Hi Madhu, Seems tricky! I think you might be best served by using explicitly circular methods for your circular data. I don't really know anything about such things (so why I'm responding to your post, I don't know!) but what little information I've gathered leads me to believe that you could use "circular statistics" to evaluate whether there's greater probability of finding a plant species over certain degrees compared to others (e.g. SE is most likely). I think the idea would be to fit a circular probability density function to your data, and see if it has a central tendency, and if so where.
You could look at some R documentation to starting finding some ideas and references: http://cran.r-project.org/web/packages/circular/index.html I think matlab also has some tools for doing this kind of thing. I think either linear regression methods have some problems, and the take home message is that for either you'd want/need to re-interpret your results in light of the initial circular nature of the data. E.g. if you just used plain degrees (and 0 = north) and you found sp1 = 0.001*(x-180)^2...that's a U shaped curve with peaks at 0 and 360...kind of strange to think of a response like that in linear space, but makes perfect sense if you re-connect (0 deg = 360 deg) the two ends--that plant likes north-facing slopes. Anyway, hopefully that's at least a little helpful. Best of luck! Andy On Sun, Jul 4, 2010 at 7:04 PM, Madhu Srinivasan <[email protected]> wrote: > Hi all, > I am currently writing one of my dissertation chapters. I collected plant > community data in a grassland ecosystem along with environmental variables > . > One of the questions I am addressing is: "How do the dominant grasses > respond to the aspect?" Aspect was the direction that the slope faced. In > the linked graphs > (http://sweb.uky.edu/~mpsrin2/aspect_fig.pdf<http://sweb.uky.edu/%7Empsrin2/aspect_fig.pdf>) > I have > displayed aspect in two ways: (1) in degrees as measured by compass > bearings, Fig. 2,and (2) converted to linear scale using: > A' = cos (45 - A) + 1, where A is the aspect in degrees (Beers et al, > 1966, > Journal of Forestry), Fig.3. The resulting index values range from 0 to 2 > (0 > = SW, 1 = SE and NW, 2 = NE), see Fig. 1. I have fitted regression lines > after determining the appropriate fit. One of my concerns is: in Fig. 3, > the > hump around A'=1.5 could either correspond to N or E, as both take the > value > 1.5 (see Fig.1). So this index of aspect does not allow me to interpret if > the plants are more abundant at N or at E facing slopes. Fig 2. allows me > to > distinguish data from the different aspects, and it is easier to explain; > but the explanatory variable here is circular, and I am concerned whether > it > is correct to apply regressions on circular data. I showed these graphs to > some of my colleagues and I got mixed responses. I would like to know which > representation is more appropriate? Right now I am leaning towards Fig. 2, > but I am concerned about the statistical appropriateness. I will include > the > explanatory Fig. 1 with either graph that I choose to finally use. > Also, if there is a better way to display/ analyze this, please let me > know. > > Thanks, > Madhu Srinivasan > Department of Biology > University of Kentucky >
