##load required libraries###
library(tidyverse)
## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr
## Warning: package 'ggplot2' was built under R version 3.1.3
## Warning: package 'readr' was built under R version 3.1.3
## Warning: package 'dplyr' was built under R version 3.1.3
## Conflicts with tidy packages ----------------------------------------------
## filter(): dplyr, stats
## lag():    dplyr, stats
library(broom)
## Warning: package 'broom' was built under R version 3.1.3
library(readxl)
## Warning: package 'readxl' was built under R version 3.1.3
library(forcats)
library(MASS)
## Warning: package 'MASS' was built under R version 3.1.3
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
##set plot themes####
source('theme_javier.R')
theme_set(theme_javier(base_size = 8))

sp <- read_excel('InteractionData_07-09-16.xlsx', 1)

###species model negative binomial####
sp_models <- sp %>%
  gather(sp, abund,-c(1:6)) %>%
  group_by(sp) %>%
  do(fit_sp = step(
    glm.nb(
      abund + 1 ~
        scale(mud) +
        I(scale(mud) ^ 2) +
        scale(CuPb) +
        I(scale(CuPb) ^ 2) +
        scale(TPTN) +
        I(scale(TPTN) ^ 2) +
        scale(TPTN):scale(CuPb) +
        scale(TPTN):scale(mud) +
        scale(CuPb):scale(mud),
      data = .
    ),
    control = glm.control(trace = 10, maxit = 1000)
  ),
  direction = 'backwards')
## Start:  AIC=3687.38
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   710.20 3686.4
## - scale(mud):scale(TPTN)   1   710.74 3686.9
## <none>                         709.20 3687.4
## - I(scale(CuPb)^2)         1   714.02 3690.2
## - scale(CuPb):scale(TPTN)  1   715.11 3691.3
## - scale(mud):scale(CuPb)   1   720.40 3696.6
## - I(scale(mud)^2)          1   721.79 3698.0
## 
## Step:  AIC=3686.38
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   711.40 3685.0
## <none>                         710.83 3686.4
## - scale(CuPb):scale(TPTN)  1   715.86 3689.4
## - I(scale(CuPb)^2)         1   716.21 3689.8
## - scale(mud):scale(CuPb)   1   721.16 3694.7
## - I(scale(mud)^2)          1   723.82 3697.4
## 
## Step:  AIC=3684.95
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         711.93 3685.0
## - I(scale(CuPb)^2)         1   716.79 3687.8
## - scale(mud):scale(CuPb)   1   721.84 3692.9
## - I(scale(mud)^2)          1   726.70 3697.7
## - scale(CuPb):scale(TPTN)  1   735.93 3706.9
## Start:  AIC=2444.17
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   468.50 2443.4
## <none>                         467.28 2444.2
## - scale(mud):scale(CuPb)   1   469.48 2444.4
## - scale(CuPb):scale(TPTN)  1   472.93 2447.8
## - I(scale(TPTN)^2)         1   478.15 2453.0
## - scale(mud):scale(TPTN)   1   479.89 2454.8
## - I(scale(mud)^2)          1   479.99 2454.9
## 
## Step:  AIC=2443.39
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         468.46 2443.4
## - scale(CuPb):scale(TPTN)  1   472.93 2445.8
## - I(scale(TPTN)^2)         1   478.34 2451.3
## - I(scale(mud)^2)          1   480.02 2452.9
## - scale(mud):scale(CuPb)   1   481.68 2454.6
## - scale(mud):scale(TPTN)   1   484.43 2457.3
## Start:  AIC=2303.55
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   429.04 2302.2
## <none>                         428.37 2303.6
## - scale(CuPb):scale(TPTN)  1   434.88 2308.1
## - I(scale(CuPb)^2)         1   436.43 2309.6
## - scale(mud):scale(TPTN)   1   436.98 2310.2
## - scale(mud):scale(CuPb)   1   449.62 2322.8
## - I(scale(mud)^2)          1   478.56 2351.7
## 
## Step:  AIC=2302.21
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         429.81 2302.2
## - scale(CuPb):scale(TPTN)  1   436.06 2306.5
## - I(scale(CuPb)^2)         1   439.55 2309.9
## - scale(mud):scale(TPTN)   1   445.51 2315.9
## - scale(mud):scale(CuPb)   1   450.76 2321.2
## - I(scale(mud)^2)          1   492.19 2362.6
## Start:  AIC=2938.77
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   598.94 2936.8
## - I(scale(TPTN)^2)         1   599.57 2937.4
## <none>                         598.93 2938.8
## - scale(mud):scale(TPTN)   1   603.86 2941.7
## - I(scale(CuPb)^2)         1   604.02 2941.9
## - I(scale(mud)^2)          1   610.65 2948.5
## - scale(mud):scale(CuPb)   1   613.86 2951.7
## 
## Step:  AIC=2936.78
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - I(scale(TPTN)^2)        1   599.82 2935.7
## <none>                        598.90 2936.8
## - scale(mud):scale(TPTN)  1   606.04 2941.9
## - I(scale(CuPb)^2)        1   606.76 2942.6
## - I(scale(mud)^2)         1   613.10 2949.0
## - scale(mud):scale(CuPb)  1   613.82 2949.7
## 
## Step:  AIC=2935.7
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        598.27 2935.7
## - I(scale(CuPb)^2)        1   606.57 2942.0
## - scale(mud):scale(CuPb)  1   613.16 2948.6
## - I(scale(mud)^2)         1   620.32 2955.8
## - scale(mud):scale(TPTN)  1   637.92 2973.3
## Start:  AIC=4062.4
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   714.96 4060.4
## - scale(mud):scale(TPTN)   1   716.35 4061.8
## <none>                         714.96 4062.4
## - scale(CuPb):scale(TPTN)  1   718.68 4064.1
## - I(scale(CuPb)^2)         1   719.64 4065.1
## - I(scale(TPTN)^2)         1   721.83 4067.3
## - I(scale(mud)^2)          1   726.48 4071.9
## 
## Step:  AIC=4060.4
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   716.33 4059.8
## <none>                         714.93 4060.4
## - scale(CuPb):scale(TPTN)  1   718.73 4062.2
## - I(scale(TPTN)^2)         1   721.80 4065.3
## - I(scale(CuPb)^2)         1   724.15 4067.6
## - I(scale(mud)^2)          1   729.21 4072.7
## 
## Step:  AIC=4059.8
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         714.47 4059.8
## - scale(CuPb):scale(TPTN)  1   717.17 4060.5
## - I(scale(TPTN)^2)         1   720.16 4063.5
## - I(scale(CuPb)^2)         1   722.63 4066.0
## - I(scale(mud)^2)          1   793.07 4136.4
## - scale(mud)               1   924.66 4268.0
## Start:  AIC=2069.51
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   389.70 2067.6
## - scale(mud):scale(TPTN)   1   390.27 2068.2
## - scale(mud):scale(CuPb)   1   390.33 2068.3
## <none>                         389.59 2069.5
## - I(scale(mud)^2)          1   391.91 2069.8
## - scale(CuPb):scale(TPTN)  1   392.76 2070.7
## - I(scale(TPTN)^2)         1   398.81 2076.7
## 
## Step:  AIC=2067.62
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   390.59 2066.5
## <none>                         389.70 2067.6
## - I(scale(mud)^2)          1   392.31 2068.2
## - scale(mud):scale(CuPb)   1   392.38 2068.3
## - scale(CuPb):scale(TPTN)  1   393.34 2069.3
## - I(scale(TPTN)^2)         1   398.93 2074.8
## 
## Step:  AIC=2066.51
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         390.34 2066.5
## - scale(mud):scale(CuPb)   1   393.27 2067.4
## - scale(CuPb):scale(TPTN)  1   395.33 2069.5
## - I(scale(TPTN)^2)         1   399.76 2073.9
## - I(scale(mud)^2)          1   403.65 2077.8
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1626.79
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   88.034 1624.8
## - scale(mud):scale(CuPb)   1   88.176 1624.9
## - I(scale(CuPb)^2)         1   88.473 1625.2
## - I(scale(mud)^2)          1   89.014 1625.8
## - I(scale(TPTN)^2)         1   89.514 1626.3
## - scale(CuPb):scale(TPTN)  1   89.770 1626.5
## <none>                         88.028 1626.8
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1624.79
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   88.200 1623.0
## - I(scale(CuPb)^2)         1   88.482 1623.2
## - I(scale(mud)^2)          1   89.657 1624.4
## - scale(CuPb):scale(TPTN)  1   89.890 1624.7
## <none>                         88.034 1624.8
## - I(scale(TPTN)^2)         1   90.134 1624.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1622.96
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   89.968 1622.7
## <none>                         88.200 1623.0
## - I(scale(CuPb)^2)         1   90.207 1623.0
## - I(scale(TPTN)^2)         1   90.334 1623.1
## - I(scale(mud)^2)          1   90.408 1623.2
## - scale(mud)               1   92.959 1625.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1622.73
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - I(scale(CuPb)^2)  1   90.233 1621.0
## - I(scale(TPTN)^2)  1   90.337 1621.1
## - scale(TPTN)       1   90.732 1621.5
## <none>                  89.968 1622.7
## - I(scale(mud)^2)   1   92.248 1623.0
## - scale(CuPb)       1   92.851 1623.6
## - scale(mud)        1   94.804 1625.6
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1620.99
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - scale(TPTN)       1   90.888 1619.7
## <none>                  90.233 1621.0
## - I(scale(mud)^2)   1   92.248 1621.0
## - scale(CuPb)       1   92.852 1621.6
## - I(scale(TPTN)^2)  1   93.063 1621.8
## - scale(mud)        1   94.942 1623.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1619.65
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - I(scale(mud)^2)   1   92.723 1619.5
## <none>                  90.888 1619.7
## - I(scale(TPTN)^2)  1   93.370 1620.1
## - scale(CuPb)       1   94.804 1621.6
## - scale(mud)        1   94.965 1621.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1619.48
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - I(scale(TPTN)^2)  1   93.420 1618.2
## <none>                  92.723 1619.5
## - scale(CuPb)       1   94.852 1619.6
## - scale(mud)        1   95.072 1619.8
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1618.18
## abund + 1 ~ scale(mud) + scale(CuPb)
## 
##               Df Deviance    AIC
## - scale(CuPb)  1   94.852 1617.6
## <none>             93.420 1618.2
## - scale(mud)   1   95.529 1618.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1617.61
## abund + 1 ~ scale(mud)
## 
##              Df Deviance    AIC
## - scale(mud)  1   95.530 1616.3
## <none>            94.852 1617.6
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1616.29
## abund + 1 ~ 1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1629.72
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   79.014 1627.7
## - scale(mud):scale(CuPb)   1   79.044 1627.8
## - scale(mud):scale(TPTN)   1   79.049 1627.8
## - I(scale(CuPb)^2)         1   79.159 1627.9
## - scale(CuPb):scale(TPTN)  1   79.164 1627.9
## - I(scale(TPTN)^2)         1   79.397 1628.1
## <none>                         79.014 1629.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1627.72
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   79.057 1625.8
## - scale(mud):scale(TPTN)   1   79.087 1625.8
## - I(scale(CuPb)^2)         1   79.169 1625.9
## - scale(CuPb):scale(TPTN)  1   79.172 1625.9
## - I(scale(TPTN)^2)         1   79.445 1626.2
## <none>                         79.014 1627.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1625.76
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   79.185 1623.9
## - scale(CuPb):scale(TPTN)  1   79.204 1623.9
## - scale(mud):scale(TPTN)   1   79.405 1624.1
## - I(scale(TPTN)^2)         1   79.596 1624.3
## <none>                         79.057 1625.8
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1623.89
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   79.206 1621.9
## - scale(mud):scale(TPTN)   1   79.539 1622.2
## - I(scale(TPTN)^2)         1   79.599 1622.3
## <none>                         79.185 1623.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1621.91
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(CuPb)             1   79.207 1619.9
## - I(scale(TPTN)^2)        1   79.702 1620.4
## - scale(mud):scale(TPTN)  1   79.725 1620.4
## <none>                        79.206 1621.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1619.91
## abund + 1 ~ scale(mud) + scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(TPTN)  1   79.812 1618.5
## - I(scale(TPTN)^2)        1   79.823 1618.5
## <none>                        79.207 1619.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1618.52
## abund + 1 ~ scale(mud) + scale(TPTN) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - I(scale(TPTN)^2)  1   79.823 1616.5
## - scale(TPTN)       1   80.282 1617.0
## - scale(mud)        1   81.319 1618.0
## <none>                  79.812 1618.5
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1616.53
## abund + 1 ~ scale(mud) + scale(TPTN)
## 
##               Df Deviance    AIC
## - scale(TPTN)  1   80.336 1615.0
## - scale(mud)   1   81.343 1616.0
## <none>             79.823 1616.5
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1615.04
## abund + 1 ~ scale(mud)
## 
##              Df Deviance    AIC
## - scale(mud)  1   81.606 1614.3
## <none>            80.336 1615.0
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1614.31
## abund + 1 ~ 1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1820.78
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   211.80 1819.4
## - scale(mud):scale(TPTN)   1   211.89 1819.5
## <none>                         211.20 1820.8
## - I(scale(mud)^2)          1   213.26 1820.8
## - scale(mud):scale(CuPb)   1   215.06 1822.6
## - scale(CuPb):scale(TPTN)  1   218.53 1826.1
## - I(scale(TPTN)^2)         1   220.85 1828.4
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1819.38
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   212.29 1817.9
## <none>                         211.80 1819.4
## - I(scale(mud)^2)          1   214.45 1820.0
## - scale(mud):scale(CuPb)   1   215.84 1821.4
## - I(scale(TPTN)^2)         1   223.50 1829.1
## - scale(CuPb):scale(TPTN)  1   225.69 1831.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1817.87
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         212.29 1817.9
## - I(scale(mud)^2)          1   215.02 1818.6
## - scale(mud):scale(CuPb)   1   216.24 1819.8
## - I(scale(TPTN)^2)         1   226.61 1830.2
## - scale(CuPb):scale(TPTN)  1   227.59 1831.2
## Start:  AIC=4457.26
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   778.54 4456.0
## <none>                         777.83 4457.3
## - scale(mud):scale(TPTN)   1   783.77 4461.2
## - I(scale(CuPb)^2)         1   784.11 4461.5
## - scale(CuPb):scale(TPTN)  1   795.54 4473.0
## - I(scale(TPTN)^2)         1   799.80 4477.2
## - I(scale(mud)^2)          1   801.31 4478.7
## 
## Step:  AIC=4455.97
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         777.82 4456.0
## - scale(mud):scale(TPTN)   1   783.12 4459.3
## - I(scale(CuPb)^2)         1   786.11 4462.3
## - scale(CuPb):scale(TPTN)  1   796.14 4472.3
## - I(scale(TPTN)^2)         1   801.22 4477.4
## - I(scale(mud)^2)          1   819.38 4495.5
## Start:  AIC=3134.99
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   708.84 3133.0
## - scale(CuPb):scale(TPTN)  1   709.23 3133.4
## - I(scale(CuPb)^2)         1   709.89 3134.1
## - I(scale(mud)^2)          1   710.77 3134.9
## <none>                         708.83 3135.0
## - scale(mud):scale(CuPb)   1   713.79 3137.9
## - scale(mud):scale(TPTN)   1   716.97 3141.1
## 
## Step:  AIC=3133
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   709.25 3131.5
## - I(scale(CuPb)^2)         1   709.82 3132.1
## <none>                         708.76 3133.0
## - I(scale(mud)^2)          1   711.03 3133.3
## - scale(mud):scale(CuPb)   1   713.82 3136.1
## - scale(mud):scale(TPTN)   1   720.87 3143.1
## 
## Step:  AIC=3131.49
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - I(scale(CuPb)^2)        1   709.16 3130.1
