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How Long Does a Short-Lived Perennial Live? A Modeling Approach

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Abstract

We have composed a “scale of ontogenesis,” i.e., the sequence of ontogenetic stages, and the life cycle graph (LCG) for Androsace albana, a monocarpic plant species that is considered a short-lived perennial, according to annual observations on permanent sample plots in an alpine lichen heath during the 2009–2016 period. There is only one reproduction event in the LCG, which eliminates any reproductive uncertainty from the data of “identified individuals” type so typical for the former projects with polycarpic species, while the monocarpic cycle excludes any returns from the generative stage to a non-flowering status. The LCG describes the ontogeny through five successive stages: seedlings, juvenile, immature, adult virginal, and generative plants, the generative plants perishing after they have flowered and produced seeds. We have constructed a matrix model of the stage-structured population that corresponds to the LCG; its calibration has reduced to calculating the vital rates directly from the data of one time step, i.e., from the censuses at two successive years of observation. Therefore, the nonautonomous model represents a set of 7 annual matrices, each giving a quantitative measure of how the local population is adapted to its environment as the dominant eigenvalue of the model matrix. Its variations have turned out quite significant from year to year, signifying either a growth or decline of the local population and, in general, its vulnerability to stress factors of the environment. Averaging the annual matrices geometrically over the whole observation period has revealed the tendency to decline and enabled us to extract certain age-specific traits (in years) from the stage-structured model using the technique of virtual absorbing Markov chains and their fundamental matrices. The mean life expectancy at various stages of the A. albana ontogeny has turned out maximal in the adult virginal plants, while the mean age at flowering equal to 13 years has exceeded the horizon of the observation time series, thus proving the technique to be efficient. The model indicates that A. albana plants spend most of their life spans as virginal adults, which characterizes the space holder strategy by Körner (2003), or the delayed-development strategy by Zhukova (1995). The model outcome gives another evidence that the A. albana population is endangered.

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REFERENCES

  1. Artyushenko, Z.T., Atlas po opisatel’noi morphologii vysshikh rastenii: semya (Atlas on Descriptive Morphology of Higher Plants: Seed), Leningrad: Nauka, 1990.

    Google Scholar 

  2. Bender, M.H., Baskin, J.M., and Baskin, C.C., Age of maturity and life span in herbaceous, polycarpic perennials, Bot. Rev., 2000, vol. 66, no. 3, pp. 311–349.

    Article  Google Scholar 

  3. Bernardelli, H., Population waves, J. Burma Res. Soc., 1941, vol. 31, pp. 1–18.

    Google Scholar 

  4. Caswell, H., Matrix Population Models: Construction, Analysis, and Interpretation, Sunderland, MA: Sinauer Associates, 2001, 2nd ed.

    Google Scholar 

  5. Cochran, M.E. and Ellner, S., Simple methods for calculating age-based life history parameters for stage-structured populations, Ecol. Monogr., 1992, vol. 62, no. 3, pp. 3455–3464.

    Article  Google Scholar 

  6. Crone, E.E., Menges, E.S., Ellis, M.M., Bell, T., Bierzychudek, P., and Ehrlen, J., How do plant ecologists use matrix population models? Ecol. Lett., 2011, vol. 14, pp. 1–8.

    Article  PubMed  Google Scholar 

  7. Crone, E.E., Ellis, M.M., Morris, W.F., Stanley, A., Bell, T., and Bierzychudek, P., Ability of matrix models to explain the past and predict the future of plant populations, Conserv. Biol., 2013, vol. 27, pp. 968–978.

    Article  PubMed  Google Scholar 

  8. Cushing, J.M. and Yicang, Z., The net reproductive value and stability in matrix population models, Nat. Resour. Model., 1994, vol. 8, no. 4, pp. 297–333.

    Article  Google Scholar 

  9. Diemer, M., Population dynamics and spatial arrangement of Ranunculus glacialis L., an alpine perennial herb, in permanent plots, Vegetatio, 1992, vol. 103, no. 2, pp. 159–166.

    Google Scholar 

  10. Dinamika tsenopopulyatsii rastenii (Dynamics of Local Plant Populations), Moscow: Nauka, 1985.

  11. Dobronets, B.S., Intervalnaya matematika (Interval Mathematics), Krasnoyarsk: Krasn. Gos. Univ., 2004.

    Google Scholar 

  12. Egorov A.V., Structure of species diversity in plant communities of the Teberda Nature Reserve. Cand. Sci. (Biol.) Dissertation, Moscow: Moscow State Univ., 2015.

