Estimating realized N within subsets of total study area

[Amanda Zak]

Hi secr group,

I have 10 study areas that I did transect surveys on, each far enough apart that animals don’t move between them. I pooled the study areas for my analysis and have identified my best-fit model. My goal is to get estimates of population density on each study area.

I planned to get estimates of realized N from region.N, using smaller masks for each study area. However, I can’t get realized estimates from region.N for masks smaller than that used to fit the model:

“Realised N is given by R(N) = n + \int_B (1 - p.(X))D(X) dX (the second term represents undetected animals). This definition strictly holds only when region B is at least as large as the region of integration used to fit the model; only with this condition can we be sure all n detected animals have centres within B.”

This shouldn’t be an issue for my study design because each study area is separate from the others and has its own buffer of 4*sigma – I know how many individuals were detected on each study area, and they should all have their centers within the smaller mask. But if I can’t get realized estimates from region.N, then I’ll need to find a workaround. If I’m understanding the help documentation correctly, then fx.total calculates D.nc the same way that region.N calculates undetected individuals. Is that right? And if so, can I use fx.total to get undetected individuals for each study area, and then add that to my number of detected individuals to get realized population size?

I’d appreciate any advice anyone has on this subject!

Thanks,

Amanda

[Murray Efford]

Hi Amanda

The quantity n in the formula for realised N is obtained by region.N() from the number of rows in the capthist to which you fitted the model - this is for your pooled dataset, not each of the 10 areas. I see two easy ways to get area-specific realised N. I demonstrate these with the first session of the infraCH skink dataset; sampling spanned two grids.

1. Split your pooled sample into 10 sessions. Then the region.N estimates are split automatically by area.

# split grids as two sessions

ch <- split(infraCH[[1]], covariates(traps(infraCH[[1]]))$Grid, bytrap = TRUE)
summary(ch, terse = TRUE)
# session-specific masks
maskch <- make.mask(traps(ch), buffer = 15, type = 'trapbuffer', spacing = 2)

# fit model that is homogeneous across sessions

fitch <- secr.fit(ch, mask = maskch, ncores = 8)

region.N(fitch)

# $S1
# estimate SE.estimate      lcl      ucl  n
# E.N 227.7262    25.28363 183.3143 282.8978 61
# R.N 207.0422    20.28635 172.3793 252.4926 61
# $S2
# estimate SE.estimate      lcl      ucl   n
# E.N 224.8617    24.96560 181.0084 279.3393 102
# R.N 245.5461    19.96045 211.4450 290.2725 102

2. Trick region.N() by substituting capthist post hoc

fit <- secr.fit(infraCH[[1]], mask = maskA, ncores = 8)
fit$capthist <- ch[[1]]

# re-using area-specific mask from (1) ...
region.N(fit, region = maskch[[1]])
# estimate SE.estimate      lcl      ucl  n
# E.N 227.7246    25.28720 183.3072 282.9049 61
# R.N 207.0406    20.29083 172.3712 252.5025 61
fit$capthist <- ch[[2]]
region.N(fit, region = maskch[[2]])
# estimate SE.estimate      lcl      ucl   n
# E.N 224.8602    24.96912 181.0015 279.3463 102
# R.N 245.5446    19.96489 211.4370 290.2823 102

More fundamentally, If your goal is to estimate population density, why are you bothering with realised N? Realised N is seductive but conceptually dubious, especially if you do not have bounded areas.

Murray

[Amanda Zak]

Thanks for the tricks, #2 worked great! I didn’t know you could just overwrite the capture history like that. I honestly wasn’t sure whether to use expected or realized and had been going back on forth on that – conceptually the expected density made more sense to me, but the realized estimates are more precise. Is realized N dubious because of the way undetected individuals are estimated?

[Murray Efford]

Why do I call realized-N dubious? At two levels

1. Density is preferable as a parameter to population size in the majority of situations, specifically when 'population size' relates to an arbitrary extent.

2. 'Realised N' is an attempt to squeeze the variance by acknowledging (conditioning on) the number actually seen. Many, possibly the majority, were not seen. That part of the 'realised N' is merely the _expected number unseen_ inferred from the model, so not really 'realised' at all.

[Zak, Amanda Leigh]

I had thought that conditioning on observed individuals would make realized estimates better, but I did notice that undetected individuals were being estimated from the expected density and that raised some questions for me.

 

Thanks for the technical help, I was able to get realized estimates at least so that I could compare them to expected and check for agreement there. And thanks for the theoretical help as well!

 

--

Amanda Zak (she/her)

Graduate Student (MSc) Ecology

236 Forest Resources Building

Pennsylvania State University

 

From: secr...@googlegroups.com <secr...@googlegroups.com> On Behalf Of Murray Efford
Sent: Sunday, December 15, 2024 8:00 PM
To: secr <secr...@googlegroups.com>
Subject: Re: Estimating realized N within subsets of total study area

 

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