Popan BiGross and B*Gross births

[j.harv3y]

Hi, (was unsure if I should post in mark or rmark forum) 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?

$`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

$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

Many thanks in advance,

Jess

[gwhite]

The "gross" estimates are the estimates with the *, and as you reported, include animals that entered and left entirely within one interval, and hence never had a chance to be captured. These are estimated based on a constant hazard function for both entry, and then departure. So this is a "gross" strong assumption.

Gary

[j.harv3y]

The "gross" estimates are the estimates with the *, and as you reported, include animals that entered and left entirely within one interval, and hence never had a chance to be captured. These are estimated based on a constant hazard function for both entry, and then departure. So this is a "gross" strong assumption.

Gary

Hi Gary,

Thanks so much for the reply. I'm afraid I'm struggling to understand the difference between BiGross and B* gross births... B* gross includes animals not encountered that may have left the system- How does is this different from BiGross? B* is so much smaller than BiGross.

Thanks again,

Jess

[gwhite]

The "*" means "gross". There is no B* Gross, only B and B*.

[j.harv3y]

Ah this is the direct readout from rmark output (both B*gross and Bi gross with very different values) - maybe this is where the confusion is.

[jlaake]

Jess

Is this from model$results$derived or from popan.derived function?

[j.harv3y]

`B* Gross Births` is from results$derived (and the same as n-hat in model output) and BiGross from popan.derived function.

Thanks so much for helping

Jess

[jlaake]

I added some quantities in popan.derived. I'll have to look at it and get back to you.

[j.harv3y]

If you could that would be amazing, thanks a million