Differences in estimated abundance/density in summary output vs. Dhat by sample.label

[Jordan Giese]

Hi all, 

I'm having an issue interpreting conflicting density estimates in R. Below is the code I'm running for hazard-rate function: 

BPC.hr <-ds(BPC, truncation = 100, transect = "point", key = "hr")
plot(BPC.hr)
summary(BPC.hr)
BPC.table<-summary(BPC.hr)$dht$individuals$bysample

I receive intuitive density estimates in the summary () output in console but when I look at Dhat at the sample label, the estimates are different by multiple orders of magnitude. For example, in the summary table, a typical density estimate is 1.99e-04 whereas at the sample label one is 7.66e-06. 

For context, these are repeated surveys across several years and I would not expect much variation across samples. I have played around with changing units between meters squared, acres, and hectares but the large difference still exists. 

Why would there be such a difference? Am I missing something in how the densities in summary() are calculated vs. Dhat by sample? 

Thank you!

Jordan 

[Eric Rexstad]

Greetings Jordan

It is not terribly common to poke about in the transect-level density estimates; not they do not have measures of uncertainty associated with them. The transect-specific densities are derived as follows:

abundance in area covered by transect (adjusted for detectability) divided by area covered by transect

The numerator for each transect would be n/P_a and the denominator would be

truncation distance * 2 * Effort

I looked at one of the "tame" data sets that ships with the Distance package, LTExercise​: line transect data with 12 replicate transects, true density 79.8 animals per km^2, just to have a look at some results.

                       Estimate          SE         CV

Average p             0.3491863  0.02160948 0.06188525

N in covered region 300.6991117 30.11199438 0.10013995

Summary statistics:

   Region Area CoveredArea Effort   n  k     ER     se.ER     cv.ER

1 Default    1      3.4368     48 105 12 2.1875 0.3169604 0.1448962

Density estimate for the study area:

Density:

  Label Estimate       se        cv      lcl      ucl       df

1 Total 87.49392 13.78541 0.1575585 62.70329 122.0859 15.32522

Density estimates by transect

> lt_hn$dht$individuals$bysample

    Region  Sample Effort Sample.Area Area  n      Nhat     Nchat      Dhat

1  Default  Line 1      5      3.4368    1 14 11.665857 40.093215 11.665857

2  Default Line 10      7      3.4368    1 23 19.165336 65.867424 19.165336

3  Default Line 11      3      3.4368    1  0  0.000000  0.000000  0.000000

4  Default Line 12      4      3.4368    1  5  4.166377 14.319005  4.166377

5  Default  Line 2      2      3.4368    1  3  2.499826  8.591403  2.499826

6  Default  Line 3      6      3.4368    1  8  6.666204 22.910409  6.666204

7  Default  Line 4      4      3.4368    1  9  7.499479 25.774210  7.499479

8  Default  Line 5      3      3.4368    1  3  2.499826  8.591403  2.499826

9  Default  Line 6      1      3.4368    1  4  3.333102 11.455204  3.333102

10 Default  Line 7      4      3.4368    1 11  9.166030 31.501812  9.166030

11 Default  Line 8      4      3.4368    1  8  6.666204 22.910409  6.666204

12 Default  Line 9      5      3.4368    1 17 14.165683 48.684618 14.165683

Note that for the estimates by transect, the Sample.Area is reported to be the same, even though the transects differ in length.  I think this might be the source of the discrepancy you describe.

For example, if I was to calculate the area sampled by transect 1 (5km by 35.8m (truncation) X 2 (both sides), I obtain a Dhat for transect 1 of

> (14/.3491863)/(35.8/1000 * 2 * 5)
[1] 111.9922

of the same order of magnitude as the 87.5 estimate reported in the summary.

Hope that helps with your interpretation.  Follow-up if anything is unclear.

---

From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of Jordan Giese <jordan...@gmail.com>
Sent: 04 October 2022 16:09
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] Differences in estimated abundance/density in summary output vs. Dhat by sample.label

 

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