# Single Species Single Season Occupancy
# Yellow-bellied toad
# Single Season Single Season occupancy
# RPresence package
# 2018-11-15 Code contributed by Carl James Schwarz (cschwarz.stat.sfu.cs@gmail.com)
library(readxl)
library(RPresence)
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.history <- readxl::read_excel(file.path("..","YellowBelliedToad.xlsx"),
sheet="detections")
# do some basic checks on your data
# e.g. check number of sites; number of visits etc
nrow(input.history)
## [1] 572
ncol(input.history)
## [1] 2
range(input.history, na.rm=TRUE)
## [1] 0 1
sum(is.na(input.history))
## [1] 0
head(input.history)
## # A tibble: 6 x 2
## V1 V2
## <dbl> <dbl>
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 1 0
# Get the site level covariates - none.
# Get the site x visit (sampling) covariates.
jdate <- readxl::read_excel(file.path("..","YellowBelliedToad.xlsx"),
sheet="JulianDate")
range(jdate)
## [1] 121 179
# Observational covariate needs to be "stacked" so that sites1...siteS for survey occastion 1
# are then followed by covariate at survey occastion 2 for sites1...siteS, etc
survey.cov <- data.frame(site =rep(1:nrow(input.history) , ncol(input.history)),
visit =as.character(rep(1:ncol(input.history), each=nrow(input.history))), # notice we make a character
jdate =as.vector(unlist(jdate)),
stringsAsFactors=FALSE)
head(survey.cov[,c("visit","site","jdate")],n=50)
## visit site jdate
## 1 1 1 139
## 2 1 2 128
## 3 1 3 130
## 4 1 4 130
## 5 1 5 128
## 6 1 6 145
## 7 1 7 145
## 8 1 8 127
## 9 1 9 130
## 10 1 10 121
## 11 1 11 121
## 12 1 12 130
## 13 1 13 123
## 14 1 14 133
## 15 1 15 133
## 16 1 16 133
## 17 1 17 133
## 18 1 18 134
## 19 1 19 130
## 20 1 20 121
## 21 1 21 123
## 22 1 22 121
## 23 1 23 156
## 24 1 24 144
## 25 1 25 144
## 26 1 26 132
## 27 1 27 144
## 28 1 28 144
## 29 1 29 132
## 30 1 30 134
## 31 1 31 125
## 32 1 32 130
## 33 1 33 129
## 34 1 34 125
## 35 1 35 127
## 36 1 36 134
## 37 1 37 131
## 38 1 38 126
## 39 1 39 134
## 40 1 40 131
## 41 1 41 133
## 42 1 42 133
## 43 1 43 133
## 44 1 44 126
## 45 1 45 133
## 46 1 46 133
## 47 1 47 133
## 48 1 48 122
## 49 1 49 136
## 50 1 50 136
str(survey.cov)
