Estimating >= 1 Detection in a Huggins Model

[bacollier]

All,
I used a Huggins Close Capture Model to estimate detection probabilities using a double counting approach with a thermal imager as the 'capture' and the spotlight as a 'recapture or new capture' method (in situations where the TI missed an individual). Using paired observers (independent observations, sampling at the same time), I wanted to estimate the probability that an individual is detected at least once by the observer pair.

I thought that I could use the formula given by MacKenzie and Kendall (2002) Ecology 83:2387-2393 on the bottom of page 2390 as they also used a Huggins model to analyze like data.

So with the MacKenzie and Kendall formula:
P_i = 1 - (1-p_1,i)*(1-p_2,i). I treated the subscripts 1 and 2 as the different observers (sampling occasion), and the subscript i representing the transect which we ran.

So, for example if the Huggins Detection Estimates for a pair of observers (thermal imager and spotlight) along 1 transect were as follows:

Thermal Imager = 0.889
Spotlight = 0.516

I though the above estimate for P_i would be:

1-(1-.889)*(1-.516) = .946-->Probability of an individual being detected at least 1 time along the transect.

I have been told that this formula was not correct as it does not account for differences in capture methods. I was working under the assumption that MacKenzie and Kendall's 'drive censuses were conducted 1 time each year after the individual were marked where initial captures were conducted using live traps, but 'recaptures' were based on resighting (2 capture methods) but I guess I was wrong.

Could someone point me in the right direction on how to estimate the probability of detecting an individual at least 1 time by the pair of observers?

Thanks,
Bret

[gwhite]

Bret:
I'm not sure why someone told you that the Huggins model does not account for differences in capture methods, as it certainly does if you run a "t" model. Note that if you are using a "b" model (i.e., a removal approach), where p1=p2, then you are not accounting for differences in capture methods.
So, as long as you properly model p1 and p2, you are accounting for capture methods. More likely the bigger issue is whether each animal has the same p1 value and the same p2 value, i.e., no individual heterogeneity in the deer population. Since you can be sure this assumption is not met, then you can be pretty sure that your estimate is biased low. With only 2 occasions, you cannot correct for individual heterogeneity. Even 4 occasioins are inadequate to correct for h.
Gary

[bacollier]

Gary,
Thanks. Using a 't' model gave me the above estimates for the TI and SL. I will need address how the population estimate will be biased low if there is individual heterogeneity.

A follow up question when you get a chance. If I had 2 pairs of observers surveying the transect (1 pair per side using the above protocol) is it possible to use those paired detection estimates based on a 't' model to estimate a overall non-detection probability for the transect?

Bret

[jlaake]

I was queried about the last 2 sentences in Gary's response so I wrote to Gary. Below is my message and his response.

Gary -

Quite awhile ago you made the following post. I was queried about the
last 2 lines of your post. Can you clarify what you meant there?
Clearly you can remove sources of heterogeneity with 2 occasions if you
use covariates. For example, you could easily stratify by sex if
detection probability varied by sex. By individual heterogeneity did
you mean each animal has it's own unique capture probability that cannot
be modelled by a finite set of covariates? Was your reference in
regards to using one of the non-parametric heterogeneity models? Or just
that there will always be some sources of undmodelled heterogeneity?

thanks--jeff

Jeff:
I was referring to the Pledger models to remove individual
heterogeneity, not the use of individual covariates. The Pledger mixture
models are pretty ineffective unless you have at least 5 occasions.

Gary