Abstract
Near-natural multilayered Abies alba Mill.–Fagus sylvatica L. forests form structural mosaics and consist of patches in different developmental stages and phases. Knowledge of the diversity of patch structure and adequate methods to describe the diameter structure is essential for modeling forest dynamics. The hypotheses tested in the study are that near-natural multilayered stands are structurally heterogeneous (i.e., tree diameter (DBH) distributions of these stands are heterogeneous) and, that in these forests the finite-mixture models are suitable for modeling the empirical DBH distributions. Diversity of patch structure was studied based on data collected from 33 sample plots. In multilayered stands, four groups of empirical DBH distributions were distinguished using hierarchical cluster analysis (HCA) and correspondence analysis (CA). Stands investigated are structurally heterogeneous; 27% multilayered stands showed the slightly rotated sigmoid (SRS) type of empirical DBH distribution, 34% the distinctly rotated sigmoid (DRS) type, 18% the bimodal M-shaped (BMS) type, and 21% the unimodal highly skewed (UHS) type. The gamma distribution, the two-component mixture gamma model, and the two-component mixture Weibull model were more flexible for the SRS type of DBH distributions. The average p-values (Chi-square test) for these theoretical distributions were 0.4712, 0.4718, and 0.4660, respectively. The two-component mixture gamma model and the two-component mixture Weibull model were a good choice for modeling the DRS, BMS, and UHS types of DBH distributions. The average p-values (Chi-square test) for these models ranged from 0.2684 to 0.4854. In near-natural multilayered Abies–Fagus forest patches of different DBH distributions occur together. The empirical DBH distributions in these stands are characterized by irregular and complicated shapes and therefore are best approximated by finite-mixture models.
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References
Anonymous (1998) World reference base for soil resources. 84 World soil resources reports. FAO, Rome
Backhaus K, Erichson B, Pinke W, Weiber R (2000) Multivariate Analysemethoden. Eine anwendungsorientierte Einführung. Springer, Berlin
Bailey RL, Dell TR (1973) Quantifying diameter distributions with the Weibull function. For Sci 19:97–104
Boyden S, Binkley D, Shepperd W (2005) Spatial and temporal patterns in structure, regeneration, and mortality of an old-growth ponderosa pine forest in the Colorado Front Range. For Ecol Manage 219:43–55
Ciołkosz A (1991) SINUS—System Informacji o Środowisku Przyrodniczym. In: Mazur S (ed) Ekologiczne Podstawy Gospodarowania Środowiskiem Przyrodniczym. Wizje—problemy—trudności. Wyd. SGGW-AR, Warszawa, pp 317–328
Cochran WG (1977) Sampling techniques. Wiley, New York
Coomes DA, Allen RB (2007) Mortality and tree-size distributions in natural mixed-age forests. J Ecol 95:27–40
Daniel TW, Helms JA, Baker FR (1979) Principles of silviculture. McGraw-Hill Publishing Company, New York
de Liocourt F (1898) De l’amenagement des Sapiniers. Bul Soc For Franche-Compté et Belfort 4:396–409
Dolezal J, Song J-S, Altman J, Janecek S, Cerny T, Srutek M, Kolbek J (2009) Tree growth and competition in a post-logging Quercus mongolica forest on Mt. Sobaek, South Korea. Ecol Res 24:281–290
Druckenbrod DL, Shugart HH, Davies I (2005) Spatial pattern and process in forest stands within the Virginia piedmont. J Veg Sci 16:37–48
Emborg J, Christensen M, Heilmann-Clausen J (2000) The structural dynamics of Suserup Skov, a near-natural temperate deciduous forest in Denmark. For Ecol Manage 126:173–189
Feeley KJ, Davies SJ, Noor MNS, Kassim AR, Tan S (2007) Do current stem size distributions predict future population changes? An empirical test of intraspecific patterns in tropical trees at two spatial scales. J Trop Ecol 23:191–198
Gądek K (2000) Lasy. In: Cieśliński S, Kowalkowski A (eds) Świętokrzyski Park Narodowy. Przyroda, Gospodarka, Kultura, Świętokrzyski Park Narodowy, Bodzentyn, pp 349–378
Goelz JCG, Leduc DJ (2002) A model describing growth and development of longleaf pine plantations: consequences of observed stand structures of structure of the model. Gen Tech Rep SRS-48. U.S. Department of Agriculture, Forest Service, Southern Research Station, Asheville
Goff FG, West D (1975) Canopy-understory interaction effects on forest population structure. For Sci 21:98–108
