Primary-session-varying Covariates in Robust Design

[brp]

We have been trapping foxes for the past 3 years. We have a robust design with 3 primary sessions (years: 2007, 2008, 2009) and 4 secondary occasions (days) within each year. I plan to use Huggins closed captures as the data type within primary sessions.

I plan to use habitat type (4 levels: MDSR, MDSG, Gfine, Gclay) and distance to road (2 levels: near, far) as grouping factors and age (3 levels: pup, juvenile, adult) and sex (2 levels: male, female) as individual covariates.

How do I include age in the input file since it is a primary-session-varying individual covariate? I have seen examples where age2007 age2008 age2009 were used as 3 covariates, but if I did that there will a large number of missing covariate values. 160 foxes were observed in only 1 year, 93 foxes were observed in 2 of the 3 years, and 64 foxes were observed all 3 years.

I have read the section in the MARK book about missing covariates, which recommends that if there are lots of missing values to code the animals into 2 groups where all the missing values are in one group. Is this what I would need to do? If so, can someone clarify the approach?

[Bill Kendall]

You do have a lot of factors to deal with. Normally age is dealt with through manipulating the diagonals of the PIMS. However, that does not work when dealing with p's in the RD, because there is a separate PIM of p's for each primary period. Therefore, if you believe age affects p, I would use the multi-strata(state) closed robust design module, and treat age as a stratum. In this case state transitions (pup -> juvenile; juvenile -> adult) are deterministic, and some are not permitted (adult -> juvenile; adult -> pup; juvenile -> pup), so there are no extra parameters to estimate (just fix transition probabilities appropriately). I'm assuming individuals only remain juveniles for one year, but if it is longer that could be accounted for.

[murray.efford]

What is the goal of your analysis and what is the spatial sampling design? From your reference to Huggins closed captures I guess that you want a measure of abundance - by which I mean population size or density - and perhaps trend in that parameter over time or space. From the reference to trapping and roads I suspect your design is geographically open. Spatially explicit capture-recapture is a suitable framework for conducting such analyses. The 'secr' package for R at www.otago.ac.nz/density allows you various options for modelling the effects you mention, and the older 'Density' software may even be sufficient. At present these do not include parameters of population turnover (survival and recruitment): robust design 'primary' sessions are treated as independent units (also called 'sessions'), so age can be scored separately within each. The main advantages of SECR are (i) you get a direct measure of density and can model density variation in space and time, or not as you wish (ii) spatially determined individual heterogeneity does not bias the estimates. If your primary interest is in survival or recruitment, or in fitting models per se, then ignore the above and go with Bill's advice.

Murray