Chapter 11 Occupancy

Occupancy modelling has been one of the mainstays of camera traps data analysis for many years, so learning how to wangle our data into occupancy-style formats is essential.

When we survey wild and free ranging populations using any sampling methodology, the probability of detecting a given individual or species if it is actually present on the landscape at the time of sampling is typically less than one. This is because wild animals are often hard to see! This issue is termed “imperfect detection”.

In order to deal with the imperfect detection issue - occupancy models separate our the counts of a given species at a site into two processes:

  1. occupancy (ψ) - which is the probability of a species occurring within a spatial unit (or “site”) during the sampling session
  2. detection probability (p) - the probability that the species will be detected given that it already occurs at a site

In order to separate out the occupancy process from the detection process, surveys need to occur at replicated ‘sites’ and we need repeated ‘visits’ to the same site. It is important to know that in camera trap studies, practitioners typically treat individual locations as sites and rather than repeated return to a location to survey it at different times, they divide the continuous camera activity data into block of time (e.g. 1 to 7 day windows).

Occupancy models were not developed specifically for camera traps - thus there are a suite of assumptions we need to make about the populations we survey when applying occupancy models. We do not adress these here. However, below we provide a list introductory resources for you to dig into the occupancy models to decide if they are appropriate for your situation:

Burton, A. Cole, et al. “Wildlife camera trapping: a review and recommendations for linking surveys to ecological processes.” Journal of Applied Ecology 52.3 (2015): 675-685.

MacKenzie, Darryl I., et al. Occupancy estimation and modeling: inferring patterns and dynamics of species occurrence. Elsevier, 2017.

Let’s focus our time on getting our data into the right formt, and applying some occupancy models!

# Check you have them and load them
list.of.packages <- c("kableExtra", "tidyr", "ggplot2", "gridExtra", "dplyr", "unmarked", "lubridate", "tibble", "sf", "gfcanalysis", "MuMIn", "spOccupancy")

new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])]
if(length(new.packages)) install.packages(new.packages)
lapply(list.of.packages, require, character.only = TRUE)

11.1 Single species occupancy model

In this example we will use the ...weekly_observations dataframe we created in the data creation section. We do this because 7 days is a time interval which occupancy models are often devided into for occupancy analyses.

# Import the weekly observations data set
week_obs <- read.csv("data/processed_data/AlgarRestorationProject_30min_independent_weekly_observations.csv", header=T)

Which, as a quick reminder, looks like this:

