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The closure assumption with SCRPassive detectors can be left out for long periods, providing more data on each animal captured and thus giving better estimates of detection parameters in spatial capturerecapture (SCR) studies. But with long study periods, the risk of animals coming and going or changing activity centres (ACs) increases.In this post I want to explore what is "closure" in SCR, why it is important, and what happens if it is violated. I'll also explore some ideas for open population models which can be used to mitigate closure issues.
New version of
A
new version of the 
12 May 2018 
saveJAGS
packagesaveJAGS
package. It has
certainly changed the way I do things. It's a wrapper for
rjags
which periodically saves the MCMC chains to files.
The advantages of that are:
3 April 2018, updated 12 May 2018 
17 March 2018 
25 December 2017 
In R, the class factor
is used for categorical variables. A factor has a levels
attribute with the names of the categories, in alphabetical
order by default, and the values are stored as integers giving
the level number.
I'll generate some simulated data for a logistic regression model (as that generalises to a lot of our other models). We have four players with different degrees of skill and a continuous covariate which does nothing.
20 December 2017 
In the simplest model, the number available for detection at site \( i \), \( N_i \), is modelled as being drawn from a Poisson distribution with parameter \( \lambda \). This is the biological model. The observation model assumes that detection of each individual is a Bernoulli trial, individuals being detected with probability \( r \). The data do not show which individuals are detected, just whether the species was detected, and that is recorded if at least one individual is observed.
27 November 2017 
In the course
of applying these ideas to maximum likelihood estimation in the
wiqid
package, a couple of new issues came up. We
will revisit logSumExp
and develop new functions to
add together two vectors and to do matrix multiplication.
31 October 2017 
If each animal produces p signs per day and signs remain visible for t days, then sign density will be:
S = D x p x t
where D is the density of animals. If we can estimate p and t, we can calculate D from S. In this post I want to provide code for estimating the persistence time of signs for retrospective studies of decay.
7 October 2017 
The solution is to work with logarithms of probabilities instead of the actual values [log(p) instead of p], eg, we routinely work with loglikelihoods. Multiplying probabilities is then simply a matter of adding up the logs. But sometimes we need to add up probabilities or calculate the complement, 1  p, and we need to do that without falling in the 0 abyss or smashing into the 1 wall.
4 August 2017 
Here's a simple example: we have 3 sites, visited 4 times per year for 2 years. This is usually shoehorned into a table with 8 columns for the visits, like this:
occasion
site 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4
A 0 1 1 3 2 0 1 1
B 1 0 1 0 3 0 2 2
C 5 2 1 1 3 4 2 1
These look like counts, but the data could be detection/nondetection (0/1) data, wind speed at each visit, or the name of the observer.
24 February 2017 
This was based on simulations with just one set of parameter values, but it does suggest that projects with limited resources should consider using unpaired cameras, as this allows more locations to be sampled.
5 February 2017, updated 17 April 2018 
24 January 2017 
jagsUI
is only 100 iterations, which was woefully
inadequate for my model. We should be specifying big numbers for
n.adapt
and small
numbers, or even zero, for n.burnin
.
27 December 2016 
17 October 2016 
7 October 2016 
secr
package to the format needed to run in JAGS or WinBUGS/OpenBUGS.
Updated 28 May 2017: You can install it from Github using the
githubinstall
package by opening R and running
library(githubinstall)
githubinstall("makeJAGSmask")
7 August 2016, updated 28 May 2017 
The issue arises because current R versions, 3.3.0 or later, are not compatible with the current default installer for JAGS. Note that the problem is with the Windows installer, not JAGS source code, and doesn't affect other platforms. A compatible installer is available, but it's not the default. See Martyn Plummer's post for more details.
10 June 2016 
People seem to run into problems with different versions of the Mac OS, R, JAGS and the rjags package. The only way to stay sane is to use recent versions of all four.
From the Apple menu, choose About This Mac; the version number appears below the name. Note whether you have v. 10.11 (El Capitan) or later. If you have an earlier version, upgrade your OS before going further.
16 Jan 2016, updated 30 Oct 2017 
BEST
and wiqid
packages with the new
version of JAGS on Ubuntu. It took me a while, but I finally
found a simple way to do this which might be of interest to
others.I already had R and JAGS 3 installed, together with
the rjags
package version 3. Installing the rjags
package within
R (or updating it with update.packages()
) installs the new
version of rjags
, v.4, which requires JAGS 4 and throws an error
if it isn't found. But the Ubuntu repository still has JAGS 3,
so you cannot update JAGS with Ubuntu Software Center.
