Does variable probability of detection compromise the use of indices in aerial surveys of medium-sized mammals?

We thank Ken England, Greg Jones, Glen Walker and Richard Mason for their assistance in aerial surveys, and Matt Hollingdale and Mark Rogers for reliable and safe helicopter piloting. Mike, Ant and Chris Martin, Donald and Doug Arnott, and Kevin Cluff kindly allowed us to count feral goats on their land. Funding of NSW Department of Primary Industries, the National Feral Animal Control Program and the Wildlife and Exotic Disease Preparedness Program is gratefully acknowledged. Remy Van de Ven, Jim Hone and Steven McLeod provided constructive comments and discussion.

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Consider the double count method of Caughley and Grice (1982). In their paper they quote estimates for p₁ and p₂, which are the unconditional detection probabilities for two observers who independently count groups of emus in an aerial survey. They use the average of these, , as an estimate for mean detection probability which is then used in a correction factor for the purpose of estimating true density. Since the estimate of average detection probability can be regarded as a function of multinomial variates, we use the delta method to derive a variance estimate for .

Suppose n is the total number of animals (or groups) detected in the survey, partitioned into S₁ = the number seen by observer 1, S₂ = the number seen by observer 2, and B = the number seen by both observers. This leaves N – S₁ – S₂ – B animals undetected, where N is the total number of animals in the survey area. The estimates for the unconditional detection probabilities are given by

The average detection probability then becomes

Using the delta method the approximate variance of (unconditional on n) will be

where each of the terms in this expression appear below.

The variance estimate follows by replacing N and the parameters p₁ and p₂ with their estimates. The following estimate for N is a suitable choice