# Brook Trout

# This is from MARK demo files on occupancy.
# Collected via electrofishing three 50 m sections of streams at 77 sites 
# in the Upper Chattachochee River basin. 
#       77 streams 3 occasions, 4 covariates: elevation, cross sectional area each occasion.

# Single Species Single Season Occupancy

# Fitting a single model using RPresence

# 2018-12-02 Code contributed by Neil Faught
library(car)
library(readxl)
library(RPresence)
## Warning: package 'RPresence' was built under R version 3.5.0
library(ggplot2)

# get the data read in
# Data for detections should be a data frame with rows corresponding to sites
# and columns to visits.
# The usual 1=detected; 0=not detected; NA=not visited is used.

input.data <- readxl::read_excel("../BrookTrout.xls",
                                 sheet="DetectionHistory",
                                 na="-",
                                 col_names=FALSE)  # notice no column names in row 1 of data file. 

head(input.data)
## # A tibble: 6 x 3
##    X__1  X__2  X__3
##   <dbl> <dbl> <dbl>
## 1  0     0        0
## 2  1.00  0        0
## 3  0     0        0
## 4  0     0        0
## 5  0     0        0
## 6  0     1.00     0
# Extract the history records
input.history <- input.data # the history extracted
head(input.history)
## # A tibble: 6 x 3
##    X__1  X__2  X__3
##   <dbl> <dbl> <dbl>
## 1  0     0        0
## 2  1.00  0        0
## 3  0     0        0
## 4  0     0        0
## 5  0     0        0
## 6  0     1.00     0
# do some basic checks on your data 
# e.g. check number of sites; number of visits etc
nrow(input.history)
## [1] 77
ncol(input.history)
## [1] 3
range(input.history, na.rm=TRUE) # check that all values are either 0 or 1
## [1] 0 1
sum(is.na(input.history))    # are there any missing values?
## [1] 0
# Get the elevation information
elevation.data <- readxl::read_excel("../BrookTrout.xls",
                                     sheet="Elevation",
                                     na="-",
                                     col_names=TRUE)  
elevation.data$Elevation <- elevation.data$Elevation/1000  # standardized it a bit
elevation.data$Site      <- 1:nrow(elevation.data)
head(elevation.data)
## # A tibble: 6 x 2
##   Elevation  Site
##       <dbl> <int>
## 1      4.27     1
## 2      4.04     2
## 3      2.03     3
## 4      3.44     4
## 5      3.04     5
## 6      2.05     6
# Get the cross sectional width
cross.data <- readxl::read_excel("../BrookTrout.xls",
                                 sheet="CrossSectionWidth",
                                 na="-",
                                 col_names=TRUE)  
head(cross.data)
## # A tibble: 6 x 3
##   Cross1 Cross2 Cross3
##    <dbl>  <dbl>  <dbl>
## 1  2.87   2.61    2.73
## 2  0.880  2.54    1.16
## 3  1.50   0.960   1.52
## 4  0.260  1.50    1.13
## 5  0.890  2.59    2.69
## 6  0.670  2.32    1.58
# Convert to a survey covariate. You need to stack the data by columns
survey.cov <- data.frame(Site=1:nrow(cross.data),
                         visit=as.factor(rep(1:ncol(cross.data), each=nrow(cross.data))),
                         Cross =unlist(cross.data), stringsAsFactors=FALSE)

