Today at Davis R Users’ Group, Rosemary Hartman took us through her work in progress fitting general additive models to organism presence/absence data. Below is her presentation and script. You can get the original script and data here

Also, check the comments below for some discussion of other options for this type of analysis, such as boosted regression trees.

## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(area.10cm, k = 6) + 
##     s(weighted.dist, k = 6) + s(bank.slope, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          3.830      3.224    1.19    0.235  
## BUBO.breedingy      -3.393      1.646   -2.06    0.039 *
## count.RACApops.1K   -0.192      0.506   -0.38    0.705  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.51    0.47
## s(vegetated.area) 3.48   3.97   3.47    0.48
## s(area.10cm)      2.20   2.66   1.17    0.70
## s(weighted.dist)  2.24   2.73   2.56    0.41
## s(bank.slope)     2.22   2.68   5.02    0.14
## 
## R-sq.(adj) =  0.597   Deviance explained = 68.5%
## UBRE score = 0.091416  Scale est. = 1         n = 42
## 
## Method: UBRE   Optimizer: outer newton
## full convergence after 14 iterations.
## Gradient range [-4.272e-07,2.326e-07]
## (score 0.09142 & scale 1).
## Hessian positive definite, eigenvalue range [2.564e-07,0.05689].
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                      k'   edf k-index p-value
## s(silt.total)     5.000 1.000   0.691    0.02
## s(vegetated.area) 6.000 3.485   1.321    0.97
## s(area.10cm)      5.000 2.200   0.742    0.02
## s(weighted.dist)  5.000 2.237   1.064    0.63
## s(bank.slope)     5.000 2.219   0.965    0.42

## Warning: basis dimension, k, increased to minimum possible

## Warning: basis dimension, k, increased to minimum possible

## Warning: basis dimension, k, increased to minimum possible

## Warning: basis dimension, k, increased to minimum possible

## Warning: basis dimension, k, increased to minimum possible

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## [1] 2
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          3.011      1.263    2.38    0.017 *
## count.RACApops.1K   -0.247      0.307   -0.80    0.421  
## BUBO.breedingy      -2.314      1.010   -2.29    0.022 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.05    0.82
## s(vegetated.area) 1.00   1.00   0.27    0.61
## s(bank.slope)     1.63   1.86   1.97    0.34
## s(area.10cm)      1.00   1.00   0.04    0.85
## s(weighted.dist)  1.80   1.96   2.34    0.30
## 
## R-sq.(adj) =  0.339   Deviance explained = 42.2%
## UBRE score = 0.21726  Scale est. = 1         n = 42
## [1] 51.12

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## [1] 3
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          3.011      1.263    2.38    0.017 *
## count.RACApops.1K   -0.247      0.307   -0.80    0.421  
## BUBO.breedingy      -2.314      1.010   -2.29    0.022 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.05    0.82
## s(vegetated.area) 1.00   1.00   0.27    0.61
## s(bank.slope)     1.63   1.86   1.97    0.34
## s(area.10cm)      1.00   1.00   0.04    0.85
## s(weighted.dist)  1.80   1.96   2.34    0.30
## 
## R-sq.(adj) =  0.339   Deviance explained = 42.2%
## UBRE score = 0.21726  Scale est. = 1         n = 42
## [1] 51.12

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## [1] 4
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          2.745      1.147    2.39    0.017 *
## count.RACApops.1K   -0.217      0.299   -0.73    0.468  
## BUBO.breedingy      -2.308      0.996   -2.32    0.020 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.06    0.81
## s(vegetated.area) 1.00   1.00   0.31    0.58
## s(bank.slope)     1.77   2.14   2.38    0.33
## s(area.10cm)      1.00   1.00   0.08    0.78
## s(weighted.dist)  1.86   2.25   2.53    0.32
## 
## R-sq.(adj) =  0.332   Deviance explained =   42%
## UBRE score = 0.22873  Scale est. = 1         n = 42
## [1] 51.61

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## [1] 5
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)          -16.5     4857.1    0.00     1.00
## count.RACApops.1K     42.4      397.8    0.11     0.92
## BUBO.breedingy      -254.6     9152.1   -0.03     0.98
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.00    0.95
## s(vegetated.area) 2.32   2.36   0.00    1.00
## s(bank.slope)     1.52   1.57   0.01    0.99
## s(area.10cm)      3.06   3.07   0.02    1.00
## s(weighted.dist)  4.00   4.00   0.02    1.00
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## UBRE score = -0.29037  Scale est. = 1         n = 42
## [1] 29.8

