Thank you JM, RK, and DB for your thoughtful responses to my questions.  I
am working on posting the file on the web and will respond as soon as it is
publicly available - (I could email it direct to those concerned as well).
Until then here is the output requested by DB and RK as well as more
information regarding sites, species, and the data:

>ds=d[d$TYPE=="s",] #separates into just sap fungi as used in the example
below
>dm=d[d$TYPE=="m",] #separates into just myc fungi (treated as distinct
populations in my analyses)

> table(table(ds$SPECIES))

    0      1    2   3   5   6
393 161  45   7   1   1
# As seen all species are not present at all the sites - this is partly why
I thought to nest SPECIES within SITE.  The sites range widely from boreal
tundra, to temperate California, to tropical forests of Borneo and Guyana.
Most fungi are not so cosmopolitan as to even potentially be present
everywhere - let alone be collected during brief collecting forays.  One
site (pine forest in CA) didn't even list  fungal names.  All fungi were
listed as mycorrhizal (m), saprotrophic (s), or of unknown ecological roles
(unk).  Most of the genera (or families) are present at all sites but that
biologically coarseness concerns me.  If, as pointed out by RK the ideal
situation would be every species present at every site then perhaps creating
a new column containing families or genera will move the dataset toward that
direction.

> xtabs(~SITE,ds)
SITE
                             Aheden                            Aheden 2
                                  4                                   0
   Ashiu (temp deciduous broadleaf)        Betsele
                                 21                                   0
                     Breuil, France                       Chiba
                                 14                                   6
                                  d                             Flakaliden
                                 23                                   0
                Glacier Bay, Alaska                Guyana
                                  4                                  20
                                  h                     heath tundra,
subarctic Sweden
                                 38                                   4
                          Kagoshima                       Kulbacksliden
                                  1                                   0
                              Kyoto                        Lamar Haines
                                 26                                  13
          Lambir (lowland tropical)               Miyajima
                                 14                                   1
                           Norikura                        Norrliden
                                  3                                   0
                            Okinawa       Ontake (subalpine coniferous)
                                  0                                   8
                              Oodai                  pine forests in CA
                                  2                                  25
                          Shirahama                     nowbowl
                                  2                                  13
                  Spruce plantation                   Stadsskogen
                                 17                                  13
                        Svartberget                     Tanigawa
                                  0                                   6
tussock tundra near Toolik Lake, AK      Vilan
                                  5                                   0
                        Woods Creek
                                 25                     # the zeros here are
because some sites have no X13C data - only X15N

I did try running models with centered predictors, as suggested by RK - see
below.  I found that the AIC scores were much larger however when the
predictors were centered using my method.  I centered by taking the mean of
mycorrhizal and saprotrophic fungal groups at each site - then I subtracted
each (m) or (s) fungus from those same group means within each site.
Because the (m) and (s) fungi have unique sources of carbon, and nitrogen
and these are reflected in their isotope values (X13C, X15N), I deemed this
centering level to be appropriatein order to preserve the magnitude of
difference between the groups.

> mix.model1  # Raw isotope values used
Linear mixed model fit by maximum likelihood
Formula: X13C ~ MAT + MAP + LAT + (1 | SPECIES) + (1 | SITE)
   Data: ds
  AIC   BIC    logLik     deviance  REMLdev
 1016 1041 -500.9     1002         1031
Random effects:
 Groups   Name        Variance Std.Dev.
 SPECIES  (Intercept) 0.62149  0.78835
 SITE     (Intercept) 0.34885  0.59063
 Residual             1.28911  1.13539
Number of obs: 283, groups: SPECIES, 215; SITE, 24

Fixed effects:
              Estimate Std. Error t value
(Intercept) -2.207e+01  1.121e+00 -19.695
MAT         -6.418e-02  3.833e-02  -1.675
MAP          3.137e-05  2.100e-04   0.149
LAT         -8.690e-03  1.778e-02  -0.489

Correlation of Fixed Effects:
          (Intr)       MAT     MAP
MAT  -0.707
MAP  -0.401  -0.247
LAT   -0.959  0.692   0.272

> mix.model1a # Group centered within each site
Linear mixed model fit by maximum likelihood
Formula: STND_13c ~ MAT + MAP + LAT + (1 | SPECIES) + (1 | SITE)
   Data: ds
  AIC   BIC    logLik     deviance  REMLdev
 2623 2649  -1305     2609         2620
Random effects:
 Groups   Name        Variance Std.Dev.
 SPECIES  (Intercept) 301.9720 17.3773
 SITE     (Intercept)   5.1294  2.2648
 Residual             327.3857 18.0938
Number of obs: 283, groups: SPECIES, 215; SITE, 24

Fixed effects:
             Estimate Std. Error t value
(Intercept) 3.463e+01  1.166e+01  2.9713
MAT         3.899e-01  4.330e-01  0.9006
MAP         2.543e-05  1.811e-03  0.0140
LAT         3.235e-01  1.867e-01  1.7324

Correlation of Fixed Effects:
         (Intr)       MAT     MAP
MAT -0.779
MAP -0.230  -0.300
LAT  -0.955   0.732   0.116

> anova(mix.model1,mix.model1a)
Data: ds
Models:
mix.model1: X13C ~ MAT + MAP + LAT + (1 | SPECIES) + (1 | SITE)
mix.model1a: STND_13c ~ MAT + MAP + LAT + (1 | SPECIES) + (1 | SITE)
                            Df      AIC         BIC          logLik  Chisq
Chi Df  Pr(>Chisq)
mix.model1.p    7      1015.85  1041.37  -500.93
mix.model1a.p  7      2623.49  2649.00 -1304.74     0      0       < 2.2e-16
***

# As seen above, the model using my centered values performed poorly.  My
interpretation is that the centering removed the very variability associated
with climate I am trying to predict!

#In addition, I compared the other models mentioned by RK using the raw
isotope values:

> anova(mix.model1,mix.model2,mix.model3)
Data: ds
Models:
mix.model1: X13C ~ MAT + MAP + LAT + (1 | SPECIES) + (1 | SITE)
mix.model2: X13C ~ (MAT + MAP + LAT)^2 + (1 | SPECIES) + (1 | SITE)
mix.model3: X13C ~ MAT * MAP * LAT + (1 | SPECIES) + (1 | SITE)
                         Df     AIC         BIC           logLik
Chisq    Chi Df   Pr(>Chisq)
mix.model1.p  7     1015.85  1041.37    -500.93
mix.model2.p 10    978.21    1014.66    -479.10   43.645      3
1.796e-09 ***
mix.model3.p 11    980.18    1020.28    -479.09   0.023        1
0.8794

# I have refrained from trying the models mentioned by DB in order to
protect his rights to not commit the "capital mistake" ;) however, the three
predictors (MAT, MAP, LAT) do indeed seem to overplot - I will try to select
only one perhaps in my final models.

# Again - thank you all for your help on this.

-- 
Jordan Mayor, Ph.D. Candidate
Ecosystem Dynamics Research Lab
Department of Botany, University of Florida
Gainesville, FL 32611

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