New Reduction-Oxidation Indices Applied to Mixtures in the Impact on Seasonal and Circadian Rhythm Studies of The Essential Oil From Leaves of Piper Gaudichaudianum Kunth (Piperaceae) – A Folk Medicine and Ritualistic Plant

Piper gaudichaudianum Kunth (Piperaceae) is widely used in Brazil as medicinal and ritualistic. In this study, chemophenetic patterns were evaluated based on leaves’ essential oils (EOs) chemical composition. Several collections were performed to accomplish circadian rhythm and seasonal studies. Besides, a predictive methodology was developed and submitted to Proof of Concept (PoC) to determine the metabolism pattern and evaluate the reduction-oxidation of complex mixtures: Weighted Average Redox Standard (S RO ) and General Mixture Redox Index (GM OR ). Fresh leaves EOs obtained by hydrodistillation were analyzed by GC-MS and GC-FID. The main identied compounds were sesquiterpenes. Nineteen terpene skeletons were registered. There was chemical composition variation at different phenological stages. EOs varied more between day and night than seasonally. Nine chemotypes are proposed based on our results and those from literature. S RO and GM RO analyzes highlighted a possible redox balance throughout day and night. Compounds per carbon skeleton diversication in EOs are matched by an increase in compounds S RO . We also report for the rst time high chemical phenotype plasticity based on EOs analysis and its implications for P. gaudichaudianum chemophenetics, chemosystematics and ecology. not enough to determine oxidation patterns during temporal variations of terpenoids. Thus, for the rst time and using P. gaudichaudianum as a model and considering the compound quantication of its EO, it was possible to develop and make a proof of concept of a new approach based on “Weighted Average Redox Standard” (S RO ) and the “General Mixture Redox Index” (GM RO ). These calculations led to correlate the production of EO compounds to the general metabolism of the species, demonstrating that there is a direction for a possible redox balance throughout the day. It was also possible to demonstrate that the diversication in the number of compounds per carbon skeleton in the P. gaudichaudianum EO is followed by an increase in the S RO of the compounds. These oxidative diversications have as their main control point the quantitative increase in biogenetic precursors. Also, chemophenetic approach of P. gaudichaudianum determine possible chemotypes. Considering carbon skeletons, it demonstrated that most chemotype diversications are centered on biogenetic derivatives or compounds with a Germacrane or Humulane Despite diversication of the skeletons of the chemotypes, the data analysis did not corroborate the existence of homogeneous spatial occurrence in the compounds expressed by the chemical phenotypes in a gradient with latitude and longitude. All data together, provide evidence of ecological, chemosystematic and chemophenetic signicance for the management and conservation of this medicinal and ritualistic species used by the Brazilian population.

Introduction oxidative steps (OS) (Emerenciano et al. 1998). In addition to performing the proof of concept in the developed indices of Weighted Average Redox Standard (S RO ) and General Mixture Redox Index (GM RO , or Ramos & Moreira´s index for mixtures). Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA) were applied to verify the interrelationship in the composition of leaf EO collected at different time and months. For chemotype analysis, information about chemical composition of EO published in the literature for P. gaudichaudianum was achieved. It was included in this paper those EO analyzes obtained by hydrodistillation from leaves; a valid number of voucher deposit and analyses by GC-MS and GC-FID. These composition data were applied to the PCA and HCA matrix to determine the chemotypes (Gottlieb et al. 1996; Sadgrove and Jones 2014). The results were processed by STATISTICA version 10 (StartSoft Inc., Tulsa, USA).

Results And Discussion
The yield and chemical composition of the EOs obtained by hydrodistillation from leaves of specimens of P. gaudichaudianum collected in the Tijuca National Park, in Rio de Janeiro/ RJ (Brazil), referring to seasonality studies (January 2017 to December 2017) and circadian rhythm (collections every 3 h in the rainy season -March 2017 -and dry season -October 2017) are shown in Tables 1 and 2, respectively. The results of Pearson's correlation between environmental abiotic variables, major compounds, chemical classes and calculated GM RO are listed in Table 3.