placename date days Alces.alces Canis.latrans Canis.lupus Cervus.canadensis Lepus.americanus Lontra.canadensis Lynx.canadensis Martes.americana Odocoileus.virginianus Oryctolagus.cuniculus Rangifer.tarandus Tamiasciurus.hudsonicus Ursus.americanus Vulpes.vulpes
ALG027 2018-W14 4 0 0 0 0 0 0 1 0 0 0 0 0 0 0
ALG027 2018-W15 7 0 0 1 0 0 0 1 0 0 0 0 0 0 0
ALG027 2018-W16 7 0 0 1 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W17 7 0 0 1 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W18 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W19 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W20 7 0 0 0 0 0 0 0 0 0 0 0 0 3 0
ALG027 2018-W21 7 0 0 1 0 0 0 0 0 0 0 0 0 8 0
ALG027 2018-W22 7 0 0 0 0 0 0 1 0 0 0 0 0 3 0
ALG027 2018-W23 7 0 0 0 0 0 0 0 0 0 0 0 0 2 0
ALG027 2018-W24 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W25 7 1 0 0 0 0 0 1 0 2 0 0 0 1 0
ALG027 2018-W26 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W27 7 0 0 1 0 0 0 1 0 0 0 0 0 1 0
ALG027 2018-W28 7 0 0 0 0 0 0 0 0 0 0 0 0 2 0
ALG027 2018-W29 7 0 0 0 0 0 0 0 0 0 0 0 0 2 0
ALG027 2018-W30 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W33 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W34 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W36 7 0 0 0 0 0 0 0 0 0 0 0 0 2 0
ALG027 2018-W37 7 0 0 0 0 0 0 1 0 0 0 0 0 0 0
ALG027 2018-W38 7 0 0 1 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W39 7 1 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG027 2018-W40 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W41 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W42 7 0 1 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W43 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W44 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W45 7 0 0 1 0 0 0 0 0 1 0 0 0 0 0
ALG027 2018-W46 7 0 0 0 1 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W47 7 0 1 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W48 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W49 7 0 0 2 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W50 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W51 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2018-W52 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W00 5 0 1 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W01 7 0 1 1 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W02 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W03 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W04 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W05 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W06 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W07 7 0 0 0 0 0 0 1 0 0 0 0 0 0 0
ALG027 2019-W08 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W09 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W10 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG027 2019-W11 7 0 0 0 0 0 0 2 0 0 0 0 0 0 0
ALG027 2019-W12 7 0 0 0 0 0 0 1 0 0 0 0 0 0 0
ALG027 2019-W13 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W13 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W14 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W15 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W16 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W17 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W18 7 3 0 0 0 0 0 0 0 2 0 0 0 1 0
ALG029 2018-W19 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W20 7 2 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W21 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W22 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W23 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W24 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W25 7 1 0 0 0 0 0 0 0 3 0 0 0 0 0
ALG029 2018-W26 7 1 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W27 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG029 2018-W28 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W29 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W30 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W33 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W34 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W36 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W37 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W38 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W39 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W40 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W41 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W42 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W43 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W44 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W45 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W46 7 0 0 0 0 0 0 0 0 2 0 0 0 0 0
ALG029 2018-W47 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W48 7 0 0 0 0 0 0 1 0 1 0 0 0 0 0
ALG029 2018-W49 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W50 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2018-W51 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2018-W52 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W00 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W01 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W02 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W03 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W04 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W05 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W06 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W07 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W08 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W09 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W10 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W11 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W12 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W13 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W14 7 0 0 0 0 0 0 0 0 2 0 0 0 0 0
ALG029 2019-W15 7 1 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG029 2019-W16 7 1 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W17 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W18 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W19 7 1 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W20 7 0 0 0 0 0 0 0 0 4 0 0 0 0 0
ALG029 2019-W21 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W22 7 1 0 0 0 0 0 0 0 0 0 0 0 2 0
ALG029 2019-W23 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W24 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W25 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W26 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W27 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W28 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W29 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W30 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG029 2019-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W33 7 0 0 0 0 0 0 0 0 2 0 0 0 0 0
ALG029 2019-W34 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W36 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W37 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W38 7 0 0 0 0 0 0 0 0 0 0 0 0 2 0
ALG029 2019-W39 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG029 2019-W40 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W41 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG029 2019-W42 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W43 7 0 0 0 0 0 0 0 0 3 0 0 0 0 0
ALG029 2019-W44 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W45 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG029 2019-W46 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W14 7 0 0 0 0 0 1 0 0 0 0 0 0 0 0
ALG031 2018-W15 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W16 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W17 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W18 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W19 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W20 7 1 0 0 0 0 0 0 1 0 0 0 0 0 0
ALG031 2018-W21 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W22 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W23 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W24 7 1 0 0 0 0 0 0 1 0 0 2 0 0 0
ALG031 2018-W25 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W26 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W27 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W28 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W29 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W30 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W33 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W34 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W36 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W37 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2018-W38 7 0 0 1 0 0 0 0 0 0 0 1 0 0 0
ALG031 2018-W39 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2018-W40 7 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ALG031 2018-W41 7 1 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2018-W42 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W43 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W44 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W45 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W46 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W47 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W48 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W49 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W50 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W51 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2018-W52 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W00 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W01 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W02 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W03 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W04 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W05 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W06 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W07 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W08 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W09 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W10 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W11 7 0 0 0 0 0 0 0 2 0 0 0 0 0 0
ALG031 2019-W12 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W13 7 1 0 2 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W14 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W15 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W16 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W17 7 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W18 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W19 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W20 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W21 7 0 0 0 0 0 0 0 1 0 0 0 0 0 0
ALG031 2019-W22 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W23 7 1 0 0 0 0 0 0 0 1 0 1 0 0 0
ALG031 2019-W24 7 0 0 1 0 0 0 0 0 0 1 1 0 0 0
ALG031 2019-W25 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2019-W26 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2019-W27 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W28 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2019-W29 7 0 0 0 0 0 0 0 0 0 0 0 0 1 0
ALG031 2019-W30 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG031 2019-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W33 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W34 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W36 7 0 0 0 0 0 0 0 0 0 0 2 0 0 0
ALG031 2019-W37 7 0 0 0 0 0 0 0 0 0 0 3 0 0 0
ALG031 2019-W38 7 0 0 0 0 0 0 0 0 0 0 3 0 0 0
ALG031 2019-W39 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W40 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W41 7 0 0 0 0 0 0 0 0 0 0 1 0 1 0
ALG031 2019-W42 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W43 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W44 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W45 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG031 2019-W46 5 0 0 0 0 1 0 0 1 0 0 0 0 0 0
ALG032 2018-W13 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W14 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W15 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W16 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W17 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W18 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W19 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W20 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W21 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W22 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG032 2018-W23 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W24 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W25 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W26 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W27 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W28 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG032 2018-W29 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG032 2018-W30 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W33 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W34 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W36 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W37 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W38 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W39 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W40 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W41 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W42 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W43 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W44 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG032 2018-W45 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W46 7 1 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W47 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W48 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W49 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W50 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W51 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2018-W52 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W00 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W01 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W02 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W03 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W04 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W05 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W06 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W07 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W08 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W09 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W10 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W11 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W12 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W13 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W14 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W15 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W16 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W17 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W18 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W19 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W20 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W21 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W22 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W23 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W24 7 0 0 0 0 0 0 0 0 1 0 0 0 0 0
ALG032 2019-W25 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W26 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W27 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W28 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W29 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG032 2019-W30 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W31 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W32 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W33 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W34 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W35 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W36 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG032 2019-W37 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 2019-W38 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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ALG073 2018-W19 7 1 0 0 0 0 0 0 0 0 0 1 0 0 0
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ALG073 2018-W22 7 0 0 0 0 0 0 0 0 0 0 2 0 0 0
ALG073 2018-W23 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG073 2018-W24 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
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ALG073 2018-W26 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG073 2018-W27 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG073 2018-W28 7 0 0 0 0 0 0 0 0 0 0 4 0 0 0
ALG073 2018-W29 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
ALG073 2018-W30 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0
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ALG073 2019-W42 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG073 2019-W43 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG073 2019-W44 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG073 2019-W45 7 0 0 0 0 0 0 0 0 0 0 2 0 0 0
ALG073 2019-W46 5 0 0 0 0 0 0 0 0 0 0 1 0 0 0

