# Abundance from capture-recapture data

For the methods in this section, we need data on detection of individual animals. That means animals need to be individually identifiable, and we know when we have detected the same animal again. The early studies were indeed “mark-recapture”: animals such as fish, small mammals and birds were given numbered tags or rings when first captured, and those were read when they were subsequently recaptured.

A fundamental assumption of all capture-recapture analysis is that animals do not lose their marks and that marks are correctly read.

With some species, animals have distinctive pelage patterns which allow individuals to be identified visually. This is exploited in camera trapping studies of tigers and leopards. It’s used for other groups where skin patterns vary, such as skinks. Analysis can be adapted for cases where only a proportion of the animals in the population are identifiable, eg, with scars.

Indirect detection of individuals from hair or faeces followed by genetic analysis can also be used.

These more recent methods do not involve literal capture of animals, so the terms detection and detector may be preferable, and we will frequently use them, though we’ll often use the old familiar terms. We are not going to relabel “camera traps” as “photographic detectors”. (Though we know of field teams being refused permission to enter no-trapping areas with camera traps.)

### Abundance vs density

In principle, abundance, the number of animals in the study area, N, and density, the number per unit area, D, are interchangeable: $D = N/A$, $N = D \cdot A$. In practice, it’s rarely that simple.

Unless your study area has boundaries which animals cannot cross, it’s not even clear what abundance means. If animals are moving in and out, do you mean the number always there, the number ever there, or something in between? With spatial capture-recapture (SCR), we can estimate the number of animals with activity centres (ACs) inside the area, as we shall see.

If using SCR to estimate density, the sampling design is important if the density estimate is to be valid. It can be tempting to focus attention on the parts of the study area where you think there are lots of animals, but that will lead to overestimates of density. If the area can be clearly separated into high and low density strata, a stratified design may be possible.

### In this section

All our models here use data augmentation and an analogy with the occupancy models in the previous section: we begin with a simple closed-capture model to explain the use of data augmentation. The rest of the models will be variants on spatial capture recapture, beginning with simple models and gradually adding complexity.

Almost all the models here assume the population doesn’t change during the study period: no births, deaths, immigration or emigration, and no change in the location of individual activity centres. This is the closure assumption.

Towards the end of the section, we’ll try to include some examples of open population models, but there is no consensus on how to handle these.