Detectability parameters for polygon detectors

questions concerning anlysis/theory using program DENSITY and R package secr. Focus on spatially-explicit analysis.

Detectability parameters for polygon detectors

Postby lenasmarques » Mon Feb 27, 2017 4:00 pm

Hello all:

I have two independent datasets of voles’ detection data, one from live-trapping and the other from non-invasive genetics of fecal samples. The main objective of this study was to compare both methods to evaluate the use of noninvasive genetics to estimate population densities of small mammals.

Both datasets were analyzed with secr independently, the trap data using a model for multi-catch traps and the noninvasive genetics data using polygon detectors with detections modeled as counts, both with exponential detection functions.

Other than comparing the density estimates obtained from each method, i would also like to compare detectability parameters, especially g0, but i am not confident if this comparison can be made in such a direct manner (as in detectability is more than 10 times higher for noninvasive genetics (g0 = 0.07) than for trapping data (g0 = 0.0036)). If this straightforward comparison cannot be made, is there any way to make the detection parameters comparable between both methods?

Thanks in advance,
Helena
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Re: Detectability parameters for polygon detectors

Postby murray.efford » Tue Feb 28, 2017 5:52 am

Hello Helena
For myself, I would be very uneasy about making a direct comparison of g0 - what would it mean? At least comparison of sigma could be construed as a comparison of trap-revealed and faecal-revealed home ranges (subject to qualification because neither behaviour - defaecation or tendency to enter a trap - is necessarily uniform across the home range). Comparisons of g0 (or better lambda0, using detectfn = 'HHN') to my mind only make sense when combined with sigma. You could devise an overall measure of detection efficiency (expected no. captures per unit effort, a function of lambda0 and sigma together) and compare that between methods. I can see that standardising 'effort' would be hard for two such radically different methods (and that is part of the problem in direct comparison of g0).
I hope this is some help - I know it stops short of giving the formula for expected number of captures - I may do that later if you want to go down that path.
Murray
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Re: Detectability parameters for polygon detectors

Postby lenasmarques » Tue Mar 21, 2017 12:59 am

Hello Murray:

Thank you for your speedy response. It was indeed helpful, at least to be aware of what I can’t do. I’ve been doing some re-reading of the bibliography, and it really doesn’t make much sense to directly compare g0 between both methods.

The initial idea was really to be able to compare detection efficiency. Our final models give us higher vole densities with the noninvasive genetics dataset. We think that’s because noninvasive genetics is more efficient in detecting voles, and it would be nice to have some metrics to confirm this. Anyway, this is not essential for us at the moment. We can just discuss our results in a different perspective.

But I have another question. You mentioned detection function HHN. I’ve used the exponential detection function in the models for the polygon detectors, because AICc of the basic model was lower when using the exponential in comparison with using the hazard exponential. Do you still advise to use the hazard exponential in this case? Or is it better to stick with the exponential? And if I continue to use the exponential, g0 still gives me a detection probability, or the expected number of captures?

Thanks,
Helena

(sorry for the long delay of my response)
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Re: Detectability parameters for polygon detectors

Postby murray.efford » Mon Mar 27, 2017 5:13 am

Sorry for the delay...

On your second paragraph -- a higher detection rate from genetic sampling is _not_ sufficient to explain a higher estimate of density. However there are related explanations that revolve around heterogeneity (differential catchability of different individuals). Most simply: if some population subclass is drastically undersampled by live trapping then it can drag down the whole estimate. There was evidence of this from pitfall trapping of voles by Charley Krebs' group way back, as you probably know. Faecal DNA seems much less susceptible to this sort of bias (depending on where you get it from - maybe young voles are less likely to use latrines). In nonspatial capture-recapture there is also a link between heterogeneity and detection rate - if all animals have high detection rates there is less scope for heterogeneity - high mean(p) implies low CV(p).