29 Dec 2015 
The idea for the sampler was developed by Nicholas Metropolis and colleagues in a paper in 1953. This was before the Gibbs sampler was proposed, but it uses the same idea of updating the parameters one by one. A better name would be "componentwise random walk Metropolis sampler". The rules for the random walk ensure that a large number of samples will be a good description of the posterior distribution.
5 March 2015 
Gibbs sampling works if we can describe the posterior for each parameter if we know all the other parameters in the model.
27 February 2015 
As our example, we'll use estimation of detection probability from data for repeat visits to a site which is known to be occupied by our target species. First, we'll describe the beta distribution, then see how that can be combined with our data. A discussion of priors will follow, and we'll finish with brief descriptions of conjugate priors for other types of data.
25 February 2015 
wiqid
package. I'll focus mainly on Bayesian
methods, but this first post will look at the likelihood, which
is used for both Bayesian analysis and maximum likelihood
estimation.We'll use a simple occupancy model. It has just two parameters and both must between 0 and 1. That means that we can plot all possible combinations of the two parameters in a simple twodimensional graph. As we'll see we need to add a third dimension, but three is still manageable.
12 February 2015 
Currently it has functions for estimating occupancy, abundance from closed captures, density from spatial capturerecaptures, and survival from markrecapture data, plus a slew of functions for species richness and alpha and beta diversity.
It is intended to be used for (1) simulations and bootstraps, (2) teaching, and (3) introducing Bayesian methods. And it should work on all platforms: Windows, Linux, and Mac.
5 January 2014 
23 December 2013 
secr
package take care of the former. Bayesian
analysis with the usual workhorses, WinBUGS, OpenBUGS and JAGS,
is straightforward if the traps are laid out in a large area of
homogenous habitat.Faced with patches of suitable habitat surrounded by inhospitable terrain, or a large extent of habitat punctuated with patches of nonhabitat, we had the choice of ML methods or one of the packages designed specifically for Bayesian SECR analysis, such as SPACECAP or SCRbayes. But then we are limited to the range of models provided by package authors: we don't have the flexibility to specify our own models that comes with WinBUGS, OpenBUGS or JAGS.
Here I present a way to incorporate patchy habitat into a BUGS/JAGS model specification.
22 Sept, updated 5 Nov 2013 
We start off with simple spinners representing a uniform distribution over a range from, say, 0 to 0.5. We discuss the problems of attaching a probability to an exact value, which leads to probability of a range of values and hence probability density.
15 September 2013 
Before the advent of SECR methods, putting all your traps into a single cluster with minimal perimeter length made sense, as you needed to estimate the area trapped animals came from to get a density. SECR estimates density directly, without needing to estimate area, so a single, large cluster may no longer be advantageous.
26 August 2013 
I've seen this asserted a couple of times, in particular in Tobler and Powell (2013, p.110), and I've myself drawn circular home ranges when discussing the interpretation of the capture parameters, but I don't think it is a necessary assumption.
8 August 2013 
Capturerecapture methods (also know as markrecapture or capturemarkrecapture) have been used to estimate the size of animal populations for many years: the first software package for analysis of this kind of data, CAPTURE (Otis et al 1978), is now 35 years old. Early methods did not use the spatial component in the data, the capture locations, and spatially explicit capturerecapture models (SECR, or just spatial capturerecapture, SCR) first appeared in 2004 (Efford 2004).
7 August 2013 
The idea is to provide an R function which is as easy to use as t.test but which gives not a mere pvalue but the kind of output Bayesians are used to  posterior probability distributions. John's BESTmcmc function uses JAGS, but handles all the preliminaries automatically and produces a result in a simple format.
9 June 2013 
As soon as cameras with "data backs" came along in the early 90s, biologists realised that they could harvest data on the activity patterns of rare, secretive forest animals. Were they diurnal, nocturnal, crepuscular, or maybe cathemeral (active all around the clock)? More recently, people have tried to get clues about how species interact  competition or preypredator interactions  from activity patterns, by examining the extent of overlap.