## - I(scale(mud)^2)         1   710.34 3131.3
## <none>                        708.55 3131.5
## - scale(mud):scale(CuPb)  1   713.81 3134.8
## - scale(mud):scale(TPTN)  1   732.80 3153.7
## 
## Step:  AIC=3130.1
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        708.35 3130.1
## - I(scale(mud)^2)         1   714.07 3133.8
## - scale(mud):scale(CuPb)  1   727.32 3147.1
## - scale(mud):scale(TPTN)  1   732.18 3151.9
## Start:  AIC=2359.69
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   454.83 2358.1
## - scale(mud):scale(TPTN)   1   455.18 2358.5
## <none>                         454.38 2359.7
## - scale(mud):scale(CuPb)   1   459.47 2362.8
## - scale(CuPb):scale(TPTN)  1   467.23 2370.5
## - I(scale(CuPb)^2)         1   470.31 2373.6
## - I(scale(TPTN)^2)         1   480.95 2384.3
## 
## Step:  AIC=2358.14
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         454.86 2358.1
## - scale(mud):scale(TPTN)   1   458.18 2359.4
## - scale(mud):scale(CuPb)   1   463.26 2364.5
## - scale(CuPb):scale(TPTN)  1   467.48 2368.8
## - I(scale(CuPb)^2)         1   472.60 2373.9
## - I(scale(TPTN)^2)         1   486.63 2387.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1704.93
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   121.67 1702.9
## - I(scale(mud)^2)          1   121.78 1703.0
## - scale(mud):scale(CuPb)   1   121.90 1703.2
## - scale(CuPb):scale(TPTN)  1   122.04 1703.3
## - I(scale(CuPb)^2)         1   122.06 1703.3
## - I(scale(TPTN)^2)         1   122.77 1704.0
## <none>                         121.66 1704.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1702.94
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   121.92 1701.2
## - I(scale(mud)^2)          1   121.95 1701.2
## - I(scale(CuPb)^2)         1   122.12 1701.4
## - scale(CuPb):scale(TPTN)  1   122.15 1701.4
## - I(scale(TPTN)^2)         1   123.04 1702.3
## <none>                         121.67 1702.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1701.19
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   122.12 1699.4
## - scale(CuPb):scale(TPTN)  1   122.49 1699.8
## - I(scale(TPTN)^2)         1   123.28 1700.5
## <none>                         121.92 1701.2
## - I(scale(mud)^2)          1   124.11 1701.4
## - scale(mud)               1   125.58 1702.8
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1699.39
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   122.70 1698.0
## - I(scale(TPTN)^2)         1   123.36 1698.6
## <none>                         122.12 1699.4
## - I(scale(mud)^2)          1   124.19 1699.5
## - scale(mud)               1   125.60 1700.9
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1697.97
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - scale(CuPb)       1   122.74 1696.0
## - I(scale(TPTN)^2)  1   124.00 1697.3
## - scale(TPTN)       1   124.34 1697.6
## <none>                  122.70 1698.0
## - I(scale(mud)^2)   1   125.71 1699.0
## - scale(mud)        1   127.86 1701.1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1696.01
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(TPTN) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - scale(TPTN)       1   124.39 1695.7
## <none>                  122.74 1696.0
## - I(scale(TPTN)^2)  1   125.51 1696.8
## - I(scale(mud)^2)   1   127.47 1698.7
## - scale(mud)        1   133.07 1704.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1695.66
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## - I(scale(TPTN)^2)  1   125.88 1695.2
## <none>                  124.39 1695.7
## - I(scale(mud)^2)   1   127.97 1697.2
## - scale(mud)        1   135.06 1704.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1695.15
## abund + 1 ~ scale(mud) + I(scale(mud)^2)
## 
##                   Df Deviance    AIC
## <none>                 125.88 1695.2
## - I(scale(mud)^2)  1   128.74 1696.0
## - scale(mud)       1   135.09 1702.4
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1840.44
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   240.70 1839.0
## - scale(mud):scale(CuPb)   1   241.59 1839.9
## - scale(mud):scale(TPTN)   1   241.81 1840.1
## <none>                         240.13 1840.4
## - I(scale(mud)^2)          1   242.51 1840.8
## - I(scale(CuPb)^2)         1   243.04 1841.3
## - I(scale(TPTN)^2)         1   243.04 1841.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1839.01
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(CuPb)  1   242.32 1838.6
## <none>                        240.70 1839.0
## - I(scale(CuPb)^2)        1   243.08 1839.4
## - I(scale(TPTN)^2)        1   243.09 1839.4
## - scale(mud):scale(TPTN)  1   243.42 1839.7
## - I(scale(mud)^2)         1   244.01 1840.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1838.62
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(CuPb)             1   242.53 1836.8
## - I(scale(CuPb)^2)        1   243.26 1837.6
## - I(scale(mud)^2)         1   244.22 1838.5
## <none>                        242.32 1838.6
## - I(scale(TPTN)^2)        1   244.82 1839.1
## - scale(mud):scale(TPTN)  1   245.85 1840.2
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1836.83
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - I(scale(CuPb)^2)        1   243.29 1835.6
## <none>                        242.53 1836.8
## - I(scale(TPTN)^2)        1   245.01 1837.3
## - I(scale(mud)^2)         1   245.27 1837.6
## - scale(mud):scale(TPTN)  1   246.16 1838.5
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1835.59
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## <none>                        243.29 1835.6
## - I(scale(mud)^2)         1   245.77 1836.1
## - scale(mud):scale(TPTN)  1   246.37 1836.7
## - I(scale(TPTN)^2)        1   246.50 1836.8
## Start:  AIC=2106.65
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   425.24 2104.9
## - scale(CuPb):scale(TPTN)  1   425.31 2105.0
## - I(scale(CuPb)^2)         1   425.74 2105.4
## <none>                         424.94 2106.7
## - I(scale(mud)^2)          1   427.75 2107.5
## - scale(mud):scale(CuPb)   1   428.74 2108.4
## - scale(mud):scale(TPTN)   1   430.32 2110.0
## 
## Step:  AIC=2104.94
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   425.37 2103.1
## - I(scale(CuPb)^2)         1   425.87 2103.6
## <none>                         425.22 2104.9
## - I(scale(mud)^2)          1   428.72 2106.4
## - scale(mud):scale(CuPb)   1   429.08 2106.8
## - scale(mud):scale(TPTN)   1   433.46 2111.2
## 
## Step:  AIC=2103.09
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - I(scale(CuPb)^2)        1   425.71 2101.6
## <none>                        425.21 2103.1
## - I(scale(mud)^2)         1   429.03 2104.9
## - scale(mud):scale(CuPb)  1   429.13 2105.0
## - scale(mud):scale(TPTN)  1   448.62 2124.5
## 
## Step:  AIC=2101.6
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        425.58 2101.6
## - I(scale(mud)^2)         1   435.42 2109.4
## - scale(mud):scale(CuPb)  1   437.62 2111.6
## - scale(mud):scale(TPTN)  1   449.45 2123.5
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1879.53
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   243.81 1877.6
## - I(scale(CuPb)^2)         1   243.85 1877.6
## - scale(mud):scale(CuPb)   1   243.93 1877.7
## - scale(mud):scale(TPTN)   1   244.12 1877.9
## <none>                         243.75 1879.5
## - scale(CuPb):scale(TPTN)  1   255.38 1889.2
## - I(scale(TPTN)^2)         1   294.51 1928.3
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1877.59
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   243.96 1875.7
## - scale(mud):scale(TPTN)   1   244.16 1875.9
## - scale(mud):scale(CuPb)   1   244.23 1876.0
## <none>                         243.81 1877.6
## - scale(CuPb):scale(TPTN)  1   256.98 1888.8
## - I(scale(TPTN)^2)         1   298.86 1930.6
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1875.74
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   244.17 1873.9
## - scale(mud):scale(CuPb)   1   244.25 1874.0
## <none>                         243.96 1875.7
## - scale(CuPb):scale(TPTN)  1   271.19 1901.0
## - I(scale(TPTN)^2)         1   301.05 1930.8
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1873.94
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(CuPb):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   244.29 1872.1
## <none>                         244.17 1873.9
## - scale(CuPb):scale(TPTN)  1   272.34 1900.1
## - I(scale(TPTN)^2)         1   341.90 1969.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1872.07
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(mud)               1   244.69 1870.5
## <none>                         244.29 1872.1
## - scale(CuPb):scale(TPTN)  1   332.08 1957.9
## - I(scale(TPTN)^2)         1   352.33 1978.1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1870.47
## abund + 1 ~ scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         244.69 1870.5
## - scale(CuPb):scale(TPTN)  1   334.23 1958.0
## - I(scale(TPTN)^2)         1   354.10 1977.9
## Warning in glm.nb(abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb)
## + : alternation limit reached
## Start:  AIC=1808.26
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   249.66 1806.5
## - I(scale(mud)^2)          1   249.79 1806.6
## - scale(mud):scale(CuPb)   1   249.86 1806.7
## <none>                         249.42 1808.3
## - scale(CuPb):scale(TPTN)  1   253.25 1810.1
## - I(scale(CuPb)^2)         1   253.40 1810.2
## - I(scale(TPTN)^2)         1   255.11 1812.0
## 
## Step:  AIC=1806.5
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   250.24 1805.1
## - I(scale(mud)^2)          1   251.27 1806.1
## <none>                         249.64 1806.5
## - I(scale(CuPb)^2)         1   254.58 1809.4
## - scale(CuPb):scale(TPTN)  1   254.81 1809.7
## - I(scale(TPTN)^2)         1   255.71 1810.6
## 
## Step:  AIC=1805.1
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         250.12 1805.1
## - scale(CuPb):scale(TPTN)  1   255.65 1808.6
## - I(scale(TPTN)^2)         1   256.07 1809.0
## - I(scale(CuPb)^2)         1   256.11 1809.1
## - I(scale(mud)^2)          1   258.87 1811.8
## - scale(mud)               1   262.17 1815.2
## Start:  AIC=2031.78
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   331.40 2029.8
## - scale(CuPb):scale(TPTN)  1   331.65 2030.0
## - scale(mud):scale(TPTN)   1   331.82 2030.2
## - I(scale(mud)^2)          1   332.36 2030.8
## <none>                         331.40 2031.8
## - I(scale(TPTN)^2)         1   335.41 2033.8
## - scale(mud):scale(CuPb)   1   337.49 2035.9
## 
## Step:  AIC=2029.79
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   331.83 2028.2
## - scale(mud):scale(TPTN)   1   331.84 2028.2
## - I(scale(mud)^2)          1   332.50 2028.9
## <none>                         331.41 2029.8
## - I(scale(TPTN)^2)         1   335.45 2031.8
## - scale(mud):scale(CuPb)   1   344.67 2041.0
## 
## Step:  AIC=2028.2
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(TPTN)  1   332.85 2027.1
## <none>                        331.98 2028.2
## - I(scale(mud)^2)         1   334.59 2028.8
## - I(scale(TPTN)^2)        1   338.96 2033.2
## - scale(mud):scale(CuPb)  1   360.87 2055.1
## 
## Step:  AIC=2027.06
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - I(scale(mud)^2)         1   335.41 2027.0
## <none>                        333.51 2027.1
## - scale(TPTN)             1   353.92 2045.5
## - scale(mud):scale(CuPb)  1   361.64 2053.2
## - I(scale(TPTN)^2)        1   379.11 2070.7
## 
## Step:  AIC=2026.96
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        334.68 2027.0
## - scale(TPTN)             1   353.95 2044.2
## - I(scale(TPTN)^2)        1   383.45 2073.7
## - scale(mud):scale(CuPb)  1   396.77 2087.1
## Start:  AIC=2451.74
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   522.65 2449.8
## - I(scale(CuPb)^2)         1   522.73 2449.9
## <none>                         522.56 2451.7
## - scale(CuPb):scale(TPTN)  1   525.99 2453.2
## - I(scale(mud)^2)          1   529.18 2456.3
## - scale(mud):scale(TPTN)   1   531.70 2458.9
## - I(scale(TPTN)^2)         1   544.53 2471.7
## 
## Step:  AIC=2449.83
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   523.28 2448.6
## <none>                         522.52 2449.8
## - scale(CuPb):scale(TPTN)  1   525.87 2451.2
## - I(scale(mud)^2)          1   531.55 2456.8
## - scale(mud):scale(TPTN)   1   531.58 2456.9
## - I(scale(TPTN)^2)         1   544.40 2469.7
## 
## Step:  AIC=2448.58
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         523.09 2448.6
## - scale(CuPb):scale(TPTN)  1   528.22 2451.7
## - scale(mud):scale(TPTN)   1   533.46 2456.9
## - I(scale(mud)^2)          1   533.82 2457.3
## - I(scale(TPTN)^2)         1   545.76 2469.2
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## Start:  AIC=1747.72
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   188.54 1745.7
## - scale(mud):scale(CuPb)   1   188.64 1745.8
## - scale(CuPb):scale(TPTN)  1   188.77 1745.9
## - I(scale(mud)^2)          1   189.62 1746.8
## - scale(mud):scale(TPTN)   1   190.01 1747.2
## - I(scale(TPTN)^2)         1   190.35 1747.5
## <none>                         188.54 1747.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1745.72
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   188.81 1744.0
## - scale(CuPb):scale(TPTN)  1   188.83 1744.0
## - I(scale(mud)^2)          1   189.64 1744.8
## - scale(mud):scale(TPTN)   1   190.12 1745.3
## - I(scale(TPTN)^2)         1   190.43 1745.6
## <none>                         188.54 1745.7
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1743.98
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   188.85 1742.0
## - I(scale(TPTN)^2)         1   190.43 1743.6
## - scale(mud):scale(TPTN)   1   190.43 1743.6
## <none>                         188.81 1744.0
## - I(scale(mud)^2)          1   190.91 1744.1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1742.02
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(CuPb)             1   189.15 1740.3
## - I(scale(TPTN)^2)        1   190.59 1741.8
## <none>                        188.85 1742.0
## - scale(mud):scale(TPTN)  1   190.85 1742.0
## - I(scale(mud)^2)         1   191.05 1742.2
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1740.33
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - I(scale(TPTN)^2)        1   190.81 1740.0
## <none>                        189.15 1740.3
## - scale(mud):scale(TPTN)  1   191.38 1740.5
## - I(scale(mud)^2)         1   192.47 1741.6
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1739.98
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(TPTN) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(TPTN)  1   191.90 1739.1
## - I(scale(mud)^2)         1   192.50 1739.7
## <none>                        190.81 1740.0
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1739.07
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(TPTN)
## 
##                   Df Deviance    AIC
## - scale(mud)       1   191.90 1737.1
## - scale(TPTN)      1   191.95 1737.1
## - I(scale(mud)^2)  1   192.71 1737.9
## <none>                 191.90 1739.1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1737.07
## abund + 1 ~ I(scale(mud)^2) + scale(TPTN)
## 
##                   Df Deviance    AIC
## - scale(TPTN)      1   192.00 1735.2
## - I(scale(mud)^2)  1   192.85 1736.0
## <none>                 191.90 1737.1
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1735.17
## abund + 1 ~ I(scale(mud)^2)
## 
##                   Df Deviance    AIC
## - I(scale(mud)^2)  1   193.13 1734.3
## <none>                 192.00 1735.2
## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached

## Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
## control$trace > : iteration limit reached
## 
## Step:  AIC=1734.31
## abund + 1 ~ 1
## 
## Start:  AIC=2643.26
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## <none>                         553.37 2643.3
## - scale(CuPb):scale(TPTN)  1   555.70 2643.6
## - scale(mud):scale(CuPb)   1   556.37 2644.3
## - scale(mud):scale(TPTN)   1   556.48 2644.4
## - I(scale(TPTN)^2)         1   556.56 2644.5
## - I(scale(mud)^2)          1   557.05 2644.9
## - I(scale(CuPb)^2)         1   565.72 2653.6
## Start:  AIC=2570.28
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   519.29 2568.6
## - scale(CuPb):scale(TPTN)  1   520.61 2569.9
## <none>                         519.00 2570.3
## - scale(mud):scale(CuPb)   1   521.28 2570.6
## - I(scale(mud)^2)          1   521.80 2571.1
## - I(scale(TPTN)^2)         1   524.66 2573.9
## - I(scale(CuPb)^2)         1   525.03 2574.3
## 
## Step:  AIC=2568.57
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         518.82 2568.6
## - scale(CuPb):scale(TPTN)  1   521.30 2569.1
## - scale(mud):scale(CuPb)   1   521.43 2569.2
## - I(scale(TPTN)^2)         1   524.89 2572.6
## - I(scale(CuPb)^2)         1   526.17 2573.9
## - I(scale(mud)^2)          1   526.50 2574.2
##without scaling opredictors####
# sp_models <- sp %>%
#   gather(sp, abund, -c(1:6)) %>%
#   group_by(sp) %>%
#   do(fit_sp = step(
#     glm.nb(
#       abund + 1 ~
#         mud +
#         I(mud ^ 2) +
#         CuPb +
#         I(CuPb ^ 2) +
#         TPTN +
#         I(TPTN ^ 2) +
#         TPTN:CuPb +
#         TPTN:mud +
#         CuPb:mud,
#       data = .
#     ),
#     control = glm.control(trace = 10, maxit = 1000)
#   ),
#   direction = 'backwards')


