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RESEARCH ARTICLE
Genetic programming based models in plant
tissue culture: An addendum to traditional
statistical approach
Meenu R. Mridula
1☯
*, Ashalatha S. Nair
1☯
, K. Satheesh Kumar
2☯
1Department of Botany, University of Kerala, Kariavattom, Thiruvananthapuram, Kerala, India,
2Department of Future Studies, University of Kerala, Kariavattom, Thiruvananthapuram, Kerala, India
☯These authors contributed equally to this work.
*m.r.meenakshi@gmail.com
Abstract
In this paper, we compared the efficacy of observation based modeling approach using a
genetic algorithm with the regular statistical analysis as an alternative methodology in plant
research. Preliminary experimental data on in vitro rooting was taken for this study with an aim
to understand the effect of charcoal and naphthalene acetic acid (NAA) on successful rooting
and also to optimize the two variables for maximum result. Observation-based modelling, as
well as traditional approach, could identify NAA as a critical factor in rooting of the plantlets
under the experimental conditions employed. Symbolic regression analysis using the software
deployed here optimised the treatments studied and was successful in identifying the complex
non-linear interaction among the variables, with minimalistic preliminary data. The presence of
charcoal in the culture medium has a significant impact on root generation by reducing basal
callus mass formation. Such an approach is advantageous for establishing in vitro culture pro-
tocols as these models will have significant potential for saving time and expenditure in plant tis-
sue culture laboratories, and it further reduces the need for specialised background.
Author summary
Trials to find out the best combination of factors that contribute to the desired response
takes up the chunk of time and resources in any plant tissue culture laboratory. The out-
put of such experiments is analysed statistically to come to a conclusion. However, with-
out prior statistical modifications, the results could be misleading. Recent reports from
several labs point out the use of artificial neural networks to circumvent this. We have
chosen to use a computational process that can predict the best combination of factors for
the desired response after randomly testing the higher and lower limit of the factors with
experiments. The magnitude of the desired response can be presumed at any concentra-
tion within this range using the models generated by symbolic regression. The procedure
provides both optimum model function as well as the optimum variable values in the
model. The variable sensitivity and percentage response add depth to the information
thus obtained. The study indicated that these models would have significant potential for
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1005976 February 27, 2018 1 / 13
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OPEN ACCESS
Citation: Mridula MR, Nair AS, Kumar KS (2018)
Genetic programming based models in plant tissue
culture: An addendum to traditional statistical
approach. PLoS Comput Biol 14(2): e1005976.
https://doi.org/10.1371/journal.pcbi.1005976
Editor: Jean-Baptiste Durand, Laboratoire Jean
Kuntzmann, FRANCE
Received: February 23, 2017
Accepted: January 15, 2018
Published: February 27, 2018
Copyright: ©2018 Mridula et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information
files. Data has also been uploaded to figshare (DOI:
10.6084/m9.figshare.5844765).
Funding: The first author (MRM) would like to
acknowledge the financial assistance from Council
of Scientific and Industrial Research, New Delhi
through Junior Research Fellowship scheme (No.
09/102/RENEWAL/2014-EMR-1). The funders had
no role in study design, data collection and
analysis, decision to publish, or preparation of the
manuscript.
saving time and expenditure in plant tissue culture laboratories for the commercial estab-
lishment of in vitro protocols.
