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Revista mexicana de ciencias agrícolas
versión impresa ISSN 20070934
Rev. Mex. Cienc. Agríc vol.11 no.1 Texcoco ene./feb. 2020 Epub 02Mar2021
https://doi.org/10.29312/remexca.v11i1.2211
Articles
Logistic model of the dynamics of the mycelial growth of the fungus ‘Totolcozcatl’ in culture media
^{1}Maestría en Agroforestería para el Desarrollo SostenibleDepartamento de SuelosUniversidad Autónoma Chapingo. Carretera TexcocoMéxico km 38.5, Chapingo, Texcoco, Estado de México. CP. 56230.
^{2}Instituto de Ecología. Xalapa, Veracruz. (victor.bandala@inecol.mx).
Edible wild mushrooms are considered a nontimber forest resource, of nutritional, ecological, cultural and economic importance for rural communities. In the mountain mesophilic forest, in Xaltepuxtla, Puebla, the looting and overexploitation of the Entoloma abortivum species, known as ‘Totolcozcatl’, place it as a threatened species. Therefore, the objective of this work was to evaluate its dynamics of average mycelial growth, in culture media using a logistic model, for its induction process. The culture media evaluated in 2018 were: malt extractyeast extractpolypeptoneagar (MYPA); meat peptonedextroseyeast extractbacteriological agar (CYM) and maltbran extract (EMS). Statistical analysis indicated that the MYPA and EMS substrate were statistically different from CYM (p< 0.05), in mycelial growth after 16 days of culture. The logistic model adjusted to the experimental data obtained in each of the substrates yielded R^{2} coefficients of determination of 0.99. The model showed that the maximum predicted growth was observed in the EMS substrate (95.94 mm) and the minimum in CYM (83.23 mm). The point of maximum growth and excessive production of hyphae added to the mycelium was obtained in the EMS substrate (47.97 and 9.59 mm), followed by MYPA (45.76 and 8.83 mm) and CYM (41.61 and 6.86 mm). Finally, it is concluded that the main important and viable alternative to the induction process of the Totolcozcatl fungus is the EMS medium.
Keywords: Entoloma abortivum (Berk. & Curtis) Donk.; culture media; growth rate
Los hongos silvestres comestibles son considerados un recurso forestal no maderable, de importancia alimenticia, ecológica, cultural y económica para las comunidades rurales. En el bosque mesófilo de montaña, en Xaltepuxtla, Puebla, el saqueo y la sobreexplotación de la especie Entoloma abortivum, conocida como ‘Totolcozcatl’, la colocan como especie amenazada. Por lo anterior, el objetivo de este trabajo fue evaluar su dinámica de crecimiento promedio micelial, en medios de cultivo mediante un modelo logístico, para su proceso de inducción. Los medios de cultivo valorados en 2018 fueron: extracto de maltaextracto de levadurapolipeptonaagar (MYPA); peptona de carnedextrosaextracto de levaduraagar bacteriológico (CYM) y extracto de maltasalvado (EMS). El análisis estadístico indicó que el sustrato MYPA y EMS fueron estadísticamente diferentes al CYM
Palabras clave: Entoloma abortivum (Berk. & Curtis) Donk.; medios de cultivo; tasa de crecimiento
Introduction
Wild mushrooms are functional and essential components of forest ecosystems and provide valuable products directly to humans. Due to its gastronomic and nutraceutical properties, its demand has been increased to the detriment of its distribution and abundance in natural ecosystems even reaching its extinction (^{Pilz et al., 1996}; ^{AlvaradoCastillo et al., 2015}).
According to ^{Sánchez and Mata (2012)}, the cultivation of edible wild mushrooms has been gaining momentum worldwide since the middle of the last century and possibly continues this trend for the following reasons: population increase, increase in demand, diversification of the fungi produced, new applications of fungi in the field of food and medicine, and attractive as an economic activity. Regarding its commercialization, ^{Contreras et al. (2018)} indicate that the price of the edible fungus Totolcozcatl (Entoloma abortivum), of terrestrial habitat, symbiote and parasite, ranges from $100.00 to $150.00 per kg, due to its scarcity in the region.
^{Alvarado et al. (2012)} mention that there are two options for the rational use of this resource and its conservation: 1) the proper management and management of natural populations; and 2) the development of techniques for domestication and commercial production. Edible wild mushrooms can be cultivated in controlled environments, since being independent of other living beings, it is enough to develop a specific lignocellulosic substrate and control the appropriate temperature, ventilation, humidity and light conditions to make them grow and fructify.
In this context, ^{Ríos and Ruiz (1993)} establish that for the propagation of edible wild mushrooms for commercial purposes, it is necessary to identify the prevailing species in the region and determine the factors that influence their development and growth. Once this has been achieved, the phases prior to its propagation are obtaining mycelium, making inoculum, preparing the substrate, inoculating the substrate, incubation and fruiting.