Essential oil yields
The EOs showed a slightly yellow color and ranged from 0.02-0.23% (w/ w) considering the seasonal and circadian analyzes (Tables 1 and 2). These values were higher compared to some of the results described in the literature for this species (0.01-0.10%) (Morais et al. 2007; Rodig and Poser 1990). Higher yield values were published for samples from Santa Maria (Rio Grande do Sul, Brazil) that ranged from 1.32 to 1.61% (Schindler et al. 2018). Intermediate values were recorded for samples collected in Atalanta (Santa Catarina, Brazil) (0.24 to 0.46%) (Santos 2009).
For the seasonal study, the highest amounts were registered for those EOs obtained in November (0.11%), December (0.14%), and January (0.12%). The study of circadian rhythm showed the highest EOs content at 6 a.m. (0.23%) in the rainy season (R) and at 12 p.m. (0.16%) in the dry season (D). There was a statistical difference between the averages throughout the day for each season (p < 0.0001), as well as between night and day (p = 0.0351). However, comparing the average yields between the dry and rainy season there was no signi cant difference (p = 0.4833). In both seasons, the night period (9 a.m. to 6 a.m.) afforded the high values of EO yield.

Seasonal variation of the essential oil
In the seasonal study, despite the predominant uniform distribution recorded throughout the year for non-oxygenated sesquiterpenes (Tables 1 and 3), in periods with greater precipitation (r = 0.701; p = 0.011) and relative humidity (r = 0.735; p = 0.006) there was an increase in non-oxygenated monoterpenes. The non-oxygenated sesquiterpenes showed correlation inversely proportional with precipitation (r = -0.591, p = 0.043) and directly to the temperature (r = 0.625, p = 0.030). The increase in the average monthly precipitation led to an increase in the concentration of oxygenated sesquiterpenes, a result con rmed by the signi cant value found in the correlations (r = -0.828; p = 0.001) ( Table 3). The EOs from the aerial parts of Peperomia galioides Kunth (Piperaceae) showed similar increase in the relative percentages of oxygenated sesquiterpenes in the period of greatest precipitation (Ramos and Moreira, 2019). Some works raise the hypothesis that plant species create mechanisms to control the biosynthetic route from the available resources; in this case, high water content in the enviroment in a compensatory way to guarantee homeostasis (Cheng et al. 2007; Barros et al. 2009;Bergma et al. 2019).
Bicyclogermacrene, E-Caryophyllene, Eudesmadiene, E-Nerolidol and α-Cadinol contents showed signi cant variation throughout the year (p < 0.01). The box plot graphic (Fig. 1) presents the variations of the EOs major compounds in the seasonal study. It was possible to observe that, even showing high annual variation, the average of Bicyclogermacrene differs from the other co-majority compounds (p < 0.01). The oxygenated sesquiterpene E-Nerolidol showed the greatest variation in content among the co-majority (Table 1, Fig. 1). P. gaudichaudianum showed its reproductive stage in the period when the average rainfall increases after the dry period, in the months of January (infructecences and in orescences) to February (infructecences) and early November (in orescences) to December (infructecences and in orescences) of 2017. It is described in the literature that reproductive phenophases occur mainly in the rainy season (Valentin-Silva and Vieira 2015). Interestingly, in P. gaudichaudianum the relative percentage of E-Nerolidol showed to increase up to four times in relation to periods of higher incidence of rain after the dry period. When testing this hypothesis, we observed directly proportional and signi cant values in Pearson's correlation between the content of E-Nerolidol with the precipitation (r = 0.769; p = 0.003) and relative humidity (r = 0.791; p = 0.002).
