A neurofuzzy logic approach for modeling plant processes - Esalq

Plant Science 179 (2010) 241–249

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Plant Science journal homepage: www.elsevier.com/locate/plantsci

A neurofuzzy logic approach for modeling plant processes: A practical case of in vitro direct rooting and acclimatization of Vitis vinifera L. Jorge Gago a , Mariana Landín b , Pedro P. Gallego a,∗ a b

Applied Plant and Soil Biology, Faculty of Biology, University of Vigo, CP 36310 Vigo, Spain Department of Pharmacy and Pharmaceutical Technology, Faculty of Pharmacy, University of Santiago, CP 15782 Santiago de Compostela, Spain

a r t i c l e

i n f o

Article history: Received 2 March 2010 Received in revised form 18 May 2010 Accepted 19 May 2010 Available online 25 May 2010 Keywords: Artificial intelligence Grapevine In vitro culture Plant model Rhizogenesis in soil

a b s t r a c t Understanding of the cause–effect relationships between culture conditions (carbon source: sucrose, plant growth regulators: type and concentration of auxins) and growth parameters (survival, root number and length, plantlet length and height, etc.) is essential for developing quality micropropagated plants. In this study, an artificial intelligence technology – neurofuzzy logic – has been employed as a modeling tool to get inside information on the effect of three variables, type of auxin, auxin concentration and sucrose concentration in the medium, on the success of in vitro direct rooting in soil and subsequent ˜ grapevine microshoots. acclimatization protocol for ‘Albarino’ The IF–THEN rule sets generated by neurofuzzy logic were completely in agreement with the findings based on statistical analysis. Additionally, neurofuzzy logic revealed significant terms not pointed out by statistics as type of auxin–sucrose concentration or type of auxin–auxin concentration interactions and advantageously generate understandable and reusable knowledge. Therefore, neurofuzzy logic is easy and rapid to apply and outcomes provided knowledge not revealed via statistical analysis leading an improvement on the understanding of the micropropagation process. © 2010 Elsevier Ireland Ltd. All rights reserved.

1. Introduction It is essential to understand the complex cause–effect relationships between plants, cultivars, media, carbon source, plant growth regulators, culture conditions, etc. for developing quality micropropagation protocols and results. Traditionally, those relationships were studied using different statistical tools according to the type of evaluated data [1]. Recently, and as a consequence of the spectacular development of computer systems in the 90s different artificial intelligence methods have also been applied in plant research [2]. In a recent study, Gago et al. [3] pointed out the effectiveness of artificial neural networks (ANNs) in modeling and optimizing different in vitro culture processes. Despite its utility, the interpretation of ANNs is not always easy. Thus, a very promising technology, neurofuzzy logic, has been introduced to help the handling complex models and to data mining [4]. These systems are hybrids and combine the strength and the adaptive learning capabilities from neural networks and the ability to generalize rules of fuzzy logic. Neurofuzzy logic technology has proven its utility in other research areas as pharmaceutics [5], in modeling complex non-linear relationships hidden in product formulation data, hav-

∗ Corresponding author. Tel.: +34 986 811976; fax: +34 986 812556. E-mail address: [email protected] (P.P. Gallego). 0168-9452/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.plantsci.2010.05.009

ing higher accuracy in prediction than statistics and helping the understanding of the complex relationships between variables. In addition, neurofuzzy logic generates understandable and reusable knowledge in an explicit format that can be applied in different scientist domains: an example of such a use is in the plant tissue culture field, where many times a full understanding of the reason for a phenomenon happening (profound knowledge) is not necessary and it could be described by simple rules as IF (condition) THEN (observed behavior). The use of fuzzy logic technology in plant research literature is still limited. Some efforts have been made to characterize and model high complex and non-linear behaviors of different processes of agroecological systems [6] using artificial neural networks, but as far as we know, no attempts have been made to apply this neurofuzzy logic technology to improve in vitro culture research by understanding, through the IF . . . THEN rules, the cause–effect relationships between culture conditions (carbon source, type and concentration of plant growth regulators, etc.) and the growth parameters (survival, root and plantlet length, height, etc.). Successful rooting in micropropagation is essential for the production of viable plants and it can be one of the first limitations in the application of this technology, for some species, to successful of ex vitro production. Auxins have been widely employed as in vitro rooting agents, playing a critical role in the regulation of diverse responses, such as emergence and lateral root initiation,