Goodburn JM, Lorimer CG (1999) Population structure in old-growth and managed northern hardwoods: an examination of the balanced diameter distribution concept. For Ecol Manage 118:11–29
Hao Z, Zhang J, Song B, Ye J, Li B (2007) Vertical structure and spatial associations of dominant tree species in an old-growth temperate forest. For Ecol Manage 252:1–11
Haughton D (1997) Packages for estimating finite mixtures: a review. Am Stat 51:194–205
Hubbell SP, Ahumada JA, Condit R, Foster RB (2001) Local neighborhood effects on long-term survival of individual trees in a neotropical forest. Ecol Res 16:859–875
Inoue S, Shirota T, Mitsuda Y, Ishii H, Gyokusen K (2008) Effects of individual size, local competition and canopy closure on the stem volume growth in a monoclonal Japanese cedar (Cryptomeria japonica D. Don) plantation. Ecol Res 23:953–964
Jaworski A (1995) Charakterystyka hodowlana drzew leśnych. Gutenberg, Kraków
Jaworski A, Podlaski R, Waga T (1999) Budowa i struktura drzewostanów o charakterze pierwotnym w rezerwacie Święty Krzyż (Świętokrzyski Park Narodowy). Acta Agr Silv Ser Silv 37:27–51
Kato J, Hayashi I (2007) Quantitative analysis of a stand of Pinus densiflora undergoing succession to Quercus mongolica ssp crispula. II. Growth and population dynamics of Q. mongolica ssp. crispula under the P. densiflora canopy. Ecol Res 22:527–533
Korpeľ Š (1982) Degree of equilibrium and dynamical changes of the forest on example of natural forests of Slovakia. Acta Fac For Zvolen 24:9–30
Korpeľ Š (1995) Die Urwälder der Westkarpaten. G Fischer-Verlag, Stuttgart
Kubota Y (1997) Demographic traits of understory trees and population dynamics of a Picea–Abies forest in Taisetsuzan National Park, northern Japan. Ecol Res 12:1–9
Leak WB (2002) Origin of sigmoid diameter distributions. U.S. Department of Agriculture, Forest Service, Northeastern Research Station, Res. Pap. NE-718. Newtown Square
Leibundgut H (1956) Empfehlungen für die Baumklassenbildung und Methodik bei Versuchen über die Wirkung von Waldpflegemaßnahmen. IUFRO Sektion 23, 10. Mitteilungen
Leibundgut H (1993) Europäische Urwälder. Wegweiser zur Naturnahen Waldwirtschaft. Verlag Paul Haupt, Bern
Liu C, Zhang L, Davis CJ, Solomon DS, Grove JH (2002) A finite mixture model for characterizing the diameter distribution of mixed-species forest stands. For Sci 48:653–661
Macdonald PDM with contributions from Du J (2004) mixdist: mixture distribution models. R package version 0.5-1. http://www.r-project.org, http://www.math.mcmaster.ca/peter/mix/mix.html
Macdonald PDM, Pitcher TJ (1979) Age-groups from size-frequency data: a versatile and efficient method of analyzing distribution mixtures. J Fish Res Board Can 36:987–1001
Maltamo M, Kangas A (1998) Methods based on k-nearest neighbor regression in estimation of basal area diameter distribution. Can J For Res 28:1107–1115
Maltamo M, Kangas A, Uuttera J, Torniainen T, Saramaki J (2000) Comparison of percentile based prediction methods and the Weibull distribution in describing the diameter distribution of heterogeneous Scots pine stands. For Ecol Manage 133:263–274
Manabe T, Nishimura N, Miura M, Yamamoto S (2000) Population structure and spatial patterns for trees in a temperate old-growth evergreen broad-leaved forest in Japan. Plant Ecol 151:181–197
Matuszkiewicz JM (2008) Zespoły leśne Polski. PWN, Warszawa
Nakashizuka T (2001) Species coexistence in temperate, mixed deciduous forests. Trends Ecol Evol 16:205–210
Nord-Larsen T, Cao QV (2006) A diameter distribution model for even-aged beech in Denmark. For Ecol Manage 231:218–225
Pacala S, Canham C, Saponara J, Silander J, Kobe R, Ribbens E (1996) Forest models defined by field measurements. II. Estimation, error analysis and dynamics. Ecol Monogr 66:1–44
Paluch JG (2007) The spatial pattern of a natural European beech (Fagus sylvatica L.)—silver fir (Abies alba Mill.) forest: a patch-mosaic perspective. For Ecol Manage 253:161–170
Parker GR, Leopold DJ, Eichenberger JK (1985) Tree dynamics in an old growth deciduous forest. For Ecol Manage 11:31–57
Pederson N, Varner JM III, Palik BJ (2008) Canopy disturbance and tree recruitment over two centuries in a managed longleaf pine landscape. For Ecol Manage 254:85–95
Piovesan G, Di Filippo A, Alessandrini A, Biondi F, Schirone B (2005) Structure, dynamics and dendroecology of an old-growth Fagus forest in the Apennines. J Veg Sci 16:13–28
Podlaski R (2005) Inventory of the degree of tree defoliation in small areas. For Ecol Manage 215:361–377
