaluation. The FluorCam consisted of a CCD camera and four fixed LED panels, one pair supplying the measuring pulse and the second pair providing actinic illumination and a saturating flash was used. Maximum quantum efficiency of photosystem II (F_v/F_m) was calculated using a custom-made protocol [28]. At the end of the short flashes, the samples were exposed to a saturating light pulse with a photosynthetic photon flux density (PPFD) of 3900 µmol/m² s that resulted in a transitory saturation of photochemistry and reduction of the primary quinone acceptor of photosystem II (PSII) [28]. After reaching steady-state emission of fluorescence, two series of fluorescence data were recorded: one series during exposure to short measuring flashes under darkness (F_o), and the second series of fluorescence emission detection was recorded at the time of saturating light flash (F_m). F_v was calculated by decreasing the F_o fluorescence values from the F_m fluorescence values. The F_v/F_m ratio was calculated by calculating the ration between F_v and F_m. The average values, and standard deviations of F_v/F_m were obtained using version 7 FluorCam software [29, 30]. F_v/F_m measurements were conducted for all four biological replicates of each treatment. In each replicate, measurements were obtained from all healthy leaves and roots of the plantlets, and the resulting values were averaged to obtain a representative value for each replicate prior to statistical analysis.

ML approach

Considering the fact that the culture media composition, light quality, plant developmental status, and culture phase system were independent variables to study the plantlet traits, we used FIS and ANFIS individually to find their optimal levels for maximizing the traits (Fig. 1). In this study, four factors, including (1) N concentrations (0.5-, 0.1-, and 0.05-fold N), (2) light spectra [blue LED (460 nm), white LED (510 nm), green LED (530 nm), white fluorescent light (550 nm), and red LED (660 nm)], (3) plantlet type, and (4) culture configuration system, were considered as input variables, while the mean values of each trait (60 data points) were considered as outputs for modeling using FIS and ANFIS approaches. For model evaluation, the input variables were classified into two categories: continuous variables (N concentrations and light spectra) and categorical variables (plantlet type and culture configuration system). Since the categorical variables each consisted of two classes [rooted vs. rootless plantlets and single-phase vs. two-phase culture systems], they were encoded numerically as 0 and 1 prior to modeling. Accordingly, each category was modeled separately, and the input corresponding to each category was used to independently model the trait four times. Three culture media, namely 1/2 MMS, MS+16P+1/10N, and MS+16P+1/20N, were included as experimental factors. As shown in Table 2; Fig. 2, only two elements (P and N) differed between the two modified media and the standard MS medium, whereas in the 1/2 MMS medium, all macro-elements were reduced by half relative to the MS medium. Therefore, among three culture media, variations in N and P relative to the MS medium were considered as continuous inputs in the modeling process. However, because P was supplied at only two levels (16- and 0.5-fold higher than the MS medium), it could not be appropriately incorporated into the models as a continuous variable. Consequently, only the three N levels were modeled directly, while the corresponding P levels were interpreted in association with the N concentration input. Furthermore, given that 16 morpho-physiological traits of Phalaenopsis leaves and roots were measured independently and that inter-trait correlations were not considered, a total of 16 separate models were developed.

To implement the FIS, we considered three Gaussian membership functions for each model input and output. For the definition of fuzzy rules and determining the mean and variance of membership functions, we constructed a Sugeno-type FIS using a data-driven fuzzy C-means (FCM) clustering algorithm and for each trait, three numbers Gaussian membership functions were defined, so the FCM number was 3, which placed in the model as low, medium, and high. Given an input–output dataset, FCM partitions the data into a number of fuzzy clusters by minimizing an objective function based on weighted Euclidean distances, where each data point belongs to all clusters with varying degrees. Each resulting cluster corresponds to a single fuzzy rule. For the antecedent part of the rules, Gaussian membership functions are generated for each input variable, with parameters derived from the cluster centers and variances. The consequent part of each rule is defined as a first-order Sugeno model, represented by a linear combination of the input variables and a constant bias term. Consequent parameters are initially estimated using least-squares optimization [19].

Since FIS might not be capable of modeling nonlinearities in the dataset correctly, we used ANFIS to assess if the combination of ANNs and FIS can improve the modeling results. ANFIS employs a hybrid learning algorithm to iteratively update the parameters of the Sugeno-type FIS based on input–output data. The fuzzy rule base consists of fixed rule structures whose antecedent parameters define the shapes and locations of the membership functions, while the consequent parameters specify linear output functions. During training, ANFIS alternates between two optimization steps. In the forward pass, antecedent parameters are held constant, firing strengths of the fuzzy rules are computed, and the consequent parameters are estimated using least-squares regression to minimize the output error. In the backward pass, the consequent parameters are fixed, and the antecedent parameters are updated via gradient descent by propagating the error backward through the network layers [20, 31].

Both algorithms were implemented in the MATLAB programming environment (R2018b, MathWorks, USA). Considering that the number of observations in the dataset was 60, the five-fold cross-validation method was employed to investigate the performance of the models in the prediction task. This method helps prevent overfitting and ensures the ability of the model to generalize. In this method, the data are divided into five subsets, with four subsets used for training and one for testing. This repeats five times in a manner that each data point in the dataset is considered for testing at least one time [15]. The performance of the model is obtained by the average performance of the five repetitions. Mean squared error (MSE) was used as the performance evaluation criterion [32]. For better analysis of MSE values, the dataset was normalized to a range between 0 and 1 before training [15].

For each plantlet type and culture system, the input space was optimized by discretizing the N concentrations (0 to 0.55× that of MS medium) and the light spectral range (400–700 nm) into 100 equal-spaced levels. This discretization yielded a comprehensive grid covering the entire response domain. All grid points were subsequently evaluated using the models, resulting in 10,000 simulations (100 × 100) to predict plantlet responses to combinations of input conditions that were not experimentally tested.

Results

Performance of the models in prediction tasks

Table 3 shows the results of five-fold cross-validation in the prediction of plant traits obtained by the FIS and ANFIS models. According to the table, both models provided acceptable performance in predicting plantlet traits. Both the MSE and R-squared (R²) values indicated the promising performance of the models. However, ANFIS has provided remarkably better prediction performance for all traits. In general, Table 3 reveals the reliability of both models for the next step, i.e., the prediction of plant behavior toward input levels that have never been investigated before in the experiments.

Table 3.

Average mean squared error (MSE) and R-squared (R²) values of the five-fold cross-validation task performed by the fuzzy inference system (FIS) and adaptive neuro-fuzzy inference system (ANFIS) models in predicting the plantlet traits

Plantlet trait	FIS		ANFIS
	MSE	R 2	MSE	R 2
Fresh weight	0.008	0.94	0.001	0.98
Dry weight	0.009	0.94	0.001	0.97
Volume	0.010	0.91	0.003	0.97
Chl a	0.007	0.94	0.002	0.98
Chl b	0.004	0.96	0.002	0.97
Total Chl	0.005	0.96	0.001	0.98
Chl a/b	0.002	0.97	0.001	0.99
Carotenoid	0.007	0.94	0.002	0.97
Anthocyanin	0.006	0.95	0.002	0.97
Soluble carbohydrate	0.007	0.93	0.003	0.97
Storage carbohydrate	0.009	0.91	0.001	0.98
Total carbohydrate	0.008	0.91	0.002	0.96
Fo	0.010	0.90	0.003	0.95
Fm	0.008	0.93	0.003	0.96
Fv	0.005	0.97	0.001	0.98
Fv/Fm	0.008	0.94	0.002	0.96

Training data summary

For leaves, the highest fresh weight (3.89 g), dry weight (0.21 g), and volume (4.59 cm³) were observed in the training dataset under T1 and T2 conditions (Table 4). In roots, the highest fresh weight (9.29 g) and volume (9.53 cm³) were observed under T41 and T42 conditions (Table 5), while the greatest dry weight (0.8 g) was observed under T21 and T22 conditions (Table 5).

