Hello,
I’m new to SECR modelling, and am trying to understand how effective sampling areas (esa) are calculated. Many thanks in advance for any insights you can provide! I’ve tried to explain my current level of understanding below, and have highlighted questions in bold.
From the Borchers and Efford 2008 paper, it seems that in the simple case where density (D) is constant and there are no covariates, the esa for each trap is the integral of the capture function (i.e. the equation for 'a' on page 379). Am I understanding that correctly?
Using the example hare dataset available in package ‘secr’ and leveraging the corresponding tutorial example, I wrote the following R code to calculate the integral of a half-normal capture function:
hareCH6 <- read.capthist("Data/hareCH6capt.txt", "Data/hareCH6trap.txt", detector = "single")
initialsigma <- RPSV(hareCH6, CC = TRUE)
fit.HN <- secr.fit (hareCH6, buffer = 4 * initialsigma, detectfn = 'HN', trace = FALSE)
logit2prob <- function(logit){ # from https://sebastiansauer.github.io/convert_logit2prob/
odds <- exp(logit)
prob <- odds / (1 + odds)
return(prob)
}
g0_logit <- coef(fit.HN)$beta[2]
g0_prob <- logit2prob(g0_logit)
sigma_log <- coef(fit.HN)$beta[3]
sigma_prob <- exp(sigma_log)
d <- seq(from = 0, to = 200, by = 1) # distance in m
capture_function <- function(d){
P <- g0_prob*exp(-(d^2)/(2*sigma_prob^2)) # see page 49 of the secr manual for this formula
return(P)
}
plot(d, capture_function(d)) # graph of the function as calculated by me above
plot(fit.HN, xval = 0:200) # graph of the function as generated automatically - good news, they match!
area_under_capture_function_curve_m2 <- integrate(capture_function, lower = 0, upper = Inf)
For the example hare dataset, this gives me: area_under_capture_function_curve_m2 = 5.275324 with absolute error < 4.6e-06.
I also noticed that the package ‘secr’ can calculate the esa directly, but presumably this is the esa for the entire trapping area (not just one trap). Am I correct in thinking that the esa calculated by the R package ‘secr’ is for the entire trapping area?
Again using the example hare dataset, I wrote the following R code to estimate the entire trapping area:
esa_all_traps_hectares <- derived(fit.HN)$estimate[1]
This gives me an esa of 46.38597 hectares.
How does this esa for the entire trapping area work, and how is it related to the ‘area under the capture function curve’ approach (i.e. where I got ~5m2 for each trap)?
On a separate but related note, would it be appropriate to look at the capture function curve and take the distance that corresponds with 95% of the area under the curve as an estimate of the radius of the effective sampling area for each trap assuming it is a circle?
A huge thanks again in advance for your help!
Much appreciated,
Laura
Hi Murray,
Thanks so much for the quick and very helpful response! Yes, you’re right that pdot is what I was looking for. I tried using pdot with various grid extents and cell sizes and was able to get fairly close to the same output as the esa function, so am feeling more confident now that I understand what the esa function is doing.
Much appreciated,
Laura
Thank you for supporting wildlife conservation,
Laura Keating
Conservation Research Analyst
T
1300 Zoo Road
NE
Calgary, AB T2E
7V6
calgaryzoo.com
As a not-for-profit charitable institution, the Calgary Zoo is a conservation leader whose mission is to take and inspire action to sustain wildlife and wild places.
Please think of the environment before printing
this e-mail.
This email may contain confidential and/or privileged
information for the sole use of the intended recipient. Any review or
distribution by others is strictly prohibited. If you have received this email
in error, please contact the sender immediately and delete all
copies.
Thank you David – very helpful!!!
Much appreciated,
Laura
Thank you for supporting wildlife conservation,
Laura Keating
Conservation Research Analyst
T
1300 Zoo Road
NE
Calgary, AB T2E
7V6
calgaryzoo.com
As a not-for-profit charitable institution, the Calgary Zoo is a conservation leader whose mission is to take and inspire action to sustain wildlife and wild places.
Please think of the environment before printing
this e-mail.
This email may contain confidential and/or privileged
information for the sole use of the intended recipient. Any review or
distribution by others is strictly prohibited. If you have received this email
in error, please contact the sender immediately and delete all
copies.
From: secr...@googlegroups.com [mailto:secr...@googlegroups.com]
On Behalf Of David Borchers
Sent: Friday, July 21, 2017 7:58 AM
To: secr <secr...@googlegroups.com>
Subject: Re: Questions re understanding the effective sampling area (esa) in package ‘secr’
To answer your questions in bold:
--