## 'data.frame': 1144 obs. of 3 variables:
## $ site : int 1 2 3 4 5 6 7 8 9 10 ...
## $ visit: chr "1" "1" "1" "1" ...
## $ jdate: num 139 128 130 130 128 145 145 127 130 121 ...
# standarize jdate
survey.cov$jdateS <- (survey.cov$jdate - 150)/10
# check that missing values in history and observer covariates align
select <- is.na(as.vector(unlist(input.history)))
survey.cov[select,]
## [1] site visit jdate jdateS
## <0 rows> (or 0-length row.names)
sum(is.na(survey.cov[!select,]))
## [1] 0
# Create the *.pao file
ybf.pao <- RPresence::createPao(input.history,
#unitcov=site_covar, # no site covariates
survcov=survey.cov,
title='ybf SSSS')
ybf.pao
## $nunits
## [1] 572
##
## $nsurveys
## [1] 2
##
## $nseasons
## [1] 1
##
## $nmethods
## [1] 1
##
## $det.data
## # A tibble: 572 x 2
## V1 V2
## <dbl> <dbl>
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 1 0
## 7 0 0
## 8 0 0
## 9 0 0
## 10 0 0
## # ... with 562 more rows
##
## $nunitcov
## [1] 1
##
## $unitcov
## TEMP
## 1 1
## 2 2
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##
## $nsurvcov
## [1] 5
##
## $survcov
## site visit jdate jdateS SURVEY
## 1 1 1 139 -1.1 1
## 2 2 1 128 -2.2 1
## 3 3 1 130 -2.0 1
## 4 4 1 130 -2.0 1
## 5 5 1 128 -2.2 1
## 6 6 1 145 -0.5 1
## 7 7 1 145 -0.5 1
## 8 8 1 127 -2.3 1
## 9 9 1 130 -2.0 1
## 10 10 1 121 -2.9 1
## 11 11 1 121 -2.9 1
## 12 12 1 130 -2.0 1
## 13 13 1 123 -2.7 1
## 14 14 1 133 -1.7 1
## 15 15 1 133 -1.7 1
## 16 16 1 133 -1.7 1
## 17 17 1 133 -1.7 1
## 18 18 1 134 -1.6 1
## 19 19 1 130 -2.0 1
## 20 20 1 121 -2.9 1
## 21 21 1 123 -2.7 1
## 22 22 1 121 -2.9 1
## 23 23 1 156 0.6 1
## 24 24 1 144 -0.6 1
## 25 25 1 144 -0.6 1
## 26 26 1 132 -1.8 1
## 27 27 1 144 -0.6 1
## 28 28 1 144 -0.6 1
## 29 29 1 132 -1.8 1
## 30 30 1 134 -1.6 1
## 31 31 1 125 -2.5 1
## 32 32 1 130 -2.0 1
## 33 33 1 129 -2.1 1
## 34 34 1 125 -2.5 1
## 35 35 1 127 -2.3 1
## 36 36 1 134 -1.6 1
## 37 37 1 131 -1.9 1
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## 115 115 1 129 -2.1 1
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## 134 134 1 150 0.0 1
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## 140 140 1 129 -2.1 1
## 141 141 1 131 -1.9 1
## 142 142 1 125 -2.5 1
## 143 143 1 124 -2.6 1
## 144 144 1 146 -0.4 1
## 145 145 1 128 -2.2 1
## 146 146 1 123 -2.7 1
## 147 147 1 123 -2.7 1
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## 149 149 1 130 -2.0 1
## 150 150 1 130 -2.0 1
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## 152 152 1 123 -2.7 1
## 153 153 1 123 -2.7 1
## 154 154 1 123 -2.7 1
## 155 155 1 123 -2.7 1
## 156 156 1 127 -2.3 1
## 157 157 1 146 -0.4 1
## 158 158 1 124 -2.6 1
## 159 159 1 131 -1.9 1
## 160 160 1 130 -2.0 1
## 161 161 1 144 -0.6 1
## 162 162 1 135 -1.5 1
## 163 163 1 135 -1.5 1
## 164 164 1 124 -2.6 1
## 165 165 1 143 -0.7 1
## 166 166 1 127 -2.3 1
## 167 167 1 135 -1.5 1
## 168 168 1 135 -1.5 1
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## 170 170 1 130 -2.0 1
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## 176 176 1 134 -1.6 1
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## 206 206 1 134 -1.6 1
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## 209 209 1 130 -2.0 1
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## 230 230 1 123 -2.7 1
## 231 231 1 130 -2.0 1
## 232 232 1 125 -2.5 1
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## 236 236 1 130 -2.0 1
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## 240 240 1 133 -1.7 1
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## 244 244 1 122 -2.8 1
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## 246 246 1 127 -2.3 1
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## 249 249 1 127 -2.3 1
## 250 250 1 127 -2.3 1
## 251 251 1 132 -1.8 1
## 252 252 1 133 -1.7 1
## 253 253 1 131 -1.9 1
## 254 254 1 133 -1.7 1
## 255 255 1 133 -1.7 1
## 256 256 1 127 -2.3 1
## 257 257 1 149 -0.1 1
## 258 258 1 126 -2.4 1
## 259 259 1 149 -0.1 1
## 260 260 1 124 -2.6 1
## 261 261 1 126 -2.4 1
## 262 262 1 149 -0.1 1
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## 264 264 1 150 0.0 1