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functionality, number and size of roots, or adventitious organ formation [7,8]. The efficiency of auxins on rooting varies with the type of auxin used and the plant species, the most common auxins having different optimal concentrations. It is important to note that the auxin optimal concentration to obtain the greatest number of roots may not be the one to produce the highest survival rate on subsequent hardening; type of auxin and its concentration can interact with other parameters as sucrose or exposition time [9,10]. Calamar and De Klerk [11] have demonstrated an interaction between auxin concentration and sucrose on adventitious root regeneration in apple microshoots concluding that the increase on sucrose concentration shifted the dose–response curve of auxin to higher values. Most of commercial laboratories traditionally used to root microcuttings in vitro, using a great number of different culture media, but because it is an intensive and expensive labour, the accounting being between 35 and 75% of the cost of micropropagation ([12] and references therein), alternatives such as in vitro rooting in soil appears to be a desirable low cost approach. Das et al. [13] have reported tea shoots direct rooting by dipping the cut ends in IBA and planting them directly in soil (peat moss 1:1 mixture) with high percentage of survival. Direct rooting in soil of Vitis ˜ has also been described recently [10]. vinifera L. cv Albarino Acclimatization of rooted plants is the subsequent obstacle for obtaining a quality micropropagation protocol. Several authors [14] have suggested that previous in vitro culture conditions, like rooting treatments, can significantly affect the survival and acclimatization of the plantlets. While efficient rooting treatments promote high percentages of rooted shoots and high quality root systems (large numbers of longer roots per shoot) frequently, in vitro formed root systems are largely non-functional and die after transplanting. The good or poor quality of the shoots at the time of planting also affects growth [15] and can be conditioned by the auxin treatment applied during rooting [16,17]. Little attention has been paid to the auxin effects on acclimatization in literature; however the selection of the optimal type, concentration and exposure time is crucial to increase the survival rates and plantlet growth [18,14]. On this basis, this paper investigates the utility of artificial intelligence technology – neurofuzzy logic – as a modeling tool used not only to understand the complex cause–effect relationships between three relevant factors: type of auxin (IBA, IAA and NAA), auxin concentration (1–50 mM) and sucrose concentration (0–9%) but also the success of direct rooting and subsequent acclimati˜ In particular, zation of microshoots of V. vinifera L. cv. Albarino. the potential application of the neurofuzzy logic approach to discover and retrieve knowledge from experimental data of in vitro plant research compared to conventional statistics data is discussed.

2. Materials and methods 2.1. Plant material and culture conditions The experiments were carried out using microshoots of V. ˜ vinifera L. “Albarino” one of the most important cultivar in the northwest Iberian Peninsula. Culture media and conditions have been described elsewhere [10]. Briefly, microshoots were proliferated in MS medium [19] containing 1 mg L−1 BAP (6benzylaminopurine), 3% sucrose and 0.8% plant agar (Duchefa® ). Media pH was set to 5.7 prior to autoclaving (121 ◦ C, 1 kg cm−2 s−1 for 15 min). Cultures were maintained under 16-h-photoperiod (50 ␮E m−2 s−1 ) and at temperatures 25 ± 2 ◦ C during the day and 22 ± 2 ◦ C at night. Microshoots longer than 2.5 cm from the proliferation stage were used as source of explants for rhizogenesis assays.