## Warning: matrix not positive definite

## [1] 6
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)         5.4778     2.5608    2.14    0.032 *
## count.RACApops.1K  -0.0673     0.4763   -0.14    0.888  
## BUBO.breedingy     -4.9379     2.1801   -2.26    0.024 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.14    0.71
## s(vegetated.area) 1.00   1.00   0.38    0.54
## s(bank.slope)     2.14   2.60   3.51    0.25
## s(area.10cm)      5.00   5.00   5.46    0.36
## s(weighted.dist)  2.13   2.64   2.50    0.40
## 
## R-sq.(adj) =  0.523   Deviance explained = 65.4%
## UBRE score = 0.13954  Scale est. = 1         n = 42
## [1] 47.86
## [1] 7
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)           6.56     366.37    0.02     0.99
## count.RACApops.1K     4.30      13.89    0.31     0.76
## BUBO.breedingy      -22.94      36.65   -0.63     0.53
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.02    0.88
## s(vegetated.area) 3.50   3.82   0.97    0.90
## s(bank.slope)     1.00   1.00   0.13    0.72
## s(area.10cm)      1.00   1.00   0.61    0.44
## s(weighted.dist)  4.02   4.21   1.32    0.88
## 
## R-sq.(adj) =      1   Deviance explained = 99.7%
## UBRE score = -0.35283  Scale est. = 1         n = 42
## [1] 27.18

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite

## [1] 8
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = i) + s(bank.slope, k = i) + 
##     s(area.10cm, k = i) + s(weighted.dist, k = i)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)         22.752    135.686    0.17     0.87
## count.RACApops.1K   -0.247     23.133   -0.01     0.99
## BUBO.breedingy     -29.877     67.934   -0.44     0.66
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     4.58   4.71   0.09    1.00
## s(vegetated.area) 3.19   3.31   0.01    1.00
## s(bank.slope)     1.00   1.00   0.06    0.80
## s(area.10cm)      2.14   2.23   0.02    0.99
## s(weighted.dist)  3.68   3.87   0.04    1.00
## 
## R-sq.(adj) =      1   Deviance explained = 99.9%
## UBRE score = -0.16157  Scale est. = 1         n = 42
## [1] 35.21
## Warning: basis dimension, k, increased to minimum possible

## Warning: matrix not positive definite

## [1] 2
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)         5.4778     2.5608    2.14    0.032 *
## count.RACApops.1K  -0.0673     0.4763   -0.14    0.888  
## BUBO.breedingy     -4.9379     2.1801   -2.26    0.024 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.14    0.71
## s(vegetated.area) 1.00   1.00   0.38    0.54
## s(bank.slope)     2.14   2.60   3.51    0.25
## s(area.10cm)      5.00   5.00   5.46    0.36
## s(weighted.dist)  2.13   2.64   2.50    0.40
## 
## R-sq.(adj) =  0.523   Deviance explained = 65.4%
## UBRE score = 0.13954  Scale est. = 1         n = 42
## [1] 47.86

## Warning: matrix not positive definite

## [1] 3
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)         5.4778     2.5608    2.14    0.032 *
## count.RACApops.1K  -0.0673     0.4763   -0.14    0.888  
## BUBO.breedingy     -4.9379     2.1801   -2.26    0.024 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.14    0.71
## s(vegetated.area) 1.00   1.00   0.38    0.54
## s(bank.slope)     2.14   2.60   3.51    0.25
## s(area.10cm)      5.00   5.00   5.46    0.36
## s(weighted.dist)  2.13   2.64   2.50    0.40
## 
## R-sq.(adj) =  0.523   Deviance explained = 65.4%
## UBRE score = 0.13954  Scale est. = 1         n = 42
## [1] 47.86
## [1] 4
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)           76.6      427.3    0.18     0.86
## count.RACApops.1K     10.1       51.7    0.20     0.84
## BUBO.breedingy       -89.3      536.3   -0.17     0.87
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.00    0.97
## s(vegetated.area) 2.65   2.70   0.03    1.00
## s(bank.slope)     3.77   3.87   0.12    1.00
## s(area.10cm)      4.51   4.54   0.19    1.00
## s(weighted.dist)  1.87   1.90   0.03    0.98
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## UBRE score = -0.19934  Scale est. = 1         n = 42
## [1] 33.63