## 265 265 1 150 0.0 1
## 266 266 1 145 -0.5 1
## 267 267 1 150 0.0 1
## 268 268 1 129 -2.1 1
## 269 269 1 131 -1.9 1
## 270 270 1 147 -0.3 1
## 271 271 1 150 0.0 1
## 272 272 1 145 -0.5 1
## 273 273 1 128 -2.2 1
## 274 274 1 121 -2.9 1
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## 295 295 1 146 -0.4 1
## 296 296 1 121 -2.9 1
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## 300 300 1 132 -1.8 1
## 301 301 1 133 -1.7 1
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## 310 310 1 128 -2.2 1
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## 314 314 1 134 -1.6 1
## 315 315 1 151 0.1 1
## 316 316 1 127 -2.3 1
## 317 317 1 151 0.1 1
## 318 318 1 126 -2.4 1
## 319 319 1 137 -1.3 1
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##
## $nsurveyseason
## [1] 2
##
## $title
## [1] "ybf SSSS"
##
## $unitnames
## [1] "unit1" "unit2" "unit3" "unit4" "unit5" "unit6" "unit7"
## [8] "unit8" "unit9" "unit10" "unit11" "unit12" "unit13" "unit14"
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## [561] "unit561" "unit562" "unit563" "unit564" "unit565" "unit566" "unit567"
## [568] "unit568" "unit569" "unit570" "unit571" "unit572"
##
## $surveynames
## [1] "1-1" "1-2"
##
## $paoname
## [1] "pres.pao"
##
## $frq
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [36] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [71] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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## [141] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [176] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [211] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [246] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [281] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [316] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [351] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [386] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [421] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [456] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [491] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [526] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [561] 1 1 1 1 1 1 1 1 1 1 1 1
##
## attr(,"class")
## [1] "pao"
# Fit some models.
# Note that formula DO NOT HAVE AN = SIGN
mod.pdot <- RPresence::occMod(model=list(psi~1, p~1), type="so", data=ybf.pao)
## PRESENCE Version 2.12.21.
summary(mod.pdot)
## Model name=psi()p()
## AIC=870.5516
## -2*log-likelihood=866.5516
## num. par=2
# look at estimated occupancy probability. RPresence gives for EACH site in case it depends on covariates
mod.pdot.psi <-mod.pdot$real$psi[1,] # occupancy probability
mod.pdot.psi
## est se lower_0.95 upper_0.95
## psi_unit1 0.2491541 0.02105004 0.210209 0.292641
# look at the estimated probability of detection. It gives an estimate for every site at very visit
mod.pdot.p <- mod.pdot$real$p[seq(1, by=nrow(input.history), length.out=ncol(input.history)),]
mod.pdot.p
## est se lower_0.95 upper_0.95
## p1_unit1 0.6595744 0.04001217 0.577406 0.7331497
## p2_unit1 0.6595744 0.04001217 0.577406 0.7331497
# alternatively
RPresence::print_one_site_estimates(mod.pdot, site = 1)
## psi()p()
## est se lower_0.95 upper_0.95
## psi_psi_unit1 0.2491541 0.02105004 0.210209 0.2926410
## p_p1_unit1 0.6595744 0.04001217 0.577406 0.7331497
# Model where p(t) varies across survey occasions
#
mod.pt.psidot <- RPresence::occMod(model=list(psi~1, p~SURVEY), type="so", data=ybf.pao)
## PRESENCE Version 2.12.21.
##
## Warning: Numerical convergence may not have been reached. Parameter esimates converged to approximately 5.83 signifcant digits.
summary(mod.pt.psidot)
## Model name=psi()p(SURVEY)
## AIC=872.3015
## -2*log-likelihood=866.3015
## num. par=3
## Warning: Numerical convergence may not have been reached. Parameter esimates converged to approximately 5.83 signifcant digits.