##get spp coefficients and rename terms####
sp_coef = tidy(sp_models, fit_sp) %>% 
  data.frame(.) %>%
  mutate(
    term = factor(term),
    term = fct_recode(
      term,
      "Intercept" = "(Intercept)",
      "Sediment" = "scale(mud)",
      "Sediment^2" = "I(scale(mud)^2)",
      "Metals" =  "scale(CuPb)",
      "Metals^2" = "I(scale(CuPb)^2)",
      "Nutrients" = "scale(TPTN)",
      "Nutrients^2" = "I(scale(TPTN)^2)",
      "Nutrients x Metals" =  "scale(CuPb):scale(TPTN)",
      "Sediment x Nutrients" =  "scale(mud):scale(TPTN)",
      "Sediment x Metals" =  "scale(mud):scale(CuPb)"
    )
  )

##subset relevant spp coefficients####
sp_coef1 <- sp_coef %>%
  dplyr::filter(term != 'Intercept' &
                  term != 'Sediment^2' &
                  term != 'Metals^2' &
                  term != 'Nutrients^2') %>%
  mutate(term = factor(term))

###Coefficient plot for species####
ggplot(sp_coef1,
       aes(
         x = estimate,
         y = fct_rev(fct_inorder(term)),
         color = term
       )) +
  geom_point() +
  geom_errorbarh(aes(
    xmin = estimate + (std.error * 1.96),
    xmax = estimate - (std.error * 1.96),
    height = .2
  )) +
  facet_wrap(~ sp) +
  geom_vline(xintercept = 0,
             lty = 2,
             col = 2) +
  ylab('') +
  xlab('Estimates') +
  geom_hline(yintercept = 3.5, lty = 2) +
  scale_color_discrete(guide = F)

