Ocena zgodności rozkładów empirycznych pierśnic drzewostanów bukowych różnych klas wieku z wybranymi rozkładami teoretycznymi

• Autorzy: Jagiello R. , Beker C. , Jagodzinski A.M.

Warianty tytułu

EN

Goodness of fit evaluation of the breast height diameter distributions of beech stands differing in age with selected theoretical distributions

• Języki publikacji: PL

Abstrakty

EN

Modelling is one of the basic activities in the field of biological sciences. The main purpose of modelling is to illustrate relationships and phenomena of biological objects (and traits describing them) and present reality as close as it is possible with expected range of error. In the paper we presented results of approximation of the selected theoretical distributions, i.e. singular (normal, log−normal, gamma, two− and three−parameter Weibull, Johnsons SB) and finite mixture (normal, log−normal, gamma and Weibull) to tree diameter distributions in beech stands (Fagus sylvatica L.). The main aim of the study was to evaluate goodness of fit of selected distributions, prove legitimacy of using mixture distributions in even−aged, single−species beech stands and find the best distribution of model diameter distribution in a whole production cycle of this kind of stands. The study was conducted in 32 sample plots located in north−western Poland in stands at the age between 9 and 140. For the evaluation χ² test, a modified error index (e) and a root mean square error (RMSE) were used. We found that the RMSE and e are related in most cases with stand density. Mean values of used indicators show that finite mixture distributions are better in comparison to singular distributions. The best fitted distributions were Johnsons SB and mixture of gamma ones. Range of error index expressed with number of trees per hectare ranges 16.5−32.8% and 7.7−27.0% for this distributions, respectively. Conversely the worst results were obtained by fitting two−parameter Weibull distribution both in singular and mixture. Future diameter distribution model based on the probability distribution should be based on Johnson SB or 3−parameter Weibull distribution from singular ones or gamma from finite mixture. In case of age class apportionment unequivocal the best result were obtained with Johnson SB and partially with mixture gamma distributions.

Słowa kluczowe

PL

lesnictwo; drzewostany bukowe; klasy wieku; buk zwyczajny; Fagus sylvatica; piersnice drzew; rozklad empiryczny; rozklad teoretyczny; ocena zgodnosci

• Wydawca: -
• Czasopismo: Sylwan
• Rocznik: 2016
• Tom: 160
• Numer: 02
• Opis fizyczny: s.107-119,rys.,tab.,bibliogr.

Twórcy

autor

Jagiello R.

• Instytut Dendrologii, Polska Akademia Nauk, ul.Parkowa 5, 62-035 Kórnik

autor

Beker C.

• Katedra Urządzania Lasu, Uniwersytet Przyrodniczy w Poznaniu, ul.Wojska Polskiego 71C, 60-625 Poznań

autor

Jagodzinski A.M.

• Instytut Dendrologii, Polska Akademia Nauk, ul.Parkowa 5, 62-035 Kórnik
• Katedra Łowiectwa i Ochrony Lasu, Uniwersytet Przyrodniczy w Poznaniu, ul.Wojska Polskiego 71D, 60-625 Poznań

