Evaluate the allocated sampling efforts

[Triciaserow]

Hi,

I have a set of data which was not designed for estimating occupancy in the first place. They were like a by-product of a project. But they were very suitable for occupancy estimation. I had an idea of using the method from MacKenzie and Royle (2005) about allocating survey efforts to evaluate if the sampling efforts in this study were good enough. To be more specific, I have finished analyzing data and had p, psi and se of both of them at hand. Given the number of survey was constant (ex. 10 days), I would like to plug in all the values and check if enough/too much sampling efforts were incorporated in the first place.

This is obviously an post-hoc evaluation, but I'm not sure if it's logically correct? Thanks.

(ps. I was focusing on standard design).

Tricia

[jhines]

Hi Tricia,

Can you give more details about what you're after? It looks like you've got estimates of occupancy (psi) and detection (p), but want to know if sampling effort is enough/too much. What do you mean by that? Enough effort for what? Do you have a target standard error you're seeking?

Jim

[Triciaserow]

The data I was given was from a camera survey, which I had finish analyzing. Take 2 species as an example:

Code: Select all

> speciesA
           p       Psi       se_p       se_Psi
A1 0.2090038 0.7917271 0.05914128 1.644753e-01
A2 0.3194914 0.9194610 0.05623518 8.182215e-02
A3 0.4120172 0.9637856 0.05617113 3.495985e-02
A4 0.4908518 0.9841868 0.05623978 1.486302e-02
A5 0.5563613 0.9940506 0.05559811 5.575551e-03
A6 0.6109906 0.9985120 0.05445608 1.397691e-03
A7 0.6579861 1.0000000 0.05297711 7.854624e-06
A8 0.6944445 1.0000000 0.05146593 7.870106e-06
A9 0.7250000 1.0000000 0.04992180 0.000000e+00

Code: Select all

> speciesB
            p       Psi       se_p     se_Psi
B1 0.09042135 0.5742533 0.07517990 0.07321705
B2 0.10374470 0.5445824 0.08030029 0.07641597
B3 0.11897139 0.5106727 0.08615217 0.08007187
B4 0.13654064 0.4715462 0.09290434 0.08429022
B5 0.15703810 0.4258987 0.10078187 0.08921163
B6 0.18126237 0.3719515 0.11009167 0.09502785
B7 0.20239517 0.3320953 0.11727589 0.09854442
B8 0.24586043 0.2280925 0.13491782 0.11053774
B9 0.29027160 0.1291894 0.15198580 0.12120080


From A1-A9 means 1-9 sample units per site, and same with B1-B9.
I created a function to calculate "s (number of site needed)" given p, Psi and se of PSI of species A & B.

Code: Select all

fun2<-function(X){    ###X==summarized output of each species   
   results<-matrix(nrow=9, ncol=1)
   for (i in 1:9){
      pstar<-(1-(1-X$p[i])^10)
      psi<-X$Psi[i]
      p<-X$p[i]
      SE<-ifelse(X$se_Psi[i]==0, 0.1466796E-004, X$se_Psi[i])   
                 ####to avoid "Inf" when calculating s with SE=0 (in speciesA's case)"
      s<-(psi/(SE^2))*((1-psi)+((1-pstar)/(pstar-10*p*((1-p)^(10-1)))))   
                ### formula given by MacKenzie and Royle (2005)
      results[i,]<-s
      }
   return(results)
}

> x<-c(1:9)   ###sampling units per grid
> data.frame(sites_surveyed=x*8, species_A=fun2(speciesA), Species_B=fun2(speciesB))

  sites_surveyed    species_A  Species_B
1              8     10.40762 228.482071
2             16     14.38984 154.490380
3             24     32.61289 105.427771
4             32     75.73178  72.792145
5             40    199.72436  50.864010
6             48    801.17672  35.735748
7             56 355122.96227  28.484875
8             64 114554.61097  15.897574
9             72  11497.85695   7.999998
> ####x*8 because I had 8 grids total#######


Given the parameter estimates (p, Psi, se of Psi) from my empirical analyses, it looks like we didn't need thousands of sampling units to achieve high p, high Psi and low se of Psi in SpeciesA. For species B with low p, low Psi and higher se of Psi, it was the other way around.

What I'm ultimately after is, what are the optimal sampling efforts for species A and B respectively given the field study we have conducted? Especially for Species B, can the method provided by MacKenzie and Royle (2005) precisely give us how many sampling units are needed if we need higher parameter estimates?

Thanks.

[jhines]

As you increase replication, I expect detection probabilities to increase, but site-occupancy should be constant and the se(Psi) should decrease. For both species, occupancy changes as you increase the number of sample-units, suggesting that the definition of a ‘site’ is changing.

For speciesA, does the first row (A1) correspond to the situation, 8 sites with 10 surveys, while the 2nd row corresponds to 16 sites with 10 surveys? Or does row 2 correspond to 8 sites with 20 surveys?

[Triciaserow]

Each row correspond to 10 surveys. So row 1 represents 8 sites with 10 surveys, and row 2 represents 16 sites with 10 surveys.

The definition of a "site" is a camera station. So in this study, a site=a station. Originally there were 9 stations per grid. These 9 stations were positioned on a 3 by 3 cells grid. The station was 300 meters from the next one. There were 8 grids total. I would like to know how the parameter estimates will change when I include only 1 stations/grid, verses 2,3,....,9 stations/grid. The outcome was what I had posted. You said that definition of site has changed, is it because of the potential violation of site independence?

SpeciesA was an abundant species with many detections. P increased as sampling units increased, and SE of both p and Psi decreased as sampling units decreased as expected. I don't understand why Psi should remain constant especially when sampling units were small (1,2,3/grid).

SpeciesB was a rare species with low p. P also had increased as sampling units increase which was what I had expected. With low detection, Psi is usually overestimated according to MacKenzie et al(2002). Notice that since species B has very low detection, I have removed detection histories contained all-zeros when subsampling because no valuable information was provided by these types of DH. I originally didn't but the results contained many high p (over 0.84) and Psi=1, which was not reasonable.

I really appreciate your time and help.

[darryl]

Hi Tricia,
I want to back up a little bit. Looking at your code for fun2 it looks like your taking estimated values for p, psi and the SE of psi as input values, then calculating what sample size would given you that observed SE, given the estimated values of psi and p. Is that right? If so, then that's a circular argument and the answer you should get is the sample size you used to estimate the data in the first place, ie 8, 16, 24, etc. If you're not then something is going wrong somewhere.
Cheers
Darryl