## Warning: matrix not positive definite

## [1] 5
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)         5.4778     2.5609    2.14    0.032 *
## count.RACApops.1K  -0.0673     0.4763   -0.14    0.888  
## BUBO.breedingy     -4.9379     2.1801   -2.26    0.024 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.14    0.71
## s(vegetated.area) 1.00   1.00   0.38    0.54
## s(bank.slope)     2.14   2.60   3.51    0.25
## s(area.10cm)      5.00   5.00   5.46    0.36
## s(weighted.dist)  2.13   2.64   2.50    0.40
## 
## R-sq.(adj) =  0.523   Deviance explained = 65.4%
## UBRE score = 0.13954  Scale est. = 1         n = 42
## [1] 47.86

## Warning: matrix not positive definite

## [1] 6
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          3.830      3.224    1.19    0.235  
## count.RACApops.1K   -0.192      0.506   -0.38    0.705  
## BUBO.breedingy      -3.393      1.646   -2.06    0.039 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     1.00   1.00   0.51    0.47
## s(vegetated.area) 3.48   3.97   3.47    0.48
## s(bank.slope)     2.22   2.68   4.07    0.21
## s(area.10cm)      2.20   2.66   1.09    0.72
## s(weighted.dist)  2.24   2.73   1.90    0.54
## 
## R-sq.(adj) =  0.597   Deviance explained = 68.5%
## UBRE score = 0.091416  Scale est. = 1         n = 42
## [1] 45.84
## [1] 7
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)          55.26     358.87    0.15     0.88
## count.RACApops.1K     5.42      99.67    0.05     0.96
## BUBO.breedingy      -87.21     624.65   -0.14     0.89
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     4.96   4.99   0.09    1.00
## s(vegetated.area) 3.99   4.02   0.02    1.00
## s(bank.slope)     1.00   1.00   0.01    0.93
## s(area.10cm)      1.86   1.96   0.02    0.99
## s(weighted.dist)  1.03   1.03   0.01    0.92
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## UBRE score = -0.24525  Scale est. = 1         n = 42
## [1] 31.7