Bibliografia

• Bailey R. L. 1980. Individual tree growth derived from diameter distribution models. Forest Science 26 (4): 626-632.
• Bailey R. L., Dell T. R. 1973. Quantifying diameter distributions with the Weibull function. Forest Science 19 (2): 97-104.
• Barnes D. J., Chu D. 2010. Introduction to Modeling for Biosciences. Springer Science + Business Media, Dordrecht – Heidelberg – New York – London.
• Bliss C. I., Reinker K. A. 1964. A lognormal approach to diameter distributions in even-aged stands. Forest Science 10 (3): 350-360.
• Burkhart H. E., Tomé M. 2012. Diameter-distribution models for even-aged stands. W: Burkhart H. E., Tomé M. [red]. Modeling Forest Trees and Stands. Springer Science + Business Media, Dordrecht – Heidelberg – New York – London. 261-297.
• Gorgoso J. J., Rojo A., Camara-Obregon A., Dieguez-Aranda U. 2012. A comparison of estimation methods for fitting Weibull, Johnson’s SB and beta functions to Pinus pinaster, Pinus radiata and Pinus sylvestris stands in northwest Spain. Forest Systems 21 (3): 446-459.
• Hafley W. L., Schreuder H. T. 1977. Statistical distributions for fitting diameter and height data in even-aged stands. Canadian Journal of Forest Research 7 (3): 481-487.
• Jagodziński A. M., Oleksyn J. 2009. Ekologiczne konsekwencje hodowli drzew w różnym zagęszczeniu. I. Wzrost i rozwój drzewostanu. Sylwan 153 (2): 75-85.
• Jaworski A., Podlaski R. 2012. Modelling irregular and multimodal tree diameter distributions by finite mixture models: an approach to stand structure characterization. Journal of Forest Research 17 (1): 79-88.
• Jopp F., Reuter H., Breckling B. [red.]. 2011. Modelling Complex Ecological Dynamics. Springer Science + Business Media, Dordrecht – Heidelberg – New York – London.
• Kerr G. 2014. The management of silver fir forests: de Liocourt (1898) revisited. Forestry 87 (1): 29-38.
• Kilkki P., Maltamo M., Mykkänen R., Päivinen R. 1989. Use of the Weibull function in estimating the basal area dbh-distribution. Silva Fennica 23 (4): 311-318.
• Liu Ch., Zhang L., Davis C. J., Solomon D. S., Gove J. H. 2002. A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. Forest Science 48 (4): 653-661.
• Macdonald P., Du J. 2014. Finite mixture distribution models. Package ‘mixdist’ ver. 0.5-4. http://ms.mcmaster.ca/ peter/mix/mix.html
• Nelson T. C. 1964. Diameter distribution and growth of loblolly pine. Forest Science 10 (1): 105-114.
• Nord-Larsen T., Cao Q. V. 2006. A diameter distribution model for even-aged beech in Denmark. Forest Ecology and Management 231 (1-3): 218-225.
• Podlaski R. 2006. Suitability of the selected statistical distributions for fitting diameter data in distinguished development stages and phases of near-natural mixed forests in the Świętokrzyski National Park (Poland). Forest Ecology and Management 236 (2-3): 393-402.
• Podlaski R. 2010a. Diversity of patch structure in Central European forests: are tree diameter distributions in near-natural multilayered Abies-Fagus stands heterogeneous? Ecological Research 25 (3): 599-608.
• Podlaski R. 2010b. Two-component mixture models for diameter distributions in mixed-species, two-age cohort stands. Forest Science 56 (4): 379-390.
• Podlaski R., Roesch F. A. 2013. Aproksymacja rozkładów pierśnic w dwugeneracyjnych drzewostanach za pomocą rozkładów mieszanych. I. Estymacja parametrów. Sylwan 157 (8): 587-596.
• Podlaski R., Zasada M. 2008. Comparison of selected statistical distributions for modeling the diameter distributions in near-natural Abies-Fagus forests in the Świętokrzyski National Park (Poland). European Journal of Forest Research 127 (6): 455-463.
• Reynolds M. R., Burk T. E., Huang W.-Ch. 1988. Goodness-of-fit tests and model selection procedures for diameter distribution models. Forest Science 34 (2): 373-399.
• Rymer-Dudzińska T., Dudzińska M. 1999. Analiza rozkładu pierśnic w drzewostanach bukowych. Sylwan 143 (8): 5-24.
• Rymer-Dudzińska T., Dudzińska M. 2001. Rozkład pierśnic drzew w nizinnych drzewostanach bukowych. Sylwan 145 (8): 13-22.
• Shiver B. D. 1988. Sample sizes and estimation methods for the Weibull distribution for unthinned slash pine plantation diameter distributions. Forest Science 34 (3): 809-814.
• Siekierski K. 1992. Evaluation of the goodness of fit of some statistical distributions to tree diameter distributions. Annals of Warsaw Agricultural University, Forestry and Wood Technology 43: 7-14.
• Zasada M. 1995. Ocena zgodności rozkładów pierśnic w drzewostanach jodłowych z niektórymi rozkładami teoretycznymi. Sylwan 139 (12): 61-69.
• Zhang L., Gove J. H., Liu Ch., Leak W. B. 2001. A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands. Canadian Journal of Forest Research 31 (9): 1654--1659.
• Zhang L., Liu Ch. 2006. Fitting irregular diameter distributions of forest stands by Weibull, modified Weibull, and mixture Weibull models. Journal of Forest Research 11 (5): 369-372.