The obtaining of mycelium is one of the determining phases of success for the propagation of the fungus, which depends largely on the culture medium providing the necessary nutrients for the development of the mycelium over time and the way in which it demands it. Therefore, the objective of this research was to evaluate the dynamics of growth of the average mycelial diameter of the fungus ‘Totolcozcatl’ in three culture media: malt extractyeast extractpolypeptoneagar (MYPA), meatdextrose peptonebacteriological yeast extract (CYM); and maltbran extract (EMS) and assess using a logistic model, which of the means provides the most favorable conditions for the development of the mycelium as a determining stage prior to its spread.
Materials and methods
Location of area of study
Issues of the species Entoloma sp. were collected in mountain mesophilic forest relics located in the Ocotitla estate, in the community of Xaltepuxtla, in the state of Puebla, between the coordinates 20° 11’ 23.06” at 20° 10’ 57.124” north latitude and 97° 58’ 5.303” at 97° 57’ 30.836” west longitude, at an average height of 1 280 meters above sea level (^{MateoGuzmán, 2018}). The climate corresponds to a semiwarm humid with rains throughout the year, precipitation of the driest month greater than 40 mm and less than 18% of winter rain with respect to the total rain and its annual average temperature ranges between 18° and 24 ° C.
Collection and disinfection of the material
Full body fungi were collected during their emergency period, which occurs between December and January, when organic substrate conditions, temperature and humidity are favorable for growth (^{Mateo, 2018}). They were covered with foil and transported in a cooler to have fresh material for insulation. In the laboratory, this process consisted of selecting whole and healthy fungi; disinfect the surface of the fungi by means of a cotton soaked in a solution of water with detergent, then with a 10% chlorine solution and finally in a 0.2% solution of veterinary gentamicin antibiotic.
Getting mycelium
The mycelium was obtained in the threeculture media using the methodology of ^{Ardon (2007)} and Silva et al. (2010), which consists of isolation by context, purification process and test of mycelium growth in culture media. This last stage consisted of: a) reseeding the strains obtained from isolation by context (vegetative) in three culture media (malt extractyeast extractpolypeptoneagar (MYPA); meat peptonedextroseyeast extract bacteriological agar (CYM) and maltbran extract (EMS); b) compare its growth in each; c) define the medium in which the mycelium best adapts and grows; d) inoculate more than five boxes by means; e) choose five of these with better appearance and absence of contaminants; f) extract a fraction of the strain in a circular form of approximately 0.5 cm; g) place it in the center of a Petri dish; h) seal it with parafilm and label it with the name of the medium and the date of inoculation; i) place the sealed and labeled box at room temperature; and j) measure the diameter of mycelial growth every two days.
Analysis of data
For the analysis of mycelial diameter growth data in the three culture media: MYPA, CYM and EMS, a oneway analysis of variance (Anova) (1V) was applied for repeated measurements (MR), Anova1VMR (^{Davis, 2002}), to determine if these have any effect on the growth of the mycelium diameter of the Totolcozcatl fungus, where the culture media correspond to the categorical factor with three levels. The method consisted of: a) checking the assumptions of homogeneity between the variances of the differences between all the possible pairs of culture medium and the normality of the errors by means of the Mauchly and ShapiroWilk sphericity test, respectively; b) apply the Greenhouse and Geisser epsilon test or the multivariate approach, in cases where the sphericity assumption is not met; and c) apply the statistical model
For each
The hypothesis tests were performed with a level of significance α= 0.05 and the comparison between means using the Bonferroni method (^{Morell, 2014}) with the SPSS software (^{IBM Corp. Released, 2012}).
Determination of the dynamics of mycelial growth
The dynamics of the growth of the fungal diameter or increase of mycelial biomass is a function of the fermentation parameters and even in the face of stress situations (^{Deacon, 2006}; ^{Huang et al., 2010}). Several models have been applied to describe the kinetics of mycelial diameter growth in different types of crops, such as the linear, exponential, logistic model, as well as modifications of these (^{ViniegraGonzález et al., 1993}; ^{Mitchell, Von Meien et al., 2004}). The differential equation proposed by ^{Sarikaya and Ladisch (1997)} was used to determine the dynamics of the growth of the average mycelial diameter.
Where: D= diameter of mycelial growth (mm); t= time (days),
The model of mycelial growth dynamics, obtained from the integration of
And this happened when t is equal to:
The parameters
Results and discussion
Determination of mycelial diameter growth
Table 1 shows the results obtained from the average growth of the mycelial diameter of the Totolcozcatl fungus in the threeculture media. The average net growth of the mycelium was 88.5, 78.3 and 89.5 mm, for the culture medium MYPA, CYM and EMS, respectively. Differentiating between the culture media, in EMS a maximum average growth diameter of 90 mm was reached at 16 days, followed by MYPA and CYM with 89 and 78.8 mm, respectively, in the same period of time.
Culture medium 
Measurement days 