In our corner of the biological world, Martin Ridout and Matt Linkie published a paper (2009) on the activity patterns of tigers, clouded leopards and golden cats in Sumatra, with a lot of technical detail on how overlap could be quantified and confidence intervals estimated. They followed up (2011) with a paper on tigers and their prey, also in Sumatra. ...
5 June 2013 
This is often a silly question: the means of real populations are almost always different, even if the difference is microscopic. More useful would be to estimate the difference and the probability that it is big enough to be of practical importance. See the BEST software for a way to do this in R.
Sometimes we are presented with confidence intervals for each of the means. This happens in particular with the standard packages we use for wildlife data analysis, where the output includes confidence intervals for each coefficient or real value. Can we infer evidence of a difference from confidence intervals in the same way as for a pvalue from a test of significance?
26 March 2013 
Sometimes people I talk to are worried because their data aren't normally distributed, and they believe that they can't use the usual techniques such as ttests or ANOVA without first transforming the data to be normal, or they must resort to nonparametric methods.
There are many good reasons for transforming data or NOT using t tests or F tests, but nonnormal data is not usually one of them!
21 Feb 2013 
A couple of people on a recent workshop had trouble with their AVG antivirus software when installing JAGS 3.3.0.
This appears to be due to AVG's paranoia: see
Martyn Plummer's comment. No malware is detected by McAfee
AntiVirus Plus or Trend Micro Office Scan. See also information
on false positives at the
AVG forum.
8 Feb 2013 
In ecology and wildlife studies, a lot of our spatial data takes the form of rasters rather than vector files. When you first add a raster in QGIS, you usually get a plain grey rectangle, or maybe just a grey outline on a white background, as most raster file formats have no styling information. To make sense of a raster, you need to change the style.
Here I'll give some hints for "quickanddirty" styling to display the contents of a raster. For a more detailed tutorial, see here.
18 Dec 2012 
In a recent post, I showed how to deal with "distance from..." data in GIS layers using the R packages for handling spatial information. The example I used there involved
1. producing a layer with distancefromnearestroad as a habitat layer so that we can calculate a probability of occupancy layer, and
2. extracting distancefromnearestroad for each of our cameras in order to model our data.
Here we will see how to do the same thing in QGIS.
16 Dec 2012 
At our recent workshop on Geographical Information Systems (GIS) using Quantum GIS we had a number of people interested in working with radio telemetry or GPS data to model animal home ranges. The home range plugin for QGIS doesn't work with current versions, at least with Windows.
It is designed to pass data to R and get the adehabitat package to do the home range estimation and pass the result back to QGIS. QGIS uses Python code, and to get it to talk to R requires a bit of software called "RPy2". This was always difficult to set up on Windows, but Python has been upgraded and RPy2 no longer works. In any case, the adehabitat package has been replaced by new packages with a wider ranger of options.
So now it's better to prepare spatial data in QGIS, read the files into R, process with adehabitatHR, write the results to new files, and load into QGIS.
13 Dec 2012 updated 5 Feb 2018 
We recently ran a workshop on Geographical Information Systems (GIS) using Quantum GIS for ecologists and wildlife researchers. For many species, distance from water, a road, forest edge, or a settlement may be an important habitat variable.
For example, we may be using automatic cameras to investigate occupancy of sites by leopards. Probability of occupancy may depend on distance from the nearest road. Given vector layers with roads and camera locations, we want to do two things:
1. produce a layer with distancefromnearestroad as a habitat layer so that we can calculate a probability of occupancy layer, and
2. extract distancefromnearestroad for each of our cameras in order to model our data.
16 Dec 2012, updated 14 Nov 2017 
I sometimes need to put formulae into my web pages, and I've been exploring the use of MathJax.
In the past I've inserted the formula into MS Word with MS Equation 3.0, doing a screen capture, cropping the image to the formula I want, saving as a .GIF file, and then displaying it on the web page as an image. So I get something like this for the Poisson distribution:
That's not ideal. If I want to change anything, I have to start all over again from Word. It's also messy if I want to put something like into the text; for a start it doesn't line up properly. MathJax allows me to type the formula in LaTeX style directly into the HTML code for my web page.
10 Dec 2012 
I have a collection of data sets for use during workshops or just to play with when trying out new statistical techniques or computer code.
A big question is what format to use, and I've changed my mind on this several times already!
After looking at this blog post by John Mount I've decided to try using tabseparated files with a .tsv extension.
8 Dec 2012 