The EO components of P. gaudichaudianum with relative percentages greater than 5% were submitted to statistical analysis. The Principal Component Analysis (PCA) of the seasonal study showed that the main components PC1 (62.1%) and PC2 (21.5%) explained 83.6% of the total chemical variation between all samples, which were classi ed into two groups, as shown in Fig. 2. Bicyclogermacrene in PC1 (-8.6) showed negative charge and positive charge with low in uence in PC2 (+ 0.7). For E-Nerolidol, positive charges were observed on PC2 (+ 5.1) for samples collected in January, February, November and December and negative charges on PC1 (-1.7) for samples collected from March to October. Compounds Eudesmadiene, α-Cadinol and E-Caryophyllene justify the variations in smaller scales, which showed moderate to low negative charges in PC axes. The samples collected in the months of April, March, and October, considered transition months between seasons in the South Hemisphere, showed more positive charges in uenced by the concentrations of E-Nerolidol. That said, Group I (January, February, November, and December) was composed with EOs constituents rich in Bicyclogermacrene and E-Nerolidol and Group II (March to October) resulted from the grouping of samples rich in Bicyclogermacrene followed by E-Caryophyllene > Eudesmadiene > α-Cadinol.
The Hierarchical Cluster Analysis (HCA) for the seasonal study is shown in Fig. 3. The clusters in the dendogram are formed from the branches corresponding to the euclidean distances of the samples in relation to the closest samples. Corroborating the results found in the PCA analisys, the samples were grouped into two clusters (Groups I and II), and it can be said that each sample group had a different chemical composition from each other. Interestingly, this separation respected the months (Group I) when the species was in the reproductive pahse and re ected the importance of E-Nerolidol in this process.
Chemical variations in the EOs from leaves of P. gaudichaudianum due to possible phenological in uence have already been reported for several species (Farhat et al. 2016;Daghbouche et al. 2020;Hazrati et al. 2020;Ramos et al. 2020). It is known that resource allocation patterns are established seasonally to respond to the different physiological demands associated with growth, defense and/ or reproduction (Gomes et al. 2019;Ramos et al. 2020). Piper mollicomum Kunth, for example, in the vegetative period showed high amounts of the oxygenated monoterpene Linalool. Once the reproductive period was established, the biosynthesis production of the oxygenated monoterpene 1,8-Cineole increased (Ramos et al. 2020).
E-Nerolidol is one of the main components of nocturnal oral bouquets called "white olfactory images", in addition to playing an important role in the protection against herbivores. In the latter case, this compound catalyzed by terpene synthase, and the subsequent oxidative degradation of alcohol by a cytochrome P-450 monooxygenase, through the intermediate route, produces 4,8-Dimethylnone-1,3,7-triene (DMNT), principal homoterpene responsible for attracting parasitoids and herbivorous predators (Balao et al. 2011). In addition, there is a premise in the literature that herbivore-induced volatile emissions would be facilitated by the ability to accurately manipulate the quantity and composition of volatiles through altered expression of genes that encode stages in their biosynthesis (Pichersky and Gershenzon 2002). For example, a study with Cucumis sativus L. (Cucurbitaceae) demonstrated that attacks by constitutive herbivores lead to the activation of genes for the decoding of E-Nerolidol synthase for the intermediate production of DMNT (Bouwmeester et al.1999).
Another point to be highlighted refers to a study that evaluated the variations of Piper herbivoria by Eois (Hübner, 1818) (specialized herbivores) in different forest patterns (dry and wet) and variations in abiotic factors. It was observed that the incidence of Eois parasitism increased signi cantly with the increase of precipitation, mainly in humid forest (Connahs et al. 2009). This leads to the hypothesis that P. gaudichaudianum, throughout its evolutionary history, has adapted in order to acquire this chemical phenotypic plasticity (increase of E-Nerolidol) as a response mechanism to environmental issues arising from the ecological pressure exerted by herbivory, as the one caused by Eois.