####Summary of spp regresssion####
sp_Summ  <- glance(sp_models, fit_sp) %>%
  mutate(Rsqr = 1 - (deviance / null.deviance)) %>%
  dplyr::select(-df.null, -BIC) %>%
  dplyr::filter(Rsqr > .1) %>%
  print(n = 20)
## Source: local data frame [13 x 7]
## Groups: sp [13]
## 
##                          sp null.deviance     logLik      AIC deviance
##                       (chr)         (dbl)      (dbl)    (dbl)    (dbl)
## 1  Anthopleura_aureoradiata     1206.7554 -1834.4753 3686.951 711.9269
## 2           Aonides_trifida      711.9496 -1212.6931 2445.386 468.4648
## 3       Arcuatula_senhousia      638.9090 -1142.1075 2304.215 429.8146
## 4     Austrominius_modestus     1172.3609 -1459.8502 2937.700 598.2667
## 5   Austrovenus_stutchburyi     1282.2567 -2021.9016 4061.803 714.4673
## 6      Hyboscolex_longiseta      249.7132  -900.9342 1819.868 212.2888
## 7      Linucula_hartvigiana      935.1958 -2218.9836 4457.967 777.8151
## 8          Macomona_liliana      826.3474 -1558.0494 3132.099 708.3472
## 9           Magelona_dakini      619.8039 -1170.0689 2360.138 454.8627
## 10      Notoacmea_elongata_      494.4091 -1043.7986 2103.597 425.5781
## 11        Orbinia_papillosa      441.6075  -930.2342 1872.468 244.6890
## 12        Paphies_australis      491.6805 -1007.4804 2028.961 334.6768
## 13 Zeacumantus_subcarinatus      658.3974 -1275.2855 2570.571 518.8195
## Variables not shown: df.residual (int), Rsqr (dbl)
sp_coef2 <-
  right_join(sp_coef1, sp_Summ, by = 'sp') %>%
  mutate(
    spp = gsub('_', ' ', sp),
    term = factor(term),
    term = fct_relevel(
      term,
      'Sediment',
      'Metals',
      'Nutrients',
      'Nutrients x Metals',
      'Sediment x Metals' ,
      'Sediment x Nutrients'
    )
  ) 
  

##save spp coefficient results####
write.csv(sp_coef2, 'sp_summary.csv', row.names = F)

##plot spp with Rsq>0.1###
sp_plot <-
  ggplot(sp_coef2,
         aes(
           x = estimate,
           y = fct_rev(fct_inorder(term)),
           color = term
         )) +
  geom_point() +
  geom_errorbarh(aes(
    xmin = estimate + (std.error * 1.96),
    xmax = estimate - (std.error * 1.96),
    height = .2
  )) +
  facet_wrap(~ spp) +
  geom_vline(xintercept = 0,
             lty = 2,
             col = 1) +
  ylab('') +
  xlab('Estimates') +
  geom_hline(yintercept = 3.5,
             lty = 2,
             col = 1) +
  scale_color_discrete(guide = F) +
  theme(strip.text = element_text(face = "italic"))


print(sp_plot)

ggsave(
  sp_plot,
  file = 'sp_plot.tif',
  device = 'tiff',
  dpi = 900,
  compression = 'lzw'
)
## Saving 7 x 5 in image
####2. Traits#####
##read data
trait <- read_excel('InteractionData_07-09-16.xlsx', 2)

