Modelling of Beetroot Seedlings with Modified Generalized Logistic Functions

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Abstract

Modified generalized logistic functions (also known as Koya-Goshu functions) were used for mathematical description of germination. These functions constitute natural modification of traditionally used Richards' function for description of plants germination that introduces a non-linear time increase in exponent and an element related to time shift. Curves were adjusted to experimental data based on minimization of the square sum of difference between experimental data and a mathematical model (the smallest squares method). Results of simulation research show that the determined parameters of curves (e.g., values of the growth parameter, time shift or upper limit of population) describing the number of seedlings as a time function stay compliant to interpretation with regard to biology of the investigated processes. Based on the research, it was stated that for control and application of plant extracts to soil, Koyu-Gosha model has better adjustment to experimental data in comparison to the generalized logistic model.

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  • Adaszyńska M. Swarcewicz M. Markowska-Szczupak A. (2013). Comparison of chemical composition and antimicrobial activity of lavender varieties from Poland. Postępy Fitoterapii2 90-96.

  • Bošković M. Baltić Ž.M. Ivanović J. Đurić J. Lončina J. Dokmanović M. Marković R. (2013). Use of essential oils in order to prevent foodborne illnesses caused by pathogens in meat. Tehnologija mesa54(1) 14-20.

  • Bozin B. Mimica-Dukic N. Simin N. Anackov G. (2006). Characterization of the volatile composition of essential oils of some Lamiaceae species and the antimicrobial and antioxidant activities of the entire oils. Journal of Agriculture and Food Chemistry54 1822-1828.

  • Brachaczek A. Kaczmarek J. Kosiada T. Jędryczka M. (2012). Występowanie suchej zgnilizny kapustnych na wybranych odmianach rzepaku ozimego i ich plon w warunkach doświadczeń łanowych w Wielkopolsce Rośliny OleisteXXXIII 56-72.

  • Bradford K.J. (1990). A water relation analysis of seed germination rates. Plant Physiologicol94 840-849.

  • Brown R.F. Mayer D.G. (1988). Representing cumulative germination. The use of the Weibull function and other empirically derived curves. Annals of Botany61 127-138.

  • Burkhart H.E. Tomé M. (2012). Modeling forest trees and stands. Springer-Verlag. London. ISBN 9789400715974.

  • Carlson T. (1913). Über geschwindigkeit und grösse der hefevermehrung in Würze. Biochemische Zeitschrift57 313-334.

  • Czerwińska E. (2015). Właściwości przeciwbakteryjne i przeciwgrzybowe wybranych roślin zielonych i ich części. Acta Scientiarum Polonorum Technica Agraria 14(1-2) 13-22.

  • Czerwińska E. Szparaga A. Deszcz E. (2015). Ocena wpływu zaprawiania wyciągami roślinnymi na zdolność kiełkowania nasion łubinu żółtego i grochu siewnego. Zeszyty Naukowe Uniwersytetu Przyrodniczego we Wrocławiu seria Rolnictwo 612 7-19.

  • Czerwińska E. Szparaga A. (2015a). Żywotność i zdrowotność nasion roślin oleistych traktowanych wyciągami roślinnymi. Acta Scientiarum Polonorum Technica Agraria14(12) 47-60.

  • Czerwińska E. Szparaga A. Deszcz E. (2015b). Ocena wpływu zaprawiania wyciągami roślinnymi na zdolność kiełkowania nasion buraków. Zeszyty Naukowe Uniwersytetu Przyrodniczego we WrocławiuRolnictwo CXII 7-20.

  • Czerwińska E. Szparaga A. Piskier T. Deszcz E. (2016). Effect of the application methods of natural plant extract on emergence of beets. Journal of Research and Applications in Agricultural Engineering61(3) 67-71.

  • Eberhardt L.L. and Breiwick J.M. (2012). Models for Population Growth Curves. ISRN Ecology2012 1-5.

  • France J. Thornley J. H. M. (1984). Mathematical Models in Agriculture. Butterworths CAB International London. ISBN 0408108681.

  • Hageseth G.T. Joyner R.D. (1975). Kinetics and thermodynamics of isothermal seed germination. Journal of. Theoretical Biology 53 51-65.

  • Hsu F.H. Nelson C.J. Chow W.S. (1984). A mathematical model to utilize the logistic function in germination and seedling growth. Journal of Experimental Botany35 1629-1640.

  • Ito T. Osumi S. (1984). An analysis of the basal area growth in even-aged pure stands based on the Richards growth function. Journal of the Japanese Society for Horticultural66(3) 99-108.

  • Koya P.R. Goshu A.T. (2013). Generalized Mathematical Model for Biological Growths. Open Journal of Modelling and Simulation1 42-53.

  • Krebs C.J. (1985). The Experimental Analysis of Distribution and Abundance. Harper and Row. New York. ISBN 0065004108.

  • Morgan B.J.T. (1976). Stochastic models of groupings changes Advances in Applied Probability8 30.

  • Mrówczyński M. Korbas M. Praczyk T. Gwiazdowski R. Jajor E. Pruszyński G. Wachowiak H. (2009). Ochrona roślin w integrowanej produkcji rzepaku. Rośliny Oleiste XXX 245-256.

  • Muszyński S. Świetlicka I. Świetlick i M. Gładyszewska B. (2015). Modelowanie kinetyki kiełkowania nasion pomidora z wykorzystaniem równania Gompertza. Acta Scientiarum Polonorum Technica Agraria14(1-2) 61-69.

  • O’Neill M.E. Thomson P.C. Jacobs B.C. Brain P. Butler R.C. Turner H. Mitakda B. (2004). Fitting and comparing seed germination models with a focus on the inverse normal distribution Austral. Journal Statistics46 349-366.

  • Odabas M.S. Mut Z. (2007). Modeling the effect of temperature on percentage and duration of seed germination grain legumes and cereals. American Journal of Physiology2 303-310.

  • Orzeszko-Rywka A. Rochalska M. (2007). Preliminary assessment of efficiency of some ecological methods of sugar beet seed dressing. Journal of Research and Applications in Agricultural Engineering52(4) 10-13.

  • Richards F.J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany10 290-300.

  • Rochalska M. i Orzeszko-Rywka A. (2009). Zastosowanie naturalnych substancji roślinnych jako zapraw nasiennych dla upraw ekologicznych. Journal of Research and Applications in Agricultural Engineering54(4) 74-80.

  • Rochalska M. Orzeszko-Rywka A. Tracz M. (2010). Estimation efficiency of powdered herbs of crop seeds treatment. Journal of Research and Applications in Agricultural Engineering55(4) 67-72.

  • Shafii B. Price W.J. (2001). Estimation of cardinal temperatures in germination data analysis. Journal of Agricultural Biological and Environmental Statistics 6 356-366.

  • Shafii B. Price W.J. Swensen J.B. Murray G.A. (1991). Nonlinear estimation of growth curve models for germination data analysis. The Third Conference On Applied Statistics In Agriculture. Kansas State University. Manhattan. KS 19-42.

  • Tsoularis A. Wallace J. (2002). Analysis of logistic growth models. Mathematical Biosciences179 21-55.

  • Tyszyńska-Kownacka D. Starek T. (1989). Zioła w polskim domu. Wydawnictwo Warta. Warszawa. ISBN 8322502303.

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