Table 4.

Training data summary and adaptive neuro-fuzzy inference system (ANFIS)-predicted optima: leaf traits

Traits		Treatments resulting in the maximum observed trait value	Empirical observed trait value1	FIS model output2				ANFIS model output2
				Light spectrum (nm)	N concentration (fold)	Plantlet type3	Trait value	Light spectrum (nm)	N concentration (fold)	Plantlet type3	Trait value
Fresh weight (g)		T1 and T2	3.89	553	0.5	R	3.69	601	0.55	R	6.91
Dry weight (g)		T1 and T2	0.21	553	0.48	R	0.2	601	0.55	R	0.35
Volume (cm3)		T1 and T2	4.59	550	0.5	R	4.36	601	0.55	R	7.33
Chl a (mg/g)		T57 and T58	0.52	460	0.04	R	0.49	400	0	R	1.35
Chl b (mg/g)		T57 and T58	0.26	457	0.04	R	0.25	400	0	R	0.68
Total Chl (mg/g)		T57 and T58	0.78	463	0.04	R	0.75	400	0	R	2.03
Chl a/b		T23 and T24	2.13	559	0.13	RL	2.08	643	0.28	RL	2.79
Carotenoid (mg/g)		T57 and T58	0.7	457	0.04	R	0.67	400	0	R	1.69
Anthocyanin (µmol/g)		T27 and T28	9.27	505	0.12	RL	8.94	700	0.25	RL	24.73
Soluble carbohydrate (mg/g)		T55 and T56	26.57	529	0.04	RL	24.69	700	0.55	RL	26.57
Storage carbohydrate (mg/g)		T31 and T32	332.51	634	0.14	RL	257.20	700	0.28	RL	843.75
Total carbohydrate (mg/g)		T31 and T32	334.57	649	0.12	RL	309.46	661	0.26	RL	767.69
Fo		T51 and T52	23833.23	643	0.025	RL	22,447	487	0.3	R	38597
Fm		T23 and T24	67319.73	559	0.12	RL	64,445	400	0.25	RL	128140
Fv		T23 and T24	48131.89	556	0.12	RL	46,165	601	0.55	RL	93046
Fv/Fm		T1 and T2	0.78	550	0.5	R	0.77	400	0	R	0.88

¹All evaluated traits were significant at the P ≤ 0.01 levels. ²The culture system configuration (single-phase vs. two-phase) showed no significant effect in either the fuzzy inference system (FIS) or adaptive neuro-fuzzy inference system (ANFIS) models. ³R Rooted plantlets and RL  Rootless plantlets

Table 5.

Training data summary and adaptive neuro-fuzzy inference system (ANFIS)-predicted optima: root traits

Traits	Treatments resulting in the maximum observed trait value	Empirical observed trait value1	FIS model output					ANFIS model output
			Light spectrum (nm)	N concentration (fold)	Plantlet type2	Culture configuration3	Trait value	Light spectrum (nm)	N concentration (fold)	Plantlet type2	Culture configuration3	Trait value
Fresh weight (g)	T41 and T42	9.29	553	0.04	R	ns	8.78	601	0.55	R	ns	13.55
Dry weight (g)	T21 and T22	0.8	550	0.08	R	ns	0.71	607	0.24	R	ns	1.09
Volume (cm3)	T41 and T42	9.53	556	0.03	R	ns	8.98	601	0.55	R	ns	14.74
Chl a (mg/g)	T49	0.31	649	0.03	R	S	0.28	700	0	R	S	0.65
Chl b (mg/g)	T9 and T10	0.17	505	0.04	R	ns	0.16	700	0.46	R	ns	0.33
Total Chl (mg/g)	T10	0.54	508	0.04	R	S	0.51	700	0	R	S	1.23
Chl a/b	T30	2.04	652	0.11	R	SL	2	610	0	R	S	2.86
Carotenoid (mg/g)	T10	0.47	661	0.5	R	SL	0.42	700	0.54	R	SL	1.02
Anthocyanin (µmol/g)	T32	11.13	649	0.12	RL	SL	10.37	700	0.29	RL	SL	47.67
Soluble carbohydrate (mg/g)	T52	29.85	652	0.04	RL	SL	27.16	700	0	RL	SL	57.99
Storage carbohydrate (mg/g)	T11 and T12	1157.26	661	0.5	RL	ns	1052.5	640	0.55	RL	ns	1392.6
Total carbohydrate (mg/g)	T11 and T12	1181.08	661	0.5	RL	ns	1039.9	640	0.55	RL	ns	1418.2
Fo	T51 and T52	17874.93	643	0.025	RL	ns	16,836	487	0.3	R	ns	28,948
Fm	T23 and T24	50489.8	556	0.12	RL	ns	48,336	400	0.25	RL	ns	96,110
Fv	T23 and T24	36098.92	559	0.125	RL	ns	34,366	601	0.55	RL	ns	69,785
Fv/Fm	T1 and T2	0.58	550	0.5	R	ns	0.58	400	0	R	ns	0.66

¹All evaluated traits were significant at the P ≤ 0.01 levels. ²R Rooted plantlets and RL  Rootless plantlets. ³S Semi-solid medium (single-phase), SL Semi-solid-Liquid medium (two-phase), and ns culture system configurations non-significant

T57 and T58 conditions showed the highest leaf Chl a (0.52 mg/g), Chl b (0.26 mg/g), and total Chl (0.78 mg/g) (Table 4). The highest Chl a/b ratio (2.13) was observed under T23 and T24 conditions (Table 4). Leaf carotenoid content (0.7 mg/g) was also the greatest under T57 and T58 conditions (Table 4). Leaf anthocyanin accumulation (9.27 µmol/g) peaked under T27 and T28 conditions (Table 4). In roots, the highest Chl a (0.28 mg/g) was observed under T49, whereas the highest Chl b (0.16 mg/g) and total Chl (0.51 mg/g) were observed under T9 and T10 conditions (Table 5). The highest Chl a/b ratio (2.04) was observed in T30 (Table 5). Root carotenoid levels (0.47 mg/g) were highest under T10 (Table 5), while root anthocyanin content (11.13 µmol/g) peaked under T32 condition (Table 5).

The highest leaf soluble carbohydrate content (26.57 mg/g FW) was observed under T55 and T56 conditions (Table 4). By contrast, the greatest leaf storage (332.51 mg/g FW) and total carbohydrate contents (334.57 mg/g FW) were observed under T31 and T32 (Table 4). In root tissue, the highest soluble carbohydrate (29.85 mg/g FW) was observed under T52 (Table 5). The largest storage (1157.26 mg/g FW) and total carbohydrate (1181.08 mg/g FW) values were observed in the dataset under T11 and T12 conditions (Table 5). The highest F_v/F_m in leaves (0.78) was observed under T1 and T2 (Table 4). For roots, the highest observed F_v/F_m (0.58) was likewise recorded under T1 and T2 conditions (Table 5).

The heatmap showed distinct yet coordinated responses of leaf and root traits in Phalaenopsis plantlets subjected to varying light spectra, culture media compositions, and plantlet types (Fig. 4). Higher values of F_v/F_m, total Chl, carotenoid of leaf and root dry weight were observed under white fluorescent light (T1 and T2, T21 and T22, then T41 and T42) (Fig. 4). In contrast, higher leaf pigment contents (total Chl and carotenoids) were observed in T37 and T38, T39 and T40, while lower root biomass was recorded under these same conditions (Fig. 4). Elevated root storage carbohydrate content was observed under T11 and T12 (Fig. 4). Higher leaf soluble carbohydrate content together with moderate root biomass was observed under T35 and T36 conditions (Fig. 4).

Fig. 4.