  13. Egorov, A.V., Onipchenko, V.G., and Tekeev, D.K., Habitat ecological properties of alpine plant species in Teberda Nature Reserve, Tr. Teberdinsk. Gos. Zapoved., 2012, no. 52.

  14. Fedorov, A.A., Kirpichnikov, M.A., and Artyushenko, Z.T., Atlas po opisatel’noi morfologii vysshikh rastenii: list (Atlas on the Descriptive Morphology of Higher Plants: Leaf), Moscow: Akad. Nauk SSSR, 1956.

    Google Scholar 

  15. Fedorov, A.A., Kirpichnikov, M.A., and Artyushenko, Z.T., Atlas po opisatel’noi morfologii vysshikh rastenii: stebel’ i koren’ (Atlas on the Descriptive Morphology of Higher Plants: Stem and Root), Moscow: Akad. Nauk SSSR, 1962.

    Google Scholar 

  16. Grime, J.P., Plant Strategies and Vegetation Processes, Chichester: Wiley, 1979.

    Google Scholar 

  17. Grime, J.P., Plant Strategies, Vegetation Processes, and Ecosystem Properties, Chichester: Wiley, 2001, 2nd ed.

    Google Scholar 

  18. Grossheim, A.A., Flora Kavkaza (Flora of the Caucasus), Leningrad: Nauka, 1967, vol. 7.

    Google Scholar 

  19. Harper, J.L. and White, J., The demography of plants, Annu. Rev. Ecol. Syst., 1974, vol. 5, pp. 419–463.

    Article  Google Scholar 

  20. Kazantseva, E.S., Population dynamics and seed productivity of short-lived alpine plants in the North-West Caucasus, Cand. Sci. (Biol.) Dissertation, Moscow: Moscow State Univ., 2016.

  21. Kazantseva, E.S., Shulakov, A.A., and Kipkeev, A.M., Anthecology of three alpine plant species of North-West Caucasus, Proc. XV Int. Sci. Conf. “Biodiversity of the Caucasus and Southern Russia,” Makhachkala, November 5–6, 2013, Makhachkala, 2013, pp. 264–265.

  22. Kazantseva, E.S., Onipchenko, V.G., Kipkeev, A.M., and Rovnaya, E.N, Parameters of seed renewal of alpine juveniles and their comparison with perennial plants, Byull. Mosk. O-va. Ispyt. Prir., Otd. Biol., 2016, vol. 121, no. 4, pp. 43–51.

    Google Scholar 

  23. Keller, R. and Vittoz, P., Clonal growth and demography of a hemicryptophyte alpine plant: Leontopodium alpinum Cassini, Alp. Bot., 2014, vol. 125, no. 1, pp. 31–40.

    Article  Google Scholar 

  24. Kemeny, J.G. and Snell, J.L., Finite Markov Chains, Berlin: Springer-Verlag, 1976.

    Google Scholar 

  25. Kipkeev, A.M., Onipchenko, V.G., Tekeev, D.K., Erkenova, M.A., and Salpagarova, F.S., Age of maturity in alpine herbaceous perennials in the North-West Caucasus, Biol. Bull. Rev., 2015, vol. 5, no. 5, pp. 505–511.

    Article  Google Scholar 

  26. Körner, C., Alpine Plant Life: Functional Plant Ecology of High Mountain Ecosystems, Berlin: Springer-Verlag, 2003, 2nd ed.

    Book  Google Scholar 

  27. Krasnaya kniga Krasnodarskogo kraya (rasteniya i griby) (The Red Data Book of the Krasnodar Krai: Plants and Fungi), Litvinskaya, S.A., Ed., Krasnodar: Dizain Byuro, 2007, 2nd ed.

    Google Scholar 

  28. Krasnaya kniga Respubliki Adygeya: Redkiye i nakhodyashchiyesya pod ugrozoy ischeznoveniya ob’’yekty zhivotnogo i rastitel’nogo mira. Chast’ 1. Rasteniya i griby (The Red Data Book of the Adygea Republic: Rare and Endangered Objects of Fauna and Flora, Part 1: Plants and Fungi), Zamotailov, A.S., Ed., Maikop: Kachestvo, 2012, 2nd ed.

