Single Season Occupancy Model

The simplest model using the ubms package

Fits the single season occupancy model of MacKenzie et al (2002) using camera trap data, unmarked and ubms
R
occupancy
ubms
unmarked
Author
Affiliation

Diego J. Lizcano

WildMon

Published

July 27, 2024

Load packages

First we load some packages

Code

library(grateful) # Facilitate Citation of R Packages
library(patchwork) # The Composer of Plots
library(readxl) # Read Excel Files
library(sf) # Simple Features for R
library(mapview) # Interactive Viewing of Spatial Data in R
library(terra) # Spatial Data Analysis
library(elevatr) # Access Elevation Data from Various APIs
library(readr)

library(camtrapR) # Camera Trap Data Management and Preparation of Occupancy and Spatial Capture-Recapture Analyses 
library(unmarked) 
library(ubms) 
library(DT)

library(kableExtra) # Construct Complex Table with 'kable' and Pipe Syntax
library(tidyverse) # Easily Install and Load the 'Tidyverse'

# source("C:/CodigoR/CameraTrapCesar/R/organiza_datos.R")

Organize the data

The workflow starts with package unmarked for organize data and continue with the package ubms for model building, selection and prediction. The first step to perform the analysis is to organize data following the unmarked package. The data should have detection, non-detection records along with the covariates.

See the unmarked::unmarkedFrameOccu function for details typing: ?unmarkedFrameOccu in your R console.

Load data

The data set was collected by Sebastián Mejía-Correa and is part of the study: Mejia-Correa S, Diaz-Martinez A. 2014. Densidad y hábitos alimentarios de la danta Tapirus bairdii en el Parque Nacional Natural Los Katios, Colombia. Tapir Conservation. 23:16–23..

Code


katios1 <- read_excel("C:/CodigoR/CameraTrapCesar/data/katios/Tbairdii_sebastian.xlsx", sheet = "danta")

View the data

Code
datatable(head(katios1))

View as map

Code
# Load Katios National Park shapefile
katios_np <- read_sf("C:/CodigoR/CameraTrapCesar/data/katios/shp/WDPA_WDOECM_Nov2024_Public_61610_shp-polygons.shp")

# make projection
projlatlon <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

katios_sf <-  st_as_sf(x = katios1 |> distinct(Longitude, Latitude, camera),
                         coords = c("Longitude", 
                                    "Latitude"),
                         crs = projlatlon)

mapview(katios_np, alpha.regions=0.1) + 
mapview(katios_sf, zcol="camera")

Cmeras location.

Function to make detection history matrix

Code


f.matrix.creator<-function(data){
  #results object
  res<-list()
  
  #get the dimensions of the matrix
  
  #list if sanpling units
  cams<-unique(data$camera)
  cams<-sort(cams)
  rows<-length(cams)
  species<-unique(data$species)
  #start and end dates of sampling periods
  # data<-data[data$Sampling.Period==year,]
  min<-min(as.Date(as.character(data$start), "%Y-%m-%d"))
  max<-max(as.Date(as.character(data$end), "%Y-%m-%d"))
  cols<-max-min+1
  
  #sampling period
  date.header<-seq(from=min,to=max, by="days")
  mat<-matrix(NA,rows,cols,dimnames=list(cams,as.character(date.header)))
  
  #for all cameras, determine the open and close date and mark in the matrix
  start.dates<-tapply(as.character(data$start),data$camera,unique)
  nms<-names(start.dates)
  # start.dates<-ymd(start.dates)
  names(start.dates)<-nms
  end.dates<-tapply(as.character(data$end),data$camera,unique)
  # end.dates<-ymd(end.dates)
  names(end.dates)<-nms
  
  #outline the sampling periods for each camera j
  for(j in 1:length(start.dates)){
    #for each camera beginning and end of sampling
    low<-which(date.header==as.Date(as.character(start.dates[j]), format = "%Y-%m-%d"))
    hi<-which(date.header==as.Date(as.character(end.dates[j]), format = "%Y-%m-%d"))
    if(length(low)+length(hi)>0){
      indx<-seq(from=low,to=hi)
      mat[names(start.dates)[j],indx]<- 0
    } else next
  }
  mat.template<-mat
  #get the species
  #species<-unique(data$bin)
  #construct the matrix for each species i
  for(i in 1:length(species)){
    indx<-which(data$species==species[i])
    #dates and cameras when/where the species was photographed
    dates<-data$date[indx]
    cameras<-data$camera[indx]
    dates.cameras<-data.frame(dates,cameras)
    #unique combination of dates and cameras 
    dates.cameras<-unique(dates.cameras)
    #fill in the matrix
    for(j in 1:length(dates.cameras[,1])){
      col<-which(date.header==as.character( dates.cameras[j,1]))
      row<-which(cams==as.character( dates.cameras[j,2]))
      mat[row,col]<-1
    }
    mat.nas<-is.na(mat)
    sum.nas<-apply(mat.nas,2,sum)
    indx.nas<-which(sum.nas==rows)
    if(length(indx.nas)>0){
      mat<-mat[,-indx.nas]
    }
    
    res<-c(res,list(mat))
    #return the matrix to its original form
    mat<-mat.template
  }
  
  names(res)<-species
  #res<-lapply(res,f.dum)
  res #object to return
}

Apply the function to get Tapirus bairdii detection matrix

Code

# filter firs year and make uniques

tbairdi <- f.matrix.creator(katios1)[[1]]

