Dealing with transience and capture heterogeneity in POPAN

[marissahutch]

Hello,

I am building POPAN models for 234 delphinids over a 5 year study (2014-2018). I am also grouping them into sexes using male, female and unknown. As expected, GOF testing revealed that both transience and trap shyness are at play. I have therefore applied a TSM effect to Phi. I believe I have set this up correctly by following the advice of other posts, however I am not sure my real parameter estimates are being calculated correctly.

This is how I set it up:

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POPAN.process <- process.data(data, model="POPAN", begin.time = 2014, groups = "sex")
POPAN.ddl <- make.design.data(POPAN.process)
POPAN.ddl$Phi$tsm = 1
POPAN.ddl$Phi$tsm[POPAN.ddl$Phi$age==0] = 0


Here is the resulting PIM:

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Phi
   par.index model.index   group age time Age Time     sex tsm
1          1           1  Female   0 2014   0    0  Female   0
2          2           2  Female   1 2015   1    1  Female   1
3          3           3  Female   2 2016   2    2  Female   1
4          4           4  Female   3 2017   3    3  Female   1
5          5           5    Male   0 2014   0    0    Male   0
6          6           6    Male   1 2015   1    1    Male   1
7          7           7    Male   2 2016   2    2    Male   1
8          8           8    Male   3 2017   3    3    Male   1
9          9           9 Unknown   0 2014   0    0 Unknown   0
10        10          10 Unknown   1 2015   1    1 Unknown   1
11        11          11 Unknown   2 2016   2    2 Unknown   1
12        12          12 Unknown   3 2017   3    3 Unknown   1


Here is my model call:

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Phi.tsm <- list(formula = ~tsm)
POPAN <- mark(POPAN.process, POPAN.ddl, model.parameters = list(Phi = Phi.tsm)


And here are my results:

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Output summary for POPAN model
Name : Phi(~tsm)p(~1)pent(~1)N(~1)

Npar :  5  (unadjusted=4)
-2lnL:  941.7069
AICc :  951.8335  (unadjusted=949.79111)

Beta
                    estimate          se          lcl         ucl
Phi:(Intercept)   18.2910370 128.7849600 -234.1274800 270.7095600
Phi:tsm          -17.2591220 128.7849600 -269.6776500 235.1594000
p:(Intercept)      0.7010789   0.1851875    0.3381114   1.0640464
pent:(Intercept)  -0.8176719   0.2883306   -1.3827999  -0.2525439
N:(Intercept)      2.1916043   0.2624869    1.6771300   2.7060786


Real Parameter Phi
                 2014     2015     2016     2017
Group:sexFemale     1 0.737287 0.737287 0.737287
Group:sexMale       1 0.737287 0.737287 0.737287
Group:sexUnknown    1 0.737287 0.737287 0.737287


Real Parameter p
                      2014      2015      2016      2017      2018
Group:sexFemale  0.6684269 0.6684269 0.6684269 0.6684269 0.6684269
Group:sexMale    0.6684269 0.6684269 0.6684269 0.6684269 0.6684269
Group:sexUnknown 0.6684269 0.6684269 0.6684269 0.6684269 0.6684269


Real Parameter pent
                      2015      2016      2017      2018
Group:sexFemale  0.1596113 0.1596113 0.1596113 0.1596113
Group:sexMale    0.1596113 0.1596113 0.1596113 0.1596113
Group:sexUnknown 0.1596113 0.1596113 0.1596113 0.1596113


Real Parameter N
                     2014
Group:sexFemale  40.94956
Group:sexMale    40.94956
Group:sexUnknown 40.94956


I understand that TSM calculates Phi separately for the first occasion versus the rest, but why is this seemingly fixed to 1? And does this account for those individuals who are only captured in the second, third, fourth or fifth occasion and not the first? Perhaps I need to use an additive or interaction effect with time? Lastly, why is the combined N values for each group (123) lower than the number of individuals included in the analysis (234)...

I am also wondering what is the best way to model capture heterogeneity. I have read that it doesn't make sense to apply TSM to capture probability (p). And I know POPAN models can't handle the individual covariate for trap dependence. Other posts have suggested using the inbuilt '~ch' term of RMark. I have trialled this and it seems to be working, but I can't find an explanation of what this is or how it works anywhere. In my case it reduced p from 0.67 to 0.48. Is this because my individuals are trap shy? Is this the best way to account for trap dependence in POPAN models?

I apologise if I am simply not understanding the theory behind these approaches. I am hoping someone with more experience is able to reassure or correct me. Any advice is greatly appreciated! Thank you

[jlaake]

Please send me the results of table(data$ch) offlist to jefflaake@gmail.com and we can discuss.

You should read the chapter on Jolly Seber models in Cooch and White if you have not already done so. It is unclear whether you have considered other models. Certainly N should not be a constant model and should be by group. It is estimating f0 the number not seen in each group and that is unlikely to ever be constant across groups. Also it is very possible that pent, probability of entry varies by time. We can discuss more offlist.