On the other hand, it is also described in the literature that the recognition of the homoterpene emission leads to a reduction in the pollinator's preference or in the pollen transfer e ciency (Chauta et al. 2017). Another issue that strengthens the argument proposed to P. gaudichaudianum is that the volatiles of leaves and in orescences can be different but act synergistically to attract visitors. Differences in the chemistry of leaves and in orescences are not unexpected, as plants are under selection to attract pollinators to owers, besides leaf herbivores defense (Parachnowitsch and Manson 2015). In study with Nicotiana attenuata Torr. ex S. Watson and Datura wrightii Regel (Solanaceae) it has been demonstrated that the presence of leaf odor further increases the attraction for the mixture of owers pollinated by moths. This interaction of mixtures of owers and leaves can, therefore, be seen as a strategy to optimize the olfactory message and, thus, improve the orientation of the food source based on odors more safely and without risk of mistaken attraction (Karpati et al. 2013 (Fig. 4). The average relative percentages in the driest period were higher than in the rainy season. However, the effects between the dry and rainy periods under the composition showed no signi cant difference (p > 0.05) (Fig. 4).
The PCA and HCA studies were applied to the compounds of the EOs from the rainy and dry periods of the circadian study and are presented in Figs. 5 and 6. The PCA showed a total variance of 90.8% and the main components PC1 and PC2 presented proportional values between themselves, 45.8% and 41.1%, respectively. The two-dimensional axial system generated by the PCA (Fig. 5) clearly showed the discrimination of two groups due to chemical variability: Group I -rich in Bicyclogermacrene, Eudesmadiene, α-Cadinol and Spathulenol; and Group II -rich in Bicyclogermacrene, E-Nerolidol and E-Caryophyllene. The HCA analysis corroborated also again with the PCA analysis, demonstrating the formation of these two groups (euclidean distance of 51.0), correlating this difference between the day (9 a.m. to 6 p.m.) and the night (9 a.m. to 6 a.m.) (Fig. 6). Analyses of the variation in a smaller euclidean distance (26.1), showed that at dusk there was a distinction between the rainy (R) and dry (D) periods, increasing the Eudesmadiene content in the dry period.
Differences were observed in the variance between day and night (paired ANOVA, F 11.77 = 25.22, p < 0.001) when testing the hypothesis observed in the multivariate analysis. The set of factors temperature, humidity, and radiation which de ne the day and night parameters, had more in uency on the chemical composition of P. gaudichaudianum EOs than the variations between the dry and rainy seasons. Analysis of all major compounds separated, showed to follow this logic (day vs night), as well as when compared to each other (p < 0.001). From this premise, patterns can be observed (Fig. 7). In both seasons, the compound Bicyclogermacrene registered constant relative percentage, with low amplitude of variation throughout the day or night, but different between the two one. It was noticeable that the period of the day increases the average content (~ 21%) of Bicyclogermacrene (Table 2; Fig. 3). The compounds Eudesmadiene, α-Cadinol and Spathulenol showed, at night, an increase of up to four times in relation to the content found during the day and with a directly proportional relation to each other (Table S2 -Supplementary Material), (Table 2; Fig. 3). During the day, the compounds E-Caryophyllene and E-Nerolidol have their percentages marked, in contrast to the nocturnal pattern. Interestingly, E-Nerolidol registered its maximum content at 12 p.m. (Table 2; Fig. 7).
Pearson's correlation analysis (Table 3) demonstrated high values of signi cant direct correlations and inversely proportional to radiation in both periods with the main compounds mentioned above. The oxygenated sesquiterpene E-Nerolidol deserves special attention, as it presented an outstanding signi cant correlation with radiation, temperature, and humidity (p < 0.01). In the literature it is reported that most plants emit spikes of volatile terpenoids at noon or in the early afternoon, regulated by light or the internal circadian clock (Dudareva et al. 2003). The increase in radiation provides an increase in the levels and emission of the stimulus by elicitation in genes related to the sesquiterpene biosynthesis. Considering our results, it is reported for the rst-time substantial evidence of the formation of a possible chronotype for the essential oil from leaves of P. gaudichaudianum (Granshaw et al., 2003). The chronotype is associated with the preference obtained or observed from certain synchronic physiological pattern, mainly, differentiated by the periods of the days and nights. The chronotype is also associated with differences in time between the various physiological events at the different spatiotemporal scales (Apostol, 2011;Shawa et al., 2018).

