الگوی توزیع زادآوری درختان براساس نظریه فرکتال در جنگل‌های گهواره، استان کرمانشاه

1.Alados, C.L., Pueyo, Y., Navas, D., Cabezudo, B., Gonzalez, A., and Freeman, D.C. 2005. Fractal analysis of plant spatial patterns: a monitoring tool for vegetation transition shifts. Biodiversity and Conservation. 14: 1453-1468.

2.Alijanpour, A., Banj Shafiei, A., and Eshaghi Rad, J. 2010. Investigation of natural regeneration characteristics in west oak forests within different levels of site factors (case study: Piranshahr region). Iranian J. of Forest. 2: 3. 209-219.(In Persian)

3.Andronache, I., Marin, M., fischer, R., Ahammer, H., Radulovic, M., ciobotaru, A.M., Jelinek, H.F., Di Ieva, A., Pintilii, R.D., Drăghici, C.C., Herman, G.V., Nicula, A.S., Simion, A.G., Loghin, V., Diaconu, D.C., and Peptenatu, D. 2019. Dynamics of forest fragmentation and connectivity Using particle and fractal Analysis. Scientific Reports. https://doi.org/ 10.1038/s41598-019-48277-z.

4.Boyden, S., Binkley, D., and Shepperd, W. 2005. Spatial and temporal patterns in structure, regeneration, and mortality of an old-growth ponderosa pine forest in the Colorado Front Range. Forest Ecology and Management. 219: 43-55.

5.Burrough, P.A. 1983. Multiscale sources of spatial variation in soil. 1. The application of fractal concepts to nested levels of soil variation. J. of Soil Science. 34: 577-597.

6.Despland, E. 2003. Fractal index captures the role of vegetation clumping in
locust swarming. Functional Ecology. 17: 315-322.

7.Dormann, C.F., McPherson, J.M., Arau, M.B., Bivand, R., Bolliger, J., Carl, G., Davies, R.G., Hirzel, A., Jetz, W., Kissling, D.W., Kuhn, L., Ohlemuller, R., Peres-Neto, P.R., Reineking, B., Schroder, B., Schurr F.M., and Wilson, R.. 2007. Methods to account for spatial autocorrelation in the nalysis of species distributional data: a review. Ecography. 30: 609-628.

8.Darabi, S., Kooch, Y., and Hosseini, M. 2014. Reaction and fractal description of soil bio-indicator to human disturbance in lowland forests of Iran. Biodiversitas. 1: 60-66.

9.Gholami, Sh., and Sayad, E. 2015. Fractal descriptive of tree canopy and soil bulk density in Zagros forests, case study: Bisotun Protected Area. Applied Ecology. 4: 12. 77-85. (In Persian)

10.Graz, P.F. 2004. The behavior of the species mingling index Msp in relation to species dominance and dispersion. European J. of Forest Research. 123: 87-92.

11.Godin, C. 2000. Representing and encoding plant architecture: a review. Annals of Forest Science.57: 05. 413-438.

12.Guzman, J.A., Sharp, L., Felipe, A., and Sanchez-Azofelifa, GA. 2020. On the relationship of fractal geometry and tree–stand metrics on point clouds derived from terrestrial laser scanning. Methods in Ecology and Evolution. 11(10): 1309-1318. https://doi.org/ 10.1111/2041-210X.1343.

13.Halley, J.M., Hartley, S., Kallimanis, A.S., Kunin, W.E., Lennon J.J., and Sgardelis, S.P. 2004. Uses and abuses of fractal methodology in ecology. Ecology Letters. 7: 254-271.

14.Henareh Khalyani, A., and Mayer, A.L. 2013. Spatial and temporal deforestation dynamics of Zagros forests (Iran) from 1972 to 2009. Landscape and Urban Planning. 117: 1-12.

15.Hosseini, A., and Hoseinzadeh, J. 2019. Investigation on regeneration behavior of Pistacia atlantica and Acer cineracens species to recognize their natural establishment pattern in Zagros forests. J. of Applied Biology. 31: 3. 41-54.

16.Imre, A.R., and Bogaert, J. 2003. The fractal dimension as a measure of the quality of habitats. Acta Boitheoretica. 52: 41-56.

17.Jayakumar, R., and Nair, K.N. 2013. Species diversity and tree regeneration patterns in tropical forests of the Western Ghats, India. International scholarly research notices, vol. 2013, 14p. https://doi.org/10.1155/2013/890862.

18.Jonckheere, I., Nackaerts, K., Muys, B., Van Aardt, J., and Coppin, P. 2006. A fractal dimension-based modeling approach for studying the effect of leaf distribution on LAI retrieval in forest canopies. Ecological Modelling. 197: 179-195.

19.Karam, A. 2010. Chaos theory, fractal & non-linear system in geomorphology.J. of Physical Geography. 3: 8. 67-82. (In Persian)

20.Kent, M., Moyeed, R.A., Reid, C.L., Pakeman, R., and Weaver, R. 2006. Geostatistics, spatial rate of change analysis, and boundary detection in plant ecology and biogeography. J. of Physical Geography. 30: 2. 201-213.

