chapman m-r variance

[ben-williams]

https://github.com/commfish/seak_sablefish/blob/a521003c509ef0d0ac0458d25f82766644e25120/r/mark_recapture.R#L1298

Use M = marks released C = fish examined for marks R = fish caught with marks

var_n = ((M+1) (C+1) (M-R) (C-R)) / ((R+1)^2 (R+2))

The CIs will then be

ll = Estimate - 1.965 * sqrt(var), ul = Estimate + 1.965 * sqrt(var)

Don't worry about small sample sizes - we don't have that issue

[jysullivan]

thanks, i'm on it!

[jysullivan]

I was only using C and R form the longline survey, which explains why the abundance estimates were so high. I'm getting much more reasonable estimates now and will update the text now to include the formula I'm using for the confidence interval.