0 
2 
4 
6 
8 
10 
12 
14 
16 

MYPA 
0.05 
8.5 
20.8 
35 
50.4 
64.8 
77 
85.3 
89 
CYM 
0.05 
7.4 
15.3 
27.4 
38.9 
51.9 
59.9 
71.1 
78.8 
EMS 
0.05 
9.3 
23 
36.2 
50.6 
66 
88.3 
90 
90 
Based on the variability observed during the development of the mycelium and the adjusted data, Figure 1 shows that the development in average mycelial diameter of the Totolcozcatl fungus was more favorable in the EMS culture medium, managing to colonize the Petri dish over a period of 14 days, followed by MYPA and CYM.
Variance analysis of repeated oneway averages (AnovaMR1V) for culture media
In order to determine if the culture media have any effect on the average growth of the mycelial diameter of the Totolcozcatl fungus, the statistical technique of the AnovaMR1V was applied to the experimental data. The culture medium corresponded to the categorical factor with three levels, that is, the culture media: 1MYPA, 2CYM and 3EMS, respectively. The growth of the average diameter of the mycelium was defined as the dependent variable; that is, petri dish 1. Effect of MYPA, petri dish 2. Effect of CYM and petri dish 3. Effect of EMS. The sample size was eight, which are times the data were taken.
In Table 2, the results of the Mauchly sphericity test indicate that the variances of the differences between each two levels of the factor are not equal. This means that the matrix of variances and covariances is not circular or spherical, since the critical level associated with the statistic (significance: 0.014) is not greater than 0.05. Consequently, the univariate F statistic was used, applying a corrective index called epsilon, which expresses the degree to which the variancecovariance matrix moves away from sphericity. Under conditions of perfect sphericity, epsilon must be worth 1. Epsilon was estimated by the GreenhouseGeisser and HuynhFeldt statistic, being the first of them more conservative. Epsilon was also estimated with the lower limit value, which expresses the value it would adopt in the case of extreme breach of the sphericity assumption.
Effect within subjects 
Mauchly W statistic 
ChiSquare Approach 
Epsilon 

GreehouseGeisser 
HuynhFeldt 
Lower limit 

Treatments 
0.239 
8.586 
2 
0.014 
0.568 
0.604 
0.5 
GL= degree of freedom; p = significance.
Therefore, the correction of the degrees of freedom of F (both in the numerator and in the denominator) was made by multiplying them by the estimated value of epsilon. Consequently, in Table 3, the results obtained in the four F statistics indicate that the null hypothesis is rejected, since the critical level associated with each of the tests is less than 0.05, this means that there are statistically significant differences in the fungus development in at least one of the three culture media.
Source 

Sum of squares Type III 
Degrees of freedom 
Mean squares 
F 
Significance 
Treatment 
Assumed sphericity 
727.85 
2 
363.92 
21.06 
0 
GreenhouseGeisser 
727.85 
1.136 
640.85 
21.06 
0.002 