## Warning: matrix not positive definite

## [1] 8
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)          89.75   12140.84    0.01     0.99
## count.RACApops.1K    -3.53    1710.88    0.00     1.00
## BUBO.breedingy     -119.62    9443.72   -0.01     0.99
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     5.76   5.80      0       1
## s(vegetated.area) 2.03   2.04      0       1
## s(bank.slope)     1.18   1.19      0       1
## s(area.10cm)      1.84   1.90      0       1
## s(weighted.dist)  1.08   1.08      0       1
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## UBRE score = -0.29122  Scale est. = 1         n = 42
## [1] 29.77
## [1] 9
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)         48.947    655.719    0.07     0.94
## count.RACApops.1K   -0.137     82.969    0.00     1.00
## BUBO.breedingy     -73.934    546.328   -0.14     0.89
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     5.75   5.84   0.02    1.00
## s(vegetated.area) 2.00   2.01   0.01    1.00
## s(bank.slope)     1.00   1.00   0.01    0.91
## s(area.10cm)      1.86   1.95   0.01    0.99
## s(weighted.dist)  1.19   1.21   0.00    0.99
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## UBRE score = -0.29492  Scale est. = 1         n = 42
## [1] 29.61
## [1] 10
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)        54.2952   102.0865    0.53     0.59
## count.RACApops.1K  -0.0411    16.5558    0.00     1.00
## BUBO.breedingy    -75.4705   126.5539   -0.60     0.55
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     6.88   7.06   0.74    1.00
## s(vegetated.area) 3.09   3.16   0.22    0.98
## s(bank.slope)     1.04   1.05   0.22    0.66
## s(area.10cm)      2.42   2.67   0.38    0.92
## s(weighted.dist)  1.00   1.00   0.30    0.58
## 
## R-sq.(adj) =      1   Deviance explained = 99.8%
## UBRE score = -0.16704  Scale est. = 1         n = 42
## [1] 34.98
## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(area.10cm, k = 6) + 
##     s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          2.175      0.974    2.23    0.026 *
## BUBO.breedingy      -1.840      0.891   -2.07    0.039 *
## count.RACApops.1K   -0.294      0.290   -1.01    0.311  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value  
## s(silt.total)     1.00   1.00   3.19   0.074 .
## s(vegetated.area) 1.00   1.00   0.46   0.499  
## s(area.10cm)      1.00   1.00   1.82   0.177  
## s(weighted.dist)  2.02   2.54   2.53   0.375  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## R-sq.(adj) =  0.279   Deviance explained = 34.1%
## UBRE score = 0.25725  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(area.10cm, k = 6) + 
##     s(weighted.dist, k = 6)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)    
## 1      34.0       36.8                           
## 2      24.6        0.1 9.41     36.6  4.2e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)          77.43     282.28    0.27     0.78
## BUBO.breedingy     -120.75     510.54   -0.24     0.81
## count.RACApops.1K     2.83      64.25    0.04     0.96
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(silt.total)     4.77   4.80   0.08    1.00
## s(vegetated.area) 2.15   2.19   0.02    0.99
## s(bank.slope)     1.22   1.25   0.06    0.88
## s(area.10cm)      3.71   3.77   0.06    1.00
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## UBRE score = -0.29299  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)
## 1      27.2      0.008                       
## 2      24.6      0.127 2.59   -0.119         
## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          2.490      1.851    1.35    0.179  
## BUBO.breedingy      -1.997      1.100   -1.82    0.069 .
## count.RACApops.1K   -0.465      0.373   -1.25    0.213  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value  
## s(silt.total)     1.00   1.00   0.03   0.852  
## s(vegetated.area) 3.29   3.81   4.86   0.276  
## s(bank.slope)     1.00   1.00   4.12   0.042 *
## s(weighted.dist)  1.40   1.70   0.81   0.591  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## R-sq.(adj) =  0.513   Deviance explained = 54.5%
## UBRE score = 0.066475  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(weighted.dist, k = 6)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)   
## 1      32.3      25.40                          
## 2      24.6       0.13 7.73     25.3   0.0012 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + s(silt.total, k = 6) + s(vegetated.area, 
##     k = 7) + s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                Estimate Std. Error z value Pr(>|z|)  
## (Intercept)       1.529      0.677    2.26    0.024 *
## BUBO.breedingy   -1.608      0.836   -1.92    0.054 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value  
## s(silt.total)     1.00   1.00   2.76   0.097 .
## s(vegetated.area) 1.00   1.00   0.30   0.583  
## s(area.10cm)      1.00   1.00   1.56   0.212  
## s(weighted.dist)  1.94   2.45   2.26   0.403  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## R-sq.(adj) =   0.26   Deviance explained = 31.8%
## UBRE score = 0.23669  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ BUBO.breeding + s(silt.total, k = 6) + s(vegetated.area, 
##     k = 7) + s(area.10cm, k = 6) + s(weighted.dist, k = 6)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)    
## 1      35.1       38.1                           
## 2      24.6        0.1 10.5     37.9  5.6e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(bank.slope, k = 6) + s(area.10cm, k = 6) + s(weighted.dist, 
##     k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          3.967      1.717    2.31    0.021 *
## BUBO.breedingy      -3.711      1.561   -2.38    0.017 *
## count.RACApops.1K   -0.085      0.412   -0.21    0.836  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                   edf Ref.df Chi.sq p-value
## s(silt.total)    1.00   1.00   0.01    0.91
## s(bank.slope)    1.90   2.32   3.93    0.18
## s(area.10cm)     4.67   4.94   6.03    0.30
## s(weighted.dist) 1.93   2.38   2.05    0.43
## 
## R-sq.(adj) =  0.512   Deviance explained = 61.4%
## UBRE score = 0.10827  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ BUBO.breeding + count.RACApops.1K + s(silt.total, 
##     k = 6) + s(bank.slope, k = 6) + s(area.10cm, k = 6) + s(weighted.dist, 
##     k = 6)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)    
## 1      29.5      21.56                           
## 2      24.6       0.13 4.94     21.4  0.00063 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(vegetated.area, 
##     k = 7) + s(bank.slope, k = 6) + s(area.10cm, k = 6) + s(weighted.dist, 
##     k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)         4.6494     2.0998    2.21    0.027 *
## BUBO.breedingy     -4.2713     1.8364   -2.33    0.020 *
## count.RACApops.1K  -0.0772     0.4423   -0.17    0.862  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value  
## s(vegetated.area) 1.00   1.00   0.14   0.707  
## s(bank.slope)     2.01   2.46   6.56   0.058 .
## s(area.10cm)      4.87   4.98   5.87   0.317  
## s(weighted.dist)  1.99   2.44   2.23   0.410  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## R-sq.(adj) =  0.524   Deviance explained = 63.3%
## UBRE score = 0.10056  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ BUBO.breeding + count.RACApops.1K + s(vegetated.area, 
##     k = 7) + s(bank.slope, k = 6) + s(area.10cm, k = 6) + s(weighted.dist, 
##     k = 6)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)    
## 1      29.1      20.50                           
## 2      24.6       0.13 4.56     20.4  0.00072 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## Warning: matrix not positive definite

