Camera-trap layout for SECR

Back to home page I have recently been looking at the design of camera-trap studies to estimate the population density of tigers when populations are very sparse. The intention is to use recently-developed spatially explicit capture-recapture (SECR) methods to analyse the data. The optimal camera-trap layout for SECR may well differ from the design used for older methods.

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.

If you wanted to estimate the density of, say, fig trees in a forest, you would probably select a large number of plots scattered randomly through the forest. This would enable you to estimate the variance of the density as well as the mean. Concentrating all your effort into a single plot, equal in area to the total of the many small plots, would be seen as a poor design. From a theoretical standpoint, scattering small clusters of traps over the study area should give better estimates.

To see how this might work in practice, I did lots of simulations with different trap layouts.

The scenario

Planned study blocks for the tiger survey would have an area of 1500 to 2500 km2, so I simulated data for an irregular, isolated block of habitat of 2000 km2. For the simulations discussed here, the area had exactly 5 tigers (0.25 tigers per 100 km2), with randomly distributed Activity Centres (ACs) subject to the constraint of a minimum distance between ACs of 5 km.

Past studies in Malaysia gave half-normal detection parameters around σ = 2.5 km and g0 = 0.02 (see here for the meaning of these), and I used these for my simulations.

The simulations

Two different trap layouts. The red + symbols are the trap locations, the black dots the activity centres, and the coloured dots and lines show where the animals were captured.

I compared the results of simulated studies with a single large cluster in the centre of the study area and several small clusters arranged in a systematic random design using the make.systematic function in the secr package. The plots above show 96 traps in a 16 x 6 cluster (left) and in 12 clusters of up to 9 traps (right). The small clusters have up to 9 traps in a 3 x 3 layout, fewer if the cluster is near the edge of the study area, but clusters of less than 4 are eliminated. Only multi-cluster layouts with 95 to 97 traps were considered for comparison with the single-cluster design.

Trap spacing was 2.5km, the same as σ; other simulations show that optimal trap spacing is around 1  σ, though the best value depends on g0 and the number of trapping occasions. I used 90 occasions (3 months) for the simulated data collection.

The activity centres of the five tigers in the study area were positioned using a Simple Sequential Inhibition (SSI) process (function rSSI in package spatstat) with minimum spacing of 5km. Then I generated capture histories using the sim.capthist function in secr, and analysed these with secr.fit.

The plot above shows the outcome of one simulation for each layout. The single large block design gets lots of recaptures of the two animals near the centre of the study area, but the multi-cluster design picks up more of the animals in the block.

Each simulation was repeated 300 times, with different activity centres and different positions of the 3 x 3 clusters; the 16 x 6 block remained in the same position in the middle of the block.

Results

Multi-cluster design gives usable data

For 8% of the simulations, the single-block design produced no usable data! In half of these, none of the five tigers in the study area was captured. For the rest, animals were captured, but each in only one location: SECR analysis only works if animals are caught in multiple locations.

So, you do the field work, spend the grant money, and at the end you have no data to analyse and no estimate of density. This did not happen with the multi-cluster design.

Density estimates from simulated data: bee-swarm plots with boxplots added. Red "bees" at the foot of the plot represent simulations giving no usable data. The horizontal dashed line shows the true value.

The density estimates for each simulated data set are shown in the bee-swarm plots above, with the simulations giving no usable data shown as "dead bees" at the bottom.

Estimates are reasonable

Both designs have a few outliers, but most of the estimates are grouped around the true value. This is surprising: in most capture-recapture studies, the sample size is taken to be the number of animals captured, which here is always ≤ 5, and in a third of the simulations it was < 4. We should not be getting reasonable estimates of three parameters (g0, σ and density) with such small samples. This is reflected in the very wide confidence intervals for density given by secr.fit, which all contain the true value, ie, they are too wide.

I think the key is that we can get reasonable estimates of capture parameters, g0 and σ, if we have enough recaptures of animals at different locations. If the homogeneity assumption holds - g0 and σ are the same for all animals - it doesn't matter if these recaptures concern a small number of animals, or even just one. With good estimates of the capture parameters, we can get a good estimate of density. This is actually implemented in secr.fit if conditional likelihood estimation is selected (argument CL = TRUE), though I did the simulations using the full likelihood.

Of course, in these simulations, g0 and σ are the same for all animals. I did more simulations where g0 and σ varied by a factor of 2 and still got reasonable estimates of density.

Multi-cluster design gives more accurate estimates

The "bees" in the bee-swarm plot above are more tightly grouped around the true value for the multi-cluster design than the single-block design. In general, the multi-cluster design gives estimates which are closer to the true value, ie, they are more accurate.

The highest outlier among the multi-cluster simulations, giving an estimated density of 0.83 animals / 100 km2, was the result of catching 4 animals, with 3 of them caught in one location each and one animal caught in only 2 locations. Few locations suggest that σ is much less than the trap spacing (the estimate of σ is just 950m when the true value is 2500m), hence capture probability is low; in spite of this low capture probability, we caught 4 animals, so there must be lots out there.

Conclusion

Multi-cluster designs are preferable to a single large cluster for SECR studies. Simulations with other cluster sizes showed that six 4 x 4 clusters were only slightly better than a single cluster, with no usable data in 4% of cases. Smaller clusters - 24 2x2 or 48 2x1 clusters - were better, giving usable data on all simulations and progressively more accurate estimates.

The problems with very small clusters are logistical. Camera failure in a small cluster can have a big impact; two traps is the minimum cluster size, and if one fails there's no cluster! Also setting up a large number of clusters would involve trekking across the whole study area, while a smaller number of clusters can be set up and maintained with targeted trips into the area.

R code to produce the graphs is here.

Comments: Please email comments to mike at mikemeredith dot net

Updated 1 Sept 2013 by Mike Meredith