Individual Covariate of Interval Length-Huggins CC

[cjardine]

Hi,

I am very new to analysis using MARK and new to model selection analysis in general so I apologize in advance if my question is too simplistic.

I am attempting to analyze point count data using the removal method. (As a disclaimer I am aware of the literature suggesting this is not necessarily the best method, my goal in performing this analysis is to determine if detection probabilities are very close to 1 in grassland ecosystems (as has been suggested in the literature) and to compare various methods of abundance estimation.)

I have data from 5min duration point counts split into three intervals, the first 3 minutes, the 4th minute and the 5th minute.

Because I have unequal sampling intervals I had originally planed to use methods outlined by Farnsworth et al 2002. However Thompson and La Sorte (Journal of Wildlife Mgmt 72(8)) state that they were able to model similar data using the Huggins closed capture models in MARK, they state “we modeled detection probability for each discrete interval with the length of the interval as a covariate”. Using the Huggins model is appealing to me because it would allow me to look at the effect of other grouping factors, (such as observer, ecoregion and year) on detection probability however I am having “trouble” conceptualizing how to execute this analysis in MARK.

I understand that to run a removal model I must run a Huggins closed capture analysis with c=0 to estimate each p

So my encounter history probabilities (as MARK sees them) would be:

100 p(1-c)(1-c)=p1
010 (1-c)p(1-c)=p2
001 p(1-c)(1-c)=p3

As all other encounter histories would have probability zero if c=0

I somehow need to include an individual covariate in my data to tell MARK that p1, p2 and p3 vary based on interval length (3, 1 and 1) I need to model the detection probability of each individual as some function of the length of the interval in which that individual was detected.
I have read Chapter 11 in the MARK book, however I am not sure how to proceed with my data. The covariate I want to include is not a continuous measure and it only has two discrete values over 3 sampling intervals (1min and 3 min).

I originally thought I needed to build the following linear model (int=interval length)

Pt = B0 + B1(int)+B2(t1) +B3(t2)+B3(int*t1)+B4(int*t2)

When I run this analysis with INT included as a covariate MARK returns P estimates of 1 for all intervals (so it is rather obvious I am making some sort of colossal error)

The problem I see is that I do not expect pt to vary only with respect to the interval length, it should vary with both interval length and per minute detection probability (p) where

pt = 1-(1-p)^interval length t

i.e. p1 = 1-(1-p)^3

However p (per minute detection probability) is essentially what I am trying to estimate, so I cannot include it in the linear model I am attempting to build.

What I *think* I need to do is include a term in my linear where the Beta is raised to the power of the interval length, but I can't see a way to do this using MARK.

Can anyone point me down the correct path or suggest where I should look to help me utilize this method (if this method is valid for my data set)?