I have a personal preference for using the detection functions expressed as hazard (HHN, HEX etc.) (difficult to explain, but hazard is additive while probability is not). I am very surprised you got a better AICc from HEX than EX. The implementation of polygon detectors was a bit confused on exactly the point you mention (g0 vs lambda0), but I have cleaned that up: if you can wait for the next release secr 3.0 in a few weeks it would be worth re-running some models as a check. But I still think HHN, HEX etc. is the cleanest formulation.

Cheers
Murray
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Re: Detectability parameters for polygon detectors

Postby lenasmarques » Tue Mar 28, 2017 10:48 pm

Hi again:

The best model for the trapping data includes a behavioral response and a time trend on detectability. Initially when I was beginning to analyze the data I ran models that included individual variables, like sex and age class, but it seems that there is no heterogeneity in catchability. Faecal DNA, on the other hand, is susceptible to other variables, that are included in the best model for the noninvasive genetics (genotyping success and the area of each searched habitat patch). So, I think that the heterogeneity in catchability is possibly not the reason for the lower density estimates obtained with live-trapping. I´ll post the print of these models in the end so you can have a look if you want.

The difference in AICc was high (12) between HEX and EX. I’ll post the print of these models also. I must discuss with my advisers the need to re-run the models using HEX instead of EX. There are more than 100 models that need to be re-run, if this is the case, and at least one month of computation time, with several models running parallel (some of these models took almost a week to run). At this point, when the paper is almost ready to submit, we need to evaluate if these extra time and effort is worthwhile.

Once again, thank you so much for your help.

Helena


Best model for the live-trapping data

Code: Select all
> print(Model58b.V3, deriv = TRUE)

secr.fit(capthist = CaptHistA.V3, model = list(D ~ 1, g0 ~ T +
    B, sigma ~ B), mask = MaskA.V3, CL = FALSE, detectfn = 2,
    start = c(2.8063528, -5.6620229, 0.1937767, 2.7593377, 1.8213741,
        -0.1933307), method = "Nelder-Mead", verify = TRUE, trace = TRUE)
secr 2.8.2, 09:57:21 01 Jul 2014

Detector type     single
Detector number   371
Average spacing   4.794238 m
x-range           521534.6 522328 m
y-range           4178202 4179022 m
Usage range by occasion
    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
min 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0
max 1 1 1 1 1 1 1 1 1  1  1  1  1  1  1  1  1  1  1  1

N animals       :  31 
N detections    :  81
N occasions     :  20
Mask area       :  11.1104 ha

Model           :  D~1 g0~T + B sigma~B
Fixed (real)    :  none
Detection fn    :  exponential
Distribution    :  poisson
N parameters    :  6
Log likelihood  :  -372.8012
AIC             :  757.6023
AICc            :  761.1023

Beta parameters (coefficients)
                  beta     SE.beta        lcl        ucl
D            2.8083653 0.189386184  2.4371752  3.1795554
g0          -5.6287007 0.015227904 -5.6585468 -5.5988545
g0.T         0.1916259 0.006550623  0.1787869  0.2044649
g0.BTRUE     2.7079777 0.017825394  2.6730406  2.7429149
sigma        1.8426776 0.010155018  1.8227741  1.8625810
sigma.BTRUE -0.2197838 0.013723621 -0.2466816 -0.1928860

Variance-covariance matrix of beta parameters
                        D            g0          g0.T      g0.BTRUE         sigma   sigma.BTRUE
D            0.0358671266 -1.394867e-04 -3.642875e-04  1.416620e-04 -1.035854e-04  1.092309e-04
g0          -0.0001394867  2.318891e-04 -1.002422e-06 -2.318122e-04 -1.625975e-07  3.123691e-07
g0.T        -0.0003642875 -1.002422e-06  4.291066e-05  7.311885e-07 -3.942257e-06  3.252029e-06
g0.BTRUE     0.0001416620 -2.318122e-04  7.311885e-07  3.177447e-04  2.490738e-07 -5.308419e-07
sigma       -0.0001035854 -1.625975e-07 -3.942257e-06  2.490738e-07  1.031244e-04 -1.029646e-04
sigma.BTRUE  0.0001092309  3.123691e-07  3.252029e-06 -5.308419e-07 -1.029646e-04  1.883378e-04