As with previous chapters, we will start by focusing on the white-tailed deer (Odocoileus virginianus).

We first need to create a site by occasion matrix for our focal species, using a 7-day occasion length. This means we need to break our camera data into seven day bins.

We can create the detection histories using the following code:

# Use white-tailed deer
focal_sp<- "Odocoileus.virginianus"

# subset to 2019
tmp_week <- week_obs[substr(week_obs$date,1,4)==2019,]

# Create the Y data  
y_dat <- tmp_week[,c("placename", "date", focal_sp)] %>% # Subset to just white-tailed deer
            pivot_wider(names_from = date, values_from = focal_sp) # Shift to wide format

# Convert it to a matrix - but only keep the date values
y_mat <- as.matrix(y_dat[,unique(tmp_week$date)])

# Update the row names
row.names(y_mat) <- y_dat$placename

The resulting data frame looks like this:

2019-W00 2019-W01 2019-W02 2019-W03 2019-W04 2019-W05 2019-W06 2019-W07 2019-W08 2019-W09 2019-W10 2019-W11 2019-W12 2019-W13 2019-W14 2019-W15 2019-W16 2019-W17 2019-W18 2019-W19 2019-W20 2019-W21 2019-W22 2019-W23 2019-W24 2019-W25 2019-W26 2019-W27 2019-W28 2019-W29 2019-W30 2019-W31 2019-W32 2019-W33 2019-W34 2019-W35 2019-W36 2019-W37 2019-W38 2019-W39 2019-W40 2019-W41 2019-W42 2019-W43 2019-W44 2019-W45 2019-W46
ALG027 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
ALG029 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 1 1 4 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 1 3 1 1 0
ALG031 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG032 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG035 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG036 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG037 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG038 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG039 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG043 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0
ALG044 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0
ALG045 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG046 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG047 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 NA NA NA NA NA NA NA NA NA NA NA NA
ALG048 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ALG049 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 NA NA NA NA NA NA NA
ALG052 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 3 1 2 0 0 1 1 5 0 0 1 0 2 3 1 1 1 1 1 0 0 0 2 1 3 0 1 1 0
ALG053 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG054 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 2 0 0 1 1 1 1 1 0 0 0 2 2 4
ALG055 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 2 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
ALG056 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
ALG057 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 6 0
ALG058 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 1 1 4 1 2 4 3 2 2 2 3 1 4 6 4 0 2 0 0 0 0 0 0 0 0 0
ALG059 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG060 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG061 0 1 0 0 1 2 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 2 1
ALG062 0 3 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 2 0 0 3 1 3 2 3 1 0 1 0 0 0 0 0 5 1 1 1 0 0 0 0 0 0 0 0 0 0
ALG063 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 1 1 1 0 0 1 1 0 1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1
ALG064 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG065 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
ALG066 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG067 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG068 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG069 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 1 0 1 0 0 0 0 0 0 2 0 0 3 4 1 0 2 1 3 1 0 0 1 1 2 3 5 0 0 2 1
ALG070 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALG071 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 2 0 0 1 0 0 1 0 0 1 0 2 0 0 4 1 0 1 0 0 2 0 2 1 0 0 1
ALG072 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
ALG073 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

It is a matrix of all the weeks the cameras were active, and whether the count of the independent detections in that interval. The fill = NA command puts a zero where there is data for a given day.

