# What is a density surface model?

### Why model abundance spatially?

• Use non-designed surveys
• Use environmental information
• Maps

## Back to Horvitz-Thompson estimation

### Horvitz-Thompson-like estimators

• Rescale the (flat) density and extrapolate

$\hat{N} = \frac{\text{study area}}{\text{covered area}}\sum_{i=1}^n \frac{s_i}{\hat{p}_i}$

• $$s_i$$ are group/cluster sizes
• $$\hat{p}_i$$ is the detection probability (from detection function)

### Hidden in this formula is a simple assumption

• Probability of sampling every point in the study area is equal
• Is this true? Sometimes.
• If (and only if) the design is randomised

### Randomisation & coverage probability

• H-T equation above assumes even coverage
• (or you can estimate)