Biosynthetic considerations and reduction-oxidation impact
In the seasonal (S) and circadian (C) study, the compounds identi ed and their respective percentages in the P. gaudichaudianum EOs were grouped according to their respective carbon skeletons ( Biosynthetic dynamics were proposed using C-skeletons throughout the year (Table 4 and Scheme 1). The precursor skeletons of Geranyl Pyrophosphate (monoterpenes) remained in low percentages throughout the year and raised only in the reproductive periods (January, February, November, and December), as well as in high precipitation season (January, March, and April). A targeting for the formation of compounds with C-skeletons from routes linked to Farnesyl Pyrophosphate, the sesquiterpenes precursor, was remarkeble. Germacrane derivatives were present in high relative percentages, suggesting that Farnesyl Pyrophosphate drives to form compounds with the central Germacrane skeleton, in relation to the carbon skeleton that differs from the precursor skeleton of Farnesane. Despite noting this fact, in the reproductive period (January, February, November and December), the biosynthetic route drives to the precursor Farnesane. This result in reproductive phase suggests the hypothesis that the metabolism is directed towards the production of basal metabolites, such as sugars for pollination reward, since these metabolites formed from Farnesane, with acyclic skeletons, demand less energy expenditure in their production than cyclic compounds. This evidence reinforces the hypotheses previously raised for the role of E-Nerolidol (acyclic) in P. gaudichaudianum as a participant in the attractiveness of pollinators.
Comparing the percentages between C-skeletons it was found that the contents of compounds with Bicyclogermacrane were in high percentages during the year, suggesting that the central precursor Germacrane has its production favored during this period. The increase in aromadandrane is linked to the decrease in Germacrane (r= -0.685; p = 0.02), suggesting that the production of compounds with aromadandrane C-skeletons, whose precursor is Bicyclogermacrane, is conditioned to displacement due to consumption, almost total, of substrates with Germacrane skeleton. Bicyclogermacrene route was reduced in August and September when the Cadinane route was favored. However, Bicyclogermacrene route harms the Cadinane route by up to two times. The C-skeleton percentages of Caryophyllane were low compared to the variation of the other sesquitepene C-skeletons. The increase in the Humulane skeleton is conditioned by the increase in the Caryophyllane skeleton, plainly by the fact that these two compounds are in a sequence of chemical transformation. Compounds with Elemane skeletons were favored in the months of May to August (intermediate rain rates) (Scheme 1).
In the circadian study the dynamics related to the production of the compounds was marked by the same pattern between day and night in both seasons (Table 5, Scheme 2). It was registered that in some periods there was an increase in the compound percentage related to the increase in abiotic factors, as previously mentioned, which indicates that the internal circadian clock also regulates the production of precursors and in the con guration of the C-skeletons of the EOs components. In the dry and rainy seasons it was possible to nd 12 and 15 C-skeletons, respectively. Geranyl pyrophosphate derivatives were favored in the rainy season.
Also, in this season, only the predecessor compounds of Myrcane's C-skeleton were favored overnight. On the other hand, in the rainy season Myrcane was favored for the daytime period, because at dusk there was a deviation from the biosynthetic route to produce Menthane and Camphane C-skeletons.