Fitted (real) parameters evaluated at base levels of covariates
       link     estimate  SE.estimate         lcl          ucl
D       log 16.582788101 3.168923e+00 11.44067739 24.036064629
g0    logit  0.003580376 5.432641e-05  0.00347546  0.003688447
sigma   log  6.313420226 6.411455e-02  6.18900352  6.440338060


Best model for noninvasive genetics

Code: Select all
> print(ModelR52.V4b, deriv = TRUE)

secr.fit(capthist = CaptXY1.V4, model = list(D ~ 1, g0 ~ sa +
    log(tarea_m2), sigma ~ 1), mask = Mask1.V4, CL = FALSE, detectfn = 2,
    start = c(3.22372542, 4.64804125, 0.04209972, -0.95883076,
        1.63094581), method = "Nelder-Mead", verify = TRUE, trace = TRUE)

secr 2.8.2, 19:01:18 20 Dez 2014

Detector type     polygon
Number vertices   265
Number polygons   21
Total area        9.867063 ha
x-range           521529.8 522347.7 m
y-range           4178147 4179094 m

N animals       :  65 
N detections    :  115
N occasions     :  4
Count model     :  Poisson
Mask area       :  11.1104 ha

Model           :  D~1 g0~sa + log(tarea_m2) sigma~1
Fixed (real)    :  none
Detection fn    :  exponential
Distribution    :  poisson
N parameters    :  5
Log likelihood  :  -204.8343
AIC             :  419.6686
AICc            :  420.6856

Beta parameters (coefficients)
                        beta     SE.beta         lcl         ucl
D                 3.22638369 0.155871514  2.92088114  3.53188624
g0                4.65592872 1.501422374  1.71319494  7.59866250
g0.sa             0.04207808 0.006365284  0.02960236  0.05455381
g0.log(tarea_m2) -0.95982951 0.182463477 -1.31745135 -0.60220767
sigma             1.63177974 0.114332966  1.40769125  1.85586824

Variance-covariance matrix of beta parameters
                             D           g0         g0.sa g0.log(tarea_m2)         sigma
D                 0.0242959287  0.039416865  2.658278e-04    -7.811774e-03 -1.743334e-04
g0                0.0394168650  2.254269144 -2.288354e-03    -2.667201e-01  3.028020e-02
g0.sa             0.0002658278 -0.002288354  4.051684e-05     3.523713e-05  8.706982e-06
g0.log(tarea_m2) -0.0078117741 -0.266720089  3.523713e-05     3.329292e-02 -3.309909e-03
sigma            -0.0001743334  0.030280196  8.706982e-06    -3.309909e-03  1.307203e-02

Fitted (real) parameters evaluated at base levels of covariates
      link    estimate SE.estimate         lcl        ucl
D      log 25.18840301  3.95012304 18.55763209 34.1883945
g0     log  0.07241937  0.02625803  0.03636664  0.1442137
sigma  log  5.11296640  0.58649624  4.08650977  6.3972502



Null model for polygon detectors, using EX

Code: Select all
> print(ModelR1.V4, deriv = TRUE)

secr.fit(capthist = CaptXY1.V4, model = list(D ~ 1, g0 ~ 1, sigma ~
    1), mask = Mask1.V4, CL = FALSE, detectfn = 2, start = NULL,
    method = "BFGS", verify = TRUE, trace = TRUE)
secr 2.10.4, 22:41:08 12 Mar 2017

Detector type     polygon
Number vertices   265
Number polygons   21
Total area        9.867063 ha
x-range           521529.8 522347.7 m
y-range           4178147 4179094 m