Heatmap showing z-score standardized variation and correlation between treatments in root dry weight (rdw), leaf maximum quantum efficiency of photosystem II (lF_v/F_m), leaf total chlorophyll (lchl a + b), leaf carotenoids (lcar), leaf soluble carbohydrates (lsoc), and root storage carbohydrates (rstc) in three-month-old in vitro plantlets. Blue and red colors represent lower and higher values relative to the mean, respectively

Response surface output

The response surface analysis revealed that optimal input conditions for leaf and root performance were systematically different between FIS and ANFIS models, consistent with an organ-resolved divergence across the continuous input space. Also, in root parameters, except for Chl a, total Chl, Chl a/b ratio, in carotenoids, anthocyanin, and soluble carbohydrates of root, the physical state of the media (single-phase vs. two-phase) had no significant effect on the remaining leaf and root traits (Table 5).

For leaf traits, the FIS model identified optimal conditions approximately under white fluorescent light region (553 –550 nm), on MS medium with lower N (0.48-0.5-fold lower N concentration⁓1/2 MMS), in rooted plantlets, corresponding to predicted fresh weight of 3.69 g (Table 4; Fig. 5A), dry weight of 0.20 g, and volume of 4.36 cm³ (Table 4). In contrast, ANFIS model indicated higher optima approximately under orange-red region (601 nm) on MS with lower N (0.55N⁓1/2 MMS) with increased predicted values of 6.91 g fresh weight (Table 4; Fig. 5B), 0.35 g dry weight, and 7.33 cm³ volume (Table 4). This shift indicates a change in optimal light quality from white fluorescent toward red-shifted conditions for leaf performance in the ANFIS response surface (Table 4). For roots, FIS predicted optimal conditions approximately under white fluorescent light region (550–556 nm) on MS containing higher P (16-fold higher P) and lower N (0.03–0.08N), in rooted plantlets, corresponding to 8.78 g fresh weight (Table 5; Fig. 5C), 0.71 g dry weight, and 8.98 cm³ volume (Table 5). ANFIS shifted the optimum toward approximately under orange-red region (601–607 nm) on MS with higher P and lower N (0.24–0.55N), in rooted plantlets, yielding higher predicted maxima of 13.55 g fresh weight (Table 5; Fig. 5D), 1.09 g dry weight, and 14.74 cm³ volume (Table 5). This indicates a corresponding shift in optimal conditions for root performance toward red-shifted light and altered nutrient balance (Table 5). Across both leaf and root traits, ANFIS consistently predicted higher performance maxima and a systematic shift in optimal light quality toward longer wavelengths compared with FIS (Tables 4 and 5).

Fig. 5.

Surface and contour plots derived from (A and C) Fuzzy inference system (FIS) and (B and D) Adaptive neuro-fuzzy inference system (ANFIS) to illustrate the optimized light spectra and nitrogen (N) concentration for maximizing fresh weight (g) in (A and B) Leaf (lfw) and (C and D) Root (rfw) of Phalaenopsis amabilis ‘Anthura Beijing’ plantlets

For leaf pigments, FIS model, identified optimal Chl accumulation under white to blue light region (559 –463 nm) on MS with higher P and lower N (0.04–0.13N) in both rooted and rootless plantlets (Table 4; Fig. 6A). In contrast, the ANFIS predicted higher theoretical maxima under 400 and 643 nm on MS with higher P and lower N (0–0.28N) (Table 4; Fig. 6B). Similarly, FIS predicted optimal carotenoid accumulation (0.67 mg/g) under 457 nm on MS with higher P and lower N (0.04N) (Table 4), whereas ANFIS predicted a maximum of 1.69 mg/g under 400 nm on MS with higher P and lacking N in rooted plantlets (Table 4). For anthocyanin, both FIS and ANFIS identified optimal conditions within the 505–700 nm under higher P and lower N (0.12–0.25N) in rootless plantlet; however, ANFIS predicted markedly higher theoretical maxima (24.73 µmol/g) than FIS (8.94 µmol/g) (Table 4; Fig. 7A and B). For roots, FIS predicted optimal Chl accumulation under 505–652 nm on MS with higher P and lower N (0.03–0.11N) (Table 5; Fig. 6C), whereas ANFIS shifted the predicted optimum toward 610–700 nm on MS with similarly elevated P and lower N (0–0.46N) (Table 5; Fig. 6D). Root carotenoid was predicted by both FIS and ANFIS under 661–700 nm on approximately 1/2 MMS (0.5N), although ANFIS predicted higher maxima (1.02 mg/g) than FIS (0.42 mg/g) (Table 5). Likewise, both models identified optimal root anthocyanin accumulation under 649–700 nm on MS with elevated P and lower N (0.12–0.29N) in rootless plantlets, with ANFIS again predicting substantially higher maxima (47.67 µmol/g) compared with FIS (10.37 µmol/g) (Table 5; Fig. 7C and D). Overall, ANFIS response surfaces consistently predicted higher pigment-related optima and a systematic shift toward red-shifted wavelengths and low N conditions relative to FIS outputs (Tables 4 and 5).

Fig. 6.

Surface and contour plots derived from (A and C) Fuzzy inference system (FIS) and (B and D) Adaptive neuro-fuzzy inference system (ANFIS) to illustrate the optimized light spectra and nitrogen (N) concentration for maximizing chlorophyll a (Chl a) (mg/g FW) in (A and B) Leaf (lchla) and (C and D) Root (rchla) of Phalaenopsis amabilis ‘Anthura Beijing’ plantlets

Fig. 7.

Surface and contour plots derived from (A and C) Fuzzy inference system (FIS) and (B and D) Adaptive neuro-fuzzy inference system (ANFIS) to illustrate the optimized light spectra and nitrogen (N) concentration for maximizing anthocyanin (µmol/g FW) in (A and B) Leaf (lantho) and (C and D) Root (rantho) of Phalaenopsis amabilis ‘Anthura Beijing’ plantlets

For leaf carbohydrates, FIS identified green spectrum (529 nm) as optimal for soluble carbohydrate (24.69 mg/g FW) (Table 4; Fig. 8A). In contrast, storage (257.2 mg/g FW) and total carbohydrate (309.46 mg/g FW) accumulation were associated with longer wavelengths under red region (634–649 nm) carbohydrate with combined single- and two-phase MS containing higher P and lower N (0.04–0.14N) in rootless plantlet (Table 4). ANFIS model predicted higher theoretical optima, including 26.57 mg/g FW soluble carbohydrate (Table 4; Fig. 8B) under far-red (700 nm), together with markedly elevated storage carbohydrate (843.75 mg/g FW) and total carbohydrate (767.69 mg/g FW) maxima under 661 nm, in combined single- or two-phase MS with elevated P and lower N (0.55–0.28N) in rootless plantlet (Table 4). For roots, FIS predicted optimal carbohydrate accumulation under red spectrum (652–661 nm) on MS with higher P and lower N (0.04–0.5N) in rootless plantlet (Table 5; Fig. 8C). ANFIS predicted substantially higher theoretical maxima for root soluble carbohydrate (57.99 mg/g FW) (Table 5; Fig. 8D), storage carbohydrate (1392.6 mg/g FW), and total carbohydrate (1418.2 mg/g FW) under red to far-red spectra (700 –640 nm) in single- and two-phase MS with higher P and lower N (0–0.55N) in rootless plantlet (Table 5). Across both leaf and root carbohydrate traits, ANFIS response surfaces consistently shifted predicted optima toward red and far-red spectral regions under elevated P and reduced N conditions, while also predicting substantially higher carbohydrate maxima relative to FIS outputs (Tables 4 and 5).

Fig. 8.