You can see that in some columns we have values > 1 - this is because we had more than one independent observation in that week. Occupancy analyses (typically) require this data to be in detection/non-dection (0 or 1) format. So lets change that here.

# Where y_mat is > 1, and where y_mat isn't NA - give it the value 1
y_mat[y_mat>1 & is.na(y_mat)==F] <- 1

However, we have lost our effort information - the number of days each camera was active in a given time period. So we need another data frame!

To get that information we need to create an effort history eff_mat:

# To create the effort matrix - inst of the Focal Species bring in the effort
eff_mat <- tmp_week[,c("placename", "date", "days")]

eff_mat <-  eff_mat %>%
  # Create a matrix based on dates and effort
  spread(date,days, fill = NA) %>% 
  # group by deloyment Location ID, then make that the row.namesd
  group_by(placename) %>%
  column_to_rownames( var = "placename") 

eff_mat <- as.matrix(eff_mat)

Check that it looks sensible:

2019-W00 2019-W01 2019-W02 2019-W03 2019-W04 2019-W05 2019-W06 2019-W07 2019-W08 2019-W09 2019-W10 2019-W11 2019-W12 2019-W13 2019-W14 2019-W15 2019-W16 2019-W17 2019-W18 2019-W19 2019-W20 2019-W21 2019-W22 2019-W23 2019-W24 2019-W25 2019-W26 2019-W27 2019-W28 2019-W29 2019-W30 2019-W31 2019-W32 2019-W33 2019-W34 2019-W35 2019-W36 2019-W37 2019-W38 2019-W39 2019-W40 2019-W41 2019-W42 2019-W43 2019-W44 2019-W45 2019-W46
ALG027 5 7 7 7 7 7 7 7 7 7 7 7 7 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
ALG029 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG031 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG032 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG035 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6
ALG036 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG037 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG038 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG039 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG043 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG044 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG045 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG046 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG047 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3 NA NA NA NA NA NA NA NA NA NA NA NA
ALG048 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG049 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 NA NA NA NA NA NA NA
ALG052 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG053 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG054 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6
ALG055 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG056 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6
ALG057 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG058 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6
ALG059 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG060 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG061 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG062 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG063 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG064 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5
ALG065 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
ALG066 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG067 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG068 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 4
ALG069 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG070 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3
ALG071 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6
ALG072 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 6
ALG073 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5

We might want to remove all of the data from the weeks where we did not get a complete sample:

y_mat[eff_mat!=7] <- NA

Now we are ready to feed this into the unmarked package.

11.1.1 Unmarked package

One of the hurdles in using the unmarked package is it uses a different style of dataframe called an unmarked dataframe. It is essentially a compillation of the different dataframes we need for the analysis (y data and covariate data). We asemmbled the Y data above, so now lets make the covariates:

locs <-  read.csv("data/processed_data/AlgarRestorationProject_camera_locations_and_covariates.csv")

# Unmarked wants your detection history, effort data and site covariates as matrices. But the order is important!
# Check the order of your matrices and covariates files matches... or you will get nonsense!
table(locs$placename == row.names(y_mat))
## 
## TRUE 
##   38

Data standardization

Unmarked models benefit from standardizing your covariates - it helps the solving algorithms converge on an appropriate solution. To do this we use the MuMIn package.

library(MuMIn)
z_locs <- stdize(locs)

Take a look at it to see what it has done!

We then need to build an ‘unmarked’ data frame. You don’t really need to know why they are different or how to use one (although it helps), knowing how to use one is sufficient.

# Build an unmarkedFramOccu
un_dat <- unmarkedFrameOccu(y = y_mat, # your occupancy data
                            siteCovs = z_locs) # Your site covariates 
## Warning: siteCovs contains characters. Converting them to factors.

We can then fit the occupancy model, lets start with a “null” model with no predictors on detection or occupancy.

