# Spatial Capture-Recapture Reasoning

Analagy for the way SECR works

Statistics

Spatial capture-recapture models are relatively new and difficult to understand. I have been asked several times, “How do SECR models work?”. In this post I give an analagy that I hope helps understand the reasoning behind SECR models.

In my analagy, Walmart is the study area. Walmart exists in a particular town that contains the population under study. Researchers cannot afford to sample everywhere in Laramie, so they set up shop in Walmart and ID people as they go in (I know, creepy, but go with it). A large fraction of people in town go to Walmart at some point. Some of us hate it and only go once a month. Some people go every day.

Here is the SECR reasoning:

**If the population is closed**: Researchers can keep a roll of everyone that goes into Walmart, and eventually they will have records (IDs) on a large fraction of the town. Closed population models estimate the fraction of people in town that never go to Walmart. Hence, closed models estimate the larger population size.**If the population is open**: My analogy is a stretch here because people do not actually live in Walmart. But, Walmart probably attracts people based on distance from their home , i.e., their Activity Center (forget about low prices and inventory as attractants in this example). Based on where researchers sight people inside Walmart (again, I’m stretching the analogy here) they estimate where those people’s activity centers are both inside and outside Walmart. From this, researchers know that they probably have a record on everyone that lives inside or close. The spatial models estimate how many people are farther away, but still visit occasionally. With all this, they estimate the number of activity centers in the area surrounding and inside Walmart, and hence estimate density. Density of activity centers. Researchers inflate this density to some area where they are sure it applies. They could multiply by the size of the town. In our case, they are only comfortable assuming the density is accurate inside Walmart. This is the key. If we only inflate density to Walmart, we are estimating the number of people in Walmart only, not in the surrounding town. There are lots of people in town, but we only estimate the number in Walmart at any given point. If we knew the size of the town and were comfortable assuming density is constant over the entire footprint of the town, we could estimate the number of people in town. In our case, if you knew turtles existed on 15 km of the Mad and were comfortable saying density on our study area is close to the average density over those 15 km, we could multiply turtles per km on the study area by 15 km to get population size.