21.Kint, V., Lust, N., Ferris, R., and Olsthoorn, A.F.M. 2000. Quantification of forest stand structure applied to Scots Pine (Pinus Sylvestris L.) Forests. Investigación Agraria: Sistemasy Recursos Forestales. 1: 147-163.

22.Kubota, Y. 2006. Spatial pattern and regeneration dynamics in a temperate Abies–Tsuga forest in southwestern Japan. Forest Research. 11: 191-201.

23.Leibhold, A.M., and Gurevitch, J.2002. Integrating the statistical analysis of spatial data in ecology. Ecography. 25: 553-557.

24.Li, B.L. 2000. Fractal geometry applications in the description and analysis of patch patterns and patch dynamics. Ecological Modelling. 132: 33-50.

25.Li, B.L. 2002. Fractal dimensions. Encyclopedia of Environmetrics.2: 821-825.

26.Loehle, C., and Li, B.L. 1996.Statistical properties of ecological and geologic fractals. Ecological Modelling. 85: 271-284.

27.Long, C., Zhao, Y., and Jafari, H. 2014. Mathematical models arising in the fractal forest gap via local fractional calculus. Abstract and Applied Analysis, vol. 2014, Article ID 782393, 6p.

28.Mandelbrot, B. 1983. The Fractal Geometry of Nature. W. H. Freeman and Co. San Francisco, 468p.

29.Maestre, F.T., Rodriguez, F., Bautista, S., Cortina, J., and Bellot, J. 2005. Spatial associations and patterns of perennial vegetation in a semi-arid steppe: a multivariate geostatistics approach. Plant Ecology. 179: 133-147.

30.Mohammadi, J. 1999. Study of the spatial variability of soil salinity in Ramhormoz area (Khuzestan) using geostatistical theory 1. Kriging. J.of Water and Soil Sciences. 2: 4. 49-64. (In Persian)

31.Mohammadi, J., and Raeisi Gahrooee, F. 2004. Fractal description of the impact of long-term grazing exclusion on spatial variability of some soil chemical properties. J. of Water and Soil Sciences, 7: 4. 25-37. (In Persian)

32.Mohammadi, J. 2006. Pedometrics: Spatial statistics, geostatistics. Pelk Press. 453p. (In Persian)

33.Mohammadi, J. 2007. Pedometrics: temporal statistics. Pelk Press. 450p.(In Persian)

34.Namiranian, M., Henareh Khalyani, A., Zahedi Amiri, Gh., and Ghazanfari, H. 2007. Study of different restoration and regeneration techniques in northern Zagros (Case study: Armardeh oak forest, Baneh). Iranian J. of Forest and Poplar Researches. 15: 4. 386-397.

35.Ngo Bieng, M.A., Perot, T., de Coligny, F., and Goreaud, F. 2013. Spatial pattern of trees influences species productivity in a mature oak-pine mixed forest. European J. of Forest Research.132: 841-850.

36.Palmer, M.W. 1988. Fractal geometry:a tool for describing spatial patterns of plant communities. Vegetation.75: 91-102.

37.Risch, A.C., Heiri, C., and Bugmann, H. 2005. Simulating structural forest patterns with a forest gap model: a model evaluation. Ecological modeling. 181: 2-3. 161-172.

38.Soleymani, S., Dargahi, D., Pourhashemi, M., Amiri, F., and Noori, N. 2012. Investigation on regeneration in different Oak (Quercus brantiiand Q. infectoria) forest types and appropriates strategy for their rehabilitation, at Salas Babajani forest, Kermanshah province. J. of Conservation and Utilization of Natural Resources. 1: 1. 65-77. (In Persian)

39.Sun, B., Zhou, SH., and Zhao, Q. 2003. Evaluation of spatial and temporal changes of soil quality based on geostatistical analysis in the hill region of subtropical China. Geoderma. 115: 85-99.

40.Thom, D., and Seidl, R. 2016. Natural disturbance impacts on ecosystem services and biodiversity in temperate and boreal forests. Biological Reviews. 91: 760-781.

41.Tiscar-Oliver, P.A. 2015. Patterns of shrub diversity and tree regeneration across topographic and stand-structural gradients in a Mediterranean forest. Forest Systems. 24: 1. 2171-9845.

42.Vedyushkin, M. 1994. Fractal properties of forest spatial structure. Vegetation. 113: 65-70.

43.Wiens, J.A., and Milne, B.T. 1989. Scaling of ‘landscapes’ in landscape ecology, or, landscape ecology from a beetle’s perspective. Landscape Ecology. 3: 87-96.

44.Zeid, B. 1990. Fractal geometry and forest measurements. P 260-266. In: V.J. LaBau and T. Cunia (eds). the State of the art methodology of forest inventory, US Dep. Agric. For. Serv. PNW-GTR-263.

45.Zeide, B. 1991. Fractal geometry in forestry applications. Forest Ecology and Management. 46: 179-188.

46.www.kermanshahmet.ir. Kermanshah regional meteorology office. Site visited on 5/10/2015.