head(survey.cov)
##         Site visit Cross
## Cross11    1     1  2.87
## Cross12    2     1  0.88
## Cross13    3     1  1.50
## Cross14    4     1  0.26
## Cross15    5     1  0.89
## Cross16    6     1  0.67
# Create the *.pao file
trout.pao <- RPresence::createPao(input.history,
                                  unitcov=elevation.data,
                                  survcov=survey.cov,
                                  title='Brook Trout SSSS')
trout.pao
## $nunits
## [1] 77
## 
## $nsurveys
## [1] 3
## 
## $nseasons
## [1] 1
## 
## $nmethods
## [1] 1
## 
## $det.data
## # A tibble: 77 x 3
##     X__1  X__2  X__3
##    <dbl> <dbl> <dbl>
##  1  0     0     0   
##  2  1.00  0     0   
##  3  0     0     0   
##  4  0     0     0   
##  5  0     0     0   
##  6  0     1.00  0   
##  7  0     0     0   
##  8  0     1.00  1.00
##  9  1.00  0     0   
## 10  0     0     0   
## # ... with 67 more rows
## 
## $nunitcov
## [1] 2
## 
## $unitcov
## # A tibble: 77 x 2
##    Elevation  Site
##        <dbl> <int>
##  1      4.27     1
##  2      4.04     2
##  3      2.03     3
##  4      3.44     4
##  5      3.04     5
##  6      2.05     6
##  7      1.82     7
##  8      3.19     8
##  9      4.41     9
## 10      3.40    10
## # ... with 67 more rows
## 
## $nsurvcov
## [1] 4
## 
## $survcov
##          Site visit Cross SURVEY
## Cross11     1     1  2.87      1
## Cross12     2     1  0.88      1
## Cross13     3     1  1.50      1
## Cross14     4     1  0.26      1
## Cross15     5     1  0.89      1
## Cross16     6     1  0.67      1
## Cross17     7     1  2.74      1
## Cross18     8     1  1.65      1
## Cross19     9     1  0.93      1
## Cross110   10     1  1.87      1
## Cross111   11     1  1.19      1
## Cross112   12     1  0.80      1
## Cross113   13     1  1.99      1
## Cross114   14     1  0.78      1
## Cross115   15     1  2.50      1
## Cross116   16     1  0.51      1
## Cross117   17     1  0.84      1
## Cross118   18     1  2.77      1
## Cross119   19     1  2.18      1
## Cross120   20     1  2.95      1
## Cross121   21     1  0.88      1
## Cross122   22     1  1.13      1
## Cross123   23     1  2.34      1
## Cross124   24     1  0.82      1
## Cross125   25     1  2.82      1
## Cross126   26     1  2.27      1
## Cross127   27     1  1.87      1
## Cross128   28     1  1.31      1
## Cross129   29     1  2.56      1
## Cross130   30     1  2.13      1
## Cross131   31     1  1.49      1
## Cross132   32     1  1.62      1
## Cross133   33     1  2.65      1
## Cross134   34     1  0.78      1
## Cross135   35     1  2.43      1
## Cross136   36     1  0.93      1
## Cross137   37     1  1.56      1
## Cross138   38     1  0.71      1
## Cross139   39     1  2.42      1
## Cross140   40     1  1.38      1
## Cross141   41     1  0.59      1
## Cross142   42     1  0.34      1
## Cross143   43     1  0.26      1
## Cross144   44     1  2.37      1
## Cross145   45     1  1.73      1
## Cross146   46     1  1.93      1
## Cross147   47     1  0.33      1
## Cross148   48     1  2.07      1
## Cross149   49     1  0.87      1
## Cross150   50     1  2.50      1
## Cross151   51     1  0.47      1
## Cross152   52     1  1.85      1
## Cross153   53     1  0.25      1
## Cross154   54     1  1.28      1
## Cross155   55     1  1.68      1
## Cross156   56     1  2.48      1
## Cross157   57     1  0.38      1
## Cross158   58     1  2.34      1
## Cross159   59     1  1.48      1
## Cross160   60     1  1.83      1
## Cross161   61     1  1.21      1
## Cross162   62     1  2.85      1
## Cross163   63     1  0.27      1
## Cross164   64     1  1.36      1
## Cross165   65     1  0.60      1
## Cross166   66     1  1.23      1
## Cross167   67     1  2.15      1
## Cross168   68     1  2.87      1
## Cross169   69     1  1.17      1
## Cross170   70     1  0.82      1
## Cross171   71     1  2.83      1
## Cross172   72     1  0.71      1
## Cross173   73     1  0.95      1
## Cross174   74     1  1.67      1
## Cross175   75     1  1.43      1
## Cross176   