  29. Kurashev, A.S., Anthecology of alpine plants in the North-Western Caucasus, Cand. Sci. (Biol.) Dissertation, Moscow: Moscow State Univ., 2012.

  30. Leslie, P.H., On the use of matrices in certain population mathematics, Biometrika, 1945, vol. 33, pp. 183–212.

    Article  PubMed  CAS  Google Scholar 

  31. Lewis, E.G., On the generation and growth of a population, Sankhya, 1942, vol. 6, pp. 93–96.

    Google Scholar 

  32. Li, C.-K. and Schneider, H., Application of Perron–Frobenius theory to population dynamics, J. Math. Biol., 2002, vol. 44, pp. 450–462.

    Article  PubMed  Google Scholar 

  33. Logofet, D.O., Convexity in projection matrices: projection to a calibration problem, Ecol. Model., 2008, vol. 216, no. 2, pp. 217–228.

    Article  Google Scholar 

  34. Logofet, D.O., Svirezhev’s substitution principle and matrix models for dynamics of populations with complex structures, Zh. Obshch. Biol., 2010, vol. 71, no. 1, pp. 30–40.

    PubMed  CAS  Google Scholar 

  35. Logofet, D.O., Complexity in matrix population models: polyvariant ontogeny and reproductive uncertainty, Ecol. Complexity, 2013a, vol. 15, pp. 43–51.

    Article  Google Scholar 

  36. Logofet, D.O., Projection matrices in variable environments: λ1 in theory and practice, Ecol. Model., 2013b, vol. 251, pp. 307–311.

    Article  Google Scholar 

  37. Logofet, D.O., Projection matrices revisited: a potential-growth indicator and the merit of indication. J. Math. Sci., 2013c, vol. 193, no. 5, pp. 671–686.

    Article  Google Scholar 

  38. Logofet, D.O. and Belova, I.N., Nonnegative matrices as a tool to model population dynamics: classical models and contemporary expansions, J. Math. Sci., 2008, vol. 155, no. 6, pp. 894–907.

    Article  Google Scholar 

  39. Logofet D.O., Ulanova, N.G., and Belova, I.N., Adaptation on the ground and beneath: does the local population maximize its λ1? Ecol. Complexity, 2014, vol. 20, pp. 176–184.

    Article  Google Scholar 

  40. Logofet, D.O., Ulanova, N.G., and Belova, I.N., Polyvariant ontogeny in woodreeds: novel models and new discoveries, Biol. Bull. Rev., 2016, vol. 6, no. 5, pp. 365–385.

    Article  Google Scholar 

  41. Logofet D.O., Ulanova, N.G., and Belova, I.N., From uncertainty to an exact number: developing a method to estimate the fitness of a clonal species with polyvariant ontogeny, Biol. Bull. Rev., 2017a, vol. 7, no. 5, pp. 387–402.

    Article  Google Scholar 

  42. Logofet, D.O., Belova, I.N., Kazantseva, E.S., and Onipchenko, V.G., Local population of Eritrichium caucasicum as an object of mathematical modeling. I. Life cycle graph and a nonautonomous matrix model, Biol. Bull. Rev., 2017b, vol. 7, no. 5, pp. 415–427.

    Article  Google Scholar 

  43. Logofet, D.O., Kazantseva, E.S., Belova, I.N., and Onipchenko, V.G., Local population of Eritrichium caucasicum as an object of mathematical modeling. II. How short does the short-lived perennial live?, Biol. Bull. Rev., 2018, vol. 8, no. 3, pp. 193–202.

    Article  Google Scholar 

  44. Markov, M.V., Populyatsionnaya biologiya rastenii (Population Biology of Plants), Moscow: KMK, 2012.

    Google Scholar 

  45. Mirkin, B.V. and Naumova, L.G., Nauka o rastitel’nosti (istoriya i sovremennoye sostoyaniye osnovnykh kontseptsiy) (The Science on Vegetation: History and Current State of the Basic Concepts), Ufa: Gilem, 1998.

    Google Scholar 

  46. Molisch, H., The Longevity of Plants (Die Lebensdauer der Pflanze), New York: E.H. Fulling, 1938.

    Google Scholar 

  47. Nakhutsrishvili, G.S. and Gamtsemlidze, Z.G., Zhizn’ rastenii v extremal’nykh usloviyakh vysokogorii: na primere Tsentral’nogo Kavkasa (Plant Life in Extreme High-Altitude Conditions by Example of the Central Caucasus), Leningrad: Nauka, 1984.