## Warning: matrix not positive definite

## Warning: matrix not positive definite
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ count.RACApops.1K + s(vegetated.area, k = 7) + s(silt.total, 
##     k = 6) + s(bank.slope, k = 5) + s(area.10cm, k = 5) + s(weighted.dist, 
##     k = 5)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)
## (Intercept)          1.074      1.926    0.56     0.58
## count.RACApops.1K   -0.338      0.343   -0.99     0.32
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value  
## s(vegetated.area) 3.46   3.97   8.07   0.087 .
## s(silt.total)     1.00   1.00   0.00   0.979  
## s(bank.slope)     1.00   1.00   3.41   0.065 .
## s(area.10cm)      1.00   1.00   0.02   0.880  
## s(weighted.dist)  1.69   2.08   0.86   0.669  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## R-sq.(adj) =   0.41   Deviance explained = 49.7%
## UBRE score = 0.15144  Scale est. = 1         n = 42
## Analysis of Deviance Table
## 
## Model 1: treatment ~ count.RACApops.1K + s(vegetated.area, k = 7) + s(silt.total, 
##     k = 6) + s(bank.slope, k = 5) + s(area.10cm, k = 5) + s(weighted.dist, 
##     k = 5)
## Model 2: treatment ~ count.RACApops.1K + BUBO.breeding + s(silt.total, 
##     k = i) + s(vegetated.area, k = 7) + s(bank.slope, k = 6) + 
##     s(area.10cm, k = 6) + s(weighted.dist, k = 6)
##   Resid. Df Resid. Dev   Df Deviance Pr(>Chi)    
## 1      31.8      28.06                           
## 2      24.6       0.13 7.28     27.9  0.00028 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Family: binomial 
## Link function: logit 
## 
## Formula:
## treatment ~ BUBO.breeding + count.RACApops.1K + s(bank.slope, 
##     k = 6) + s(vegetated.area, k = 7) + s(weighted.dist, k = 6)
## 
## Parametric coefficients:
##                   Estimate Std. Error z value Pr(>|z|)  
## (Intercept)          2.918      2.071    1.41    0.159  
## BUBO.breedingy      -2.159      1.129   -1.91    0.056 .
## count.RACApops.1K   -0.397      0.383   -1.04    0.300  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Approximate significance of smooth terms:
##                    edf Ref.df Chi.sq p-value
## s(bank.slope)     1.71   2.13   3.99    0.15
## s(vegetated.area) 3.34   3.85   4.20    0.35
## s(weighted.dist)  1.63   2.01   0.99    0.61
## 
## R-sq.(adj) =  0.543   Deviance explained = 58.1%
## UBRE score = 0.017961  Scale est. = 1         n = 42
##                 AICc df               dAICc weight 
## fish1           49.4 9.69075868652962  0.0  0.66781
## fishlakes4.logr 51.4 9.69801565275897  2.0  0.23978
## fishlakes5.logr 55.2 6.94476085279448  5.8  0.03658
## fishlakes8.logr 55.7 10.1502612087597  6.3  0.02826
## fishlakes2.logr 57.2 8.02172340100704  7.8  0.01338
## fishlakes6.logr 58.4 12.4918149689505  9.0  0.00742
## fishlakes7.logr 58.9 12.8639006849105  9.5  0.00570
## fishlakes.logr  62.2 17.4287814751962 12.9  0.00107

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