HuynhFeldt 
727.85 
1.208 
602.35 
21.06 
0.001 

Límite inferior 
727.85 
1 
727.85 
21.06 
0.003 

Error (treatment) 
Assumed sphericity 
241.972 
14 
17.28 


GreenhouseGeisser 
241.972 
7.95 
30.44 



HuynhFeldt 
241.972 
8.458 
28.61 



Límite inferior 
241.972 
7 
34.57 
Comparison of means by means of the Bonferroni test
The results obtained from the twototwo comparisons between the culture media according to the critical levels associated with each comparison indicate that there are only significant differences between the culture medium 2 with respect to 1 and 3, while between 1 and 3 no there are differences (Table 4). This first analysis indicated that the MYPA and EMS culture media are the most favorable for the growth of the average mycelial diameter of the Totolcozcatl fungus than the CYM.
Treatment (I) 
Treatment (J) 
Mean difference (IJ) 
Standard error 
Significance^{b} 
95% confidence interval for the difference^{b} 

Límite inferior 
Límite superior 

1 
2 
10.006* 
1.81 
0.003 
4.344 
15.669 
3 
2.831 
1.306 
0.201 
6.916 
1.254 

2 
1 
10.006* 
1.81 
0.003 
15.669 
4.344 
3 
12.838* 
2.825 
0.008 
21.672 
4.003 

3 
1 
2.831 
1.306 
0.201 
1.254 
6.916 
2 
12.838* 
2.815 
0.008 
4.003 
21.672 
^{b}= setting for multiple comparisons= Bonferroni.
The differences found in the development of diameter growth between the three means used are associated with their chemical composition. The EMS medium has nutritional characteristics that favor the development of the species, since it provides nutrients such as maltose, glucose and mainly wheat bran, which supplies cellulose, polysaccharides and hemicellulose, which, in the natural habitat of the fungus, cellulose is always present in decomposing matter (^{Mateo, 2018}). This favors fungi to increase the branching of their hyphae and, consequently, the amount of biomass and the surface area of the mycelium (^{Harris, 2008}). On the contrary, if nutrients are limited, the mycelium tends to be less branched (^{Prosser and Tough, 1991}).
Determination of the dynamics of mycelial growth
The model adjusted to the growth data measured as the average mycelial diameter of the Totolcozcatl fungus, in the three culture media was the logistic one, which coincided with what was stated by ^{Sarikaya and Ladisch (1997)}, who mention that the mycelial diameter measurements present a good fit with a logistic model, though, this adjustment is best when the area of the colonies is used as a variable.
According to ^{Madigan et al. (2004)}, this characteristic behavior of microbial development, evidences three stages. The first is latency, associated with the synthesis of enzymes that allow the use of nutrients from the culture medium. The second is exponential, obtaining in this the maximum growth point
Regarding the dynamics of the development of the diameter of the mycelium of the Totolcozcatl fungus in the MYPA medium, in Figure 2, the adjusted model indicates that its maximum growth, also known as load capacity, was achieved in K= 91.51 mm, in a period 16 days. While the point at which hyphae grow rapidly from one time to another was
According to ^{Madigan et al. (2004)}, at the beginning, the sufficiency of resources, in space and food, allows hyphae to grow in number and individually almost without restrictions, geometrically, since each unit of increased diameter means a decrease in the availability of resources. Consequently, the speed with which the hyphae was growing is gradually reduced until all the resources of the growth medium are consumed as quickly as they are produced, and the mycelium stops growing.
This point is known as carrying capacity as mentioned above (K; Figure 2a). If you consider only the number of hyphae (biomass) that is added to the mycelium from one time to another (surplus production), it increased in the early stages, reaching a maximum and began to decrease symmetrically to the initial part, reaching zero when the size of the mycelium reached the value of
The model adjusted to the experimental data with the CYM and EMS culture medium (Figure 3 and 4) indicate that its loading capacity and the point of maximum growth was close to (K= 83.23 mm and
Conclusions
The adjusted mathematical models that explain the mycelial growth in each culture medium, in terms of goodness of fit, revealed a high percentage of the variability of the logarithms of the counts or measurements of the hyphae over time. Likewise, these functions allowed estimating: point of maximum growth (K) of the mycelium (in diameter), at which point the hyphae grow rapidly from one time to another, surplus production or number of hyphae added to the mycelium in each culture medium and less time in which it is reached. Based on these results, it is concluded that the EMS medium is the most viable medium for the Totolcozcatl fungus induction process.
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Received: November 01, 2019; Accepted: January 01, 2020