# Fit general model all variables
m0 <- occu(formula = ~1 # detection formula first
                     ~1, # occupancy formula second,
                data = un_dat)

Then view the results.

summary(m0)
## 
## Call:
## occu(formula = ~1 ~ 1, data = un_dat)
## 
## Occupancy (logit-scale):
##  Estimate    SE    z P(>|z|)
##     0.668 0.345 1.94  0.0527
## 
## Detection (logit-scale):
##  Estimate     SE     z  P(>|z|)
##     -1.37 0.0749 -18.3 1.34e-74
## 
## AIC: 1170.366 
## Number of sites: 38
## optim convergence code: 0
## optim iterations: 26 
## Bootstrap iterations: 0

The estimate you see for both occupancy and detection probability is on the log-link scale. If we want to calculate the occupancy probability, we can use the backTransform() function:

backTransform(m0, type = "state")
## Backtransformed linear combination(s) of Occupancy estimate(s)
## 
##  Estimate     SE LinComb (Intercept)
##     0.661 0.0773   0.668           1
## 
## Transformation: logistic

So the probability that a white-tailed deer occupies one of the survey locations is ~0.66. For the detection probability we specify “det”:

backTransform(m0, type = "det")
## Backtransformed linear combination(s) of Detection estimate(s)
## 
##  Estimate     SE LinComb (Intercept)
##     0.203 0.0121   -1.37           1
## 
## Transformation: logistic

The probability that we detect a white-tailed deer in a given unit of time (7-days), given that it is there to be detected, is ~0.2.

Let’s fit a couple of other models!

First with a continuous covariate on the occupancy probability, then a categorical one too:

# Occupancy is influence by line of sight
m1 <- occu(formula = ~1 # detection formula first
                     ~z.line_of_sight_m, # occupancy formula second,
                data = un_dat)

# Occupancy is influenced by the feature_type a camera is deployed on
m2 <- occu(formula = ~1 # detection formula first
                     ~feature_type, # occupancy formula second,
                data = un_dat)

We can perform model selection on these different scenarios in the same way as in the habitat use chapter - using the MuMIn package:

model.sel(m0,m1,m2)
## Model selection table 
##    p(Int) psi(Int) psi(z.lin_of_sgh_m) psi(ftr_typ) df   logLik   AICc
## m1 -1.368  0.70530             -0.5664               3 -581.839 1170.4
## m0 -1.368  0.66830                                   2 -583.183 1170.7
## m2 -1.367  0.01785                                +  4 -581.769 1172.8
##    delta weight
## m1  0.00  0.464
## m0  0.33  0.394
## m2  2.37  0.142
## Models ranked by AICc(x)

The best supported model contains z.line_of_sight_m, although the improvement on the null model is minimal.

11.1.2 Plotting predictions

We can observe the relationship between our covariates and our occupancy probabilities through the use of a dummy dataframes (which we will call new_dat). A dummy dataframe is essential just a dataframe built up of dummy data - which lies within the upper and lower limits of the covariates we already have. We wouldn’t want to extrapolate beyond our data! We can then plot the results:

# Generate new data to predict from 
new_dat <- cbind(expand.grid(
                  z.line_of_sight_m=seq(min(z_locs$z.line_of_sight_m),max(z_locs$z.line_of_sight_m), # add more covariates here if the model is more complex
                  length.out=25)))

# Make the predicted values for the data you supplied                 
new_dat <- predict(m1, type="state", newdata = new_dat, appendData=TRUE)


#Plot the results

p1 <- ggplot(new_dat, aes(x = z.line_of_sight_m, y = Predicted)) + # mean line
  geom_ribbon(aes(ymin = lower, ymax = upper), alpha = 0.5, linetype = "dashed") + #Confidence intervals
  geom_path(size = 1) +
  labs(x = "Line of sight", y = "Occupancy probability") + # axis labels
  theme_classic() +
  coord_cartesian(ylim = c(0,1))

p1

As with our habitat use model, white-tailed deer (Odocoileus virginianus) occupancy appears to decrease with increasing line of sight.

11.1.3 On your own

Let’s explore some of the models we fit in the habitat use chapter in the occupancy framework. We have not included any detection covariates in this example dataset, so hold that constand for now!

NOT IN R Tobler, M. et al. Spatiotemporal hierarchical modelling of species richness and occupancy using camera trap data. J. Appl. Ecol. (2015).

11.2 Spatial occupancy model: spOccupancy

COMING SOON

Whilst unmarked has been the workhorse for implementing occupancy models in R, there is a new kid on the block - spOccupancy.

One of the benefits of spOccupancy is that they have a huge amount of resources to help you learn and fit models too: the spOccupancy website

11.2.1 Multi species model

COMING SOON