Lets extract percent tree cover 2012 to be used as site covariate

The covariate is coming from MODIS. MOD44B Version 6 Vegetation Continuous Fields (VCF). https://lpdaac.usgs.gov/products/mod44bv006/

We plot the cameras as sf object on top the map and extract the values using the function terra::extract

Code
# load the raster map
per_tree_cov <- rast("C:/CodigoR/WCS-CameraTrap/raster/latlon/Veg_Cont_Fields_Yearly_250m_v61/Perc_TreeCov/MOD44B_Perc_TreeCov_2012_065.tif")

# extract values per camera
per_tre <- terra::extract(per_tree_cov, katios_sf)

# assign values to the sf object
katios_sf$per_tree_cov <- per_tre$MOD44B_Perc_TreeCov_2012_065 
#  fix 200 issue
# ind <- which(sites$per_tree_cov== 200)
# sites$per_tree_cov[ind] <- 0

Create unmarked frame object

Lets use the unmarked package to make an unmarkedFrameOccu object.

Code
umf <- unmarkedFrameOccu(y=tbairdi, 
                         siteCovs=data.frame(
                           per_tree_cov=katios_sf$per_tree_cov)
                           # road_den=sites$roads),
                         # obsCovs=list(effort=ej)
                      )

plot(umf)

Sites against days (observation)

Sites against days (observation)
Code

unmarked::summary(umf)
#> unmarkedFrame Object
#> 
#> 27 sites
#> Maximum number of observations per site: 93 
#> Mean number of observations per site: 45.52 
#> Sites with at least one detection: 10 
#> 
#> Tabulation of y observations:
#>    0    1 <NA> 
#> 1206   23 1282 
#> 
#> Site-level covariates:
#>   per_tree_cov  
#>  Min.   :66.00  
#>  1st Qu.:73.00  
#>  Median :78.00  
#>  Mean   :76.07  
#>  3rd Qu.:78.00  
#>  Max.   :80.00

Fit models

lets use ubms package to fit several models. We contrast the null model (no covariates) against a model with percent tree cover to explain the occupancy. For this example we are not using covariates for the detection part.

Code
# fit_0 <- occu(~1~1, data=umf) # unmarked

fit_j0 <- stan_occu(~1~1, data=umf, chains=3, iter=100000, cores=3)
fit_j2 <- stan_occu(~1~scale(per_tree_cov), data=umf, chains=3, iter=100000, cores=3)

Model selection

Code
# compare models
models <- list("p(.)psi(.)" = fit_j0, # put names
                "p(.)psi(per_tree_cov)" = fit_j2) # put names

mods <- fitList(fits = models)

## see model selection as a table
datatable( 
  round(modSel(mods), 3)
  )

The model p(.)psi(per_tree_cov) is the “better”.

Estimates for the null model

Estimated values for the null model p(.)psi(.) are: 0.4403455, 0.0439675 for occupancy, and detection probability respectively.

Details of the best model

Code
fit_j2
#> 
#> Call:
#> stan_occu(formula = ~1 ~ scale(per_tree_cov), data = umf, chains = 3, 
#>     iter = 1e+05, cores = 3)
#> 
#> Occupancy (logit-scale):
#>                     Estimate    SD   2.5% 97.5% n_eff Rhat
#> (Intercept)            -0.40 0.585 -1.494 0.811 89171    1
#> scale(per_tree_cov)     1.34 0.707  0.148 2.917 87437    1
#> 
#> Detection (logit-scale):
#>  Estimate    SD  2.5% 97.5% n_eff Rhat
#>     -3.09 0.262 -3.64 -2.62 94232    1
#> 
#> LOOIC: 216.987
#> Runtime: 75.721 sec

we conclude MCMC chains have converged if all R>1.05
Convergence here is not that good…

Model convergence

Let see the chains.

Code
traceplot(fit_j2, pars=c("beta_state"))

the chains should be converging

Chains trace plot. The chains should be converging

not that good…

Evaluate model fit

Statistic (p) should be near 0.5 if the model fits well.

Code

# eval
fit_top_gof <- gof(fit_j2, draws=500, quiet=TRUE)
fit_top_gof
#> MacKenzie-Bailey Chi-square 
#> Point estimate = 713919507.838
#> Posterior predictive p = 0.136

# plot(fit_top_gof)

0.14 is not that bad.

Model inference

No covariate for detection, and percent of forest tree cover in occupancy.

Code
# ubms::plot_effects(fit_j2, "det")
ubms::plot_effects(fit_j2, "state")

The predictor is percent tree cover

Prediction of occupancy with percent tree cover

The error band is large but there is a clear trend.

