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var <- (n1)*(n2)*(n1-m)*(n2-m)/(m)^2/(m)
where n1, n2, and m are as conventionally defined:
n1 = number captured on first visit
n2 = number captured on second visit
m = number captured on both visits
If I try using the Huggins model in MARK with one primary period and two secondary periods the SE based on the proposed variance formula above matched the SE returned by MARK. So, I think the above formula is correct. However, I would feel much more comfortable if someone verified that formula above or if I could find that formula in a paper or book.
I suspect MARK is using maximum likelihood to obtain the variance. I have not yet tried programming a multinomial version of the Lincoln-Petersen into optim in R to see whether I can obtain the same SE that MARK returns.
Could someone email me a copy of Chapman 1951, Lincoln 1930 (and maybe Petersen (1896)? I cannot locate those publications either. I suspect one or more of them includes the above proposed formula for the variance.
Chapman, D.G. (1951). Some properties of the hypergeometric distribution with applications to zoological sample censuses.
Lincoln, F. C. (1930). Calculating Waterfowl Abundance on the Basis of Banding Returns. United States Department of Agriculture Circular. 118: 1–4.
Petersen, C. G. J. (1896). The Yearly Immigration of Young Plaice Into the Limfjord From the German Sea, Report of the Danish Biological Station (1895), 6, 5–84.
If I get the R code in optim to work and return a SE that matches MARK I will post it here.
Thank you sincerely,
Mark
mark.wayne.miller@gmail.com