Surface and contour plots derived from (A and C) Fuzzy inference system (FIS) and (B and D) Adaptive neuro-fuzzy inference system (ANFIS) to illustrate the optimized light spectra and nitrogen (N) concentration for maximizing soluble carbohydrate (mg/g FW) in (A and B) Leaf (lsoc) and (C and D) Root (rsoc) of Phalaenopsis amabilis ‘Anthura Beijing’ plantlets

For leaves, FIS identified optimal conditions at approximately white fluorescent light region (550 nm) approximately on 1/2 MMS (0.5N) in rooted plantlets, corresponding to a predicted F_v/F_m value of 0.77 (Table 4; Fig. 9A). In contrast, ANFIS predicted a higher theoretical optimum (F_v/F_m = 0.88) approximately under blue region (400 nm), on MS with higher P and lacking N (Table 4; Fig. 9B). For roots, FIS predicted similar optimal conditions (MS with 0.5-fold lower N under 550 nm in rooted plantlets), corresponding to a predicted F_v/F_m value of 0.58 (Table 5; Fig. 9C). The ANFIS model predicted a higher theoretical maximum of F_v/F_m (0.66) under 400 nm illumination combined with MS with elevated P and lacking N in rooted plantlets (Table 5; Fig. 9D). Across both leaf and root traits, ANFIS response surfaces consistently predicted higher F_v/F_m maxima and shifted optimal conditions toward blue-light wavelengths under elevated P and low N conditions relative to FIS outputs (Tables 4 and 5).

Fig. 9.

Surface and contour plots derived from (A and C) Fuzzy inference system (FIS) and (B and D) Adaptive neuro-fuzzy inference system (ANFIS) to illustrate the optimized light spectra and nitrogen (N) concentration for maximum quantum efficiency of photosystem II (F_v/F_m) in (A and B) Leaf (lF_v/F_m) and (C and D) Root (rF_v/F_m) of Phalaenopsis amabilis ‘Anthura Beijing’ plantlets

Discussion

Enhanced predictive performance of ANFIS over FIS

FIS demonstrated relatively weak predictive performance for the morpho-physiological traits of Phalaenopsis leaves and roots under varying culture conditions (Tables 4 and 5). This can be attributed to several well-documented limitations inherent to conventional FIS architectures. First, traditional FIS models typically rely on fixed membership functions (MFs) and rules that are predefined, often derived from expert knowledge, rather than being learned or adaptively optimized from the empirical data. As a result, such static rule sets and non-tuned MFs are often unable to approximate the highly nonlinear and interactive relationships among multiple biological inputs and outputs, particularly in complex plant physiological systems. This limitation has been extensively discussed in comparative studies, which have shown that the lack of adaptive tuning in MF parameters and rule consequents significantly constrains the accuracy of conventional FIS relative to data-driven methods such as ANFIS [33].

Second, when the number of input variables (traits) increases, the so-called “curse of dimensionality” becomes a critical issue for FIS. The number of potential fuzzy rules expands exponentially with the number of input variables, especially when each input is represented by multiple membership functions. This exponential growth not only complicates model construction and interpretability but also increases the risk of overfitting, thereby further reducing the generalization performance of the FIS [33]. This limitation further reduces the generalizability of FIS models when dealing with high-dimensional datasets.

Third, FIS performance is highly sensitive to the selection of MF types, such as triangular, Gaussian, bell-shaped, and to their initial parametrization. In the absence of systematic optimization, suboptimal MF structures or poorly tuned parameters can degrade model fitting accuracy, resulting in larger residual errors. Previous studies have shown that even minor variations in MF configuration can produce marked differences in predictive performance between ANFIS and conventional FIS models [34].

Fourth, biological datasets are inherently noisy, often containing measurement error, and complex nonlinear interactions among multiple inputs. FIS models based on manually defined rules are typically less robust to such variability and interaction effects; in contrast, ANFIS dynamically learns both MF parameters and rule weights from data, allowing it to minimize modeling error and achieve superior predictive accuracy. Evidence from several in vitro plants culture modeling studies supports this advantage, for example, the application of ANFIS coupled with ANFIS-NSGAII in Chrysanthemum somatic embryogenesis demonstrated significantly higher performance under similarly noisy and interactive conditions [35].

Fifth, many implementations of FIS lack rigorous model validation procedures, such as cross-validation or independent test datasets. In several studies, model performances have been evaluated solely on training data, which can obscure overfitting and lead to an overestimation of predictive accuracy. ANFIS-based approaches commonly employ hold-out or k-fold cross-validation schemes and report the results on independent test sets, consistently demonstrating superior generalization ability [34].

Given these methodological limitations, the superior predictive performance of ANFIS observed in the present dataset is expected. ANFIS possesses an inherent capacity to adapt membership function parameters and rule weights through data-driven learning, effectively controlling model complexity while capturing nonlinear relationships, interactions and noise. This adaptability enables ANFIS to more accurately model the intricate input-output relationships among factors such as light spectrum, culture medium compositions, plantlet types, and culture system configurations, as well as the associated morphological and physiological traits.

Organ-resolved optimum divergence and practical implications

The present study revealed a clear organ-resolved divergence in the optimal light spectra and nutrient compositions governing morpho-physiological responses in Phalaenopsis plantlets. Leaf associated traits, particularly growth (Fig. 5A and B), photosynthetic efficiency (Fig. 9A and B), and pigment accumulation, were generally optimized under white and blue light combined with N reduction (Table 4), whereas root associated traits (Table 5) and carbohydrate storage responses (Tables 4 and 5), exhibited stronger optima under red light enriched conditions combined with elevated P and reduced N availability. Importantly, these divergent responses indicate that practitioners cannot simultaneously maximize all physiological traits within a single culture condition, but instead must prioritize either leaf photosynthetic performance or root biomass and storage metabolism depending on the propagation objective. The ML-derived response surfaces further demonstrated that leaf related traits were governed predominantly by relatively stable physiological regimes, whereas root growth, carbohydrate accumulation, and source-sink interactions exhibited context-dependent responses. Consequently, the FIS model generally aligned more closely with experimentally observed optima under physiologically stable conditions, while ANFIS more effectively captured latent interaction patterns among light quality, nutrient availability, plantlet type, culture system configuration in organ-specific metabolism (Tables 4 and 5). These findings indicate that optimization of Phalaenopsis tissue culture systems requires not only empirical treatment evaluation but also mechanistic interpretation of physiological interactions captured through ML-based modeling. Overall, the integration of ML-derived optima with physiological interpretation demonstrates that light quality and nutrient availability regulate Phalaenopsis development through tightly coordinated source-sink interactions linking leaf photosynthetic activity with root metabolic storage. Importantly, these interactions are governed by physiological regimes that cannot be fully inferred from treatment means alone.

Mechanistic validation of ML-predicted optima

Interpretation of light spectra, nutrient composition, and plantlet types interactions

the FIS model identified 550–553 nm (white fluorescent region) combined with moderate N reduction as an optimal condition for leaf growth (Table 4; Fig. 5A) suggests that biomass accumulation is favored under relatively stable, near-linear physiological responses. This prediction is physiologically consistent with the broad spectra distribution of white fluorescent light encompasses efficiently absorbed by Chl, thereby enhancing photosynthetic performance and promoting leaf expansion and biomass accumulation (Table 4). This mechanistic interpretation is consistent with previous studies on Phalaenopsis and Dendrobium, where broad-spectrum or mixed-light conditions enhanced photosynthetic efficiency and morphogenesis compared to monochromatic spectra [36, 37]. Likewise, Mahdavi et al. (2025) reported a 387% increase in leaf area under nutrient-optimized conditions (medium with 100, 7.4, and 2.1% increase in NO₃⁻, P, and K, respectively) [1]. It should be noted that, besides N and P modifications, differences in other macro-nutrient as K, magnesium (Mg), calcium (Ca), and sulfur (S) concentrations (Table 2; Fig. 2A) resulting from the use of 1/2 MMS medium may also have contributed to some of the observed physiological responses. While the ANFIS model predicted a theoretical maximum in orange-red wavelengths (~601–607 nm) for leaf growth (Table 4; Fig. 5B), this likely reflects latent interactions between red light signaling and nutrient assimilation efficiency, particularly through phytochrome-mediated regulation of photosynthate allocation [38]. However, the experimentally observed superiority of white fluorescent light likely results from its balanced activation of both photosystems (PS) and the reduced risk of photoinhibition.

