Jess, This is an interesting idea that could work. For irregularly shaped sites, those bounded by topography or man-made boundaries, the area could be filled progressively from the center outward until the boundaries in any direction is met and area additions stopped there, while the rest of the site would continue to be incrementally filled. You said that the curve tended to be logarithmic in shape - the areas plotted on the x-axis would then be a linear progression. I am wondering about whether this is applied to areas of vastly different sizes in your literature research? I am thinking that some small pockets of trees may be 2 or more orders of magnitude smaller than the largest sites - say a 10 acre site vs. the Smokies or a drainage basin. If you look at area, it increases with exponentially with distance (radius) from the center. Perhaps we could look at making the x-axis, the area axis, be a logarithmic scale instead of linear. This would make true logarithmic progressions plot as straight lines rather than curves, and would allow a lot to show more detail at smaller areas, and allow the plot to progress through multiple orders of magnitude. I am just thinking out loud. I am sure you have a better grasp of the math and certainly the ecology literature than I do.
Ed Join me in the Eastern Native Tree Society at http://www.nativetreesociety.org and in the Primal Forests - Ancient Trees Community at: http://primalforests.ning.com/ ----- Original Message ----- From: Jess Riddle To: [email protected] Sent: Saturday, September 27, 2008 12:10 PM Subject: [ENTS] Re: Rucker Index Thoughts (area) Ed, Will, all; The first solution that comes to mind for the area dependency of the Rucker Index is to produce Rucker Index-Area curves. I'm borrowing this idea from the ecology literature where a analogous problem occurs with species richness, the total number of species. Species richness for a site is dependent on the size of the site, and the number of species found, even for a small site, is dependent on the sampling effort, especially where species are often cryptic such as with fungi. To address those problems, plots are constructed with species richness on the y-axis and either area or sampling effort, which could be number of days sampled, time spent sampling, or number of samples, on the x-axis. A curve is then fit to the data, so the species richness for different sized sites or different sampling intensities can be interpolated or extrapolated. The curve usually takes a logarithmic form, increasing rapidly at first but then appearing to approach an asymptote. We could apply that same strategy to Rucker Indices by first calculating the Rucker Index for the core of the site, then expanding the area until new trees enter the Rucker Index and recalculating, and repeating that process until the entire site was included. The results would be plotted with RI on the y-axis and area on the x-axis a curve fit to that data. When comparing sites, we could then interpolate the RI of the large site at the area of the smaller site, or give an estimated RI for all sites at some standard area. Jess On Fri, Sep 26, 2008 at 2:04 PM, Edward Forrest Frank <[EMAIL PROTECTED]> wrote: > Will, > > I have thought and thought about the acreage issue. That is one reason I > encouraged you and Jess to look at subdivisions of GSMNP to reduce the size > of the block that is considered a site. Thus you can have RI for subsites > more comparable in size with other locations and still have a combined RI > for the entire park. Even within a defined site, you would need to know > where all the trees were located because if the site was looked at in terms > of acreage, you would want to define the least amount of acreage that would > include the greatest Rucker Index - sort of a balance. Then there is the > question of shape. In an ideal forest the area could be defined by a circle > as a minimum edge, maximum area shape, but in practice, the boundaries we > consider are irregular. They may follow a narrow valley, or a drainage > basin, or a square patch of remnant forest. If people have ideas of how to > do it, it certainly is worth talking about. As it is, I would suggest that > the "site" be defined as a discrete area whose boundaries are established by > the person or group involved in the measurement (The boundaries should be > described as best possible). This would include both productive and less > productive areas. More productive areas could be defined as a subsite, or a > separate site. Then along with the Rucker Index an acreage for the "site" > could be listed to provide a good context for the size of the area versus > the rucker index numbers. It is information that can added and is useful, > but on the other hand some of the best locations may have a high Rucker > Index in a relatively small area - I am not really convinced that a Rucker > Index per size of an area would be informative. > > Ed > > > Join me in the Eastern Native Tree Society at > http://www.nativetreesociety.org > and in the Primal Forests - Ancient Trees Community at: > http://primalforests.ning.com/ > > ----- Original Message ----- > From: Will Blozan > To: [email protected] > Sent: Friday, September 26, 2008 12:27 PM > Subject: [ENTS] Re: Rucker Index Thoughts > > Ed, > > > > Great thoughts. I support the reasoning for the R5 and R20 indices. If only > there was some way to incorporate the area needed to obtain a certain Rucker > Value. An R5 acre, R10 acre, R20 acre index? --~--~---------~--~----~------------~-------~--~----~ Eastern Native Tree Society http://www.nativetreesociety.org You are subscribed to the Google Groups "ENTSTrees" group. To post to this group, send email to [email protected] To unsubscribe send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/entstrees?hl=en -~----------~----~----~----~------~----~------~--~---