N animals       :  65 
N detections    :  115
N occasions     :  4
Count model     :  Poisson
Mask area       :  11.1104 ha

Model           :  D~1 g0~1 sigma~1
Fixed (real)    :  none
Detection fn    :  exponential
Distribution    :  poisson
N parameters    :  3
Log likelihood  :  -243.6708
AIC             :  493.3416
AICc            :  493.7351

Beta parameters (coefficients)
            beta   SE.beta       lcl        ucl
D      2.4809079 0.1391105  2.208256  2.7535594
g0    -0.9366488 0.1337347 -1.198764 -0.6745336
sigma  1.5666668 0.1027948  1.365193  1.7681410

Variance-covariance matrix of beta parameters
                  D           g0         sigma
D      0.0193517297 -0.008350741 -0.0004722569
g0    -0.0083507409  0.017884971  0.0027955625
sigma -0.0004722569  0.002795562  0.0105667740

Fitted (real) parameters evaluated at base levels of covariates
      link   estimate SE.estimate       lcl       ucl
D      log 11.9521105   1.6707404 9.0998353 15.698410
g0     log  0.3919391   0.0526511 0.3015667  0.509394
sigma  log  4.7906535   0.4937581 3.9164777  5.859949



Null model for polygon detectors, using HEX

Code: Select all
> print(ModelR1.V4Z, deriv = TRUE)

secr.fit(capthist = CaptXY1.V4, model = list(D ~ 1, g0 ~ 1, sigma ~
    1), mask = Mask1.V4, CL = FALSE, detectfn = 16, start = NULL,
    method = "BFGS", verify = TRUE, trace = TRUE)
secr 2.10.4, 05:26:57 08 Mar 2017

Detector type     polygon
Number vertices   265
Number polygons   21
Total area        9.867063 ha
x-range           521529.8 522347.7 m
y-range           4178147 4179094 m

N animals       :  65 
N detections    :  115
N occasions     :  4
Count model     :  Poisson
Mask area       :  11.1104 ha

Model           :  D~1 lambda0~1 sigma~1
Fixed (real)    :  none
Detection fn    :  hazard exponential
Distribution    :  poisson
N parameters    :  3
Log likelihood  :  -249.7629
AIC             :  505.5259
AICc            :  505.9193

Beta parameters (coefficients)
             beta   SE.beta       lcl       ucl
D        2.531826 0.1418696  2.253766  2.809885
lambda0 -1.086550 0.1299047 -1.341158 -0.831941
sigma    1.526036 0.1170496  1.296623  1.755449

Variance-covariance matrix of beta parameters
                    D      lambda0         sigma
D        0.0201269873 -0.008856176 -0.0002039613
lambda0 -0.0088561763  0.016875236  0.0025374188
sigma   -0.0002039613  0.002537419  0.0137006034

Fitted (real) parameters evaluated at base levels of covariates
        link   estimate SE.estimate       lcl        ucl
D        log 12.5764453  1.79323091 9.5235369 16.6080077
lambda0  log  0.3373786  0.04401262 0.2615426  0.4352037
sigma    log  4.5999069  0.54026658 3.6569267  5.7860451
lenasmarques
 
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Re: Detectability parameters for polygon detectors

Postby murray.efford » Wed Mar 29, 2017 2:38 am

Hi

It's unseemly to get into an argument about your model set and data (you know them better than me), but I have my doubts about the wisdom of running 100 models - perhaps we could discuss some of those choices offline. I agree it is not smart to re-fit all those models.

I really would like to understand the reason for the AIC difference between EX and HEX. Could you possibly send me the R objects CaptXY1.V4 and Mask1.V4 in confidence? Possibly
Code: Select all
 save(CaptXY1.V4 , Mask1.V4, file = 'dataformurray.RData')


Murray
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Posts: 507
Joined: Mon Sep 29, 2008 7:11 pm
Location: Dunedin, New Zealand


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