For root development, The ANFIS predicted higher theoretical maxima under 601–607 combined with high P and moderately reduced N (Table 5), suggesting that red light can further stimulate root expansion, though its effect may on the balance between light intensity, nutrient interaction and tissue differentiation volumetric expansion. P is a vital component and key constituent of ATP, nucleic acids, and phospholipids, all of which are essential for cellular energy metabolism, division in root meristems, and root elongation [30]. Reduced N availability may have minimized N-induced osmotic or oxidative stress and the risk of N-induced toxicity, allowing P to exert its full stimulatory effect on root growth [30]. However, the experimentally observed preference for white fluorescent light indicates that root growth is also dependent on baseline photosynthetic support from leaves, reinforcing the importance of systemic leaf-root physiological integration (Table 5). It should be acknowledged that the superior performance observed under white fluorescent light treatment may not be attributed solely to its spectral properties. In the present study, the white fluorescent light represented a distinct light source compared to all LED based treatments (white, red, blue, and green) (Table 1). Therefore, differences in leaf and root responses may have been partially influenced by intrinsic differences between fluorescent and LED technologies, such as spectral distribution characteristics, photon diffusion patterns, and thermal output [39]. As a result, the observed effects of white fluorescent light should be interpreted with caution, and further studies directly comparing white LED and white fluorescent light under identical conditions are needed to disentangle spectral effects from light-source effects. The presence of roots in plantlets is crucial for nutrient and water uptake, which directly impacts leaf development. Rooted plantlets exhibit superior physiological performance, likely due to enhanced water uptake that supports sustained leaf expansion and carbohydrate metabolism. This observation aligns with reports highlighting the positive influence of root presence on aerial organ growth, like leaf in orchids [6]. The absence of significant culture medium configuration (single-phase vs. two-phase) on root growth further indicates that nutrient composition and light spectrum are the dominant factors governing root development. Collectively, the combined ML experimental evidence demonstrates that leaf development is dominated by relatively stable physiological constraints, whereas root development related traits exhibit strong light-nutrient interactions that are more effectively captured by ANFIS than by FIS (Tables 4 and 5).

Light-nutrient crosstalk governs pigment differentiation

The ANFIS model identified blue light spectra combined with low N (0N) and high P availability as high-sensitivity region for maximizing leaf pigment-related traits (Table 4). Chl and carotenoid accumulation in Phalaenopsis leaves by activating blue-light photoreceptors such as cryptochromes and phototropins, which enhance the transcription of genes involved in Chl biosynthesis and Chl-binding proteins. This, in turn, increases chloroplast development and photosynthetic efficiency [40, 41]. Blue light also stimulates the expression of key enzymes in the carotenoid biosynthetic pathway, such as phytoene synthase (PSY), and promotes plastid differentiation toward chloroplast-type organelles [40, 41]. Importantly, the stronger predictive gain of ANFIS for pigment related traits compared to more conservative physiological ratios (e.g., Chl a/b) (Table 4), suggests that these pigment accumulation processes exhibit environmental sensitivity, which is consistent with the observed strong response under blue-enriched spectra. Based on the experimentally observed results, the highest pigment contents were recorded under blue light combined with MS medium containing 16-fold P and 1/20-fold N (Table 4). In contrast, higher N supply (1/10N) under the same light condition resulted in significantly lower pigment accumulation (Table 4), indicating a strong interaction between N availability and blue light in regulating pigment biosynthesis. Although N is essential for Chl synthesis, moderate N limitation may enhance N use efficiency and promote pigment accumulation under certain conditions [42]. Moreover, ANFIS predictions indicated that pigment accumulation is maximized under a nutrient regime characterized by relatively (Table 4). This agrees with the physiological shift in carbon (C) allocation from growth toward pigment biosynthesis by adjusting the C:N:P stoichiometry, where increased ATP availability and supporting the synthesis of isoprenoid precursors [42]. The ML model captured interaction between light quality and nutrient availability that is not explicitly evident from treatment means alone, suggesting that pigment biosynthesis is governed by strong light-nutrient interaction effects rather than additive responses. Anthocyanin accumulation in leaves under white LED illumination (Table 4), particularly in rootless plantlets, reflects both experimentally observed stress physiology and ML-indicated reduced efficiency under broad-spectrum lighting. White LEDs emit broad-spectrum radiation encompassing green, blue, and far-red wavelengths, which activate both cryptochrome and phytochrome signaling pathways and induce photoprotective flavonoid biosynthesis, often through reactive oxygen species (ROS)-mediated signaling [43]. In rootless plantlets, limited nutrient and water uptake intensifies oxidative stress and sugar accumulation, leading to upregulation of R2R3-MYB/bHLH transcription factors that regulate anthocyanin biosynthesis [44]. The comparatively lower predictive efficiency of ANFIS for broad-spectrum treatments suggests that such stress-induced metabolic responses are more variable and less predictable than pigment responses under optimized narrow-band conditions.

In contrast, the ANFIS model identified red light as particularly favorable for root-associated pigment accumulation (Table 5), likely promotes phytochrome activation and plastid differentiation. This enhances gene networks Chl and carotenoid accumulation even in subterranean or non-foliar tissues exposed to in vitro light conditions [45]. Additionally, ML-derived response surfaces indicated a stronger sensitivity of root pigment traits to red and far-red balance compared to leaf traits (Tables 4 and 5), suggesting tissue-specific light perception. Red light can also increase translocation of photosynthates and sugar signaling to roots, providing more C scaffold for isoprenoid (carotenoid) and phenylpropanoid (anthocyanin) pathways in root cells under the studied nutrient regimes [45]. The model further suggested that high P availability supports ATP production and phosphorylated intermediates essential for pigment biosynthesis, while low N reduces growth dilution effects, together promoting the secondary metabolite accumulation in roots [30, 42]. These interactions highlight that pigment accumulation in roots is governed by a distinct light-nutrient interaction network compared to leaves, which was effectively captured by the ML framework.

Physiological mechanisms underlying carbohydrate allocation

The ANFIS model showed a substantially greater predictive improvement over FIS for storage carbohydrate traits (Table 4). Experimentally, the highest leaves soluble carbohydrate concentration was observed under green LED illumination (530 nm) combined with elevated P (16-fold) and very low N (0.05-fold) levels in T55 and T56 (Table 4). Importantly, both FIS and ANFIS identified low N and high P conditions as favorable for carbohydrate accumulation, while ANFIS predicted stronger optima, suggesting that carbohydrate metabolism responds to interactive thresholds rather than simple additive nutrient effects (Table 4). Limited N availability is known to suppress protein synthesis and cell expansion, resulting in an excess of photosynthetically fixed C that accumulates in soluble sugar forms such as sucrose and glucose [46, 47]. Concurrently, high P enhances ATP production and the activation of key photosynthetic enzymes, thereby supporting increased CO₂ assimilation and carbohydrate biosynthesis [48]. The FIS model correctly identified green light as optimal for soluble carbohydrates (Table 4; Fig. 8A) and red light as optimal for storage and total carbohydrates consistent with experimentally observed responses (Table 4). Under green light, Chl pigments exhibit relatively lower absorption efficiency, which may allow a greater proportion of photons to penetrate deeper into the leaf tissues. This altered light distribution could potentially contribute to enhanced photosynthetic activity in lower cell layers and thereby promote overall C assimilation and soluble sugar accumulation [49, 50]. However, it should be noted that in vitro plantlets possess simplified and less differentiated tissue architecture compared to mature leaves. Similar findings were reported in Dendrobium orchids, where green light significantly increased soluble carbohydrate and protein content under in vitro conditions [51]. In contrast, the ANFIS model consistently predicted red light as the optimal condition across all carbohydrate-related traits (Table 4), indicating a stronger weighting of red-light-mediated C partitioning pathways in the learned response surface. Red LED illumination (640–661 nm) promoted higher accumulation of storage and total carbohydrate in leaves [52]. Red light activates phytochrome signaling pathway, which upregulates starch biosynthetic genes such as AGPase, SS, and SBE while downregulating sugar catabolic enzymes [53]. Moreover, N limitation combined with P enrichment elevates the C/N ratio, diverting C flux toward starch and polysaccharide biosynthesis rather than amino acid production [42].