    Google Scholar 

  48. Onipchenko, V.G., Alpine Vegetation of the Teberda Nature Reserve, the Northwest Caucasus (Veröffentlichungen des Geobotanischen Institutes der Eidgenössische Technische Hochschule), Zurich: Stiftung Rübel, 2002, no. 130.

  49. Onipchenko, V.G., Funktsional’naya fitotsenologiya: sinekologiya rasteniy (Functional Phytocenology: Synecology of the Plants), Moscow: Krasand, 2013.

    Google Scholar 

  50. Onipchenko, V.G. and Komarov, A.S., Population dynamics and life history features of three alpine plant species in the Northwest Caucasus, Zh. Obshch. Biol., 1997, vol. 58, no. 6, pp. 64–75.

    Google Scholar 

  51. Onipchenko, V.G., Zernov, A.S., and Vorob’eva, F.M, Vascular plants of the Teberda Nature Reserve: annotated list of species, in Flora i fauna zapovednikov (Flora and Fauna of Nature Reserves), Moscow: Inst. Probl. Ekol. Evol., Ross. Akad. Nauk, 2011, no. 99A.

  52. Pavlov, V.N. and Onipchenko, V.G., High altitude vegetation, Itogi Nauki Tekh., Ser.: Bot., 1987, vol. 7, pp. 3–38.

    Google Scholar 

  53. Pierce, S., Negreiros, D., Cerabolini, B.E.L., et al., A global view and measurement of plant ecological strategies from leaf economics and size traits, Funct. Ecol., 2017, vol. 31, no. 2, pp. 444–457.

    Article  Google Scholar 

  54. Polevaya geobotanika (Field Geobotany), Lavrenko, E.M. and Korchagin, A.A., Eds., Moscow: Akad. Nauk SSSR, 1960, vol. 2.

  55. Polivariantnost’ razvitiya organizmov, populyatsii i soobshchestv (Polyvariant Development of Organisms, Populations, and Communities), Yoshkar-Ola: Mariisk. Gos. Univ., 2006.

  56. Popova, A.S., Biology of short-lived alpine plants (exemplified with the Teberda Nature Reserve), MSc Dissertation, Pushchino, 2010.

  57. Populyatsionnaya ekologiya i introduktsiya rastenii (Population Ecology and Introduction of the Plants), Semkina, L.A. and Mamaeva, S.A., Eds., Yekaterinburg: Ural. Fil., Ross. Akad. Nauk, 2003, no. 2.

  58. Rabotnov, T.A., Duration of the virgin period in the life span of herbaceous perennials in natural conenoses, Byull. Mosk. O-va. Ispyt. Prir., Otd. Biol., 1946, vol. 51, no. 2, pp. 41–48.

    Google Scholar 

  59. Rabotnov, T.A., The life cycle of perennial herbaceous plants and their population structures, Nauchno-Metod. Zap. Glav. Uprav. Zapoved. RSFSR, 1949, no. 12, pp. 91–98.

  60. Rabotnov, T.A., Life cycle of perennial herbaceous plants in meadow phytocenosises, Tr. Bot. Inst., Akad. Nauk SSSR, Ser. 3. Geobot., 1950a, no. 6, pp. 7–204.

  61. Rabotnov, T.A., The phytocenological analysis of the population structure, Probl. Bot., 1950b, no. 1, pp. 465–483.

  62. Salguero-Gómez, R., Jones, O.R., Archer, C.A., et al., The COMPADRE plant matrix database: an online repository for plant population dynamics, J. Ecol., 2015, vol. 103, pp. 202–218.

    Article  Google Scholar 

  63. Semenova, G.V. and Onipchenko, V.G., Soil seed bank of an alpine lichen heath in the Northwestern Caucasus: species richness, Oecol. Mon., 1996, vol. 5, no. 2, pp. 83–86.

    Google Scholar 

  64. Shetekauri, Sh., Spatial distribution characteristics of glacial relief flora in the high mountains of the Caucasus, Feddes Repertorium, 1998, vol. 109, pp. 465–472.

    Article  Google Scholar 

  65. Shidakov, I.I. and Onipchenko, V.G., Comparative analysis of alpine plant leaf traits in the Teberda Nature Reserve, Byull. Mosk. O-va Ispyt. Prir., Otd. Biol., 2007, vol. 112, no. 4, pp. 42–50.