2.2. In vitro direct rooting (in soil) Two sequential assays were carried out. Firstly, the effect of three different auxins: IAA, IBA and NAA in a broad range of concentrations (1, 15, 25 and 50 mM) and a control treatment (without auxins) was studied. Microshoots longer than 2.5 cm were quick-dipped on their basal side, into a filtered-sterilized auxin concentrated solution and placed directly into the culture vessels with a sterilized planting mixture (perlite:compost 1:1) supplemented with 3% sucrose for 28 days under the culture conditions described previously for plant culture conditions [10]. Secondly, to reduce the factorial design, microshoots longer than 2.5 cm were dipped only with the optimal concentration of each auxin obtained from the previous assay (25 mM IAA, 15 mM IBA and 1 mM NAA) and placed directly into sterilized planting mixture supplemented, in this case, with 0, 1.5, 3.0, 6.0 and 9.0% sucrose (w/v) to examine el effect of sucrose in rhizogenesis. Culture conditions were those described previously [10]. After 28 days, root length and root number parameters (outputs) were recorded for modeling the effect of the factors (inputs) studied on in vitro rooting in soil. 2.3. Acclimatization Plantlets were acclimatized after the rhizogenesis phase. They were carefully transferred to minipots containing steam-sterilized planting mixture (perlite:compost 1:1), and placed in a growth room (Sanyo model SGC066.CFX.F) under 16-h-photoperiod. The light was provided by fluorescent lamps (Phillips TLD32W/83HF) with light intensity of 80 ± 10 ␮E m−2 s−1 . Temperature was 25 ± 2 ◦ C during the day and 20 ± 2 ◦ C at night. The initial value of RH was set to 100% and decreased gradually over 21 days to 60%. After 21 days, two parameters were recorded to analyze the effect of the factors (inputs) studied on acclimatization (outputs): percentage of survival and height (the mean height of plantlets) from acclimatization stage. 2.4. Experimental design and statistical analysis Each rooting treatment consisted of five replicates of three explants each and was repeated at least twice. Optimal rooting was determined based on two parameters (outputs): root length and number of roots at 28 days. Optimal acclimatization was determined based on another two parameters (outputs): survival percent and plantlet height at 21 days. Survival as binary data (dead or alive) were analyzed using binary logistic regression (p < 0.05) procedure in the software pack˜ et al. [20]. Proliferation paramage SPSS 16.0 as suggested by Ibánez eter as count data (number of roots per shoots) usually do not follow a normal distribution, therefore a suitable alternative is used. The Poisson regression model (p < 0.05) which relates the logarithm of the mean count to the combination of the factor effects of a particular case of generalized linear models [1,20], was carried out using generalized linear models procedure in SPSS 16.0. Treatments were compared by multiple comparisons adjusted by the sequential Sidak method (p < 0.05). Finally, growth parameters, as continuous data (root length and plantlets height in cm), can take any value within a range and therefore the length was evaluated through oneway analysis of variance (ANOVA). One-way ANOVA procedure in SPSS 16.0 was used to study the variability of group means and post hoc comparisons of pairs by Tukey’s test (p < 0.05) [1]. 2.5. Neurofuzzy logic A commercial neurofuzzy logic software, FormRules v3.31 supplied by Intelligensys Ltd, 2008, UK was used in this study. A


243

Fig. 1. Graphical example of the significant submodels and their domains developed by neurofuzzy logic for the output root length. (A) Simplest submodels generated pointing out the significant input interactions A × S and A × C (A: type of auxin; S: sucrose and C: auxin concentration) affecting this output; (B) three domains established for the discrete input type of auxin (A); (C) three domains established for the continuous inputs sucrose concentration (S) and (D) five domains established for the continuous inputs auxin concentration (C), respectively driven by the membership degree estimated by neurofuzzy model.

separate model is developed for each property, and a model assessment criterion is used to prevent over-fitting to the data. The accuracy of the neurofuzzy logic model is assessed using the ANOVA correlation coefficient (R2 ) for each output.

n 2 (yi − yˆ i ) R = 1 − i=1 n 2 2

i=1

(yi − y¯ i )

where y¯ is the mean of the dependent variable, and yˆ is the predicted value from the model. The larger the value of the Train Set R2 , the more the model captured the variation in the training data. Values between 70 and 99.9% are indicative of reasonable model predictabilities [21]. In this paper, type of auxin (IAA, IBA and NAA), its concentration (0, 1, 15, 25 and 50 mM), and percentage of sucrose in the medium (0, 1.5, 3.0, 6.0 and 9.0%), were introduced as ingredients and/or process conditions (inputs) whereas the root length, and number of roots, at 28 days (to characterize the rooting) and survival percent and plantlet height at 21 days (to characterize acclimatization) were selected as properties (outputs). FormRules v3.31 is the implementation of the ASMOD (Adaptative Spline Modeling of Observation Data) algorithm [22]. This method uses global partitioning that involves splitting the model into smaller submodels. Various models and submodels are examined, starting from a set of the simplest modes. The models are sums or products of the basic functions, giving submodels that depend only on a subset of the inputs. Complex models are intensely simplified to make them as simple as possible and perform easily understandable rules (Fig. 1). One principle of fuzzy logic consists in dividing the input range of a variable between several subspaces (fuzzy subsets) to which a symbolic name is attached. As an example, in Fig. 1B–D it can be seen that for the discrete variable type of auxin (input A) three domains were established named; IAA, IBA and NAA. For the continuous variables as percentage of sucrose and auxin concentration (inputs S and C) three domains (named “low”, “medium” and “high”) and five domains (“low 1(5)”, “medium 2(5)”, medium 3(5), medium 4(5), “high 5(5)”) were established (Fig. 1C and D), respectively. The output of neurofuzzy logic technology is a predictive model and usually a set of “IF . . . THEN” rules with different values of membership degree [23]. For each of these rules a “membership

