## POPAN Bigross and B* gross births

posts related to the RMark library, which may not be of general interest to users of 'classic' MARK

### POPAN Bigross and B* gross births

Hi, I'm a bit confused with the different 'birth' derived POPAN parameters. I've looked through chapter 12 of the mark book and also read the Schwarz and Arnason 1996 paper but haven't had much luck.

What is the difference between BiGross and B* Gross births (which is the same as B-hat?) ? Could someone provide the correct definitions please?

The definitions from Schwarz and Arnason 1996 are:

-Bi number of animals that enter after sample time i and survive to sample time i + 1,
i = O. ... , k - 1. The Bi are referred to as the net births. Bo is defined as the number
of animals alive just prior to the first sample time.

-Bi* gross number of animals that enter between sampling occasions i and i + 1. These include
animals that enter and die before the next sampling occasion.

I can't seem to find a definition of Bi Gross anywhere.

Also, with Net births, each group is consistent across years. Does this mean that net births are, for example, 5.75 between i and i+1 or is this across the whole of the study period?

>results\$derived

\$`B* Gross Births`
estimate se lcl ucl
6 6.356789e+00 7.441877e-01 5.057372e+00 7.990071e+00
7 5.910371e+00 6.636054e-01 4.746143e+00 7.360183e+00
8 6.983769e+00 8.504516e-01 5.505715e+00 8.858618e+00
9 6.045344e+00 6.892532e-01 4.838198e+00 7.553677e+00
10 6.696976e+00 8.443284e-01 5.235804e+00 8.565920e+00

16 7.016028e+00 1.448408e+00 4.701040e+00 1.047101e+01
17 4.768665e+00 9.751729e-01 3.207053e+00 7.090675e+00
18 8.821659e+00 1.820427e+00 5.911833e+00 1.316371e+01
19 5.624325e+00 1.245842e+00 3.662444e+00 8.637137e+00
20 8.095871e+00 1.822230e+00 5.236397e+00 1.251684e+01

\$`B Net Births`
estimate se lcl ucl
6 5.747887e+00 6.318783e-01 4.636741e+00 7.125307e+00
7 5.747887e+00 6.318783e-01 4.636741e+00 7.125307e+00
8 5.747887e+00 6.318783e-01 4.636741e+00 7.125307e+00
9 5.747887e+00 6.318783e-01 4.636741e+00 7.125307e+00
10 5.747887e+00 6.318783e-01 4.636741e+00 7.125307e+00

16 3.226884e+00 3.547387e-01 2.603083e+00 4.000172e+00
17 3.226884e+00 3.547387e-01 2.603083e+00 4.000172e+00
18 3.226884e+00 3.547387e-01 2.603083e+00 4.000172e+00
19 3.226884e+00 3.547387e-01 2.603083e+00 4.000172e+00
20 3.226884e+00 3.547387e-01 2.603083e+00 4.000172e+00

>popan.derived

\$BiGross
sex injury occasion estimate se
2 M major 1 28.26056 3.159481e+00
2.1 M major 2 34.61735 2.462664e+00
2.2 M major 3 40.52772 1.819467e+00
2.3 M major 4 47.51149 1.125427e+00
2.4 M major 5 53.55684 6.113182e-01
2.5 M major 6 60.25381 7.421704e-01

5 M none 1 15.86558 1.773744e+00
5.1 M none 2 22.88161 1.574671e+00
5.2 M none 3 27.65027 1.656681e+00
5.3 M none 4 36.47193 2.821646e+00
5.4 M none 5 42.09626 3.581685e+00
5.5 M none 6 50.19213 4.992593e+00

Apologies if this has already been posted, I couldn't find it!

Jess
j.harv3y

Posts: 45
Joined: Mon Oct 08, 2018 4:45 am

### Re: POPAN Bigross and B* gross births

Obviously I need to add that to the documentation.  It was something I needed but right now I'm not sure what I used it for.  It is the cumulative value of Bi*. The first value will match the initial number in the population and then it accumulates the gross number entering.  So it is an accumulation of individuals ever in the population at some point. Notice how the last value is NGross. Here is an example with the dipper data.
> library(RMark)
> data(dipper)
> dp=process.data(dipper,model="POPAN")
> mod=mark(dp,model="POPAN")
summary for POPAN model
Name : Phi(~1)p(~1)pent(~1)N(~1)

Npar :  4
-2lnL:  705.5656
AICc :  713.6435

Beta
estimate        se       lcl       ucl
Phi:(Intercept)  0.2382582 0.1016105 0.0391017 0.4374147
p:(Intercept)    2.2914682 0.3323916 1.6399806 2.9429557
pent:(Intercept) 0.6683265 0.2233363 0.2305874 1.1060656
N:(Intercept)    2.7195521 0.4296113 1.8775139 3.5615902

Real Parameter Phi
1         2         3         4         5         6
0.5592844 0.5592844 0.5592844 0.5592844 0.5592844 0.5592844

Real Parameter p
1        2        3        4        5        6        7
0.908168 0.908168 0.908168 0.908168 0.908168 0.908168 0.908168

Real Parameter pent
2         3         4         5         6         7
0.1535493 0.1535493 0.1535493 0.1535493 0.1535493 0.1535493

