{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T05:04:38Z","timestamp":1790053478297,"version":"4.0.1"},"reference-count":49,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:00:00Z","timestamp":1789776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u0327\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","award":["E-26\/201.141\/2022"],"award-info":[{"award-number":["E-26\/201.141\/2022"]}]},{"name":"Funda\u0327\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado do Rio de Janeiro","award":["E-26\/200.537\/2026"],"award-info":[{"award-number":["E-26\/200.537\/2026"]}]},{"name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","award":["306417\/2025-1"],"award-info":[{"award-number":["306417\/2025-1"]}],"id":[{"id":"https:\/\/ror.org\/03swz6y49","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","award":["306861\/2023-2"],"award-info":[{"award-number":["306861\/2023-2"]}],"id":[{"id":"https:\/\/ror.org\/03swz6y49","id-type":"ROR","asserted-by":"crossref"}]},{"award":["306417\/2025-1"],"award-info":[{"award-number":["306417\/2025-1"]}],"id":[{"id":"https:\/\/ror.org\/03swz6y49","id-type":"ROR","asserted-by":"publisher"}]},{"award":["306861\/2023-2"],"award-info":[{"award-number":["306861\/2023-2"]}],"id":[{"id":"https:\/\/ror.org\/03swz6y49","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Federal University of Bahia","award":["PRPPG 010\/2024"],"award-info":[{"award-number":["PRPPG 010\/2024"]}],"id":[{"id":"https:\/\/ror.org\/03k3p7647","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Federal University of Bahia","award":["MCTI\/FINEP\/FNDCT\/A\u00e7\u00e3o Transversal\/CT-Agro\u201401\/2024\u20142629\/24"],"award-info":[{"award-number":["MCTI\/FINEP\/FNDCT\/A\u00e7\u00e3o Transversal\/CT-Agro\u201401\/2024\u20142629\/24"]}],"id":[{"id":"https:\/\/ror.org\/03k3p7647","id-type":"ROR","asserted-by":"crossref"}]},{"award":["PRPPG 010\/2024"],"award-info":[{"award-number":["PRPPG 010\/2024"]}],"id":[{"id":"https:\/\/ror.org\/03k3p7647","id-type":"ROR","asserted-by":"publisher"}]},{"award":["MCTI\/FINEP\/FNDCT\/A\u00e7\u00e3o Transversal\/CT-Agro\u201401\/2024\u20142629\/24"],"award-info":[{"award-number":["MCTI\/FINEP\/FNDCT\/A\u00e7\u00e3o Transversal\/CT-Agro\u201401\/2024\u20142629\/24"]}],"id":[{"id":"https:\/\/ror.org\/03k3p7647","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Molecules"],"abstract":"<jats:p>Plant chemodiversity is generally evaluated through metabolite richness, relative abundance, compositional dissimilarity, and biosynthetic organization. However, these descriptors characterize chemical states without explicitly identifying which metabolites, chemical classes, or biosynthetic pathways gain or lose relative representation during transitions between states. Here, we introduce Chemical Game Theory as an operational analogy inspired by the relative-performance principle of replicator dynamics. Metabolites are treated as elementary chemical strategies, biosynthetic pathways constitute higher-order strategies, and normalized chromatographic abundances define their frequencies within a mixture. A centered log-ratio quantity, termed realized chemical payoff within this framework, retrospectively quantifies whether a component gained or lost proportional representation relative to the abundance-weighted mean log change in the system. It is not inferred from a payoff matrix and does not represent Darwinian fitness, interaction strength, or absolute biosynthetic production. Shannon diversity describes metabolite-level coexistence, whereas the General Biosynthetic Diversity Index, GBDI, characterizes abundance-weighted pathway organization and intrapathway diversification. The framework was applied to previously published GC-MS and GC-FID profiles of essential oils from leaves and four developmental stages of the reproductive organ of Piper mollicomum Kunth, sampled over five months. Leaves had the highest numerical mean Shannon diversity and GBDI, although the Shannon difference was not statistically significant. The reproductive stages followed temporally variable compositional trajectories. Across the five descriptive monthly blocks, the terpenoid route gained relative representation during the Stage I to II and Stage III to IV transitions, whereas the mixed category declined. Chemical dominance, Shannon diversity, GBDI, and realized payoff captured related but non-equivalent dimensions of relative chemical organization. As a proof of concept, Chemical Game Theory provides a quantitative language for retrospective analysis of compositional redistribution. Its proposed use for prioritizing plant material and its transferability to other chromatographic platforms require validation with independent datasets, biological replication, absolute quantification, and bioactivity-guided experiments.