

We've created 35 home ranges for individual birds that we tracked during
the pre-breeding season. Each home range is based on an individual
utilization distribution (UD) that we've used to predict relative at each
100 x 100 m pixel. Each pixel also has associated habitat attributes, such
as water depth and percent emergent vegetation. We also have bird-level
variables (age [categorical] and relative body condition [continuous]).
We're now trying to relate habitat use (UD value) to habitat attributes and
individual quality (with age and body condition as proxies). We've modeled
the data with individual bird as a random effect to account for the related
nature of pixels within an individual's home range. We then imposed a
rational quadratic correlation structure to the lme model to account for
the spatial autocorrelation among pixels (corRatio was best fit compared to
other structures available in nlme). When we look at variograms for each
model we don't see any improvement in residual correlation, but our beta
estimates for the effects of habitat on selection change significantly.

Here is what our data look like:

>head(hrdata)

    XMIN   XMAX    YMIN    YMAX  BirdID DEP SUB H2O EDGE    UDval Age
BCIndex Year_  logUDval
1 430400 430500 4942900 4943000 1653957   0   0   0    0 0.012085   1
-18.82793     0 -4.415790
2 430400 430500 4943000 4943100 1653957   0   0   0    0 0.012856   1
-18.82793     0 -4.353945
3 430400 430500 4943100 4943200 1653957   0   0   0    0 0.014132   1
-18.82793     0 -4.259314
4 430400 430500 4943200 4943300 1653957   0   0   0    0 0.014939   1
-18.82793     0 -4.203780
5 430400 430500 4943300 4943400 1653957   0   0   0    0 0.016364   1
-18.82793     0 -4.112671
6 430400 430500 4943400 4943500 1653957   0   0   0    0 0.017369   1
-18.82793     0 -4.053068

Model statements:
Form <- formula(logUDval ~ DEP + EDGE + SUB:H2O + Year_ + Age + BCIndex)
m1.lme<-lme(Form, random = ~ 1|BirdID, method="REML", data=hrdata)
m1.lme.ratio<-lme(Form, random = ~ 1|BirdID, correlation = corRatio(form =
~XMIN + YMIN), method="REML", data=hrdata)

Model summaries:

Summary of LME with no spatial autocorrelation structure

Linear mixed-effects model fit by REML
 Data: hrdata
       AIC      BIC    logLik
  50535.09 50605.97 -25258.54

Random effects:
 Formula: ~1 | BirdID
        (Intercept)  Residual
StdDev:   0.6385548 0.8809287

Fixed effects: list(Form)
                  Value             Std.Error         DF    t-value
p-value
(Intercept)       -1.8712232  0.20935222  19415  -8.938158        0.0000
DEP               0.0014205   0.00028237  19415       5.030507    0.0000
EDGE              0.0028367   0.00029345  19415       9.666943    0.0000
Year_1      -0.3690599  0.23942499        31    -1.541443   0.1334
Age1        -0.2452163  0.23423909        31    -1.046863   0.3033
BCIndex           0.0018829   0.00283624        31    0.663880    0.5117
SUB:H2O           0.0037672   0.00030599  19415       12.311448   0.0000
 Correlation:
        (Intr) DEP    EDGE   Year_1 Age1   BCIndx
DEP     -0.018
EDGE    -0.018 -0.201
Year_1  -0.667 -0.016  0.002
Age1    -0.740  0.001 -0.002  0.361
BCIndex -0.011 -0.003  0.003  0.105 -0.085
SUB:H2O -0.014 -0.433  0.069  0.010 -0.002 -0.003

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-1.8954412 -0.8640309 -0.0985262  0.7541542  2.8349462

Number of Observations: 19453
Number of Groups: 35

************************************************************************

Summary of LME with rational quadratic spatial autocorrelation structure

Linear mixed-effects model fit by REML
 Data: hrdata
        AIC       BIC   logLik
  -74203.99 -74125.23 37111.99

Random effects:
 Formula: ~1 | BirdID
        (Intercept)  Residual
StdDev:   0.5266185 0.5505424

Correlation Structure: Rational quadratic spatial correlation
 Formula: ~XMIN + YMIN | BirdID
 Parameter estimate(s):
   range
405.6316
Fixed effects: list(Form)
                  Value             Std.Error         DF
t-value           p-value
(Intercept)  -2.4777143 0.18583575  19415             -13.332819   0.0000
DEP          -0.0000045       0.00001259  19415             -0.357142
0.7210
EDGE          0.0000032       0.00000281  19415             1.150247
0.2501
Year_1       -0.3041446       0.21134054        31          -1.439121
0.1601
Age1              -0.2356964  0.20706315        31          -1.138283
0.2637
BCIndex            0.0013983  0.00250764        31           0.557623
0.5811
SUB:H2O     -0.0000001  0.00000827  19415             -0.006635   0.9947
 Correlation:
        (Intr) DEP    EDGE   Year_1 Age1   BCIndx
DEP     -0.001
EDGE     0.000 -0.283
Year_1  -0.672 -0.001  0.001
Age1    -0.743  0.000  0.000  0.368
BCIndex -0.012  0.000  0.001  0.102 -0.079
SUB:H2O -0.001 -0.287  0.267  0.001  0.000  0.001

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-1.5110519 -0.2035459  1.0313164  2.4303284  5.6538601

Number of Observations: 19453
Number of Groups: 35


We don't understand why there appears to be no improvement in spatial
autocorrelation but our results have changed so dramatically. Any ideas on
why we're running into this issue would be greatly appreciated.

Thanks,

Jeff Warren
Wildlife Biologist
27650 B South Valley Rd
Lima, Montana 59739
(406) 276-3536 ext. 304
(406) 548-8487 cell

"Without data, all you are is just another person with an opinion"
--Unknown
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