During the day (dry or rainy), Farnesyl Pyrophosphate derivatives were higher from 9 a.m. to 3 p.m. for the compounds with C-skeleton equal to the precursor (Farnesene), which demands less energy for the plant. Again, we emphasize that this period is the one with the highest luminous incidence, reinforcing the hypothesis that there has been a completely change in metabolism for the routes involved with photosynthesis (basal metabolism), consequently, reducing the energy effort for specialized metabolism. During this same period, the displacement for production of most Bicyclogermacranes is constant and relatively greater in the dry season, a route that is commonly active in the plant. From 3 p.m. to 18 p.m., there was exclusive drive to produce the Caryophyllane Cskeleton (including under most of the Bicyclogermacrane C-skeleton).
At night from 9 p.m. to 6 a.m. there was a deviation from the Germacrane route, favoring the routes of Cadinane and Eudesmane C-skeletons. In addition, the displacement of Bicyclogermacrane to produce C-skeleton compounds from Aromadendrane was favored. These two changes, described previously, justify the signi cant reduction in the values of the majority in the EO composition.
Based on our results for P. gaudichaudianum EO, it is possible to postulate that there was a diurnal propensity for acyclic and monocyclic C-skeletons, which requires lower energy costs for construction and structural specialization for production. At night, the opposite pattern was observed, favoring the production of bicyclic and tricyclic C-skeletons, which demand greater expenditure on energy in construction and structural specialization for production. These ndings Previously reported studies on this kind of chemosystematic analysis, based on evolutionary correlation, postulate that the production and diversity of specialized metabolites reach the maximum in more advanced taxa. However, in groups that present these diversi cations in metabolites, evolution tends to nd oxidative balance, always maintaining one or two unoxidized classes. For example, there are Flavonoids and Terpenoids (Emerenciano et al., 2006); Iridoides (Das et al., 1987) and Limonoides Gottlieb, 1982). In other groups, the variations may be in the diversity of the produced skeletons. In general, even at a lower hierarchical level than family, this fact may have occurred with P. gaudichaudianum. But an in-depth chemosystematic analysis is missing to comprove it.
Furthermore, as already mentioned, this analysis based on N OX and OS is a static approach that points out only the absence and presence of compounds in the mixture. The Redox Theory developed by Gottlieb (1989) and studied for decades, demonstrated that the evolution of micromolecules occurs through the oxidation of highly oxidized compounds. It is postulated that oxidative pathways in plants occur in parallel with a protective mechanism against oxidative degradation, re ected directly in the role of atmospheric oxygen (Gottlieb and Kaplan, 1993). These ndings led to the development and application of static quantitative methodologies (Chemosystematic) to assess the evolutionary advances of species based on micromolecules patterns (Gottlieb 1982 The results of the GM RO or EM RO calculations from the seasonal and circadian studies of EOs of P. gaudichaudianum are presented in Tables 1 and 2. It was possible to register variation between − 6.4 to -3.6 in the studies (S: -5.6 to -3,6; C: -6.4 to -3.6).
In the annual variation (January to December 2017) it was registered averages of GM RO , with signi cant difference (p < 0.01). Note that the reproductive period (January, February, November, and December) coincided with the highest values of GM RO (greatest oxidation). After periods with high rainfall, the GM RO values show a decrease (greater reduction). In the same period, there were decrease in the diversity of substances present in the EOs. However, the results of Pearson's correlation for the annual variation did not show signi cant values, but they predict adaptive tendencies of the specimen in space. D: -6.4 to -4.2) and greater oxidation at night (R: -3.9 to -3.7; D: − 4.3 to − 3.6). Pearson's correlation showed signi cant correlations between relative humidity, precipitation, and radiation. These results describe the natural metabolic movement that leads to a possible redox balance throughout the day. In addition, our GM RO results reinforce the protection hypothesis that specialized metabolites exert under stress conditions to minimize the formation of reactive oxygen species (ROS) and reactive nitrogen species (RNS). All these variations aim to guarantee the full functioning and maintenance of plant physiology (Dietz and Pfannchmidt 2011).
A study comparing the effects of adaptation and damage to vine leaves showed that the metabolism of isoprenoids was modulated according to UV-B rates.