Real Parameter N
1
309.1735
> mod\$results\$derived
\$`B* Gross Births`
estimate       se     lcl      ucl
1 62.59513 2.036819 58.7286 66.71622
2 62.59513 2.036819 58.7286 66.71622
3 62.59513 2.036819 58.7286 66.71622
4 62.59513 2.036819 58.7286 66.71622
5 62.59513 2.036819 58.7286 66.71622
6 62.59513 2.036819 58.7286 66.71622

\$`B Net Births`
estimate       se     lcl      ucl
1 47.47338 1.267814 45.0528 50.02402
2 47.47338 1.267814 45.0528 50.02402
3 47.47338 1.267814 45.0528 50.02402
4 47.47338 1.267814 45.0528 50.02402
5 47.47338 1.267814 45.0528 50.02402
6 47.47338 1.267814 45.0528 50.02402

\$`N Population Size`
estimate       se      lcl       ucl
1  24.33322 5.060679 16.25696  36.42169
2  61.08258 2.529974 56.32173  66.24586
3  81.63591 2.694208 76.52378  87.08956
4  93.13107 3.849885 85.88587 100.98747
5  99.56013 4.849039 90.50067 109.52648
6 103.15581 5.568714 92.80586 114.66001
7 105.16681 6.056550 93.95021 117.72256

\$`Gross N* Population Size`
estimate       se    lcl      ucl
1  399.904 10.85389 379.19 421.7495

> popan.derived(dp,mod)
\$N
Occasion         N       se      LCL       UCL
1        1  24.33323 5.060678 14.41430  34.25215
2        2  61.08258 2.529973 56.12383  66.04132
3        3  81.63591 2.694207 76.35527  86.91656
4        4  93.13107 3.849885 85.58530 100.67685
5        5  99.56014 4.849038 90.05602 109.06425
6        6 103.15581 5.568714 92.24113 114.07049
7        7 105.16682 6.056550 93.29598 117.03765

\$N.vcv
[,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
[1,] 25.610466 11.033476  3.069674 -1.278718 -3.651624 -4.945710 -5.650991
[2,] 11.033476  6.400764  4.545214  3.918762  3.798447  3.859819  3.966103
[3,]  3.069674  4.545214  7.258751  9.832480 11.862582 13.328331 14.332857
[4,] -1.278718  3.918762  9.832480 14.821614 18.552497 21.165151 22.920567
[5,] -3.651624  3.798447 11.862582 18.552497 23.513174 26.969432 29.283801
[6,] -4.945710  3.859819 13.328331 21.165151 26.969432 31.010570 33.715288
[7,] -5.650991  3.966103 14.332857 22.920567 29.283801 33.715288 36.681797

\$Nbyocc
Occasion         N       se      LCL       UCL
1        1  24.33323 5.060678 14.41430  34.25215
2        2  61.08258 2.529973 56.12383  66.04132
3        3  81.63591 2.694207 76.35527  86.91656
4        4  93.13107 3.849885 85.58530 100.67685
5        5  99.56014 4.849038 90.05602 109.06425
6        6 103.15581 5.568714 92.24113 114.07049
7        7 105.16682 6.056550 93.29598 117.03765

\$Nbyocc.vcv
[,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
[1,] 25.610466 11.033476  3.069674 -1.278718 -3.651624 -4.945710 -5.650991
[2,] 11.033476  6.400764  4.545214  3.918762  3.798447  3.859819  3.966103
[3,]  3.069674  4.545214  7.258751  9.832480 11.862582 13.328331 14.332857
[4,] -1.278718  3.918762  9.832480 14.821614 18.552497 21.165151 22.920567
[5,] -3.651624  3.798447 11.862582 18.552497 23.513174 26.969432 29.283801
[6,] -4.945710  3.859819 13.328331 21.165151 26.969432 31.010570 33.715288
[7,] -5.650991  3.966103 14.332857 22.920567 29.283801 33.715288 36.681797

\$NGross
[1] 399.904

\$NGross.vcv
[1] 117.8068

\$BiGross
occasion  estimate        se
1        1  24.33323  5.060678
2        2  86.92835  4.498152
3        3 149.52348  4.811812
4        4 212.11861  5.862675
5        5 274.71374  7.340684
6        6 337.30887  9.038672
7        7 399.90399 10.853883

\$BiGross.vcv
[,1]     [,2]     [,3]     [,4]      [,5]      [,6]       [,7]
[1,] 25.610466 20.84760 16.08474 11.32188  6.559014  1.796151  -2.966712
[2,] 20.847603 20.23337 19.61914 19.00490 18.390671 17.776438  17.162204
[3,] 16.084740 19.61914 23.15353 26.68793 30.222327 33.756724  37.291121
[4,] 11.321877 19.00490 26.68793 34.37096 42.053984 49.737011  57.420037
[5,]  6.559014 18.39067 30.22233 42.05398 53.885641 65.717297  77.548954
[6,]  1.796151 17.77644 33.75672 49.73701 65.717297 81.697584  97.677870
[7,] -2.966712 17.16220 37.29112 57.42004 77.548954 97.677870 117.806787

jlaake

Posts: 1197
Joined: Fri May 12, 2006 12:50 pm
Location: Escondido, CA