Spatial model

Taking in to account spatial autocorrelation.

Code
# convert to UTM
katios_utm = st_transform(katios_sf, 21818)
katios_cord <- st_coordinates(katios_utm)
site_cov <- as.data.frame(cbind(per_tree_cov=scale(katios_sf$per_tree_cov),
                  katios_cord))

names(site_cov) <- c("per_tree_cov", "X", "Y")

with(site_cov, RSR(X, Y, threshold=1, plot_site=27))

Spatial autocorrelation.

Spatial autocorrelation.
Code

form <- ~1 ~per_tree_cov + RSR(X, Y, threshold=1)
umf2 <- unmarkedFrameOccu(y=tbairdi, siteCovs=site_cov)
# fit_spatial <- stan_occu(form, umf2, chains=3, cores=3, seed=123) # error

Spatial model do not run… Error at Building RSR matrices: TridiagEigen: eigen decomposition failed. Probably to few sites.

Predict occupancy in a map

Lets use a raster map with percent tree cover to predict the occupancy and see the resulting occupancy as a map.

Code
# cut large raster 
box <- ext(-77.18,-77.11, 7.800, 7.89) # make a box xmin, xmax, ymin, ymax
library(raster)
per_tree_cov_cut <- raster(crop(per_tree_cov, box))# cut raster using the box
# put correct name
names(per_tree_cov_cut) <- "per_tree_cov"

# predict in ubms
map_occupancy <- ubms::predict(fit_j2,
                               submodel="state",
                               newdata=per_tree_cov_cut,
                               transform=TRUE)

katios_occu <- map_occupancy[[1]] # assign just prediction
katios_occu[katios_occu >= 0.9] <- NA # convert river to NA

# make a palette 9 colors yellow to green
pal <- grDevices::colorRampPalette(RColorBrewer::brewer.pal(9, "YlGn"))
# plot map
mapview(katios_np, alpha.regions=0.1) +
mapview(katios_occu, col.regions= pal, alpha = 0.5) + mapview(katios_sf, cex=2)

Predicted occupancy map.

Package Citation

Code
pkgs <- cite_packages(output = "paragraph", out.dir = ".") #knitr::kable(pkgs)
pkgs

We used R version 4.3.2 (R Core Team 2023) and the following R packages: camtrapR v. 2.3.0 (Niedballa et al. 2016), devtools v. 2.4.5 (Wickham et al. 2022), DT v. 0.33 (Xie, Cheng, and Tan 2024), elevatr v. 0.99.0 (Hollister et al. 2023), kableExtra v. 1.4.0 (Zhu 2024), mapview v. 2.11.2 (Appelhans et al. 2023), patchwork v. 1.3.0 (Pedersen 2024), quarto v. 1.4.4 (Allaire and Dervieux 2024), raster v. 3.6.30 (Hijmans 2024a), RColorBrewer v. 1.1.3 (Neuwirth 2022), rmarkdown v. 2.28 (Xie, Allaire, and Grolemund 2018; Xie, Dervieux, and Riederer 2020; Allaire et al. 2024), sf v. 1.0.17 (Pebesma 2018; Pebesma and Bivand 2023), styler v. 1.10.3 (Müller and Walthert 2024), terra v. 1.7.78 (Hijmans 2024b), tidyverse v. 2.0.0 (Wickham et al. 2019), ubms v. 1.2.7 (Kellner et al. 2021), unmarked v. 1.4.3 (Fiske and Chandler 2011; Kellner et al. 2023).

Sesion info

Session info 
#> ─ Session info ───────────────────────────────────────────────────────────────────────────────────────────────────────
#>  setting  value
#>  version  R version 4.3.2 (2023-10-31 ucrt)
#>  os       Windows 10 x64 (build 19045)
#>  system   x86_64, mingw32
#>  ui       RTerm
#>  language (EN)
#>  collate  Spanish_Colombia.utf8
#>  ctype    Spanish_Colombia.utf8
#>  tz       America/Bogota
#>  date     2024-11-07
#>  pandoc   3.2 @ C:/Program Files/RStudio/resources/app/bin/quarto/bin/tools/ (via rmarkdown)
#> 
#> ─ Packages ───────────────────────────────────────────────────────────────────────────────────────────────────────────
#>  ! package           * version  date (UTC) lib source
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#>  D ── DLL MD5 mismatch, broken installation.
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#> ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────

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Citation

BibTeX citation:
@online{j._lizcano2024,
  author = {J. Lizcano, Diego},
  title = {Single {Season} {Occupancy} {Model}},
  date = {2024-07-27},
  url = {https://dlizcano.github.io/cametrap/posts/2024-07-29-sigle-season-occupancy/},
  langid = {en}
}
For attribution, please cite this work as:
J. Lizcano, Diego. 2024. “Single Season Occupancy Model.” July 27, 2024. https://dlizcano.github.io/cametrap/posts/2024-07-29-sigle-season-occupancy/.