In roots, the highest soluble, storage, and total carbohydrate concentrations were observed under red LED light combined with low N (0.05-fold) and high P (16-fold) levels (Table 5). ANFIS-derived optima further suggested that root carbohydrate accumulation is particularly sensitive to red-light–nutrient interactions (Table 5), consistent with the strong source-sink regulation governing belowground C allocation. Red light enhances source-sink dynamics by promoting the translocation of photosynthates from leaves to roots via phytochrome-mediated regulation of sucrose transporters [54], while elevated P further supports sucrose metabolism in roots by enhancing the activities of sucrose synthase, thereby facilitating the conversion of soluble sugars to storage polysaccharides [55]. Conversely, N limitation restricts protein synthesis and cellular proliferation, leading to increased partitioning of C into non-structural carbohydrate reserves [56]. The tendency of ANFIS to converge on red light as a universal optimum in leaf and root (Tables 4 and 5), suggests that carbohydrate metabolism in this system is governed more strongly by source-sink regulation and phytochrome-driven C partitioning than by pigment-level light absorption effects alone.

In rootless plantlets, the absence of sink tissues (i.e., roots) restricts carbohydrate translocation, resulting in sugar accumulation of soluble sugars within leaf tissues. This physiological response has been reported previously for Phalaenopsis, where rootless protocorms accumulate excess soluble sugars and starch due to reduced C export [3, 57]. Such carbohydrate retention represents an adaptive mechanism to maintain osmotic balance and energy homeostasis under restricted sink demand, ensuring metabolic stability despite restricted assimilate partitioning. Importantly, this condition represents a feedback state captured more effectively by ANFIS than by FIS, further emphasizing the importance of sink limitation in regulating carbohydrate dynamics.

Organ-specific regulation of PSII efficiency under different light and nutrient conditions

The highest observed leaf F_v/F_m (0.78) (Table 4) in rooted Phalaenopsis plantlets cultured under white fluorescent light in single- and two-phase 1/2 MMS (T1 and T2) reflects a physiologically stable state in which balanced spectral quality and moderate N availability jointly sustain optimal PSII photochemical efficiency [58]. Importantly, the FIS model accurately captured this optimum at 550 nm combined with moderate N reduction (Table 4; Fig. 9A), indicating that leaf PSII efficiency follows a relatively smooth and near-linear response surface governed by coordinated photosystem excitation and N-dependent protein synthesis [58]. Mechanistically, white/broad-spectrum light promotes coordinated expression of photosynthetic genes, stabilizes PSII reaction centers and facilitates the efficient assembly of light-harvesting complexes [58]. These processes are highly dependent on both spectral quality and N availability, as N is essential for the synthesis of D1/D2 core proteins and Chl protein complexes [58]. Under moderate N conditions (0.5-fold lower N; 1/2 MMS), nutrient resources appear sufficient to sustain PSII repair and turnover, thereby producing high F_v/F_m values in leaf tissues [58]. By contrast, the ANFIS model projected a theoretical maximum at F_v/F_m of 0.88 under blue illumination (~400 nm) combined with MS with elevated P, and unless N (Table 4; Fig. 9B), representing an idealized physiological state rather than an experimentally dominant condition. This divergence between FIS and ANFIS suggests that PSII efficiency is governed by two distinct regimes: a stable, physiologically constrained regime captured by FIS (broad spectrum with moderate N), and acclimatory regime captured by ANFIS (blue light driven photoprotective activation). Blue light signaling via cryptochrome and phototropin pathways can enhance PSII repair capacity and photoprotective acclimation, but only becomes fully effective when sufficient metabolic resources (e.g., N-dependent protein synthesis capacity) are available. Therefore, the ANFIS prediction reflects a potential upper biological limit rather than a commonly expressed experimental optimum (Table 4; Fig. 9B). Consistent with this interpretation, previous studies of Ko et al. (2020), as they reported that after blue light acclimation, Phalaenopsis aphrodite led to elevated leaf anthocyanin accumulation, enhanced chloroplast avoidance movement, and increased Chl fluorescence variables including F_v/F_m, electron transport rate (ETR), Chl, catalase activity, and sucrose accumulation [41].

Root F_v/F_m values in T1 and T2 are consistently lower than those of leaves (0.58) (Table 5), reflecting intrinsic physiological and structural differences between leaf mesophyll and root tissues. Roots plastids are fewer in number and less differentiated than chloroplasts (Fig. 10); even under in vitro illuminated, they exhibit lower alters photosynthetic capacity and reduced PS stoichiometry, resulting in inherently reduced maximal photochemical efficiency compared with leaf tissues [6]. The FIS model identified 550 nm combined with moderate N availability (0.5-fold lower N) as optimal for root F_v/F_m (Table 5; Fig. 9C) likely reflects a physiological balance in which broad-spectrum white light promotes limited plastid differentiation without inducing spectral stress, while sufficient N supply supports the synthesis of core PSII proteins required for basal photochemical function in root plastids [58]. By contrast, the ANFIS model predicted a higher theoretical optimum under blue wavelengths (~400 nm) combined with N deprivation (0N) and elevated P levels (Table 5; Fig. 9D). This scenario reflects acclimatory hypothesis in which blue light signaling could activate acclimation pathways leading to improve PSII efficiency in root tissues-provided that energetic and biosynthetic precursors such as ATP, phosphorylated intermediates, and C skeletons are adequately available [59, 60]. In practice terms, root metabolism in Phalaenopsis is inherently constrained by its dependence on photoassimilate supply from leaves and by its specialized epiphytic anatomy (i.e., the presence of velamen). These structural and metabolic features limit photosynthetic competence in roots, even under in vitro illumination, resulting in lower PSII repair capacity and restricted ETR relative to leaves (Fig. 10) [6, 59]. Therefore, under realistic culture conditions, the ANFIS-predicted enhancement at 0N is unlikely to manifest unless compensatory mechanisms sustain N-dependent protein turnover and reflects an extrapolation artifact rather than a physiologically realistic condition (Table 5), indicating that the model may overemphasize extreme parameter interactions beyond the experimentally observed range.

Fig. 10.

Schematics conceptual model of photosynthetic processes in leaf and root chloroplasts of Phalaenopsis. Leaf chloroplasts exhibit a canonical, photosystem II (PSII)-driven linear electron flow (LEF), resulting in substantial oxygen evolution, high production of ATP and NADPH, and a fully active Calvin–Benson cycle with Rubisco supporting net carbon (C) assimilation and carbohydrate export. In contrast, root chloroplasts show reduced PSII activity and predominantly rely on photosystem I (PSI)-centered cyclic electron flow (CEF), which enhances proton translocation and ATP synthesis without concomitant NADPH production or oxygen evolution. Consequently, the Calvin cycle in roots operates at low flux and is depicted as smaller, reflecting its limited role in respiratory CO₂ refixation and local metabolic support rather than bulk C fixation. Differences in chlorophyll (Chl) abundance are indicated by darker green leaf chloroplasts compared with paler root chloroplasts. Arrows color denote: LEF (green), CEF (blue), production of metabolic product (yellow), and utilization of metabolic product (red). This schematic represents a conceptual interpretation based on literature and physiological inference and has not been directly validated experimentally in this study

Ultimately, the superior PSII performance of rooted plantlets underscores the fundamental role of an intact root system in maintaining nutrient and water fluxes to the aerial organs under in vitro conditions. Continuous nutrient uptake, particularly of N, which supports D1 protein turnover and prevents chronic photoinhibitory damage, thereby preserving higher F_v/F_m values and ensuring sustained photosynthetic stability [61].