degree” is defined which specifies how a “low value” belongs to that fuzzy subset (from 0 to 1). These are the gradual transitions of membership functions between neighboring subsets that gave this technique the so called fuzzy qualifier. The symbolic names are used commonly by neurofuzzy logic technology to promote the importance of the significance against the precision. However, when precise information is needed, the different domains can be observed and quantitatively determining the membership degree of a specific point in the spectrum of the input in the fuzzy subset predicted by the model (Fig. 1B–D). This technology also contains various statistical fitness criteria including Cross Validation (CV), Minimum Description Length (MDL), Structural Risk Minimization (SRM), Leave One Out Cross Validation (LOOCV) and Bayesian Information Criterion (BIC). All of them were investigated to obtain the model that gave the best R2 , for simultaneously measuring the four rooting and acclimatization parameters, and the simplest and more intelligible rules. The best results were found when SRM was used. The training process was conducted in the same way as reported in a previous study by Shao et al. [23]. More details on the parameters are available in the user’s manual of FormRules v3.31 at Intelligensys website (http://www.intelligensys.ac.uk). Minimization parameters are summarized in Table 1. Neurofuzzy logic allowed us to discover and integrate knowledge hidden from all data collected from complex and non-linear processes such rhizogenesis and subsequent acclimatization of micropropagated plants. Data of each of the four parameter studied (root number, root length, survival and plantlet height) were Table 1 The training parameters setting with FormRules v3.31. Minimization parameters Ridge regression factor: 1e−6 Model selection criteria Structural Risk Minimization (SRM) C1 = 0.84–0.3; C2 = 4.8 Number of set densities: 2 Set densities: 2, 3 Adapt nodes: TRUE Max. inputs per submodel: 4 Max. nodes per input: 15

244


Table 2 Effect of IAA, IBA and NAA and sucrose at different concentrations on root number per shoot and root length (mm) during rhizogenesis, and survival and shoot height ˜ microshoots at 28 days and at 21 days, respectively. Different letters mean statistically significant differences at p < 0.05 within all the during acclimatization of cv. Albarino treatments tested per column. A

[A] mM

S (%)

Rhizogenesis

Acclimatization

Root number per shoot Experiment 1 Control IAA

IBA

NAA

Experiment 2 IAA

IBA

NAA

0 1 15 25 50 1 15 25 50 1 15 25 50

3 3 3 3 3 3 3 3 3 3 3 3 3

1.5 3.2 4.9 8.4 5.3 4.1 7.3 6.3 8.4 3.9 5.9 9.8 10.2

25 25 25 25 25 15 15 15 15 15 1 1 1 1 1

0 1.5 3 6 9 0 1.5 3 6 9 0 1.5 3 6 9

2.8 8.4 6.5 7.0 5.3 1.6 5.7 5.9 8.0 7.6 1.3 3.2 3.4 3.2 2.1

A

A A A A A A

B B B B B B B B B B

C C C C C C C C C

C A A A

A A A A

B B B B

Root length (mm) D D

D

D

C C C

B B B B

C C

B B B

C C C C

D D

C D D D D D

19.7 53.4 30.6 26.7 27.8 38.3 26.0 12.6 14.2 31.9 12.3 12.3 4.7 12.3 43.5 30.0 54.8 42.8 10.0 22.8 25.0 22.2 34.1 8.00 29.8 38.9 48.0 29.6

separately provided as outputs to FormRules v3.31 while neurofuzzy logic models were trained using the parameters described in Table 1. Consequently, four sets of “IF . . . THEN” rules were subsequently generated, one for each output.

3. Results and discussion 3.1. Data analysis using conventional statistics High survival (>70%) and rooting percentages (control 45%, auxin × sucrose treatments >50%) during the rhizogenesis stage were obtained. Results are in agreement with those suggesting that the rhizogenesis of microshoots of some grapevine genotypes does not always require the presence of exogenous auxins, but when they are added to the medium better results are obtained [24]. Further, high survival percentages during the acclimatization stage in all treatments (40–93%) under the conditions studied were also achieved. Table 2 shows the in vitro culture results for the parameters selected. As it can be inferred from its observation it is difficult to draw clear and simple conclusions about the effect of variables studied on the rooting and acclimatization simultaneously. The mean root number per shoot after 21 days varies between 1.5 for the control sample and 10.2 after the 50 mM NAA treatment. When analyzing the root number as count data, using Poison’s regression (p < 0.05), statistically significant differences between sucrose and auxin, both type and concentration treatments were observed (Table 2). The multiple comparison test (p < 0.05) has demonstrated that the auxin concentration increase promotes a significant improvement in the number of roots per shoot and also that the auxins have different optimal concentrations with regard to this parameter.