mod.pt.psidot$real$psi[1:5,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.2490413 0.02103535 0.2101233 0.2924982
## psi_unit2 0.2490413 0.02103535 0.2101233 0.2924982
## psi_unit3 0.2490413 0.02103535 0.2101233 0.2924982
## psi_unit4 0.2490413 0.02103535 0.2101233 0.2924982
## psi_unit5 0.2490413 0.02103535 0.2101233 0.2924982
mod.pt.psidot$real$p[seq(1, by=nrow(input.history), length.out=ncol(input.history)),]
## est se lower_0.95 upper_0.95
## p1_unit1 0.6458334 0.04881285 0.5455004 0.7347859
## p2_unit1 0.6739130 0.04887346 0.5720059 0.7616658
print_one_site_estimates(mod.pt.psidot, site = 1)
## psi()p(SURVEY)
## est se lower_0.95 upper_0.95
## psi_psi_unit1 0.2490413 0.02103535 0.2101233 0.2924982
## p_p1_unit1 0.6458334 0.04881285 0.5455004 0.7347859
fitted(mod.pt.psidot, param="psi")[1,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.2490413 0.02103535 0.2101233 0.2924982
# Model where p varies by julian date in a linear form
#
mod.pjdate.psidot <- RPresence::occMod(model=list(psi~1, p~jdateS), type="so", data=ybf.pao)
## PRESENCE Version 2.12.21.
summary(mod.pjdate.psidot)
## Model name=psi()p(jdateS)
## AIC=868.8199
## -2*log-likelihood=862.8199
## num. par=3
mod.pjdate.psidot$real$psi[1:5,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit2 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit3 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit4 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit5 0.2486579 0.02095048 0.2098931 0.2919368
mod.pjdate.psidot$real$p[seq(1, by=nrow(input.history), length.out=ncol(input.history)),]
## est se lower_0.95 upper_0.95
## p1_unit1 0.6692831 0.04026427 0.5862319 0.7429731
## p2_unit1 0.5190084 0.08523262 0.3559219 0.6781425
print_one_site_estimates(mod.pjdate.psidot, site = 1)
## psi()p(jdateS)
## est se lower_0.95 upper_0.95
## psi_psi_unit1 0.2486579 0.02095048 0.2098931 0.2919368
## p_p1_unit1 0.6692831 0.04026427 0.5862319 0.7429731
fitted(mod.pjdate.psidot, param="psi")[1:5,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit2 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit3 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit4 0.2486579 0.02095048 0.2098931 0.2919368
## psi_unit5 0.2486579 0.02095048 0.2098931 0.2919368
# Model where p varies by julian date in a quadrat form
# Notice we need the I() around the square term in the model to force R to evaluate it properly
mod.pjdate2.psidot <- RPresence::occMod(model=list(psi~1, p~jdateS + I(jdateS^2)), type="so", data=ybf.pao)
## PRESENCE Version 2.12.21.
summary(mod.pjdate2.psidot)
## Model name=psi()p(jdateS P I(jdateS^2))
## AIC=821.0628
## -2*log-likelihood=813.0628
## num. par=4
mod.pjdate2.psidot$beta
## $psi
## est se
## A1_psi -1.160932 0.107143
##
## $psi.VC
## [,1]
## [1,] 0.01148
##
## $p
## est se
## B1_p1 1.509602 0.294376
## B2_p1.p.jdateS -0.721760 0.197863
## B3_p1.p.I(jdateS^2) -0.479987 0.092650
##
## $p.VC
## B1_p1 B2_p1.p.jdateS B3_p1.p.I(jdateS^2)
## B1_p1 0.086657 0.002244 -0.012017
## B2_p1.p.jdateS 0.002244 0.039150 0.014409
## B3_p1.p.I(jdateS^2) -0.012017 0.014409 0.008584
##
## $VC
## A1_psi B1_p1 B2_p1.p.jdateS B3_p1.p.I(jdateS^2)
## A1_psi 0.011480 -0.007676 0.000309 0.000826
## B1_p1 -0.007676 0.086657 0.002244 -0.012017
## B2_p1.p.jdateS 0.000309 0.002244 0.039150 0.014409
## B3_p1.p.I(jdateS^2) 0.000826 -0.012017 0.014409 0.008584
mod.pjdate2.psidot$real$psi[1:5,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit2 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit3 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit4 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit5 0.238498 0.01945928 0.2024693 0.2786974