76     1  1.73      1
## Cross177   77     1  0.52      1
## Cross21     1     2  2.61      2
## Cross22     2     2  2.54      2
## Cross23     3     2  0.96      2
## Cross24     4     2  1.50      2
## Cross25     5     2  2.59      2
## Cross26     6     2  2.32      2
## Cross27     7     2  1.13      2
## Cross28     8     2  1.78      2
## Cross29     9     2  0.86      2
## Cross210   10     2  1.18      2
## Cross211   11     2  2.83      2
## Cross212   12     2  2.89      2
## Cross213   13     2  1.16      2
## Cross214   14     2  2.49      2
## Cross215   15     2  1.51      2
## Cross216   16     2  0.92      2
## Cross217   17     2  2.31      2
## Cross218   18     2  0.66      2
## Cross219   19     2  2.80      2
## Cross220   20     2  1.58      2
## Cross221   21     2  2.42      2
## Cross222   22     2  0.48      2
## Cross223   23     2  2.44      2
## Cross224   24     2  1.88      2
## Cross225   25     2  1.21      2
## Cross226   26     2  0.95      2
## Cross227   27     2  1.97      2
## Cross228   28     2  2.06      2
## Cross229   29     2  1.74      2
## Cross230   30     2  1.71      2
## Cross231   31     2  1.33      2
## Cross232   32     2  1.25      2
## Cross233   33     2  0.31      2
## Cross234   34     2  1.02      2
## Cross235   35     2  2.18      2
## Cross236   36     2  1.12      2
## Cross237   37     2  0.95      2
## Cross238   38     2  0.62      2
## Cross239   39     2  2.78      2
## Cross240   40     2  2.44      2
## Cross241   41     2  0.75      2
## Cross242   42     2  1.89      2
## Cross243   43     2  1.18      2
## Cross244   44     2  1.64      2
## Cross245   45     2  2.57      2
## Cross246   46     2  2.37      2
## Cross247   47     2  1.44      2
## Cross248   48     2  1.24      2
## Cross249   49     2  0.26      2
## Cross250   50     2  0.79      2
## Cross251   51     2  1.72      2
## Cross252   52     2  2.10      2
## Cross253   53     2  2.26      2
## Cross254   54     2  1.39      2
## Cross255   55     2  2.18      2
## Cross256   56     2  1.25      2
## Cross257   57     2  2.50      2
## Cross258   58     2  2.67      2
## Cross259   59     2  2.51      2
## Cross260   60     2  2.83      2
## Cross261   61     2  2.30      2
## Cross262   62     2  0.35      2
## Cross263   63     2  2.11      2
## Cross264   64     2  0.94      2
## Cross265   65     2  1.05      2
## Cross266   66     2  1.04      2
## Cross267   67     2  0.74      2
## Cross268   68     2  1.96      2
## Cross269   69     2  1.05      2
## Cross270   70     2  1.41      2
## Cross271   71     2  0.93      2
## Cross272   72     2  1.13      2
## Cross273   73     2  1.54      2
## Cross274   74     2  2.24      2
## Cross275   75     2  1.85      2
## Cross276   76     2  1.10      2
## Cross277   77     2  2.19      2
## Cross31     1     3  2.73      3
## Cross32     2     3  1.16      3
## Cross33     3     3  1.52      3
## Cross34     4     3  1.13      3
## Cross35     5     3  2.69      3
## Cross36     6     3  1.58      3
## Cross37     7     3  1.73      3
## Cross38     8     3  1.42      3
## Cross39     9     3  1.47      3
## Cross310   10     3  2.37      3
## Cross311   11     3  2.89      3
## Cross312   12     3  0.77      3
## Cross313   13     3  1.51      3
## Cross314   14     3  1.35      3
## Cross315   15     3  2.21      3
## Cross316   16     3  0.78      3
## Cross317   17     3  0.39      3
## Cross318   18     3  0.43      3
## Cross319   19     3  2.57      3
## Cross320   20     3  2.43      3
## Cross321   21     3  2.70      3
## Cross322   22     3  0.72      3
## Cross323   23     3  0.86      3
## Cross324   24     3  0.48      3
## Cross325   25     3  0.88      3
## Cross326   26     3  0.85      3
## Cross327   27     3  2.34      3
## Cross328   28     3  2.52      3
## Cross329   29     3  3.00      3
## Cross330   30     3  2.06      3
## Cross331   31     3  2.51      3
## Cross332   32     3  1.38      3
## Cross333   33     3  1.25      3
## Cross334   34     3  1.21      3
