> Therefore, it may be useful to relate standard deviation of >diameter and available stand characteristics such as average >diameter, stand density, and age. > If you know anything about this issue (including >references), I, and probably other netters, would appreciate >hearing from you. The diameter distribution methods used in the New Zealand STANDPAK, mentioned by Euan Mason, are described in: 1) Goulding, C.J. and Shirley, J.W. 1979. A method to predict the yield of log assortments for long term planning. Pp. 301-315 in Elliott, D.A. (ed) "Mensuration for Management Planning of Exotic Forest Plantations", New Zealand Forest Service, Forest Research Institute Symposium No. 20. 2) Goulding, C.J. 1986. ? In: Levak, H. (ed), "1986 Forestry Handbook". New Zealand Institute of Foresters (Inc.), Wellington. 1986. 3) Garcia, O. 1984. New class of growth models for even-aged stands: Pinus radiata in Golden Downs Forest. New Zealand Journal of Forestry Science 14:65-88. These do exactly what Boris was talking about, estimating distributions from stand-level data. 1) and 2) (not entirely sure about the contents of 2, I do not have it at hand) follow earlier unpublished work by Clutter and Allison, and by Levak, using regressions on the stand variables to estimate the basal area of the minimum dbh tree and the variance of the individual tree basal areas. Together with the mean basal area, these values are then used to calculate the parameters of a 3-parameter Weibull distribution of basal areas, which is subsequently converted to a distribution of diameters. In 3) a regression for the coefficient of variation of the basal areas (equation 22), together with the mean basal area, are used to obtain a two-parameter Weibull (if you plot Weibulls with the same mean and variance but different location parameters on top of each other you will se why!) Working with basal area distributions instead of diameters has been found to give more stable relationships, and also makes the method-of-moment estimators to be almost fully efficient (the shape parameter is larger.) Of course, if the tree basal areas follow a 2-parameter Weibull so do the diameters (this is not true with three parameters). Now, despite what my New Zealand friends said, I believe that this kind of approach will give you distribution estimates as good as you have the right to expect. The real problem is that talking about tree diameter distributions in general does not make much sense. To repeat it one more time, usually TREE SIZES ARE NOT RANDOMLY DISTRIBUTED ON THE GROUND. Competition induces short-range negative spatial correlations (the neighbor of a large tree is likely to be small). It seems to me that this is pretty obvious to any forester, and it is explicitly built-in in individual-tree (distance-dependent) growth models. Often more noticeable, microsite variation induces a somewhat longer-range positive correlation (trees close by are likely to grow in more similar conditions than trees further apart). This one has been totally ignored in all the individual-tree growth models I know of. The consequence of all this is that the distribution of tree sizes in a stand (what we usually want) can be, an usually is, totally different from the distribution in sample plots (what we usually get). More generally, a "diameter distribution" will vary unpredictably with the size of the piece of land considered: Garcia, O. 1992. What is a diameter distribution? In: Minowa, M. and Tsuyuki, S. (eds.) "Proceedings of the Symposium on Integrated Forest Management Information Systems". Japan Society of Forest Planning Press. (see also reference 3, above, and page 1896 in Can.J.For.Res. 24, 1894-1903, 1994.) And these are not just theoretical niceties, there is increasing empirical evidence that the effects can be quite substantial. There is no denying that distributions of output products are important for forest management, and we would very much like to have them. But realistically, we must content ourselves with rather rough estimates, and no amount of mathematical or statistical sophistication will change that. Besides the spatial structure issues, it is "well-known" that decent estimates of anything beyond second moments requires samples of astronomical size. It seems possible, however, to estimate stand-level variances from inventory plot data when there are several plots in the stand, and that is a subject worth pursuing. It never ceases to amaze me that nobody seems to see facts that are so obvious. But I suppose that playing with distributions has already become a minor industry, and it is such a fun! As Kendall and Stuart noticed in The Advanced Theory of Statistics, "the fitting of distributions to observational data has a certain intrinsic interest which is apt to outrun its statistical usefulness". My apologies for this long diatribe. Now that I got it out of my system, on with your next diameter distribution publication! ------- Oscar Garcia - Visiting Professor - og@kvl.dk The Royal Veterinary and Agricultural University (KVL) Department of Economics and Natural Resources, Unit of Forestry Thorvaldsensvej 57, DK-1871 Frederiksberg C, Denmark Tel. +45 35 28 22 47. Fax +45 31 35 78 33
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