Hi Tom,
Cool study!
One thing that you migth want to think about is that your plants are
discrete entities, you do not have a continuous random field. A marked
point process on the otherhand is more in line with your variables. The
locations of your plants are the points, number of nodules, biomass, etc.
and local nitrogen level are the marks. A slight complication is that the
soil variables are continous, so you are associating a point process with
an estimated continuous random variable. I don't know if there is much
literature on that, i believe Steve Rathbun at U. Georgia wrote some stuff
about that, I have the tech report, I don't know if he published it.
In regards to the permutation tests you were talking about, you can
incorporate spatial information, there is quite a bit written about this,
look for papers by Peter Smouse, Robert Sokal, and Brian Manly in the
80's. Also go down the hall and talk to Monty Slatkin, he has done quite a
bit in spatial population genetics ;)
Lastly, interms of a reccomended software package, use R
(http://cran.r-project.org) there are packages for geostatistics (Rgeo),
and point processes (splancs) and best of all it is free!
Nicholas
On Wed, 4 Jul 2001, Tom Juenger wrote:
> Hi;
>
> My name is Tom Juenger. I'm a postdoc at UC Berkeley in the Integrative
> Biology Department. I study plant evolutionary ecology. Most of my
> research focuses on how plants interact with other species (pollinators,
> herbivores, bacteria etc). I'm fairly new to spatial statistical
> approaches in ecology, but I'm very interested in learning more. I have a
> set of observations that I'm currently starting to analyze and thought it
> might be helpful to bounce a few thoughts off of the geostats group.
> Please cut me some slack for the simplicity of my questions - I'm just
> getting started.
>
> I've been studying a neat plant that occurs in sand dune habitats just
> north of the San Francisco Bay area. The plant is a lupine. Many species
> in this group form a symbiotic relationship with bacteria in specialized
> root organs called nodules. The general understanding is that the bacteria
> can fix atmospheric nitrogen which it then supplies to the plant, while the
> plant fixes carbon through photosynthesis which it shares with the
> bacteria. This is probably an important interaction in this habitat as sand
> dunes have few mineral resources. I'm very interested in how tightly
> co-evolved or adapted this interaction is and whether environmental factors
> influence the cost or benefits of the symbiosis. For example, do plants
> restrict their interaction with the bacteria when they already occur in
> soil patches that are high in plant available nitrogen. Do certain plant
> genotypes prefer certain bacterial genotypes?
>
> I've collected two years of (x y) coordinate data in a natural population
> of lupines. The thought is to use these data as a pilot study to direct
> some future experimental manipulations. I created a nice 10 m x 20 m grid
> over a plant population. In 2000, I mapped the location of all Lupinus
> bicolor (an annual lupine) individuals to the nearest cm (oh, my knees
> hurt......over 2,000 plants!). I also placed small ion-exchange membranes
> in the soil to estimate plant available nitrate, ammonium, and phosphorus.
> These membranes were placed so that a membrane was planted systematically
> at each 1 m spacing over the entire grid and at a .5 m spacing in 4 dense
> subplots (this ends up being @ 400 sampling points). At the end of the
> season, I randomly harvested at least one (and often two) plants per square
> meter over the entire plot. I've measured plant biomass and the number of
> nodules on all harvested plants. I repeated this sampling in 2001,
> although the density of plants dropped dramatically, presumably due to the
> dry year we are having. I have also collected tissue from both the harvest
> plants and their nodules - we are currently developing genetic markers to
> "dna fingerprint" both the bacteria and the plant from each of the
> harvested individuals.
>
> I'm interested in a suite of questions. First, I'd like to say something
> about the spatial structuring of soil resources. I've been using PROC
> Variogram in SAS for some preliminary investigations of the soil resource
> data. Does anyone have a suggestion on how to bin my samples for
> calculating variograms. It seems logical to pick 0.5 (my smallest
> "inter-membrane" distance) and yet then I have very different sample sizes
> across the distance categories? The data is very non-normal with a skewed
> distribution - many low values and a few large values. The variograms seem
> to be very dependent on the inclusion of the high outliers, and yet I do
> not have a good reason to just throw them out. Is there any particular
> rule of thumb I should follow...........or am I in the realm of opinion.
> Alternatively, I'm really only interested in the relative amount of soil
> resources across space - should I think about a rank transformation? or
> other transformations?
>
> It makes sense to use variograms and a geostats approach to look at spatial
> pattens in the soil resources - nitrogen COULD have been measured at each
> point so the notion of a random spatial field makes sense to me. However,
> I'm not sure if this applies to the plant characteristics. For example,
> there can only be nodules where a plant occurs. In some sense this is a
> point process. Does it still make sense to fit variograms for nodule
> production across space? Would this sort of analysis be interpreted as an
> "average" nodule number across space. Is there some way I could adjust
> this analysis if I was interested in "absolute" numbers of nodules in the
> soil (given I know exact numbers of plants and their location)? I
> apologize if that question seems ill formed - I'm not sure I've thought
> through the problem completely.
>
> A major question I have is whether nodule production is correlated with
> soil nitrogen levels. Many ecologist would just go in the field and pull
> up plants, count nodules, measure N in the soil, ignore the locations of
> sampling, and test for a correlation. I get the idea that this could be a
> problem given the the pairs of points might not be independent given
> spatial correlation - I have heard people speak about co-kriging. I have
> the impression this method is often used to predict one variable (often an
> expensive variable to measure) based on measuring a different variable
> (often a cheap variable to measure). Is this an approach I should
> investigate for this question? Are there other means of calculating a
> correlation between variables, controlling for their spatial correlation?
>
> We are still working on the dna fingerprinting but hope to ask whether
> particular plant genotypes are correlated with bacterial genotypes - this
> is a nice test of co-adaptation. The fingerprinting will let us categorize
> the sampled plants and bacteria into "clones" (nominal identifiers A,B,C, D
> for plants and bacteria). One approach would be to test for a
> nonparametric correlation between the plant and bacteria clones using a
> permutation test - but this would not include the problem of spatial
> correlation in the occurrences of the various genotypes. Would there be a
> corresponding non-parametric test for a correlation, controlling for
> spatial locations?
>
> SAS is a bit clunky - do you folks have any suggestions on software I
> should investigate?
>
> Once again, I apologize for my naive questions and for the rambling email.
> I'd love to hear any thoughts or suggestions you may have.
>
> Take care
> Tom J.
>
>
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CH3
|
N Nicholas Lewin-Koh
/ \ Dept of Statistics
N----C C==O Program in Ecology and Evolutionary Biology
|| || | Iowa State University
|| || | Ames, IA 50011
CH C N--CH3 http://www.public.iastate.edu/~nlewin
\ / \ / [EMAIL PROTECTED]
N C
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CH3 O Graphics Lab
School of Computing
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The Real Part of Coffee [EMAIL PROTECTED]
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