<\/jats:p>","DOI":"10.3390\/molecules31183325","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T14:12:09Z","timestamp":1789999929000},"page":"3325","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Chemical Game Theory: Linking Metabolite Diversity, Biosynthetic Architecture, and Realized Payoffs"],"prefix":"10.3390","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3060-0395","authenticated-orcid":false,"given":"Davyson de Lima","family":"Moreira","sequence":"first","affiliation":[{"name":"Research Institute of the Rio de Janeiro Botanical Garden, Rua Pacheco Le\u00e3o 915, Jardim Bot\u00e2nico, Rio de Janeiro 22460-030, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6474-2033","authenticated-orcid":false,"given":"Daniel de Brito","family":"Machado","sequence":"additional","affiliation":[{"name":"Research Institute of the Rio de Janeiro Botanical Garden, Rua Pacheco Le\u00e3o 915, Jardim Bot\u00e2nico, Rio de Janeiro 22460-030, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4443-1008","authenticated-orcid":false,"given":"Ygor Jess\u00e9","family":"Ramos","sequence":"additional","affiliation":[{"name":"Farm\u00e1cia da Terra Laboratory, Faculty of Pharmacy, Federal University of Bahia, Rua Bar\u00e3o de Jeremoabo, 147, Ondina, Salvador 40170-115, BA, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"conceptualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7576-226X","authenticated-orcid":false,"given":"Renato Crespo","family":"Pereira","sequence":"additional","affiliation":[{"name":"Department of Marine Biology, Universidade Federal Fluminense, Campus do Valonguinho, Outeiro de S\u00e3o Jo\u00e3o Batista, s\/n, Centro, Niter\u00f3i 24020-141, RJ, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.sajb.2013.06.006","article-title":"Evolution of secondary metabolites in legumes (Fabaceae)","volume":"89","author":"Wink","year":"2013","journal-title":"S. Afr. J. Bot."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2831","DOI":"10.1016\/j.phytochem.2007.09.017","article-title":"From waste products to ecochemicals: Fifty years research of plant secondary metabolism","volume":"68","author":"Hartmann","year":"2007","journal-title":"Phytochemistry"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1146\/annurev-arplant-042110-103814","article-title":"Convergent evolution in plant specialized metabolism","volume":"62","author":"Pichersky","year":"2011","journal-title":"Annu. Rev. Plant Biol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1111\/nph.12526","article-title":"Explaining intraspecific diversity in plant secondary metabolites","volume":"201","author":"Moore","year":"2014","journal-title":"New Phytol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/ele.13422","article-title":"The many dimensions of phytochemical diversity: Linking theory to practice","volume":"23","author":"Wetzel","year":"2020","journal-title":"Ecol. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e1635","DOI":"10.1002\/ecm.1635","article-title":"Understanding the chemodiversity of plants: Quantification, variation, and ecological function","volume":"94","author":"Anaia","year":"2024","journal-title":"Ecol. Monogr."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2478","DOI":"10.1111\/nph.18685","article-title":"Quantifying chemodiversity considering biochemical and structural properties of compounds with the R package CHEMODIV","volume":"237","author":"Junker","year":"2023","journal-title":"New Phytol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Moreira, D.L., Pereira, R.C., and Ramos, Y.J. (2026). Beyond chemodiversity: A General Biosynthetic Diversity Index for plant metabolic architecture in ecology, evolutionary, and bioprospection. Molecules, 31.","DOI":"10.3390\/molecules31122188"},{"key":"ref_9","unstructured":"von Neumann, J., and Morgenstern, O. (1944). Theory of Games and Economic Behavior, Princeton University Press."},{"key":"ref_10","unstructured":"Osborne, M.J., and Rubinstein, A. (1994). A Course in Game Theory, MIT Press."},{"key":"ref_11","unstructured":"Weibull, J.W. (1995). Evolutionary Game Theory, MIT Press."