###Gamma glm for traits####
traits_models <- trait %>% gather(trait, abund,-c(1:6)) %>%
  group_by(trait) %>%
  do(fit_trait = step(
    glm(
      abund + 1 ~
        scale(mud) +
        I(scale(mud) ^ 2) +
        scale(CuPb) +
        I(scale(CuPb) ^ 2) +
        scale(TPTN) +
        I(scale(TPTN) ^ 2) +
        scale(TPTN):scale(CuPb) +
        scale(TPTN):scale(mud) +
        scale(CuPb):scale(mud),
      family = Gamma('log'),
      data = .
    )
  ),
  direction = 'both')
## Start:  AIC=3766.84
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   1142.0 3766.7
## <none>                         1137.2 3766.8
## - scale(mud):scale(TPTN)   1   1145.4 3768.1
## - scale(CuPb):scale(TPTN)  1   1147.7 3769.0
## - I(scale(CuPb)^2)         1   1152.2 3770.7
## - I(scale(mud)^2)          1   1167.4 3776.7
## - scale(mud):scale(CuPb)   1   1173.6 3779.1
## 
## Step:  AIC=3768.72
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
## Start:  AIC=5873.41
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   775.03 5871.5
## <none>                         774.96 5873.4
## - scale(mud):scale(CuPb)   1   777.55 5873.7
## - scale(CuPb):scale(TPTN)  1   777.79 5873.9
## - I(scale(CuPb)^2)         1   780.32 5876.2
## - I(scale(mud)^2)          1   785.44 5880.7
## - I(scale(TPTN)^2)         1   787.92 5882.9
## 
## Step:  AIC=5871.49
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         775.03 5871.5
## - scale(mud):scale(CuPb)   1   777.57 5871.7
## - scale(CuPb):scale(TPTN)  1   777.83 5872.0
## - I(scale(CuPb)^2)         1   780.61 5874.4
## - I(scale(mud)^2)          1   788.88 5881.8
## - I(scale(TPTN)^2)         1   794.86 5887.1
## Start:  AIC=5350.55
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## <none>                         365.69 5350.6
## - scale(CuPb):scale(TPTN)  1   368.23 5352.6
## - I(scale(mud)^2)          1   368.89 5353.7
## - I(scale(TPTN)^2)         1   369.26 5354.3
## - scale(mud):scale(CuPb)   1   371.94 5358.6
## - scale(mud):scale(TPTN)   1   377.21 5367.1
## - I(scale(CuPb)^2)         1   379.04 5370.0
## Start:  AIC=6192.93
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   401.47 6191.2
## - scale(CuPb):scale(TPTN)  1   401.58 6191.4
## - scale(mud):scale(CuPb)   1   402.39 6192.8
## <none>                         401.34 6192.9
## - I(scale(CuPb)^2)         1   403.97 6195.5
## - scale(mud):scale(TPTN)   1   405.24 6197.7
## - I(scale(TPTN)^2)         1   407.08 6200.9
## 
## Step:  AIC=6191.21
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   401.85 6189.9
## - scale(mud):scale(CuPb)   1   402.41 6190.8
## <none>                         401.47 6191.2
## - I(scale(CuPb)^2)         1   403.98 6193.6
## - I(scale(TPTN)^2)         1   408.50 6201.4
## - scale(mud):scale(TPTN)   1   409.11 6202.5
## 
## Step:  AIC=6189.97
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(CuPb)  1   402.84 6189.7
## <none>                        401.85 6190.0
## - I(scale(CuPb)^2)        1   404.15 6192.0
## - scale(mud):scale(TPTN)  1   409.18 6200.8
## - I(scale(TPTN)^2)        1   419.56 6218.9
## 
## Step:  AIC=6189.97
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
## Start:  AIC=5030.58
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   399.52 5029.0
## <none>                         399.27 5030.6
## - scale(CuPb):scale(TPTN)  1   400.84 5031.0
## - scale(mud):scale(CuPb)   1   404.66 5036.9
## - I(scale(TPTN)^2)         1   405.46 5038.2
## - scale(mud):scale(TPTN)   1   409.14 5043.8
## - I(scale(CuPb)^2)         1   409.98 5045.1
## 
## Step:  AIC=5029.09
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         399.52 5029.1
## - scale(CuPb):scale(TPTN)  1   400.86 5029.2
## - I(scale(TPTN)^2)         1   405.60 5036.5
## - scale(mud):scale(CuPb)   1   407.70 5039.7
## - I(scale(CuPb)^2)         1   411.04 5044.9
## - scale(mud):scale(TPTN)   1   413.24 5048.3
## Start:  AIC=6138.61
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   328.65 6137.3
## - scale(mud):scale(CuPb)   1   328.96 6138.0
## <none>                         328.32 6138.6
## - I(scale(TPTN)^2)         1   330.30 6141.0
## - scale(mud):scale(TPTN)   1   331.36 6143.4
## - scale(CuPb):scale(TPTN)  1   331.72 6144.2
## - I(scale(CuPb)^2)         1   335.19 6151.9
## 
## Step:  AIC=6137.42
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   329.02 6136.2
## <none>                         328.65 6137.4
## - I(scale(TPTN)^2)         1   331.54 6141.8
## - scale(CuPb):scale(TPTN)  1   333.02 6145.1
## - I(scale(CuPb)^2)         1   335.21 6149.9
## - scale(mud):scale(TPTN)   1   336.32 6152.4
## 
## Step:  AIC=6136.33
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         329.02 6136.3
## - I(scale(TPTN)^2)         1   331.57 6140.0
## - scale(CuPb):scale(TPTN)  1   333.54 6144.3
## - I(scale(CuPb)^2)         1   337.72 6153.5
## - scale(mud):scale(TPTN)   1   339.34 6157.1
## Start:  AIC=5066.69
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   361.11 5065.0
## - scale(mud):scale(CuPb)   1   361.31 5065.4
## - I(scale(TPTN)^2)         1   361.94 5066.7
## <none>                         360.98 5066.7
## - scale(CuPb):scale(TPTN)  1   362.69 5068.2
## - I(scale(CuPb)^2)         1   363.81 5070.5
## - I(scale(mud)^2)          1   366.91 5076.9
## 
## Step:  AIC=5064.98
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   361.38 5063.5
## - I(scale(TPTN)^2)         1   361.98 5064.8
## <none>                         361.11 5065.0
## - scale(CuPb):scale(TPTN)  1   362.69 5066.2
## - I(scale(CuPb)^2)         1   363.81 5068.5
## - I(scale(mud)^2)          1   374.03 5089.5
## 
## Step:  AIC=5063.58
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   362.29 5063.4
## <none>                         361.38 5063.6
## - scale(CuPb):scale(TPTN)  1   363.14 5065.2
## - I(scale(CuPb)^2)         1   364.68 5068.4
## - I(scale(mud)^2)          1   385.12 5110.3
## - scale(mud)               1   423.79 5189.8
## 
## Step:  AIC=5063.61
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN)
## 
## Start:  AIC=4924.52
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   731.01 4922.5
## - scale(mud):scale(TPTN)   1   732.02 4923.5
## <none>                         731.00 4924.5
## - I(scale(CuPb)^2)         1   734.70 4926.0
## - scale(CuPb):scale(TPTN)  1   742.67 4933.4
## - I(scale(mud)^2)          1   743.03 4933.7
## - I(scale(TPTN)^2)         1   747.36 4937.7
## 
## Step:  AIC=4922.54
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   732.03 4921.5
## <none>                         731.01 4922.5
## - I(scale(CuPb)^2)         1   738.94 4927.9
## - scale(CuPb):scale(TPTN)  1   742.77 4931.5
## - I(scale(TPTN)^2)         1   747.64 4936.0
## - I(scale(mud)^2)          1   748.80 4937.1
## 
## Step:  AIC=4921.73
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         732.03 4921.7
## - I(scale(CuPb)^2)         1   739.22 4926.5
## - scale(CuPb):scale(TPTN)  1   742.78 4929.8
## - I(scale(TPTN)^2)         1   761.38 4947.2
## - I(scale(mud)^2)          1   765.31 4950.9
## - scale(mud)               1   777.02 4961.9
## Start:  AIC=5202.93
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   659.04 5201.0
## - I(scale(CuPb)^2)         1   659.61 5201.4
## <none>                         659.00 5202.9
## - I(scale(TPTN)^2)         1   661.55 5203.1
## - scale(CuPb):scale(TPTN)  1   662.09 5203.5
## - scale(mud):scale(CuPb)   1   662.51 5203.9
## - scale(mud):scale(TPTN)   1   663.58 5204.8
## 
## Step:  AIC=5200.99
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   659.61 5199.5
## <none>                         659.04 5201.0
## - I(scale(TPTN)^2)         1   661.89 5201.4
## - scale(CuPb):scale(TPTN)  1   662.09 5201.6
## - scale(mud):scale(CuPb)   1   662.79 5202.1
## - scale(mud):scale(TPTN)   1   666.39 5205.2
## 
## Step:  AIC=5199.72
## abund + 1 ~ scale(mud) + scale(CuPb) + scale(TPTN) + I(scale(TPTN)^2) + 
##     scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         659.61 5199.7
## - I(scale(TPTN)^2)         1   662.33 5200.0
## - scale(mud):scale(CuPb)   1   663.34 5200.8
## - scale(CuPb):scale(TPTN)  1   664.90 5202.1
## - scale(mud):scale(TPTN)   1   671.68 5207.7
## Start:  AIC=4790.66
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   570.57 4788.7
## <none>                         570.54 4790.7
## - scale(mud):scale(CuPb)   1   578.77 4796.0
## - I(scale(CuPb)^2)         1   580.27 4797.3
## - I(scale(TPTN)^2)         1   585.89 4802.3
## - I(scale(mud)^2)          1   586.22 4802.6
## - scale(mud):scale(TPTN)   1   592.15 4807.9
## 
## Step:  AIC=4788.71
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        570.57 4788.7
## - scale(mud):scale(CuPb)  1   579.28 4794.5
## - I(scale(CuPb)^2)        1   582.68 4797.5
## - I(scale(mud)^2)         1   587.37 4801.7
## - I(scale(TPTN)^2)        1   591.53 4805.5
## - scale(mud):scale(TPTN)  1   593.51 4807.2
## Start:  AIC=6144.73
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   712.72 6143.1
## - scale(CuPb):scale(TPTN)  1   713.47 6143.9
## <none>                         712.33 6144.7
## - scale(mud):scale(CuPb)   1   717.11 6147.5
## - I(scale(CuPb)^2)         1   718.18 6148.6
## - I(scale(TPTN)^2)         1   720.66 6151.1
## - I(scale(mud)^2)          1   724.25 6154.6
## 
## Step:  AIC=6143.2
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   713.64 6142.1
## <none>                         712.72 6143.2
## - scale(mud):scale(CuPb)   1   717.12 6145.6
## - I(scale(CuPb)^2)         1   718.20 6146.7
## - I(scale(mud)^2)          1   727.48 6156.0
## - I(scale(TPTN)^2)         1   729.28 6157.8
## 
## Step:  AIC=6142.31
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(CuPb)
## Warning: glm.fit: algorithm did not converge
##                          Df Deviance    AIC
## <none>                        713.64 6142.3
## - I(scale(CuPb)^2)        1   718.32 6145.0
## - scale(mud):scale(CuPb)  1   718.57 6145.3
## - I(scale(mud)^2)         1   728.50 6155.2
## - I(scale(TPTN)^2)        1   756.13 6183.0
## - scale(TPTN)             1   882.58 6310.0
## Start:  AIC=4204.81
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## <none>                         1149.2 4204.8
## - I(scale(TPTN)^2)         1   1154.6 4205.0
## - scale(mud):scale(TPTN)   1   1155.2 4205.3
## - I(scale(CuPb)^2)         1   1159.1 4206.9
## - scale(CuPb):scale(TPTN)  1   1161.4 4207.8
## - I(scale(mud)^2)          1   1161.8 4208.0
## - scale(mud):scale(CuPb)   1   1189.8 4219.5
## Start:  AIC=4847.04
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   942.83 4845.4
## - I(scale(CuPb)^2)         1   944.23 4846.4
## <none>                         942.34 4847.0
## - scale(mud):scale(TPTN)   1   945.29 4847.1
## - scale(CuPb):scale(TPTN)  1   950.98 4851.0
## - I(scale(TPTN)^2)         1   967.04 4862.1
## - I(scale(mud)^2)          1   973.93 4866.9
## 
## Step:  AIC=4845.51
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(CuPb)^2)         1   944.51 4844.7
## - scale(mud):scale(TPTN)   1   945.32 4845.2
## <none>                         942.83 4845.5
## - scale(CuPb):scale(TPTN)  1   951.92 4849.8
## - I(scale(TPTN)^2)         1   969.34 4861.9
## - I(scale(mud)^2)          1   992.66 4878.0
## 
## Step:  AIC=4845.09
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   946.48 4844.4
## <none>                         944.51 4845.1
## - scale(CuPb):scale(TPTN)  1   960.51 4854.2
## - I(scale(TPTN)^2)         1   970.45 4861.0
## - I(scale(mud)^2)          1   992.69 4876.4
## 
## Step:  AIC=4844.94
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         946.48 4844.9
## - scale(CuPb):scale(TPTN)  1   960.52 4852.8
## - I(scale(TPTN)^2)         1  1015.52 4891.3
## - I(scale(mud)^2)          1  1029.76 4901.3
## - scale(mud)               1  1064.97 4925.9
## Start:  AIC=6004.41
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   785.76 6002.4