Survival (%) C

D

A B B A

B

B

C C C C C

D D D D

C D D

D A A A

E E

B B

C C

B

C

B

C C C C

D D D D

E E E E

E

E A A

B B B B

C

C

62.0 86.1 75.0 65.8 41.6 72.4 91.5 72.7 75.0 84.8 78.9 77.3 73.3 46.9 81.0 85.0 93.3 92.8 43.9 72.0 89.2 63.5 68.4 39.2 53.8 81.4 62.9 68.4

Height (cm) C

A

B B B

C D

B

C

B B B B B B

C

A

A

C D

A A A A

B B

D A

B B B

C C C C

A

B B

C C

D D

2.3 4.5 3.7 8.1 3.8 4.2 6.8 3.9 4.5 5.4 2.7 2.8 3.0 2.4 4.0 7.1 4.6 2.9 2.2 4.0 5.8 3.8 3.8 2.1 4.7 4.7 3.2 3.5

B B

C C

D D D

B B B B B B

C C

D D

C C C C C C

D D

C C

D D

C C

D D D D

A

A

A

B B B

B B B B

C C C C

B B

C C C C

B

D D D

D D D D D D

In experiment 2, when a selected concentration of auxins was employed (25 mM IAA, 15 mM IBA, 1 mM NAA) results show that the presence of sucrose (Table 2) has a positive effect in improving the number of roots with respect to the control however, sucrose concentration had no significant effect on root number. On the other hand, a reduction in this parameter can be noted for IAA and NAA auxins at the highest sucrose concentrations. On the contrary, when root length results (continuous data) were analyzed using ANOVA (p < 0.05), a significant inhibitory effect of auxins was observed (Table 2). The multiple comparison by the Tukey test (p < 0.05) pointed out the non-linear effect of IAA, IBA or NAA concentration on the root length of shoots, the highest values for this parameter being obtained with low values of auxin concentration. Despite the presence of sucrose also having a significant effect (Table 2) on root length, compared to the controls no clear trend can be deduced from the data. Results agree with other author’s findings [9,25] pointing out that auxins have a double effect on rhizogenesis, while increasing the number of roots they simultaneously reduce size, blocking root growth. Moreover, a small addition of sucrose promotes an increase in the number of roots and length per shoot however more than 6% the effect seems to reverse. In carob tree (Ceratonia siliqua L.), after testing different types and concentrations of sugars to determine the best conditions for in vitro rooting and acclimatization, with 5% sucrose the best rooting response was obtained [26]. Calamar and De Klerk [11] in apple microshoots observe that sucrose was required for rooting but there were no significant effects in a broad range of concentrations. Acclimatization parameters analysis does not also contribute to establishing clear trends on the effects of the variables studied. Percentage of survival (binary data) results analyzed by binary logistic regression (p < 0.05) point out a significant effect of auxin concen-


245

Fig. 2. Experimental versus predicted values by neurofuzzy logic for the different parameters studied.

tration, sucrose and the interaction of the type of auxin and its concentration (Table 2). The multiple comparison test (p < 0.05) has demonstrated that the highest survival percentages were obtained at different auxin concentrations depending on the hormone used, these being low for IAA and NAA (1 mM) and medium for IBA (15 mM). A significant effect of sucrose concentration on survival percentage was observed compared to controls, but the highest survival percentages were achieved at different sucrose concentrations depending on the type of hormone, especially for IAA treatments which promoted survivals on acclimatization stage between 81 and 92.8% at any of the sucrose concentrations studied. Finally, when analyzing the plantlet height (continuous data), the ANOVA (p < 0.05) tests point to a significant effect of the three variables studied and the interaction of the type of auxin and its concentration. However, the multiple comparison test (p < 0.05) has revealed little differences between treatments, the most remarkable highest effect being obtained when medium (25 mM IAA) or (15 mM IBA) and low auxins concentrations (1 mM NAA) were used and/or 3% of sucrose was added to the medium. Additionally, it is important to note that no significant differences in plantlets height, compared to controls, were found for the most of treatments. These results are in agreement to previous studies pointing out that in vitro culture conditions, like auxin type, concentration, sugars and other additions, can significantly affect the final ex vitro survival and vigor of the micropropagated plantlets [10,14–18]. In this paper data reveal that auxin and sucrose are required for improving the acclimatization, however infraoptimal and supraoptimal conditions of these factors can negatively affect the plantlets during the acclimatization stage. In addition, it is important to point out that each auxin showed different optimal concentrations. Statistical analysis indicates the different effects but, in our opinion does not help in estimating the most suitable combination of the three factors to produce the best results in both rhizogenesis and acclimatization, and also it is no easy task to fully understand the process and/or get inside information on the knowledge in vitro rooting in soil and acclimatization of grapevine. When, as in this case, the result variability is high, it is a really high complex task to extract conclusions from the data and understand the whole process and/or the interactions between factors. The key question to be answered for the most of plant tissue culture researchers is: “Which is the optimal factor combination for achieving the most suitable