    Google Scholar 

  66. Shishkin, B.K. and Bobrov, E.G., Androsace genus, in Flora SSSR (Flora in the USSR), Shishkin, B.K. and Bobrov, E.G., Eds., Moscow: Akad. Nauk SSSR, 1952, vol. 18, pp. 221–243.

    Google Scholar 

  67. Shkhagapsoev, S.Kh., Morfostruktura podzemnykh organov rastenii pervichnoobnazhennykh sklonov Kabardino-Balkarii (Morphological Structure of the Underground Organs of Plants on the Primary Slopes of Kabardino-Balkaria), Nalchik: Kabardino-Balkar. Gos. Univ., 1999.

  68. Sizov, I.E., Onipchenko, V.G., and Komarov, A.S., Life span indirect evaluation of three alpine perennial plants, Oecol. Mo., 1999, vol. 8, nos. 1–2, pp. 21–26.

  69. Sovremennye podkhody k opisaniyu struktury rasteniya (Modern Approaches to Description of the Plant Structures), Savinykh, N.P. and Bobrovykh, Yu.A., Eds., Kirov: Loban’, 2008.

    Google Scholar 

  70. Tsenopopulyatsii rastenii: osnovnye ponyatiya i struktura (Plant Cenopopulations: General Terms and Structure), Uranov, A.A. and Serebryakova, T.I., Eds., Moscow: Nauka, 1976.

    Google Scholar 

  71. Uranov, A.A., Age spectrum of phytocoenopopulations as a function of time and energetic wave processes, Biol. Nauki, 1975, no. 2, pp. 7–34.

  72. Vorob’eva, F.M. and Onipchenko, V.G., Vascular plants of Teberda Nature Reserve, in Flora i fauna zapovednikov (Flora and Fauna of Nature Reserves), Gubanov, I.A., Ed., Tula: Grif i K, 2001, no. 99, pp. 1–100.

  73. Witte de, L.C. and Stöcklin, J., Longevity of clonal plants: why it matters and how to measure it, Ann. Bot., 2010, vol. 106, pp. 859–870.

  74. Zernov, A.S., Flora Severo-Zapadnogo Kavkaza (Flora of the Northwest Caucasus), Moscow: KMK, 2006.

    Google Scholar 

  75. Zernov, A.S., Opredelitel’ sosudistykh rastenii Karachaevo-Cherkesskoi Respubliki (Guide for Identification of Vascular Plants of the Karachay-Cherkessia Republic), Moscow: KMK, 2015.

    Google Scholar 

  76. Zhmylev, P.Yu., Alekseev, Yu.E., Karpukhina, E.A., and Balandin, S.A., Biomorfologiya rastenii: illustrirovannyi slovar’ (Plant Biomorphology: Illustrated Dictionary), Tula: Grif i K, 2005, 2nd ed.

    Google Scholar 

  77. Zhukova, L.A., Polyvariance of the meadow plants, in Zhiznennye formy v ekologii i sistematike rastenii (Life Forms in Ecology and Plant Systematics), Moscow: Mosk. Gos. Pedagog. Inst., 1986, pp. 104–114.

    Google Scholar 

  78. Zhukova, L.A., Populyatsionnaya zhizn’ lugovykh rastenii (Population Life of Meadow Plants), Yoshkar-Ola: Lanar, 1995.

    Google Scholar 

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ACKNOWLEDGMENTS

This study was supported in the field data mining part by the Russian Foundation for Basic Research, project no. 14-04-00214; in the modeling part by project nos. 13-04-01836 and 16-04-00832. Data processing and writing texts with the support by the Russian Science Foundation, project no. 14-50-00029.

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  1. Laboratory of Mathematical Ecology, Institute of Atmospheric Physics, Russian Academy of Sciences, 119017, Moscow, Russia

    D. O. Logofet & I. N. Belova

  2. Biological Department, Moscow State University, 119234, Moscow, Russia

    E. S. Kazantseva & V. G. Onipchenko

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Logofet, D.O., Kazantseva, E.S., Belova, I.N. et al. How Long Does a Short-Lived Perennial Live? A Modeling Approach. Biol Bull Rev 8, 406–420 (2018). https://doi.org/10.1134/S2079086418050043

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