## - scale(CuPb):scale(TPTN)  1   785.78 6002.4
## - I(scale(CuPb)^2)         1   786.62 6003.1
## - scale(mud):scale(TPTN)   1   787.06 6003.5
## - I(scale(mud)^2)          1   787.50 6003.9
## <none>                         785.76 6004.4
## - I(scale(TPTN)^2)         1   798.21 6012.8
## 
## Step:  AIC=6002.41
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   785.78 6000.4
## - scale(mud):scale(TPTN)   1   787.15 6001.6
## - I(scale(CuPb)^2)         1   787.39 6001.8
## - I(scale(mud)^2)          1   787.99 6002.3
## <none>                         785.76 6002.4
## - I(scale(TPTN)^2)         1   798.34 6010.9
## 
## Step:  AIC=6000.44
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(TPTN)  1   787.47 5999.9
## - I(scale(mud)^2)         1   788.03 6000.3
## <none>                        785.78 6000.4
## - scale(CuPb)             1   789.62 6001.7
## - I(scale(CuPb)^2)        1   796.13 6007.1
## - I(scale(TPTN)^2)        1   803.03 6012.9
## 
## Step:  AIC=6000.31
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## <none>                  787.47 6000.3
## - scale(CuPb)       1   790.67 6001.0
## - I(scale(CuPb)^2)  1   799.59 6008.4
## - I(scale(mud)^2)   1   802.76 6011.1
## - I(scale(TPTN)^2)  1   830.63 6034.4
## - scale(mud)        1   831.47 6035.1
## - scale(TPTN)       1   903.26 6095.2
## Start:  AIC=6064.84
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   558.55 6063.0
## <none>                         558.41 6064.8
## - scale(mud):scale(CuPb)   1   560.48 6065.1
## - I(scale(TPTN)^2)         1   560.73 6065.4
## - scale(CuPb):scale(TPTN)  1   562.72 6067.5
## - scale(mud):scale(TPTN)   1   564.30 6069.3
## - I(scale(CuPb)^2)         1   568.09 6073.4
## 
## Step:  AIC=6063.05
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## <none>                         558.55 6063.1
## - scale(mud):scale(CuPb)   1   560.53 6063.2
## - I(scale(TPTN)^2)         1   561.90 6064.7
## - scale(CuPb):scale(TPTN)  1   563.31 6066.2
## - I(scale(CuPb)^2)         1   568.16 6071.5
## - scale(mud):scale(TPTN)   1   571.19 6074.8
## Start:  AIC=4190.16
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   384.82 4188.2
## - scale(mud):scale(CuPb)   1   385.42 4188.8
## - I(scale(mud)^2)          1   386.20 4189.6
## - scale(mud):scale(TPTN)   1   386.78 4190.2
## <none>                         384.78 4190.2
## - I(scale(CuPb)^2)         1   389.16 4192.5
## - scale(CuPb):scale(TPTN)  1   395.26 4198.6
## 
## Step:  AIC=4188.24
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   385.43 4186.9
## - I(scale(mud)^2)          1   386.67 4188.1
## <none>                         384.82 4188.2
## - scale(mud):scale(TPTN)   1   388.20 4189.6
## - I(scale(CuPb)^2)         1   389.27 4190.7
## - scale(CuPb):scale(TPTN)  1   399.40 4200.8
## 
## Step:  AIC=4187.53
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   386.74 4186.8
## <none>                         385.43 4187.5
## - scale(mud):scale(TPTN)   1   389.74 4189.8
## - scale(CuPb):scale(TPTN)  1   399.66 4199.8
## - I(scale(CuPb)^2)         1   402.20 4202.3
## 
## Step:  AIC=4188.27
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN)
## 
## Start:  AIC=5825.15
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   495.23 5824.1
## - scale(CuPb):scale(TPTN)  1   495.90 5824.8
## - I(scale(CuPb)^2)         1   496.06 5825.0
## <none>                         494.44 5825.2
## - scale(mud):scale(CuPb)   1   497.18 5826.3
## - I(scale(mud)^2)          1   502.75 5832.8
## - I(scale(TPTN)^2)         1   504.05 5834.3
## 
## Step:  AIC=5824.47
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   496.26 5823.7
## - I(scale(CuPb)^2)         1   496.34 5823.8
## <none>                         495.23 5824.5
## - scale(mud):scale(CuPb)   1   497.44 5825.0
## - I(scale(mud)^2)          1   503.52 5832.1
## - I(scale(TPTN)^2)         1   513.08 5843.2
## 
## Step:  AIC=5824.19
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - I(scale(CuPb)^2)        1   496.62 5822.6
## <none>                        496.26 5824.2
## - scale(mud):scale(CuPb)  1   498.96 5825.3
## - I(scale(mud)^2)         1   504.13 5831.3
## - I(scale(TPTN)^2)        1   542.16 5875.4
## - scale(TPTN)             1   559.22 5895.2
## 
## Step:  AIC=5822.8
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        496.62 5822.8
## - scale(mud):scale(CuPb)  1   505.23 5830.8
## - I(scale(mud)^2)         1   512.91 5839.6
## - I(scale(TPTN)^2)        1   542.26 5873.6
## - scale(TPTN)             1   560.29 5894.5
## Start:  AIC=5081.78
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   818.36 5080.1
## - scale(CuPb):scale(TPTN)  1   820.55 5081.7
## <none>                         817.93 5081.8
## - I(scale(CuPb)^2)         1   821.32 5082.2
## - I(scale(TPTN)^2)         1   822.27 5082.9
## - I(scale(mud)^2)          1   822.44 5083.0
## - scale(mud):scale(CuPb)   1   833.20 5090.7
## 
## Step:  AIC=5080.24
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   820.72 5079.9
## <none>                         818.36 5080.2
## - I(scale(CuPb)^2)         1   822.76 5081.4
## - I(scale(TPTN)^2)         1   823.02 5081.6
## - I(scale(mud)^2)          1   831.78 5087.9
## - scale(mud):scale(CuPb)   1   835.99 5090.9
## 
## Step:  AIC=5080.75
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(CuPb)
## 
## Start:  AIC=5883.45
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   437.77 5881.5
## - I(scale(CuPb)^2)         1   437.87 5881.6
## - scale(mud):scale(TPTN)   1   437.90 5881.7
## - scale(mud):scale(CuPb)   1   438.09 5882.0
## <none>                         437.75 5883.4
## - I(scale(TPTN)^2)         1   442.14 5888.1
## - I(scale(mud)^2)          1   447.12 5895.7
## 
## Step:  AIC=5881.49
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - I(scale(CuPb)^2)        1   437.87 5879.6
## - scale(mud):scale(TPTN)  1   437.96 5879.8
## - scale(mud):scale(CuPb)  1   438.09 5880.0
## <none>                        437.77 5881.5
## - I(scale(TPTN)^2)        1   444.75 5890.1
## - I(scale(mud)^2)         1   447.73 5894.7
## 
## Step:  AIC=5879.67
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(TPTN)  1   438.12 5878.1
## <none>                        437.87 5879.7
## - scale(mud):scale(CuPb)  1   443.07 5885.6
## - I(scale(TPTN)^2)        1   444.76 5888.2
## - I(scale(mud)^2)         1   448.82 5894.4
## 
## Step:  AIC=5878.14
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## <none>                        438.12 5878.1
## - scale(mud):scale(CuPb)  1   443.09 5883.8
## - I(scale(mud)^2)         1   455.44 5902.7
## - I(scale(TPTN)^2)        1   475.22 5933.0
## - scale(TPTN)             1   508.56 5984.0
## Start:  AIC=4679.44
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(CuPb):scale(TPTN)  1   554.36 4677.5
## - scale(mud):scale(CuPb)   1   554.50 4677.7
## - I(scale(CuPb)^2)         1   554.90 4678.2
## - scale(mud):scale(TPTN)   1   555.24 4678.7
## <none>                         554.34 4679.4
## - I(scale(TPTN)^2)         1   556.42 4680.3
## - I(scale(mud)^2)          1   557.07 4681.2
## 
## Step:  AIC=4677.46
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(CuPb)  1   554.52 4675.7
## - scale(mud):scale(TPTN)  1   555.27 4676.7
## - I(scale(CuPb)^2)        1   555.44 4677.0
## <none>                        554.36 4677.5
## - I(scale(mud)^2)         1   557.27 4679.5
## - I(scale(TPTN)^2)        1   557.51 4679.8
## 
## Step:  AIC=4675.7
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(CuPb)             1   555.58 4675.2
## - scale(mud):scale(TPTN)  1   555.64 4675.3
## <none>                        554.52 4675.7
## - I(scale(CuPb)^2)        1   557.68 4678.1
## - I(scale(TPTN)^2)        1   557.71 4678.1
## - I(scale(mud)^2)         1   558.81 4679.6
## 
## Step:  AIC=4675.3
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(mud):scale(TPTN)
## 
##                          Df Deviance    AIC
## - scale(mud):scale(TPTN)  1   556.60 4674.7
## <none>                        555.58 4675.3
## - I(scale(TPTN)^2)        1   558.79 4677.8
## - I(scale(CuPb)^2)        1   560.34 4680.0
## - I(scale(mud)^2)         1   562.78 4683.5
## 
## Step:  AIC=4674.83
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2)
## 
##                    Df Deviance    AIC
## <none>                  556.60 4674.8
## - I(scale(TPTN)^2)  1   560.51 4678.3
## - I(scale(CuPb)^2)  1   560.72 4678.6
## - I(scale(mud)^2)   1   613.65 4752.4
## - scale(TPTN)       1   647.94 4800.2
## - scale(mud)        1   722.11 4903.7
## Start:  AIC=2956.2
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(CuPb)   1   908.16 2954.2
## - scale(mud):scale(TPTN)   1   908.35 2954.3
## - I(scale(mud)^2)          1   909.84 2954.5
## - I(scale(TPTN)^2)         1   916.30 2955.7
## <none>                         907.93 2956.2
## - I(scale(CuPb)^2)         1   926.87 2957.6
## - scale(CuPb):scale(TPTN)  1   942.88 2960.5
## 
## Step:  AIC=2954.42
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN) + 
##     scale(mud):scale(TPTN)
## 
##                           Df Deviance    AIC
## - scale(mud):scale(TPTN)   1   909.07 2952.6
## - I(scale(mud)^2)          1   909.97 2952.7
## - I(scale(TPTN)^2)         1   916.30 2953.9
## <none>                         908.16 2954.4
## - scale(CuPb):scale(TPTN)  1   944.27 2958.9
## - I(scale(CuPb)^2)         1   961.47 2962.1
## 
## Step:  AIC=2953.31
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   910.21 2951.5
## - scale(mud)               1   913.96 2952.2
## <none>                         909.07 2953.3
## - I(scale(TPTN)^2)         1   925.36 2954.3
## - scale(CuPb):scale(TPTN)  1   944.27 2957.7
## - I(scale(CuPb)^2)         1   961.47 2960.8
## 
## Step:  AIC=2952.41
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     I(scale(TPTN)^2) + scale(CuPb):scale(TPTN)
## 
##                           Df Deviance    AIC
## <none>                         910.21 2952.4
## - I(scale(TPTN)^2)         1   926.35 2953.3
## - scale(mud)               1   939.05 2955.6
## - scale(CuPb):scale(TPTN)  1   947.89 2957.2
## - I(scale(CuPb)^2)         1   963.44 2960.0
## Start:  AIC=5756.99
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + I(scale(TPTN)^2) + scale(TPTN):scale(CuPb) + 
##     scale(TPTN):scale(mud) + scale(CuPb):scale(mud)
## 
##                           Df Deviance    AIC
## - I(scale(TPTN)^2)         1   535.17 5755.2
## - I(scale(mud)^2)          1   536.67 5756.6
## <none>                         534.96 5757.0
## - scale(mud):scale(CuPb)   1   541.17 5760.9
## - scale(mud):scale(TPTN)   1   544.56 5764.1
## - scale(CuPb):scale(TPTN)  1   544.62 5764.1
## - I(scale(CuPb)^2)         1   556.74 5775.6
## 
## Step:  AIC=5755.32
## abund + 1 ~ scale(mud) + I(scale(mud)^2) + scale(CuPb) + I(scale(CuPb)^2) + 
##     scale(TPTN) + scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + 
##     scale(mud):scale(CuPb)
## 
##                           Df Deviance    AIC
## - I(scale(mud)^2)          1   536.67 5754.7
## <none>                         535.17 5755.3
## - scale(mud):scale(CuPb)   1   541.24 5759.1
## - scale(mud):scale(TPTN)   1   546.49 5764.0
## - scale(CuPb):scale(TPTN)  1   551.41 5768.7
## - I(scale(CuPb)^2)         1   559.51 5776.3
## 
## Step:  AIC=5755.66
## abund + 1 ~ scale(mud) + scale(CuPb) + I(scale(CuPb)^2) + scale(TPTN) + 
##     scale(CuPb):scale(TPTN) + scale(mud):scale(TPTN) + scale(mud):scale(CuPb)
###get coefficients for models and change factor names###
trait_Coef  <- tidy(traits_models, fit_trait, conf.int = T) %>%
  data.frame(.) %>% 
  mutate(
    term = factor(term),
    term = fct_recode(
      term,
      "Intercept" = "(Intercept)",
      "Sediment" = "scale(mud)",
      "Sediment^2" = "I(scale(mud)^2)",
      "Metals" =  "scale(CuPb)",
      "Metals^2" = "I(scale(CuPb)^2)",
      "Nutrients" = "scale(TPTN)",
      "Nutrients^2" = "I(scale(TPTN)^2)",
      "Nutrients x Metals" =  "scale(CuPb):scale(TPTN)",
      "Sediment x Nutrients" =  "scale(mud):scale(TPTN)",
      "Sediment x Metals" =  "scale(mud):scale(CuPb)"
    )
  )

