# SECR : spatially explicit capture recapture

Back to home page I've a couple of ideas for blog posts on SECR (spatially explicit capture-recapture), and this post sets out the basic concepts of SECR which I will need to refer to in later posts.

Capture-recapture methods (also know as mark-recapture or capture-mark-recapture) 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 capture-recapture models (SECR, or just spatial capture-recapture, SCR) first appeared in 2004 (Efford 2004).

Estimating the number of animals in a population would be easy if you could be sure that all animals were captured in a trapping exercise, ie, if capture probability, p = 1. This is rarely the case, and we have to correct the number actually captured to allow for p < 1. The basic idea of mark-recapture is to capture, mark and release a known number of animals in the population. In a subsequent trapping exercise, the proportion of the marked animals you capture allows you to estimate the capture probability and hence the number of animals not captured. This simple model assumes that all animals are equally catchable, that all have the same p, and more sophisticated models have been developed which allow for heterogeneity in capture probability.

A major source of heterogeneity is due to individual animal's movement patterns and trap locations. A animal with several traps in its home range will have a higher capture probability than an animal with only one trap in its home range. More generally, the probability of capture in a specific trap depends on its location relative to the movement of the animal. SECR models incorporate this spatial element.

### How SECR works

SECR assumes that:

1. each animal has an Activity Centre (AC);
1. capture probability is a function of the distance between the trap and the animal's AC.

Most models assume that the capture probability is highest when the trap is placed exactly at the animal's AC and declines as the distance between trap and AC increases. The half-normal function (see plot below) is usually a pretty good fit, but a variety of functions are available, including annular functions, where capture probability peaks at some distance from the AC. We'll see other detection functions in a later post. The half-normal (or Gaussian) detection function is described by two parameters: g0, the probability of capture when the distance between the animal's AC and the trap is zero, and the scale parameter, σ (the Greek letter "sigma"). For animals which move over large areas, such as tigers, σ may be several kilometers, while for lizards it may be only a few metres. (Technically, for the half-normal curve, σ indicates the point where the curve changes from becoming more and more steep as the distance increases to becoming less steep.)

To estimate the capture parameters, g0 and σ, for an animal, we need to capture it at several different locations. Although in principle g0 and σ are characteristics of individual animals, we need values for all the animals in the study area, including those never captured. The simplest models assume that these parameters are the same for all animals.

Provided g0 and σ can be estimated, we can estimate the density of animals, D, the number of animals per unit area.

More sophisticated models can be built, allowing  g0 or σ or both to vary with time, capture history, or covariates, and including covariates for density.

### Assumptions

1. Animals do not lose their marks and animals are correctly identified (as with all mark-recapture methods).
2. Trap locations are recorded accurately, as are any covariates used.
3. Each animal has an Activity Centre and probability of capture depends on the distance between the trap and the AC.
4. Closure: no births, deaths, immigration or emigration during the study, and activity centres do not change.
5. Detectors are randomly placed with respect to the location of activity centres.
6. Detections are independent.
7. No unmodelled heterogeneity: for the simplest models, that means that g0 and σ are the same for all animals and density is uniform.

### Implementation

Maximum likelihood methods are implemented in program DENSITY and in the R package secr, both authored by Murray Efford. The secr package has a wider range of options than DENSITY, and it provides a range of tools for simulating data in R.

Bayesian analysis can be implemented in BUGS (ie, WinBUGS, OpenBUGS or JAGS). Until recently, BUGS models could only be written for rectangular areas of habitat, and the R package SPACECAP was developed to provide a Bayesian implementation for irregular patches of habitat. However, simple methods are now available to deal with irregular habitat patches in BUGS.