Introduction
Relatively more straightforward and efficient empirical modeling techniques based on input-
output models are gaining popularity to conventional statistical methods across various disci-
plines [1]. This surge is due to its relative ease of use and understanding. Genetic programming
(GP) is an approach which uses the concept of biological evolution to handle a problem with
many fluctuating variables. Computational optimisation techniques have recently debuted in
plant tissue culture research as studied in neural networks models [2]. Symbolic regression was
one of the earliest applications of GP and continues to be widely considered [3]. A broad array
of scientific fields like Biology, Chemistry, Environmental Science, Neurology and Psychology
reports the use of symbolic regression [4–9]. However, plant tissue culture data has not yet been
analysed using symbolic regression. The data generated from plant tissue culture experiments
includes continuous, count, binomial or multinomial and predominantly the information is val-
idated using analysis of variance method (ANOVA) [2,10]. ANOVA is adequate for normally
distributed continuous data; but without prior manipulation, it is erroneous to analyze count,
binomial or multinomial data [11]. Neuro-fuzzy logic is the standard practice by which compu-
tational modeling is achieved in plant tissue culture [2,12]. In this context, genetic algorithm
based symbolic regression remains unevaluated. Unlike conventional regression analysis which
optimises parameters for a pre-defined model, symbolic regression avoids imposing any apriori
assumptions. In generalised linear model (GLM) regression, the dependent variable is repre-
sented as linear combination of the given set of basic functions and optimise the coefficients to
fit the data. However, symbolic regression searches for both a set of basic functions and coeffi-
cients. The added value of symbolic regression, compared to GLM, lies in its ability to quickly
and accurately find an optimal set of basic functions [13,14]. The algorithm infers the model
from the data by combining variables and mathematical operators and generates an empirical
formula which is a mathematical equation that predicts observed results derived from con-
ducted experiments. GP combines previous equations and forms new ones. Thus it produces
models with interpretable structure, relating to input and output variables from a data set with-
out pre-processing and identifying critical parameters and hence shed insight into the underly-
ing processes involved in a given system [15]. Symbolic regression can recognise and model
complex non-linear relationships between the inputs and outputs of biological processes even
in the presence of disturbances and potential for parallel processing. The preliminary data gen-
erated from experiments during rooting of in vitro regenerated plantlets in Wrightia tinctoria
was employed to study the utility of symbolic regression to analyze plant tissue culture data.
The effect of two variables - NAA and charcoal on root proliferation was considered. The data-
sets were subjected to usual statistical analysis as well as observation based modeling via sym-
bolic regression. Moreover, we aimed to optimise the process by examining the influencing
factors. We propound the use of symbolic regression-based model prediction as an addendum
to data analysis method for plant tissue culture experiments.
Materials and methods
Culture conditions
The genetic variability was kept minimum by using a single field grown ortet, thus minimising
statistical errors [16]. Nodal regions derived from the fresh flushes of growth from the ortet, two
Symbolic regression to plant tissue culture data: An addendum to routine approach
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1005976 February 27, 2018 2 / 13
Competing interests: The authors have declared
that no competing interests exist.
weeks after lopping one major branch served as the explants [17]. The nodal explants were condi-
tioned over a period of 4 months (subculture/four weeks) on MS medium (1962) [18], pH 5.8 and
2μM each of BAP and NAA for shoot multiplication. For rooting experiments individual shoots
were transferred on MS medium containing 2 μM BAP with NAA (2, 4 and 6 μM, respectively)
and charcoal (0.01, 0.03, 0.05, 0.07, 0.09 and 0.11%, respectively) in 250 ml culture flasks in 50 ml
of sterilized medium (pH 5.8). The cultures were maintained at 25±2˚C in a culture room with
40 μmolm
−2
s
−1
irradiances and a photoperiod of 8 hrs with 55±5% of relative humidity.
Experimental design
The plant tissue culture database, containing 21 conditions, followed a factorial design for two
variables- concentration of NAA (2, 4 and 6 μM) and charcoal (0,0.01, 0.03,0.05,0.07,0.09
and 0.11%) in the medium. Each treatment consisted of 5-7 explants in a culture flask with
three replicates. The subculture was done at the end of four weeks and five parameters were
recorded to analyze the effects of the variables on rooting such as basal callus diameter (mm)
(BC), the percentage of shoots rooted (R), the length of the longest root (cm) (RL), the number
of roots (NR) and the number of lateral roots (NLR) (S1).
Statistical analysis
All experiments were conducted using Randomised Block Design (RBD). Continuous data were
analysed using multiple linear regression in R and posthoc comparisons of pairs performed by
Tukey’s test (p>0.05). Count data were analysed using Poisson regression model. Pearson’s Chi-
squared test for count data was employed to access statistical significance of the variables.