results for the parameters studied?” In our opinion, with a data set with no clear trends and great variability, neurofuzzy logic technology essentially helps to reveal hidden knowledge in the topic studied. 3.2. Neurofuzzy logic model A commercial neurofuzzy logic software FormRules® was used as an attempt to model the effect of the three variables or inputs (type of auxin, auxin concentration and sucrose concentration) on the rhizogenesis and acclimatization parameters selected. Neurofuzzy logic models were successfully and simultaneously developed applying the training parameters for the four outputs indicated in Table 1. In Fig. 2 the correlations between the predicted values from the neurofuzzy logic model and the experimental values for root number (Fig. 2A) and root length (Fig. 2B) in rhizogenesis and survival (Fig. 2C) and plantlet height (Fig. 2D) in the acclimatization stage are illustrated. Their linearity together with the slope, close to 1, indicates a good fit of the model to the data. Additionally, the ANOVA correlation coefficient calculated from predicted and observed values for the training data (training R2 ) range from 90.0923 to 95.1739 for the different rooting and acclimatization parameters, assessing the accuracy of neurofuzzy logic models (Table 3). Table 3 also presents the inputs included by the FormRules submodels. Its comparison with the significant terms indicated by the statistics reveals, at first glance, that interactions between auxin type and concentration of auxin or sucrose do have an important effect on the parameters studied meaning that a clear difference in behavior of the three hormones on both processes. As we stated in the introduction of this work, the output of neurofuzzy logic technology is a predictive model and a set of “IF . . . THEN” rules with values of membership degrees [23], which can assist on decision-making and/or on understanding the biological process. Four sets of “IF . . . THEN” rules were extracted from the submodels for each output studied: root number and length; survival and plantlet height (see Tables 4–7). Some of the contributing inputs included in the submodels have a complex effect which is expressed through various fuzzy input sets. Neurofuzzy linguistic set membership is labeled according to the following scheme: the first set is called Low 1(m), where m

246


Table 3 Significant variables from traditional statistics (>0.05%), significant inputs from neurofuzzy logic submodels and training R2 computed for each output. Inputs: A: type of auxin; C: auxin concentration; and S: sucrose. Parameters or outputs

Significant terms by traditional statistic

Inputs from neurofuzzy logic submodels

Training R2

Root number/shoot

A C S A C S C S A×C A C S A×C

C A×S

90.0923

A×C A×S

95.1739

A×C A×S

93.8093

A×C A×S

92.2700

Root length (mm)

Survival on acclimatization (%)

Height (cm)

denotes the total number of sets. The following sets are labeled as MID 2(m), MID 3(m) . . . and the last one HIGH m(m) (see Section 2 for details). Table 4 presents the rules set for root length on rhizogenesis showing two submodels; the interactive effect of the auxin type and concentration (A × C; Table 3) and the interaction between auxin type and sucrose concentration (A × S; Table 3). Again all the interactions between variables had not been indicated by the statistics. When analyzing and interpreting the rule in Table 5, two general approaches can be carried out:

• Optimization of auxin concentration is a key factor in controlling root growth at the rooting stage: very low or high concentrations clearly reduce root length. IF auxin concentration is medium 2(5) AND auxins are either IAA, IBA or NAA THEN root length is HIGH (1.00) (rules 2, 7 and 12 of submodel 1). IF auxin concentration is any other AND the type of auxin is any of tested THEN root length is always low with 1.00 membership degree. • Sucrose is clearly required for root growth. IF auxin is IAA, IBA or NAA AND sucrose concentration is medium or high THEN root length is high (1.00).