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hofbauer, J., and Sigmund, K. (1998). Evolutionary Games and Population Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9781139173179"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Nowak, M.A. (2006). Evolutionary Dynamics: Exploring the Equations of Life, Belknap Press of Harvard University Press.","DOI":"10.2307\/j.ctvjghw98"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1073\/pnas.36.1.48","article-title":"Equilibrium points in n-person games","volume":"36","author":"Nash","year":"1950","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0025-5564(78)90077-9","article-title":"Evolutionarily stable strategies and game dynamics","volume":"40","author":"Taylor","year":"1978","journal-title":"Math. Biosci."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Maynard Smith, J. (1982). Evolution and the Theory of Games, Cambridge University Press.","DOI":"10.1017\/CBO9780511806292"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1111\/ele.12071","article-title":"Game theory and plant ecology","volume":"16","author":"McNickle","year":"2013","journal-title":"Ecol. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1046\/j.0022-0477.2001.00609.x","article-title":"Tragedy of the commons as a result of root competition","volume":"89","author":"Gersani","year":"2001","journal-title":"J. Ecol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"diaa008","DOI":"10.1093\/insilicoplants\/diaa008","article-title":"Optimal plant defence under competition for light and nutrients: An evolutionary modelling approach","volume":"2","author":"Evers","year":"2020","journal-title":"In Silico Plants"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"ply035","DOI":"10.1093\/aobpla\/ply035","article-title":"Toleration games: Compensatory growth by plants in response to enemy attack is an evolutionarily stable strategy","volume":"10","author":"McNickle","year":"2018","journal-title":"AoB Plants"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e382","DOI":"10.1002\/pld3.382","article-title":"Allelopathy as an evolutionary game","volume":"6","author":"McCoy","year":"2022","journal-title":"Plant Direct"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e49810","DOI":"10.3897\/rio.6.e49810","article-title":"Ecology and evolution of intraspecific chemodiversity of plants","volume":"6","author":"Eilers","year":"2020","journal-title":"Res. Ideas Outcomes"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"e14365","DOI":"10.1111\/ele.14365","article-title":"The evolution of chemodiversity in plants: From verbal to quantitative models","volume":"27","author":"Thon","year":"2024","journal-title":"Ecol. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1893","DOI":"10.1104\/pp.104.049981","article-title":"Biochemistry of plant volatiles","volume":"135","author":"Dudareva","year":"2004","journal-title":"Plant Physiol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/nph.12145","article-title":"Biosynthesis, function and metabolic engineering of plant volatile organic compounds","volume":"198","author":"Dudareva","year":"2013","journal-title":"New Phytol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.tree.2005.05.001","article-title":"Facing herbivory as you grow up: The ontogeny of resistance in plants","volume":"20","author":"Boege","year":"2005","journal-title":"Trends Ecol. Evol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1039\/C8NP00065D","article-title":"Selection and characterization of botanical natural products for research studies: A NaPDI Center recommended approach","volume":"36","author":"Kellogg","year":"2019","journal-title":"Nat. Prod. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1038\/s41573-020-00114-z","article-title":"Natural products in drug discovery: Advances and opportunities","volume":"20","author":"Atanasov","year":"2021","journal-title":"Nat. Rev. Drug Discov."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1039\/C9NP00004F","article-title":"Innovative omics-based approaches for prioritisation and targeted isolation of natural products","volume":"36","author":"Wolfender","year":"2019","journal-title":"Nat. Prod. Rep."