Symbolic regression
Each of the observed parameters is modeled as a function of NAA and charcoal concentrations
using symbolic regression and GLM for comparison. To obtain a global optimum, we have also
modelled the combination (R+RL+NR+NRL-BC) by taking rooting factors together after nor-
malisation by employing both GLM and symbolic regression. The optimum model for each
case was generated by genetic programming based symbolic regression using the software pack-
age Eureqa (Version 0.98 beta) with 50% of the data randomly selected as training data, and
3-fold cross-validated with randomly selected 25% of the remaining data [19–21]. Correspond-
ing to each symbolic regression model of the data partition, we have also obtained generalised
linear model by including x, y, xy, 1/x, 1/y, sin(x), cos(x), sin(y), cos(y), xy sin(x), xy cos(x), xy
sin(y), xy cos(y) into the set of basic functions and cross-validated similarly. The remaining 25%
the data was used for testing and reporting error [19–21]. The Target expression used to gener-
ate the regression model was the minimal equation z = f(x, y) where ‘x’ corresponds to NAA
concentration and ‘y’ corresponds to charcoal concentrations, and ‘z’ represents each of the five
observed parameters and their combination. The models were based on the primary and trigo-
nometric building blocks, with the R
2
goodness of fit as the error metric [22,23]. Root Mean
Squared Error (RMSE) was calculated for the test data sets. Sensitivity represents the relative
impact of the variable on the parameter studied within this model and was calculated by the
local method using the partial derivatives [24]. Given a model equation of the form z = f(x, y),
the influence metrics of x on z was;
Sensitivity ¼@z
@x:sðxÞ
sðzÞ;evaluated at all input data points;
Symbolic regression to plant tissue culture data: An addendum to routine approach
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The percentage positive was calculated as percentage of data points where sðxÞ
sðzÞ>0and per-
centage negative was calculated as percentage of data points where sðxÞ
sðzÞ<0; where @z
@xwas the
partial derivative of z with respect to x, σ(x) was the standard deviation of x in the input data, σ
(z) was the standard deviation of z, |x| denoted the absolute value of x, and
xdenoted the mean
of x [25]. The ‘fmin’ function in MATLAB (R2012b) was used to obtain the maximum value of
each of these functions.
Results and discussion
The average values obtained for the five growth parameters observed during the study were
given as the basal callus diameter (Table 1), the percentage of shoots rooted (Table 2), the
length of longest roots (Table 3) and the number of roots and the number of lateral roots
(Table 4). The miniscule alphabets within a column indicated the significant influence of char-
coal and majuscule alphabets in the row represented the significant interaction of NAA. The
shoots inoculated on MS medium with 0% charcoal (control) showed maximum basal callus
formation (Fig 1). The shoots inoculated on MS medium supplemented with 4μM NAA and
0.07% charcoal showed the maximum percentage of rooting (Fig 2).
Multiple linear regression demonstrated a significant effect of NAA and its interaction with
charcoal on basal callus (p>0.001), the percentage of shoots rooted (p>0.05) and root length
(p>0.01) (Tables 1–3). The individualistic effect of NAA for the number of roots and lateral
roots were found to be significant at p>0.05 and p>0.001 respectively (Table 4). The interac-
tion of NAA and charcoal was not significant for the same parameters studied. Mathematical
Table 1. Mean of basal callus diameter after four weeks of culture under the conditions studied. Means followed
by similar letters; a, b and c (within each column) and A and B (in each row) are not significantly different by Tukey’s
multirange test (p>0.05).
Basal callus
Diameter (mm)
Charcoal NAA
2 4 6
0 10.06 c A 11.40 d B 11.33 c B
0.01 2.25 b AB 2.40 c B 2. b A
0.03 1.61 a A 2.38 c B 1.43 a A
0.05 1.57 a A 1.54 b A 1.32 a A
0.07 1.32 a A 1.36 ab A 1.22 a A
0.09 1.34 a A 1.12 ab A 1.27 a A
0.1 1.44 a A 1.28 a A 1.24 a A
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Table 2. Mean of the percentage of shoots rooted after four weeks of culture under the conditions studied. Means
followed by similar letters; a, b and c (within each column) and A Band C (in each row) are not significantly different
by Tukey’s multirange test (p>0.05).
Percentage of
shoots rooted
Charcoal NAA
246
0 0 a A 0 a A 0 a A
0.01 0 a A 0 a A 0 a A
0.03 0 a A 10.76 a B 12.96 b B
0.05 43.9 c B 47.6 c B 12.8 b A
0.07 39.93 c B 50 c C 28 c A
0.09 27.43 b B 31.7 b B 9.4 ab A
0.1 28.3 b B 23.23 b B 0 a A
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Symbolic regression to plant tissue culture data: An addendum to routine approach
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functions were successfully developed using symbolic regression to understand the correlation
between the two variables for each of the parameters considered and is contrasted with those
obtained by traditional regression models (Table 5). To analyze the effect of each of the vari-
ables on the parameter studied; variable sensitivity measures were calculated along with its
percentage impact. Its sensitivity denoted the relative impact within this model that a variable
has on the target variable. The individualistic effect of the two input variables on the output
parameter was pointed out as percentage positive or negative of that input variable (Table 6).