Rules set generated by neurofuzzy logic model for root number data revealed two submodels, that is two different and independent effects of the inputs (Table 5). The submodel 1 indicates that, independently to the auxin studied, low auxin concentration leads a low root number, while medium and high auxin concentrations produce high root numbers and membership degrees. From submodel 2 it can also be deduced that there is an interaction between the type of auxin and sucrose, which had not been detected by statistics (A × S; Table 3). This interaction reveals a dissimilar behavior of auxins, which present different optimal sucrose concentrations. By interpreting the rules in Table 5 useful knowledge was discovered: • Auxins improve the number of roots. Root number is positively correlated with increments in auxin concentration. IF auxin concentration is low THEN root number is low with 100% confidence or membership; on the contrary IF auxin concentration is medium or high THEN root number is also high with 100% and 91% membership degree, respectively. • Sucrose is clearly required for rooting. Low sucrose concentrations lead low number of roots per shoots with a 100%

Table 4 Rules for root length during rooting generated by neurofuzzy logic. Best combinations have been highlighted. Rules Submodel 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Submodel 2 1 2 3 4 5 6 7 8 9

Auxin type

Auxin concentration (mM)

IF

IAA IAA IAA IAA IAA IBA IBA IBA IBA IBA NAA NAA NAA NAA NAA

Low 1(5) Medium 2(5) Medium 3(5) Medium 4(5) High 5(5) Low 1(5) Medium 2(5) Medium 3(5) Medium 4(5) High 5(5) Low 1(5) Medium 2(5) Medium 3(5) Medium 4(5) High 5(5)

IF

IAA IAA IAA IBA IBA IBA NAA NAA NAA

Sucrose %

Low Medium High Low Medium High Low Medium High

Root length

Membership degree

THEN

Low High Low Low Low Low High Low Low Low Low High Low Low Low

1.00 1.00 1.00 0.92 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

THEN

Low High High High High High Low High High

0.54 1.00 1.00 0.84 1.00 1.00 1.00 1.00 1.00


247

Table 5 Rules for root number per shoot during rooting generated by neurofuzzy logic. Best combinations have been highlighted. Rule Submodel 1 1 2 3 Submodel 2 1 2 3 4 5 6 7 8 9

Auxin (type)

Sucrose (%)

Low Medium High

IF

IF


IAA IAA IAA IBA IBA IBA NAA NAA NAA

Low Medium High Low Medium High Low Medium High

membership degree when the type of auxin is IAA or IBA. A medium or high value of sucrose (%) promotes a higher number of roots with a medium membership degree (from 54 to 86%) for any auxin treatment (for example rules 2, 3, 5, 6, 8 and 9 of submodel 2).

The rules in Tables 4 and 5 are completely in agreement with our previous conclusions on rhizogenesis from statistics and also with the findings in the literature [11,25] and references therein. Neurofuzzy logic rules easily allow the conclusion that the treatment with any of the auxins studied improves the number of roots per shoot but if the concentration is excessive the length of the roots could be negatively affected. On the other hand, the effect of sucrose is quantitatively different depending on the hormone used but generally a medium or high amount of sucrose is required to produce a high number of long roots. Table 6 shows the rules set for survival in the acclimatization stage showing two submodels: the interactive effect of the auxin type and auxin concentration (A × C; Table 3) in submodel 1 and the

Root number/shoot

Membership degree

THEN

Low High High

1.00 1.00 0.91

THEN

Low High High Low High High Low High High

1.00 0.69 0.88 1.00 0.69 0.86 0.65 0.69 0.54

interaction of auxin type and sucrose in submodel 2 (A × S; Table 3). Only the first interaction could be detected by statistical analysis. When analyzing and interpreting the submodels, two general rules were discovered: • Optimization of auxin concentration is also a key factor in controlling survival at the acclimatization stage: very low or high auxin concentrations clearly reduce survival percentages but the survival parameter is dependent on the hormone applied IAA or NAA having a narrower optimal range of concentrations than IBA with regard to percentage of survival at acclimatization (rules 2, 7–9 and 12 of submodel 1). • Sucrose is also clearly required for survival. IF auxin is IAA, IBA or NAA AND sucrose concentration is medium or high THEN survival is high, although the membership degrees are different depending on the rule. Table 7 presents the rules set for plantlet height illustrating two submodels: the interactive effect of the auxin type and concentration (A × C; Table 3) in submodel 1 and auxin type and sucrose in

Table 6 Rules for survival during acclimatization generated by neurofuzzy logic. Best combinations have been highlighted. Rule Submodel 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Submodel 2 1 2 3 4 5 6 7 8 9 10 11 12

Auxin type


IF



IF

IAA IAA IAA IAA IBA IBA IBA IBA NAA NAA NAA NAA

Sucrose (%)

Low 1(4) Medium 2(4) Medium 3(4) High 4(4) Low 1(4) Medium 2(4) Medium 3(4) High 4(4) Low 1(4) Medium 2(4) Medium 3(4) High 4(4)

