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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