芦苇生长格局分形特征的初步研究

PRELIMINARY STUDY ON FRACTAL CHARACTER OF GROWTH PATTERN OF REED

应用非线性科学中的分形几何理论，以黄淮海平原封丘试区的芦苇为例，研究芦苇生长格局的分形特征。计算表明，芦苇大小分布的分形维数在0．6235—0．8761之间。统计分析表明，其分布格局可明显地分为两个时期：在芦苇生长的初期，其大小分布较为均匀（分维＞0.8），而在芦苇生长的中后期（6月底以后），大小分布差异较大（分维＜0.7）。

The researches about reed (Phragmites communis) growth were mainlyconcentrated on seasonal dynamics, investigation of large area resource, and comparison of different ecological forms of reed. The study on size distribution of reed,however, was scarcely reported. By means of fractal geometric theory of non-linear science, we studied the fractal character of growth pattern of reed, for the purpose of quantitatively exploring the mechanism of reed growth. The classical method of studying size distribution is to draw histogram and then to fit distribution curve. It is well known, however, that the obtained histogram is strongly depended on the number of class interval and its correspondent width. The determination of rational number and width of class interval is somewhat arbitrary, since it is gotten according to analyst’s experience. In general, there are a certain similarity among histograms described at different class number of class interval and width somehow. It implies that we could use the fractal geometry to analyze the relationship among them, and reach more reliable conclusion.The data we used in our analyses is from the monthly sampling in Caogang Lake (114°E, 35°N), an emergent macrophyte dominated lake in Fengqiu Experimental Area of the Huanghuaihai Plain, Henan Province, P. R.China The way to calculate fractal dimension (FD) of reed growth is box-dimension (BD) and information dimension (ID).Because the longest reed occasionally exceeds 400 cm, for the reason of convenience,we define the largest scale S=400 cm. Halving the scale S until it could recognize each individual reed (S<1 cm), the relationship betWeen different scale S and the number of samples fallen in each S and their correspondent entropy were calculated,respectively (cf. Tab. 1,2). The slope of each regression is the FD at different growth stages. In order to answer whether the difference between FD at any two different growth stages is significant t-test was carried out to judge if the regressions are parallel. The common slope of tWo regressions, i.e., the common FD of reed at any two growth stages was therefore calculated while the functions are parallel (cf. Tab. 3 and 4). The results showed that the difference between two samplings in May and those among three samplings in June and later were not remarkable for both BD or ID. It was noted, however, that the difference between samplings in and after May is significant. It was demonstrated that the fractal dimension of size distribution of reed tanged from 0.6235 to 0.8761. The distribution pattern could be statistically divided as two significant periods: the size of reed is quite welldistributed at the beginning of reed growth (fracial dimension>0.8), but is irregular in the middle and later growth season (fractal dimension<0.7). These results are benefit to reach the goal of rational use of reed resources and to protect the biodiversity in wehand ecosystem.