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1038\/s41592-020-0933-6","article-title":"Feature-based molecular networking in the GNPS analysis environment","volume":"17","author":"Nothias","year":"2020","journal-title":"Nat. Methods"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"de Brito Machado, D., Felisberto, J.S., de Queiroz, G.A., Guimar\u00e3es, E.F., Ramos, Y.J., and Moreira, D.L. (2024). From leaves to reproductive organs: Chemodiversity and chemophenetics of essential oils as important tools to evaluate Piper mollicomum Kunth chemical ecology relevance in the Neotropics. Plants, 13.","DOI":"10.3390\/plants13172497"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Aitchison, J. (1986). The Statistical Analysis of Compositional Data, Chapman and Hall.","DOI":"10.1007\/978-94-009-4109-0"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Gloor, G.B., Macklaim, J.M., Pawlowsky-Glahn, V., and Egozcue, J.J. (2017). Microbiome datasets are compositional: And this is not optional. Front. Microbiol., 8.","DOI":"10.3389\/fmicb.2017.02224"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s00049-016-0227-8","article-title":"A chemo-ecologists\u2019 practical guide to compositional data analysis","volume":"27","author":"Heethoff","year":"2017","journal-title":"Chemoecology"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1023866030544","article-title":"Dealing with zeros and missing values in compositional data sets using nonparametric imputation","volume":"35","year":"2003","journal-title":"Math. Geol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.chemolab.2015.02.019","article-title":"zCompositions: R package for multivariate imputation of left-censored data under a compositional approach","volume":"143","year":"2015","journal-title":"Chemom. Intell. Lab. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1080\/01621459.1937.10503522","article-title":"The use of ranks to avoid the assumption of normality implicit in the analysis of variance","volume":"32","author":"Friedman","year":"1937","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"80","DOI":"10.2307\/3001968","article-title":"Individual comparisons by ranking methods","volume":"1","author":"Wilcoxon","year":"1945","journal-title":"Biom. Bull."},{"key":"ref_39","first-page":"65","article-title":"A simple sequentially rejective multiple test procedure","volume":"6","author":"Holm","year":"1979","journal-title":"Scand. J. Stat."},{"key":"ref_40","unstructured":"Van Rossum, G., and Drake, F.L. (2009). Python 3 Reference Manual, CreateSpace."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","article-title":"Array programming with NumPy","volume":"585","author":"Harris","year":"2020","journal-title":"Nature"},{"key":"ref_42","unstructured":"van der Walt, S., and Millman, J. (2010). Data structures for statistical computing in Python. Proceedings of the 9th Python in Science Conference, SciPy."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: Fundamental algorithms for scientific computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nat. Methods"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCSE.2007.55","article-title":"Matplotlib: A 2D graphics environment","volume":"9","author":"Hunter","year":"2007","journal-title":"Comput. Sci. Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1002\/pca.843","article-title":"Circadian rhythm of anti-fungal prenylated chromene in leaves of Piper aduncum","volume":"16","author":"Morandim","year":"2005","journal-title":"Phytochem. Anal."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1500","DOI":"10.1590\/S0103-50532007000800008","article-title":"Biosynthetic origin of the isoprene units in chromenes of Piper aduncum (Piperaceae)","volume":"18","author":"Leite","year":"2007","journal-title":"J. Braz. Chem. Soc."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3209","DOI":"10.1002\/jssc.201500106","article-title":"Prediction of response factors for gas chromatography with flame ionization detection: Algorithm improvement, extension to silylated compounds, and application to the quantification of metabolites","volume":"38","author":"Leocata","year":"2015","journal-title":"J. Sep. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0022-5193(66)90013-0","article-title":"The Measurement of Diversity in Different Types of Biological Collections","volume":"13","author":"Pielou","year":"1966","journal-title":"J. Theor. Biol."}],"container-title":["Molecules"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1420-3049\/31\/18\/3325\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T04:27:38Z","timestamp":1790051258000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1420-3049\/31\/18\/3325"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,19]]},"references-count":49,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["molecules31183325"],"URL":"https:\/\/doi.org\/10.3390\/molecules31183325","relation":{},"ISSN":["1420-3049"],"issn-type":[{"value":"1420-3049","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,19]]}}}