For the parameter basal calli diameter, the percentage positive value for variable ‘y’ was zero.
In other words, there was zero percent chance of basal calli mass increasing with increasing
concentration of charcoal; or that basal calli mass decrease with increasing concentration of
charcoal (Fig 3). The model predicted that increase in charcoal concentration had a conse-
quent increase in root length and root number in 50% of all the trials while the same promoted
rooting percentage and lateral root number in 75% of the trials. Root number and root length
decreased with increasing concentration of NAA in 100% of the trials. Rooting percentage
and lateral root numbers increased with increasing NAA concentration in 50% of all the trials.
Table 3. Mean of the length of longest roots after four weeks of culture under the conditions studied. Means fol-
lowed by similar letters; a, b and c (within each column) and A and B (in each row) are not significantly different by
Tukey’s multirange test (p>0.05).
Length of
longest
roots (mm)
Charcoal NAA
2 4 6
0 0 a A 0 a A 0 a A
0.01 0 a A 0 a A 0 a A
0.03 0 a A 7.88 b B 1.72 a A
0.05 26.4 c C 17.94 c B 6.9 ab A
0.07 41.78 d B 41.67 d B 14.4 b A
0.09 18.17 b B 10.1 b A 6.8 a A
0.1 7.38 a B 3.13 ab AB 0 a A
https://doi.org/10.1371/journal.pcbi.1005976.t003
Table 4. Mean of the number of roots and number of lateral roots after four weeks of culture under the conditions
studied. The row and the column variables are statistically significantly associated at p>0.05 (Number of roots) and
p>0.001(Number of lateral roots), by Pearson’s Chi-squared Test for Count Data.
Number of Roots
Charcoal NAA
2 4 6
0 0 0 0
0.01 0 0 0
0.03 0 0.4 0.6
0.05 5 2.4 1.2
0.07 1.5 1.4 0.8
0.09 1 1.13 0.8
0.1 0.8 0.6 0
Number of lateral Roots
0 0 0 0
0.01 0 0 0
0.03 0 0 0
0.05 0.4 0.43 0
0.07 5 0.6 1.1
0.09 0.6 2.7 2.2
0.1 0 1.96 0
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Symbolic regression to plant tissue culture data: An addendum to routine approach
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The function obtained and the 3D plots thus generated could be used to predict the combi-
nations of input variables giving optimum results. The best response for rooting percentage
Fig 1. In vitro plants of W.tinctoria- Shoot inoculated in the absence of charcoal showing profuse basal callusing (left); against shoot inoculated in
the presence of charcoal showing reduced/no basal callus mass (right).
https://doi.org/10.1371/journal.pcbi.1005976.g001
Symbolic regression to plant tissue culture data: An addendum to routine approach
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was predicted at 3.7 μM NAA and 0.08% charcoal (Fig 4). The root length showed a non-linear
pattern, and the highest value for its function was estimated with 2.8 μM NAA and 0.05%
charcoal (Fig 5). The maximum root number was determined for 1.7 μM NAA and 0.06%
charcoal (Fig 6). The maximum value of the function generated for lateral root number was
with 6.3 μM NAA and 0.08% charcoal (Fig 7). The global optimum modelled upon the com-
bination (R+RL+NR+NRL-BC) indicated the results as 2.44 μM NAA and 0.03% charcoal
(Fig 8).
Fig 2. Maximum rooting observed in the shoots inoculated on MS medium supplemented with 4 μM NAA and 0.07% charcoal.
https://doi.org/10.1371/journal.pcbi.1005976.g002
Symbolic regression to plant tissue culture data: An addendum to routine approach
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The conclusion obtained by traditional statistics suggested that charcoal had a positive and
stimulatory effect in rooting of shoots by reducing basal callus (Table 1). Percentage of shoots
rooted and root length showed a significant impact with the combination of NAA and char-
coal (Tables 2and 3). In the present study, NAA has a significant effect on rooting as shown by
the number of roots and lateral roots (Table 4). Similar results were reported in Acacia leu-
cophloea and Cinnamomum verum [26,27]. With traditional statistics, we were not able to esti-
mate the combination/s of both variables in producing the best results or able to identify the
relative impact of a particular variable on the output parameter. Modeling of plant tissue cul-
ture data is practised using regression analysis where first an initial function is approximated
and the data fitted to that function to obtain the optimum parameters [11,28,29]. In this proce-
dure even when one gets the optimum parameter values, the model prediction was limited by
the probable wrong selection of the model function. In contrast, symbolic regression
Table 5. Functions and error matrix obtained through symbolic regression and multiple linear regression.
