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

Many faces of randomisation

plot of chunk randomisation

Randomisation & coverage probability

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