In addition, this study associated the damages caused to the generation of ROS with the increase of the excitation energy (Gil et al. 2012). In the literature it is described that volatile terpenoids (Monoterpenes and Sesquiterpenes) are quickly combined with ROS and that these reactions are stimulated by changes in light and temperature conditions (Gil et al. 2012;Jaiswal et al. 2020). Likewise, the data obtained from GM RO at the macro metabolic level corroborate the Redox Theory with a quantitative parameter, which postulates that at the oxidation level, the specialized metabolism requires the existence of binary antioxidant systems: meaning that there will be a balance to guarantee a proportion of different classes of compounds in the redox system. Therefore, compounds may vary in quantity (abundance) or in reducing power (high potential), to achieve "general reducing power", considered a metabolic homeostasis (Gottlieb and Kaplan 1993).
This theoretical statement led to the question: does the diversi cation of the number of compounds by carbon skeletons during different periods (seasonal and circadian study) lead to an increase in oxidation or a reduction in the compounds of the EOs from leaves of P. gaudichaudianum? The number of compounds in each carbon skeleton and the S RO values obtained in seasonal and circadian studies did not have normal distributions (Kolmogorov-Smimov test), so Spearman's nonparametric test was applied to correlate them (Fig. 9) and to answer the question. It was possible to observe a signi cant inversely proportional correlation between the tested parameters, suggesting that the diversi cation of the carbon skeleton is followed by an increase in the S RO of the compounds. However, the scatterplot ( Fig. 9)

Chemophenetic aspects in Piper gaudichaudianum
Based on data from this study and those from literature, sixty (n = 60) EOs chemical composition (Table S3 -Supplementary Material) from P. gaudichaudianum leaves were compiled. The data were processed and analyzed by PCA and HCA and are shown in Figs. 10 and 11, respectively.
The C-skeletons via MEP and MEV with the highest qualitative occurrence (presence and absence) were Caryophyllane (n = 58), Aromadendrane (n = 56), Humulane (n = 56) and Germacrane (n = 55). The propensity for routes in the production of compounds with Humulane and Caryophyllane C-skeletons is found qualitatively and quantitatively in the samples (n = 59). Exception for PR1, in which the production of the Longipinane C-skeleton was favored, a tricyclic compound structurally more complex than Humulane, that is the Longipinane precursor.
Correlating the relative percentage of the compounds by the C-skeleton and the latitude (Lt) and longitude (Lg) (data from literature and from our study), it was Germacrane; Bicyclogermacrane (RJ1 to RJ28, RS3 and RS4) and Aromadandrane (RO). However, when the precursor was Humulane (RS2, SP) it followed the biosynthetic pathway for the formation of Caryophyllane (PR3-1) or Longipinane (PR1). Thyme (Thymus vulgaris L.), a pioneer and invasive species in several countries, showed phenotypic chemical modulations in the terpenes present in the EO in different geographical positions and under evaluation in the edge effect. It was reported that the chemical response of plasticity was mainly related to environmental factors and that the most important mechanism for successful plant invasion at the forest edge is associated with the presence of the carvacrol type chemotype (Nielsen et al. 2013). This is in favor of the argument of the structural (skeleton) spatial diversi cation of the chemotypes present in P. gaudichaudianum, which also has pioneering characteristics.