Comparative photochemical and C metabolic differentiation between leaves and roots

Growth and biomass: Roots of Phalaenopsis exhibited significantly greater fresh and dry biomass and volumetric expansion than leaves across most treatments (Tables 4 and 5). Importantly, this pattern was captured more accurately by the ANFIS model than by FIS (Tables 4 and 5), indicating that root biomass accumulation is governed by strongly sink-driven processes, whereas leaf growth follows comparatively more stable and near-linear physiological responses [6]. This consistent pattern underscores their role as dominant sink organs that actively import photoassimilates from leaves and convert them into reserve carbohydrates such as starch, leading to substantial mass accumulation [6, 30]. The velamen and cortical parenchyma of roots also store large amounts of water, explaining the greater fresh weight and volume compared with the thinner, photosynthetically specialized leaves [6]. In contrast, leaves function primarily as source tissue, optimizing light capture and C fixation rather than biomass accumulation. Their cellular architecture, dominated by chloroplast-rich mesophyll and limited storage parenchyma, favors efficient photosynthetic output and assimilate export at the expense of tissue density and water retention [62]. Elevated P availability (16-fold higher P) in the culture medium stimulated ATP-dependent sucrose transport and starch biosynthesis, particularly in roots, thereby amplifying their sink strength and biomass production [63].

Pigment composition and organ-specific photoreceptor responses: Leaves accumulated markedly higher levels of Chl and carotenoids than roots (Tables 4 and 5), reflecting their primary role as the primary photosynthetic organ and their possession of abundant, well-developed chloroplasts with dense thylakoid membrane systems (Fig. 10) [40, 64]. This organ-specific distribution was reflected in the ML-results, where leaf pigment traits showed relatively smaller differences between FIS and ANFIS (Tables 4 and 5), indicating a more constrained and stable response surface compared to root-associated traits. In contrast, root plastids are less differentiated and possess limited light-capture geometry, constraining Chl biosynthesis even under in vitro illumination (Fig. 10) [6]. Carotenoid synthesis, which occurs within plastids, follows this same pattern (Tables 4 and 5), being more pronounced in leaves due to the greater number and functional maturity of their chloroplasts [41, 64]. Interestingly, Phalaenopsis roots frequently exhibited comparable or even higher anthocyanin levels than leaves (Tables 4 and 5), a response likely triggered by light- and nutrient-induced stress signaling under in vitro conditions. This response aligns with ANFIS predicted stress sensitivity, where root pigment regulation appears more strongly influenced by interaction effects between light quality and nutrient limitation (Table 5). Accumulation of soluble sugars and ROS can activate R2R3-MYB/bHLH transcription factors that drive anthocyanin biosynthesis as a photoprotective mechanism [44]. The velamen and photosynthetic cortex in Phalaenopsis roots enable limited photosynthesis and can induce anthocyanin formation to mitigate oxidative stress, modulate light penetration, and protect internal tissues from photodamage [65].

F_v/F_m: The significantly higher F_v/F_m observed in leaves (⁓0.78) (Table 4) compared to roots (⁓0.58) (Table 5) demonstrates the superior integrity and dynamics of PSII in leaf chloroplasts [6]. Importantly, ANFIS predicted a higher theoretical upper limit for leaf (Table 4; Fig. 9B) and root F_v/F_m (Table 5; Fig. 9D) under blue light conditions, whereas FIS closely matched experimentally observed white fluorescent light optima (Tables 4 and 5), indicating that PSII efficiency operates under two regimes: a stable physiological regime and a photoprotective acclimation regime. Leaves possess densely stacked grana and highly efficient PSII reaction centers that facilitate rapid charge separation and stable excitation energy transfer (Fig. 10) [66]. In contrast, root plastids exhibit sparse thylakoid organization and reduce PSII abundance, resulting in limited electron transport capacity and slower D1 protein turnover, which together diminish PSII quantum efficiency (Fig. 10) [67]. Within leaf tissues, higher cytochrome b₆f (Cytb₆f) content and faster plastoquinone (PQ) oxidation sustain linear electron flow (LEF) and minimize photoinhibition (Fig. 10) [66]. Conversely, root plastids possess smaller PQ pools and slower PQH₂ oxidation kinetics, which elevate the likelihood of charge recombination and ROS formation [67]. Moreover, the limited Calvin-cycle activity and NADP⁺ availability in roots restrict downstream electron sinks, causing over-reduction of PSII/PSI components and further decreasing F_v/F_m (Fig. 10). Leaves maintain rapid D1 turnover, supported by greater N and ATP availability, which facilitates continuous PSII repair and preserves high quantum yield [66, 67].

Carbohydrate partitioning and Calvin–Benson cycle activity: Roots accumulated substantially greater storage and total carbohydrate pools than leaves in several treatment condition (Tables 4 and 5), consistent with their function as dominant C sinks [6]. This pattern was strongly nonlinear in the ML analysis, with ANFIS outperforming FIS (Tables 4 and 5), indicating that carbohydrate partitioning is governed by interaction-dependent source–sink dynamics rather than additive effects of light and nutrients. In contrast, leaves function as C sources under red and green light by driving Calvin–Benson cycle activity and producing triose phosphates that are exported as sucrose. Red light enhances electron transport and ATP/NADPH production, increasing C fixation and export capacity (Fig. 10) [68]. Roots, possessing fewer plastids and substantially lower Rubisco content (as inferred from their limited photosynthetic capacity compared to leaves), exhibit limited autonomous C fixation. However, they maintain a high capacity for sucrose conversion into starch through sucrose synthase and ADP-glucose pyro-phosphorylase (AGPase)–mediated pathways (Fig. 10) [6]. Consequently, under conditions of high photosynthetic source activity and N limitation (i.e., elevated C:N ratio), excess C is preferentially allocated and stored as non-structural carbohydrates in root tissue [69]. In the present experiment, under green light, where phloem loading and assimilate export are reduced, as observed in rootless plantlets, soluble carbohydrate levels increased markedly in leaves (Table 4), reflecting limited sink demand and constrained sucrose translocation [49]. This condition represents a feedback state captured more effectively by ANFIS than FIS, highlighting the importance of sink limitation in regulating carbohydrate dynamics.