mod.pjdate2.psidot$real$p[seq(1, by=nrow(input.history), length.out=ncol(input.history)),]
## est se lower_0.95 upper_0.95
## p1_unit1 0.84848319 0.03502429 0.76652424 0.9052286
## p2_unit1 0.06359119 0.05217745 0.01204526 0.2744444
print_one_site_estimates(mod.pjdate2.psidot, site = 1)
## psi()p(jdateS P I(jdateS^2))
## est se lower_0.95 upper_0.95
## psi_psi_unit1 0.2384980 0.01945928 0.2024693 0.2786974
## p_p1_unit1 0.8484832 0.03502429 0.7665242 0.9052286
fitted(mod.pjdate2.psidot, param="psi")[1:5,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit2 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit3 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit4 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit5 0.238498 0.01945928 0.2024693 0.2786974
# Model averaging
models<-list(mod.pdot,
mod.pjdate.psidot,
mod.pjdate2.psidot,
mod.pt.psidot)
results<-RPresence::createAicTable(models)
summary(results)
## Model DAIC wgt npar neg2ll warn.conv warn.VC
## 1 psi()p(jdateS P I(jdateS^2)) 0.00 1 4 813.06 0.00 0
## 2 psi()p(jdateS) 47.76 0 3 862.82 0.00 0
## 3 psi()p() 49.49 0 2 866.55 0.00 0
## 4 psi()p(SURVEY) 51.24 0 3 866.30 5.83 0
RPresence::modAvg(results, param="psi")[1:5,]
## est se lower_0.95 upper_0.95
## psi_unit1 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit2 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit3 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit4 0.238498 0.01945928 0.2024693 0.2786974
## psi_unit5 0.238498 0.01945928 0.2024693 0.2786974
# look at detectability
ma.p <- RPresence::modAvg(results, param="p")
# we need to extract the site and survey and merge with survey.cov to get jdate
head(ma.p)
## est se lower_0.95 upper_0.95
## p1_unit1 0.8484832 0.03502429 0.7665242 0.9052286
## p1_unit2 0.6844583 0.04539391 0.5896187 0.7660759
## p1_unit3 0.7375308 0.04103923 0.6496855 0.8097969
## p1_unit4 0.7375308 0.04103923 0.6496855 0.8097969
## p1_unit5 0.6844583 0.04539391 0.5896187 0.7660759
## p1_unit6 0.8520140 0.03678740 0.7647029 0.9107098
ma.p$site <- as.numeric( substring(row.names(ma.p), 4+regexpr("unit", row.names(ma.p))))
ma.p$visit<- substr(row.names(ma.p),2,2)
head(ma.p)
## est se lower_0.95 upper_0.95 site visit
## p1_unit1 0.8484832 0.03502429 0.7665242 0.9052286 1 1
## p1_unit2 0.6844583 0.04539391 0.5896187 0.7660759 2 1
## p1_unit3 0.7375308 0.04103923 0.6496855 0.8097969 3 1
## p1_unit4 0.7375308 0.04103923 0.6496855 0.8097969 4 1
## p1_unit5 0.6844583 0.04539391 0.5896187 0.7660759 5 1
## p1_unit6 0.8520140 0.03678740 0.7647029 0.9107098 6 1
ma.p <- merge(ma.p, survey.cov)
head(ma.p)
## site visit est se lower_0.95 upper_0.95 jdate jdateS
## 1 1 1 0.84848319 0.03502429 0.76652424 0.9052286 139 -1.1
## 2 1 2 0.06359119 0.05217745 0.01204526 0.2744444 173 2.3
## 3 10 1 0.39317523 0.07733181 0.25554528 0.5501516 121 -2.9
## 4 10 2 0.85565245 0.03560442 0.77111973 0.9125069 143 -0.7
## 5 100 1 0.57788162 0.05717818 0.46373085 0.6842772 125 -2.5
## 6 100 2 0.79403668 0.03758781 0.71073631 0.8581368 133 -1.7
ggplot(data=ma.p, aes(x=jdate, y=est))+
ggtitle("Estimated detection as a function of julian date")+
geom_point()+
geom_ribbon(aes(ymin=lower_0.95, ymax=upper_0.95), alpha=0.2)+
ylim(0,1)