Parameter Symbolic regression Linear regression
Function R
2
RMSE Function R
2
RMSE
Basal callus
diameter (BC)
1.17 + 0.12/(0.01 + y) 0.98 0.09 739.5 x – 51540 y + 73390 Sin(y) – 0.56 Sin(x) -29450 Cos(y) –
1190 xy + 1673 x Sin(y) – 14130 y Sin(y) +739.3 x Cos(y) -21970 y
Cos(y) + 0.7174 y Sin(x) -350.2 xy Sin(y) -487.8 xy Cos(y)
+294660
0.98 0.56
Percentage of
shoots rooted (R)
4.43 x + 4738572.57 y
4
+ 88353.22 y
2
-
18.33 – 1270650.34 y
3
– 21.85 y x
2
0.73 0.94 70990 x + 619700 y -904900 Sin(y) + 0.294 Sin (x) + 278000 Cos
(y) -157200 xy + 229300 x Sin(y) + 137300 y Sin (y) -70990 x Cos
(y) + 285300 y Cos(y) -27.01 y Sin(x) -34940 x y Sin (y) -72090 x y
Cos(y) -278000
0.60 1.11
Length of longest
roots (mm) (RL)
2.28 -22.58 cos(40.39 y)/(1.25 x + x cos(5.06 y)
+ sin(1.84 - x))
0.75 1.28 46840 x + 530000 y -768300 Sin(y) -1.7 Sin(x) + 263300 Cos (y)
-98130 xy + 142600 x Sin(y) + 129200 y Sin(y) + 129200 y Sin(y)
-46840 + 238500 y Cos(y) -4.134 y Sin(x) -22990 x y Sin (y) -44490
x y Cos(y) -263300
0.85 7.85
Number of roots
(NR)
14.83 y
2
+ 14.78 y
2
sin(10.50 + 6375y) – 4.80
y – 1.92 x y -19.2 y sin(5.5 + 88.86y) – 1.95 x y
sin(6.3-183.03y)
0.82 0.76 5984 x + 56560 y -83160 Sin(y) + 0.09042 Sin(x) + 22980 Cos(y)
-14110 xy + 20670 x Sin (y) + 11420 y Sin(y) -5984 x Cos (y)
+ 26590 y Cos(y) -0.3519 y Sin (x) -2959 x y SIn (y) -6560 x y Cos
(y) -22980
0.63 1.03
Number of lateral
roots (NRL)
0.04 + 2208.78 x y
3
- 3559.64 y
4
– 0.39 y x
2
–
17758.21 x y
4
0.96 0.02 7025 x + 56710 y -82060 Sin(y) + 0.467 Sin (x) + 28560 Cos(y)
-14700 x y + 21340 x Sin(y) + 13970 y Sin(y) -7025 x Cos(y)
+ 25370 y Cos(y) -2.28 y Sin(x)-3443 xy Sin(y)-6652 xy Cos (y)
-28560
0.68 1.40
Normalised (R+RL
+NR+NRL-BC)
1.24 sin(3.24 + 3.42 x
3
y
2
sin(y) - 3.77y
2
cos(x)) 0.80 0.92 8604 x + 15570y – 19520 xy – 2.067 sin(x) – 22750 sin(y) +6988
cos(y) + 3453 y sin(x) -8606 x cos(y)– 4249 xy sin(y) -9014 xy cos
(y) - 6988
0.78 1.99
The variable x represents NAA concentration and y represents charcoal concentration
https://doi.org/10.1371/journal.pcbi.1005976.t005
Table 6. Variable sensitivity values of the parameters studied through symbolic regression.
Parameters Sensitivity Percentage positive Percentage negative
x y x y x y
Basal calli diameter (mm) - 1.65 - 0 - 100
Percentage of shoots rooted 0.7 1.78 50 75 50 25
Length of longest roots (mm) 0.3 1.4 0 50 100 50
Number of roots 0.21 1.26 0 50
100 50
Number of lateral roots 0.18 1.94 50 75 50 25
Normalised 0.13 1.64 50 75 50 25
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Symbolic regression to plant tissue culture data: An addendum to routine approach
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procedures work simultaneously on model specification problem and the problem of fitting
coefficients [30]. Thus it provides both optimum model function as well as the optimum vari-
able values in the model. The simple relations derived from GP were more accessible to analyze
the relationships between the input and output variables [31]. Observation-based predictive
models using GP identified that the individualistic effect of charcoal was significant in all the
output parameters. A previous investigation suggested basal callus mass formation as one of
the primary constraints in the culture of this tree species [32]. In the present study, charcoal
has a positive and stimulatory effect in rooting by reducing basal callus formation in shoots.