Conclusions
P. gaudichaudianum EOs content as well as the relative percentage of the compounds are in uenced by the circadian rhythm and season. The highest content was achieved in the months of December to February, and at 6 a.m. in the rainy season and at 12 p.m. in the dry season. The major identi ed compound was Bicyclogermacrene, with variations of E-Caryophyllene, Eudesmadiene, E-Nerolidol, α-Cadinol and Spathulenol. We report for the rst time the high chemical phenotype plasticity presented by P. gaudichaudianum in a different time scale. It was possible to correlate changes in chemical composition at different phenological stages and under different abiotic factors. The variation between the dry and rainy periods did not strongly in uence in the chemical composition, however, there were signi cant variations in the volatiles between day and night. More complex terpenes (bicyclic and tricyclic) were biosynthetized during the nighttime. That said, a possible chronotype based on the chemical composition of EOs is described for the rst time in the genus Piper. We demonstrated that C-skeleton types are an important tool for chemophenetic analyzes and their percentage of occurrence showed trends of signi cant variation in the biosynthetic routes throughout the seasonal and circadian rhythm. Static models of chemosystematic analysis (considering oxidative steps) are not enough to determine oxidation patterns during temporal variations of terpenoids. Thus, for the rst time and using P. gaudichaudianum as a model and considering the compound quanti cation of its EO, it was possible to develop and make a proof of concept of a new approach based on "Weighted Average Redox Standard" (S RO ) and the "General Mixture Redox Index" (GM RO ). These calculations led to correlate the production of EO compounds to the general metabolism of the species, demonstrating that there is a direction for a possible redox balance throughout the day. It was also possible to demonstrate that the diversi cation in the number of compounds per carbon skeleton in the P. gaudichaudianum EO is followed by an increase in the S RO of the compounds. These oxidative diversi cations have as their main control point the quantitative increase in biogenetic precursors.
Also, chemophenetic approach of P. gaudichaudianum allowed to determine nine possible chemotypes. Considering carbon skeletons, it was demonstrated that most chemotype diversi cations are centered on biogenetic derivatives or compounds with a Germacrane or Humulane skeleton. Despite the diversi cation of the skeletons of the chemotypes, the data analysis did not corroborate the existence of homogeneous spatial occurrence in the compounds expressed by the chemical phenotypes in a gradient with latitude and longitude. All data together, provide evidence of ecological, chemosystematic and chemophenetic signi cance for the management and conservation of this medicinal and ritualistic species used by the Brazilian population. Figure 1 Box plot analyses of the major compounds (%) registered in the essential oils from leaves of Piper gaudichaudianum Kunth (Piperaceae) collected monthly for the seasonality study (January to December 2017). Means followed by different letters are signi cantly different according to Tukey test (p < 0.05).

Figure 2
Biplot (Principal Component Analysis -PCA) resulting from the analysis of the essential oils obtained from leaves of Piper gaudichaudianum Kunth (Piperaceae) collected for the seasonsonality study monthly, from January to December 2017.

Figure 3
Dendrogram representing the similarity relation of the essential oils composition from leaves Piper gaudichaudianum Kunth (Piperaceae) collected for the seasonality study monthly, from January to December 2017.

Figure 4
Box plot analyses of the major compounds (%) present in the essential oils from leaves of Piper gaudichaudianum Kunth (Piperaceae) in the circadian rhythm study from 12 a.m. to 12 p.m., during Rainy (March) and Dry (October) seasons. Means followed by different letters are signi cantly different using Tukey test (p < 0.05).   Box plot analyses of the major compounds (%) present in the essential oils from leaves of Piper gaudichaudianum Kunth (Piperaceae) in the circadian rhythm study from days (9 a.m. to 6 p.m.) and nights (9 p.m. to 6 a.m.), during March (Mar, rainy season) and October (Oct, dry season). Means followed by different letters are signi cantly different using Tukey test (p < 0,05).

Figure 8
Radar plot representation of the General Mixture Redox Index obtained from essential oils from leaves of Piper gaudichaudianum Kunth (Piperaceae) in the circadian rhythm study from 12 a.m. to 12 p.m., during March (Mar, rainy season) and October (Oct, dry season).

Figure 9
Correlation between compound numbers for carbon skeleton and Weighted Average Redox Standard (SRO) for the compounds identi ed in the essential oils from leaves of Piper gaudichaudianum Kunth (Piperaceae) in the seasonality and circadian rhythm studies.