Adaptive modulation of source-sink balance and leaf-root coordination

A strong positive correlation between F_v/F_m, total Chl, carotenoid of leaf and root dry weight under white fluorescent light (T1 and T2, T2 and T22, T41 and T42) (Fig. 4) indicates efficient C assimilation and allocation. Importantly, the FIS model closely matched the experimentally observed optimum under broad spectrum white light combined with elevated P and reduced N (Tables 4 and 5), suggesting that balanced shoot-root development in Phalaenopsis is governed primarily by a relatively stable physiological regime under these conditions. In contrast, ANFIS predicted alternative theoretical optima characterized by stronger interactions between photochemical efficiency and sink-driven biomass accumulation (Tables 4 and 5). This is consistent with prior reports demonstrating that broad-spectrum white light enhances balanced shoot–root development by optimizing photosynthetic efficiency and carbohydrate translocation [37]. Under these conditions, improved photochemical performance in leaves likely increases sucrose export, thereby supporting greater root biomass accumulation and metabolic activity [70]. Elevated P availability enhances ATP and NADPH turnover, sustaining higher photosynthetic energy conversion and assimilate flow toward roots [48]. In contrast, reduced N levels limit excessive vegetative expansion, promoting a more balanced source-sink equilibrium between leaf and root metabolism. Under blue LED illumination (T37 and T38, T39 and T40) (Fig. 4), however, although leaf Chl and carotenoid contents increased while root biomass decreased (Fig. 4), particularly in the rootless plantlets (T39 and T40). ANFIS captured this response more strongly than FIS (Tables 4 and 5), suggesting that blue light responses involve highly allocation trade-offs between pigment biosynthesis and sink development. Blue light activates the cryptochrome-mediated signaling pathway that enhances pigment biosynthesis and stomatal differentiation [71]. However, in the absence of a functional sink, as rootless plantlets, excessive C assimilation can trigger feedback inhibition of carbohydrate export and utilization [57]. Consequently, the correlation between photosynthetic pigment accumulation and root growth becomes weak or negative when roots are absent (Fig. 4), emphasizing the critical role of functional tissues in maintaining optimal photosynthetic balance. Under red light LED treatments (T11 and T12) (Fig. 4), rootless plantlets exhibited increased root storage carbohydrate despite moderate F_v/F_m values (Fig. 4), suggesting that red light promotes C fixation and starch accumulation via phytochrome-mediated regulation of carbohydrate metabolism. ANFIS-derived optima further indicated that red-light-driven carbohydrate accumulation behaves as a storage-oriented response (Tables 4 and 5). This interpretation is consistent with previous studies demonstrating that phytochrome signaling enhances C fixation efficiency and starch biosynthesis under red light conditions [68]. In contrast, green LED treatments (T35 and T36) (Fig. 4) enhanced both leaf soluble sugar levels and moderate root biomass, particularly in rootless plantlets, indicating improved coordination between sugar production and utilization between source and sink organs. Green light penetrates deeper into mesophyll tissues, stimulating photosynthesis in lower chloroplasts and facilitating sucrose translocation to roots [72].

Overall, the observed correlations in the heatmap highlight that Phalaenopsis plantlets coordinate their leaf photosynthetic capacity and root metabolic storage through tightly integrated source-sink regulation (Fig. 4). Importantly, the ML models revealed that these interactions are governed by physiological regimes that cannot be fully inferred from experimental treatment means alone. This integration of ML-derived response surfaces with physiological interpretation provides a more mechanistic understanding of how light quality and nutrient availability jointly regulate adaptive growth responses under in vitro conditions.

Model-biology divergence and practical limitations of ANFIS predictions

The ANFIS model predicted several theoretical optima that diverged from experimentally observed physiological behavior, most notably the prediction of maximal F_v/F_m values under blue light conditions combined with complete N deprivation (0N) (Tables 4 and 5; Fig. 9B and D). Although ANFIS identified this condition as a mathematical optimum, this prediction contradicts established physiological knowledge regarding the essential role of N in PSII stability and repair [58]. N is required for synthesis and turnover of D1/D2 core proteins, Chl-protein complexes, and enzymes involved in photosynthetic electron transport [58]. Under complete N deprivation, sustained PSII repair and photochemical stability are physiologically unlikely, particularly under prolonged in vitro culture conditions. This divergence between ANFIS prediction and biological reality is scientifically important because it reveals the practical boundaries of ML-based extrapolation in plant tissue culture systems [73]. ANFIS effectively captured latent interaction patterns within the experimental dataset; however, under extreme parameter combinations that were weakly represented or biologically constrained, the model appears to overemphasize mathematical interactions beyond physiologically realistic limits. Therefore, the ANFIS-predicted optima under 0N conditions should not be interpreted as directly applicable cultivation protocols, but rather as theoretical upper-bound scenarios reflecting strong responses. The divergence also highlights an important distinction between predictive optimization and mechanistic biological feasibility. While ML models can successfully identify hidden multidimensional relationships among nutrient composition, light spectra, plantlet type, and culture system configuration [4, 15], physiological interpretation remains essential for determining whether predicted optima are biologically sustainable. In the present study, experimentally observed optima under white fluorescent light and moderate N reduction likely represent physiologically stable operating regimes (Tables 4 and 5), whereas ANFIS-derived extreme optima reflect nonlinear extrapolations beyond the dominant biological response domain (Tables 4 and 5; Fig. 9B and D).

Conclusions

The results demonstrate that the adaptive ANFIS consistently outperformed the conventional FIS across all 16 predicted traits. Based on prediction results, ANFIS provided more reliable prediction of relationships among light quality, nutrient composition, plantlet type, and culture configuration. In addition, ANFIS generated smoother and more distinct response surfaces, enabling more precise identification of treatment combination optimal regions in comparison with FIS.

Direct experimental observations provide clear, actionable guidelines for in vitro propagation of Phalaenopsis amabilis. For maximum leaf growth and photochemical efficiency, T1 and T2 conditions (1/2 MS under white fluorescent light in rooted plantlets) produced the highest leaf fresh weight (3.89 g) and F_v/F_m (0.78). For enhanced leaf pigment accumulation, T57 and T58 (MS+16P+1/20N under blue LED light in rooted plantlets) are recommended. For maximum root biomass, T41 and T42 (MS+16P+1/20N under white fluorescent light in rooted plantlets) resulted in the highest root fresh weight (9.29 g). For maximum root carbohydrate storage, T11 and T12 (1/2 MS under red LED in rootless plantlets) produced the highest storage carbohydrate content (1157.26 mg/g). These conditions optima directly applicable for protocol optimization in commercial and research propagation systems.

Beyond experimentally verified optima, ANFIS produced unvalidated predictions identifying additional high-response regions, including a predicted increase in leaf biomass under ~601 nm light combined with moderate N reduction, and enhanced root carbohydrate accumulation under red-far and red enriched conditions with elevated P and reduced N. These outputs represent model-generated hypotheses requiring experimental validation before practical application. Importantly, a central design insight emerges from both observed and predicted response surfaces, optimal conditions for leaf development and root development are systematically distinct and partially conflicting. Conditions that maximize leaf growth and photochemical performance do not simultaneously optimize root biomass and carbohydrate storage. This trade-off constitutes the most actionable outcome of the modelling framework and provides a practical guideline for targeted, organ-specific optimization strategies in orchid tissue culture systems.

Abbreviations

ANFIS

Adaptive Neuro-Fuzzy Inference System

ANNs

Artificial Neural Networks

C

Carbon

Chl

Chlorophyll

CEF

Cyclic Electron Flow

ETR

Electron Transport Rate

Cytb₆f

Cytochrome b₆f

FW

Fresh Weight

FCM

Fuzzy C-Means

FIS

Fuzzy Inference System

1/2 MMS

Half-strength Modified Murashige and Skoog culture medium

LEF

Linear Electron Flow

ML

Machine Learning

F_v/F_m

Maximum quantum efficiency of photosystem II

MSE

Mean Squared Error

MFs

Membership Functions

MS

Murashige and Skoog culture medium

N

Nitrogen

P

Phosphorus

PS

Photosystems

PSI

Photosystem I

PSII

Photosystem II

PSY

Phytoene Synthase

PQ

Plastoquinone

PLBs

Protocorm-Like Bodies

ROS

Reactive Oxygen Species

R²

R-squared

TDZ

Tidiazoron

Authors' contributions

A.M.B. conceived the study, conducted experiments, analyzed data, and drafted the manuscript. S.D.D. supervised the project, contributed to experimental design, interpretation, and manuscript revision. K.A.V contributed to experimental design, analyzed the data using machine-learning method, and manuscript revision. S.A. contributed to experimental design, performed photosynthetic measurements, and assisted with data collection. K.V. provided laboratory facilities, contributed to project conceptualization, and critically revised the manuscript. All authors read and approved the final manuscript.

Funding

The authors declare that there is no funding source associated with this study.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.