trait_coef1 <- trait_Coef %>%
  dplyr::filter(term != 'Intercept' &
                  term != 'Sediment^2' &
                  term != 'Metals^2' &
                  term != 'Nutrients^2') %>%
  mutate(term = factor(term))


##Color coef plot for traits####
ggplot(trait_coef1,
       aes(
         x = estimate,
         y = fct_rev(fct_inorder(term)),
         color = term
       )) +
  geom_point() +
  geom_errorbarh(aes(xmin = conf.low,
                     xmax = conf.high),
                 height = .2) +
  facet_wrap(~ trait) +
  geom_vline(xintercept = 0,
             lty = 2,
             col = 1) +
  ylab('') +
  geom_hline(yintercept = 3.5, lty = 2) +
  scale_color_discrete(guide = F)

trait_Summ = glance(traits_models, fit_trait) %>%
  mutate(Rsqr = 1 - (deviance / null.deviance)) %>%
  dplyr::filter(Rsqr > 0.1) %>%
  print(n = 22)
## Source: local data frame [22 x 9]
## Groups: trait [22]
## 
##                 trait null.deviance df.null    logLik      AIC      BIC
##                 (chr)         (dbl)   (int)     (dbl)    (dbl)    (dbl)
## 1            Attached     2076.4288     747 -1874.362 3768.723 3814.897
## 2            Calified     1113.7541     747 -2925.747 5871.493 5917.667
## 3                Deep      426.6548     747 -2664.277 5350.554 5401.345
## 4             Deposit      466.6612     747 -3086.986 6189.972 6226.911
## 5    Depth_to_surface      479.8139     747 -2504.543 5029.087 5075.261
## 6       Freely_motile      437.1190     747 -3059.163 6136.326 6177.882
## 7               Large      541.8180     747 -2523.804 5063.609 5100.548
## 8             Limited      878.6001     747 -2451.867 4921.733 4963.290
## 9              Medium      830.8049     747 -2590.861 5199.722 5241.279
## 10   Permanent_burrow      705.4543     747 -2384.355 4788.709 4834.883
## 11    Round/Globulose     1108.9903     747 -3062.156 6142.313 6183.870
## 12          Sedentary     2073.4195     747 -2091.407 4204.813 4255.605
## 13 Simple_hole_or_pit     1268.4554     747 -2414.470 4844.940 4881.879
## 14              Small      990.9262     747 -2992.153 6000.306 6037.246
## 15        Soft-bodied      710.1602     747 -3021.525 6063.051 6109.225
## 16   Surface_to_depth      583.8680     747 -2086.135 4188.270 4225.209
## 17 Surface_to_surface      726.7398     747 -2903.398 5822.795 5859.735
## 18         Suspension     1567.4824     747 -2531.374 5080.748 5122.305
## 19           Top_2_cm      649.1362     747 -2931.071 5878.143 5915.082
## 20             Trough      765.3053     747 -2330.413 4674.826 4707.148
## 21     Tube_structure     1354.9574     747 -1468.206 2952.413 2989.352
## 22          Worm_like      621.0322     747 -2868.830 5755.660 5797.217
## Variables not shown: deviance (dbl), df.residual (int), Rsqr (dbl)
###joint with summary and filter Rsq>0.1###
trait_coef2 <-
  right_join(trait_coef1, trait_Summ, by = 'trait') %>%
  mutate(Trait = gsub('_', ' ', trait),
  term = factor(term),
  term = fct_relevel(
    term,
    'Sediment',
    'Metals',
    'Nutrients',
    'Nutrients x Metals',
    'Sediment x Metals' ,
    'Sediment x Nutrients'
  )
) 

##save results###
write.csv(trait_coef2, 'trait_summary.csv', row.names = F)

##coef plot for traits####
trait_plot <-
  ggplot(trait_coef2,
         aes(
           x = estimate,
           y = fct_rev(fct_inorder(term)),
           color = term
         )) +
  geom_point() +
  geom_errorbarh(aes(
    xmin = conf.low,
    xmax = conf.high,
    height = .2
  )) +
  facet_wrap(~ Trait) +
  geom_vline(xintercept = 0,
             lty = 2,
             col = 2) +
  ylab('') +
  xlab('Estimates') +
  geom_hline(yintercept = 3.5,
             lty = 2,
             col = 2) +
  scale_color_discrete(guide = F)

###save plot as tiff###
print(trait_plot)

ggsave(
  trait_plot,
  file = 'trait_plot.tif',
  device = 'tiff',
  dpi = 900,
  compression = 'lzw'
)
## Saving 7 x 5 in image