Survival

Membership degree

THEN

Low High Low Low Low Low High High High Low Low High Low Low Low

1.00 1.00 1.00 0.56 1.00 1.00 1.00 0.60 1.00 0.92 1.00 1.00 0.70 0.77 0.92

THEN

Low High High High Low High High High Low High High High

1.00 1.00 1.00 1.00 1.00 1.00 0.50 0.56 1.00 1.00 0.95 0.89

248


Table 7 Rules for plantlet height during acclimatization generated by neurofuzzy logic. Best combinations have been highlighted. Rule Submodel 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Submodel 2 1 2 3 4 5 6 7 8 9 10 11 12

Auxin type


IF



IF

IAA IAA IAA IAA IBA IBA IBA IBA NAA NAA NAA NAA

Sucrose (%)

Low 1(4) Medium 2(4) Medium 3(4) High 4(4) Low 1(4) Medium 2(4) Medium 3(4) High 4(4) Low 1(4) Medium 2(4) Medium 3(4) High 4(4)

submodel 2 (A × S; Table 3). Once again, the latter interaction could not be detected by statistical analysis. Conclusions from those rules are as follows: • Optimization of auxin concentration is a key factor in controlling plantlet height: very low or very high concentrations clearly reduce height percentage. IF auxin is IAA, IBA or NAA AND its concentration is medium 2(5) THEN plantlet height is HIGH (1.00) (rules 2, 7 and 12 of submodel 1). IF low or high concentrations of auxin are used THEN plantlet height is always low. • Optimization of sucrose concentration is key factor in controlling plantlet height: very low or high concentrations clearly reduce height. IF auxin is IAA, IBA or NAA AND sucrose concentration is medium 2(4) THEN plantlet height is high with a membership degree of 1.00, IF low or high concentration of sucrose THEN plantlet height is always low. The rules in Tables 6 and 7 also are completely in agreement with our previous conclusions on acclimatization from statistics. Neurofuzzy logic rules easily allow us to conclude that the treatment with auxins during the rhizogenesis stage have an optimal concentration range permitting high survival percentages and high plantlets at the acclimatization stage which were different for the hormones studied. Additionally, medium concentration of sucrose is required to improve acclimatization parameters. Finally, a new set of rules can be generated, for assisting decision-making for researchers, by selecting the combinations of

Height

Membership degree

THEN

Low High Low Low Low Low High Low Low Low Low High Low Low Low

1.00 1.00 1.00 0.64 1.00 1.00 1.00 0.63 1.00 1.00 1.00 1.00 1.00 1.00 1.00

THEN

Low High High Low Low High High Low Low High Low Low

1.00 1.00 1.00 1.00 1.00 1.00 0.72 0.57 1.00 1.00 0.62 0.50

inputs that produce simultaneously the optimal rhizogenesis and acclimatization parameters; high mean number of roots, high mean root length, high mean survival percentage on acclimatization and also a high mean plantlets height (Table 8). From the results a general rule can be established for optimization: IF auxin (IAA, IBA or NAA) concentration is medium 2(5) AND sucrose is medium 2(4) THEN all parameter on rooting and acclimatization (root number and length, survival and plantlet height) are HIGH with high levels of membership. In the present study, neurofuzzy logic to an in vitro rooting and acclimatization of the V. vinifera experiment data set has applied. Compared to statistical analysis neurofuzzy logic has a higher accuracy in identifying interaction effects; it is less time consuming and extremely helpful when the number of experiment is large. In fact, different kind of data (binary, discrete and continuous) can be analyzed using a unique and easy to use technology. Moreover, successful and simultaneous models were promptly obtained from neurofuzzy logic, for all the outputs studied simultaneously, with a low normalized error. Additionally, through the IF . . . THEN rule sets generated by neurofuzzy logic, understandable and reusable knowledge is generated on the complex non-linear effects of the variables of the process, which can be increased by including additional information or new inputs, such as additional auxin types, substrate, physical conditions, etc. in the data set. Finally, neurofuzzy logic technology allowed answers the questions on the optimal factors combination for achieving the most suitable results for the parameters studied.

Table 8 Combinations of inputs producing the optimal result simultaneously for all outputs during in vitro rooting in soil and acclimatization obtained from neurofuzzy logic technique. Membership degrees in parentheses.

IF

Auxin


IAA

Medium Medium Medium Medium Medium

IBA NAA

2(5) 2(5) 2(5) 2(5) 2(5)

Sucrose (%)

Root number

Root length (mm)

Survival (%)

Height (cm)

Medium 2(4) Medium 2(4) Medium 3(4) Medium 2(4) Medium 3(4)

High (0.88) High (0.80) High (0.80) High (0.71) High (0.71)




THEN


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