Podlaski R (2007) Accuracy assessment of a small-area method for estimating the spatial distribution of the degree of tree damage. Environ Monit Assess 135:339–351
Podlaski R (2008a) Characterization of diameter distribution data in near-natural forests using the Birnbaum–Saunders distribution. Can J For Res 38:518–527
Podlaski R (2008b) Dynamics in Central European near-natural Abies–Fagus forests: does the mosaic-cycle approach provide an appropriate model? J Veg Sci 19:173–182
Podlaski R, Zasada M (2008) Comparison of selected statistical distributions for modelling the diameter distributions in near-natural Abies–Fagus forests in the Świętokrzyski National Park (Poland). Eur J For Res 127:455–463
Pretzsch H (2001) Models for pure and mixed forests. In: Evans J (ed) The forests handbook. Blackwell Science, London, pp 210–228
R Development Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, AT. ISBN 3-900051-07-0. http://www.R-project.org
Rubin BD, Manion PD, Faber-Langendoen D (2006) Diameter distributions and structural sustainability forests. For Ecol Manage 222:427–438
Runkle JR (1985) Disturbance regimes in temperate forests. In: Pickett STA, White P (eds) The ecology of natural disturbance and patch dynamics. Academic Press, Orlando, pp 17–33
Shimatani K, Satoko Kawarasaki S, Manabe T (2008) Describing size-related mortality and size distribution by nonparametric estimation and model selection using the Akaike Bayesian Information Criterion. Ecol Res 23:289–297
Shorohova E, Kuuluvainen T, Kangur A, Jõgiste K (2009) Natural stand structures, disturbance regimes and successional dynamics in the Eurasian boreal forests: a review with special reference to Russian studies. Ann For Sci 66:201
Sierpiński Z (1977) Przyczyny zamierania jodły w Górach Świętokrzyskich. Sylwan 121(11):29–41
Splechtna BE, Gratzer G (2005) Natural disturbances in Central European forests: approaches and preliminary results from Rothwald, Austria. For Snow Landsc Res 79:57–67
Stephens SL, Gill SJ (2005) Forest structure and mortality in an old-growth Jeffrey pine-mixed conifer forest in north-western Mexico. For Ecol Manage 205:15–18
von Oheimb G, Westphal C, Tempel N, Härdtle W (2005) Structural pattern of a near-natural beech forest (Fagus sylvatica) (Serrahn, north-east Germany). For Ecol Manage 212:253–263
Wang X, Hao Z, Zhang J, Lian J, Li B, Ye J, Yao X (2009) Tree size distributions in an old-growth temperate forest. Oikos 118:25–36
Watt AS (1947) Pattern and process in the plant community. J Ecol 35:1–22
Weber P, Rigling A, Bugmann H (2007) Radial growth responses to drought of Pinus sylvestris and Quercus pubescens in an inner-Alpine dry valley. J Veg Sci 18:777–792
Weber P, Bugmann H, Fonti P, Rigling A (2008) Using a retrospective dynamic competition index to reconstruct forest succession. For Ecol Manage 254:96–106
West DC, Shugart HH, Ranney RW (1981) Population structure of forests over a large area. For Sci 27:701–710
Westphal C, Tremer N, von Oheimb G, Hansen J, von Gadow K, Härdtle W (2006) Is the reverse J-shaped diameter distribution universally applicable in European virgin beech forests? For Ecol Manage 223:75–83
Wolfram S (2003) The Mathematica book. Wolfram Media/Cambridge University Press, Cambridge
Zasada M, Cieszewski CJ (2005) A finite mixture distribution approach for characterizing tree diameter distributions by natural social class in pure even-aged Scots pine stands in Poland. For Ecol Manage 204:145–158
Zhang LJ, Liu C (2001) Use of a finite mixture model in describing irregular diameter distributions of forest stands. In: Proceedings of IUFRO conference on forest modelling for ecosystem management, forest certification, and sustainable management. Faculty of Forestry, University of British Columbia, Vancouver
Zhang LJ, Gove JH, Liu C, Leak WB (2001) A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands. Can J For Res 31:1654–1659
Zieliński R (1972) Tablice statystyczne. PWN, Warszawa
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I thank Dr. A. Lang for his English grammatical improvements in my manuscript. I also thank the editor and two anonymous reviewers for constructive comments, suggestions, and corrections.
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Podlaski, R. Diversity of patch structure in Central European forests: are tree diameter distributions in near-natural multilayered Abies–Fagus stands heterogeneous?. Ecol Res 25, 599–608 (2010). https://doi.org/10.1007/s11284-010-0690-6
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DOI: https://doi.org/10.1007/s11284-010-0690-6