For each of the functions, generated values can be obtained by increasing /decreasing the
Fig 3. The plot generated for parameters predicted by symbolic regression model for W.tinctoria plantlets as a
function of NAA and charcoal concentration showing basal calli diameter (mm). The cyan coloured dot indicates
the optimum concentration predicted by the model function.
https://doi.org/10.1371/journal.pcbi.1005976.g003
Fig 4. The plot generated for parameters predicted by symbolic regression model for W.tinctoria plantlets as a
function of NAA and charcoal concentration showing rooting percentage. The cyan coloured dot indicates the
optimum concentration predicted by the model function.
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Symbolic regression to plant tissue culture data: An addendum to routine approach
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variables by a unit. After randomly testing the higher and lower limit of the additives with
experiments, the magnitude of the observed parameters can be presumed at any concentration
of the additives within this range using the models generated. It can be extended to analyze
synergistic interactions between two parameters by testing whether increasing both variables
by a unit, gives a higher or a lower value than the sum of the values obtained by increasing
each individually by a unit. The basic requirement for any empirical model includes interpret-
ability, robustness and reliability [33]. Symbolic regression gave comparably lesser RMSE val-
ues in comparison to multiple linear regression, thus adding validity to its use. In plant tissue
culture obtaining an optimum model is crucial when one needs to find the optimum experi-
mental parameters for large-scale production. The procedure adopted in the work can also be
Fig 5. The plot generated for parameters predicted by symbolic regression model for W.tinctoria plantlets as a
function of NAA and charcoal concentration showing the length of the longest roots (mm). The cyan coloured dot
indicates the optimum concentration predicted by the model function.
https://doi.org/10.1371/journal.pcbi.1005976.g005
Fig 6. The plot generated for parameters predicted by symbolic regression model for W.tinctoria plantlets as a
function of NAA and charcoal concentration showing the number of roots. The cyan coloured dot indicates the
optimum concentration predicted by the model function.
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Symbolic regression to plant tissue culture data: An addendum to routine approach
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extended to similar experiments as it is general and computationally efficient. The analysis pre-
dicted the optimum concentration of medium for micropropagation of the selected tree spe-
cies from the model plots derived from the preliminary experimental data. The study indicated
that these models would have significant potential for saving time and expenditure in plant tis-
sue culture laboratories for the commercial establishment of in vitro protocols in tree species.
Fig 7. The plot generated for parameters predicted by symbolic regression model for W.tinctoria plantlets as a
function of NAA and charcoal concentration showing the number of lateral roots. The cyan coloured dot indicates
the optimum concentration predicted by the model function.
https://doi.org/10.1371/journal.pcbi.1005976.g007
Fig 8. The plot generated for the combination of all parameters studied, by symbolic regression model for W.
tinctoria plantlets as a function of NAA and charcoal concentration. The cyan coloured dot indicates the optimum
concentration predicted by the model function.
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Symbolic regression to plant tissue culture data: An addendum to routine approach
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Supporting information
S1 Data. The minimal data set used for the analysis. Legends NAA, CH, BC, R, RL, NR and
NRL represent the concentration of NAA, concentration of charcoal, basal callus diameter,
percentage of shoots rooted, length of longest roots, number of roots and number of lateral
roots, respectively.
(CSV)
Author Contributions
Conceptualization: Meenu R. Mridula, K. Satheesh Kumar.
Data curation: Meenu R. Mridula.
Formal analysis: Meenu R. Mridula, K. Satheesh Kumar.
Funding acquisition: Ashalatha S. Nair.
Investigation: Meenu R. Mridula, Ashalatha S. Nair.
Methodology: K. Satheesh Kumar.
Project administration: Ashalatha S. Nair.
Resources: Ashalatha S. Nair, K. Satheesh Kumar.
Software: Meenu R. Mridula, K. Satheesh Kumar.
Supervision: Ashalatha S. Nair, K. Satheesh Kumar.
Validation: K. Satheesh Kumar.
Visualization: K. Satheesh Kumar.
Writing – original draft: Meenu R. Mridula.
Writing – review & editing: Ashalatha S. Nair.
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