## Cross335   35     3  1.44      3
## Cross336   36     3  0.26      3
## Cross337   37     3  2.51      3
## Cross338   38     3  1.35      3
## Cross339   39     3  1.74      3
## Cross340   40     3  2.02      3
## Cross341   41     3  0.46      3
## Cross342   42     3  0.35      3
## Cross343   43     3  2.76      3
## Cross344   44     3  0.78      3
## Cross345   45     3  2.41      3
## Cross346   46     3  1.22      3
## Cross347   47     3  0.28      3
## Cross348   48     3  0.32      3
## Cross349   49     3  2.97      3
## Cross350   50     3  0.51      3
## Cross351   51     3  2.67      3
## Cross352   52     3  0.92      3
## Cross353   53     3  1.42      3
## Cross354   54     3  0.85      3
## Cross355   55     3  2.03      3
## Cross356   56     3  0.53      3
## Cross357   57     3  0.58      3
## Cross358   58     3  0.72      3
## Cross359   59     3  1.77      3
## Cross360   60     3  1.40      3
## Cross361   61     3  2.76      3
## Cross362   62     3  2.44      3
## Cross363   63     3  2.73      3
## Cross364   64     3  1.36      3
## Cross365   65     3  1.25      3
## Cross366   66     3  2.92      3
## Cross367   67     3  2.71      3
## Cross368   68     3  0.38      3
## Cross369   69     3  1.39      3
## Cross370   70     3  0.86      3
## Cross371   71     3  0.78      3
## Cross372   72     3  2.90      3
## Cross373   73     3  1.05      3
## Cross374   74     3  2.90      3
## Cross375   75     3  1.62      3
## Cross376   76     3  2.25      3
## Cross377   77     3  0.64      3
## 
## $nsurveyseason
## [1] 3
## 
## $title
## [1] "Brook Trout SSSS"
## 
## $unitnames
##  [1] "unit1"  "unit2"  "unit3"  "unit4"  "unit5"  "unit6"  "unit7" 
##  [8] "unit8"  "unit9"  "unit10" "unit11" "unit12" "unit13" "unit14"
## [15] "unit15" "unit16" "unit17" "unit18" "unit19" "unit20" "unit21"
## [22] "unit22" "unit23" "unit24" "unit25" "unit26" "unit27" "unit28"
## [29] "unit29" "unit30" "unit31" "unit32" "unit33" "unit34" "unit35"
## [36] "unit36" "unit37" "unit38" "unit39" "unit40" "unit41" "unit42"
## [43] "unit43" "unit44" "unit45" "unit46" "unit47" "unit48" "unit49"
## [50] "unit50" "unit51" "unit52" "unit53" "unit54" "unit55" "unit56"
## [57] "unit57" "unit58" "unit59" "unit60" "unit61" "unit62" "unit63"
## [64] "unit64" "unit65" "unit66" "unit67" "unit68" "unit69" "unit70"
## [71] "unit71" "unit72" "unit73" "unit74" "unit75" "unit76" "unit77"
## 
## $surveynames
## [1] "1-1" "1-2" "1-3"
## 
## $paoname
## [1] "pres.pao"
## 
## $frq
##  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [36] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [71] 1 1 1 1 1 1 1
## 
## attr(,"class")
## [1] "pao"
# Model where occupancy varies with elevation of stream
mod.elev <- RPresence::occMod(model=list(psi~Elevation, p~1), 
                            type="so", data=trout.pao)
## PRESENCE Version 2.12.21.
summary(mod.elev)
## Model name=psi(Elevation)p()
## AIC=210.1568
## -2*log-likelihood=204.1568
## num. par=3
head(mod.elev$real$psi)
##                 est         se lower_0.95 upper_0.95
## psi_unit1 0.8385830 0.08074740 0.61740368  0.9435824
## psi_unit2 0.7918434 0.08754743 0.57323101  0.9150643
## psi_unit3 0.1953217 0.07164442 0.09036233  0.3722981
## psi_unit4 0.6257368 0.09111721 0.43816822  0.7818603
## psi_unit5 0.4904815 0.08492637 0.33089709  0.6520298
## psi_unit6 0.1993520 0.07204241 0.09321430  0.3762035
mod.elev$real$p[seq(1, by=nrow(input.history), length.out=ncol(input.history)),]
##                est         se lower_0.95 upper_0.95
## p1_unit1 0.5363987 0.06035689  0.4182753   0.650574
## p2_unit1 0.5363987 0.06035689  0.4182753   0.650574
## p3_unit1 0.5363987 0.06035689  0.4182753   0.650574
# plot occupancy as a function of elevation of stream
plotdata = data.frame(mod.elev$real$psi, Elevation = elevation.data$Elevation)

ggplot(data=plotdata, aes(x=Elevation, y=est))+
  ggtitle("Occupancy as a function of elevation")+
  geom_point()+
  geom_ribbon(aes(ymin=lower_0.95, ymax=upper_0.95), alpha=0.2)+
  ylim(0,1)+
  ylab("Estimated occupancy")