Estimating survival for binned age classes

[tasha]

Hello,

We are wanting to estimate annual survival for juvenile and adult prairie dogs over a six year period but are having some issues obtaining the desired output when modeling age transitions in a robust model in RMark.

We have 6 years of mark-recapture data. Within each year animals are trapped for 9 days. Upon first capture each individual is identified as a juvenile (pup of the year, <1) or adult (specific age is unknown, 1+). As seen in the script below we have binned age from 0-1 for juveniles and from 1-5 for adults. Using this method our top model includes time:plot+age+sex which gives us annual survival estimates for male and female juveniles (per plot). For adults in each plot this model gives us an a separate estimate for each age in each year.
Rather than having a separate estimate for each of the "adult age classes" what we would like is a single annual survival estimate for all adults (age 1-5 combined). We are just wondering if there is an easy way to bin adults all together to just obtain one annual survival estimate for adults … or do we just have to average the output we have?

Any advice would be hugely appreciated and we apologize if we have over looked something simple…

Thanks so much,
T&T


Sample of Script:

Survival_Age_Core=import.chdata("C:/tara local data/RMark YAY Files/Interior/Annual_Survival_Age_Core.txt",
field.types=c("f","f","f","f"))
summary(Survival_Age_Core)

Survival_Age_Core.process=process.data(Survival_Age_Core,begin.time=2007,groups=c
("plot","Sex","age"),initial.age=c(1,0),age.var=3,
model="Robust",time.intervals=c(0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0))

Survival_Age_Core.ddl=make.design.data(Survival_Age_Core.process)
Survival_Age_Core.ddl=add.design.data(Survival_Age_Core.process,Survival_Age_Core.ddl,
"S","age",bins=c(0,1,5),right=FALSE,name="JA")

Survival_Age_Core.ddl
Survival_Age_Core_GammasPCTimeSexColonyS.models=function()
{
S.One=list(formula=~-1+time:plot+Sex+age)

Sample OutPut for the female adults in the first plot "gEC-01":

Real Function Parameters of { S(~time:plot + Sex + age)Gamma''(~1)Gamma'()p(~session:time + plot + c)c()N(~-1 + group:session) }
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1:S gEC-01FemaleAdult 0.3847042 0.0753165 0.2510030 0.5384274
2:S gEC-01FemaleAdult 0.8044735 0.0893442 0.5747384 0.9260661
3:S gEC-01FemaleAdult 0.5931664 0.0917264 0.4090411 0.7543728
4:S gEC-01FemaleAdult 0.6834327 0.1405612 0.3766498 0.8852361
5:S gEC-01FemaleAdult 0.4341965 0.2145278 0.1217147 0.8095044
6:S gEC-01FemaleAdult 0.8668798 0.0641666 0.6865004 0.9508971
7:S gEC-01FemaleAdult 0.6109438 0.0717103 0.4650469 0.7393519
8:S gEC-01FemaleAdult 0.8046907 0.0819940 0.5970814 0.9197111
9:S gEC-01FemaleAdult 0.2910371 0.1175448 0.1184776 0.5563155
10:S gEC-01FemaleAdult 0.7130896 0.0586221 0.5863356 0.8133667
11:S gEC-01FemaleAdult 0.8160909 0.0727763 0.6317401 0.9198624
12:S gEC-01FemaleAdult 0.4392833 0.0987200 0.2631578 0.6321561
13:S gEC-01FemaleAdult 0.8753637 0.0510995 0.7371574 0.9462027
14:S gEC-01FemaleAdult 0.4576367 0.0794637 0.3105904 0.6124540
15:S gEC-01FemaleAdult 0.5718236 0.0791401 0.4147809 0.7156177

We are interpreting the above as
1: = survival from yr1 to yr2 of those first captured in yr 1 (so 1 yr olds)
2: = survival from yr2 to yr3 of those first capture in yr 2 (so 1 yr olds)
3: = survival from yr2 to yr3 of those first captured in yr 1 (so 2 yr olds)
4: = survival from yr3 to yr4 of those first capture in yr 3 (so 1 yr olds)
5: = survival from yr3 to yr4 of those first captured in yr 2 (so 2 yr olds)
6: = survival from yr3 to yr4 of those first captured in yr 1 (so 3 yr olds)
...

So can we somehow group the adult age classes to just get 5 estimates (one for each year) rather than 15!
Thanks

[jlaake]

Either use JA that you defined in place of age in your formula

Code: Select all

S.One=list(formula=~-1+time:plot+Sex+JA)


or specify bins for age in make.design.data.

Code: Select all

Survival_Age_Core.ddl=make.design.data(Survival_Age_Core.process,
    parameters=list(S=list(age.bins=c(0,1,5))),right=FALSE)


Currently, you binned JA but left age unbinned so when you used age in the formula it is giving you a different value for each age in years. You should look at your design data (Survival_Age_Core.ddl$S) because I don't think c(0,1,5) will span all ages so it will contain NA values and won't work. With 6 years of data and an initial age of 1, S will range up to age=6.

--jeff

[tasha]

Hello

Thank-you very much for your last advice, it ran and we think it worked but we are a little confused about the output (see a sample below).
Our data goes from 2007 to 2012 so as expected we have 5 annual survival estimates for each group (sex, age, plot), However we do not know exactly how to interpret each of the columns under the “Parameter” heading.
For example:
For Adult Females in Plot A, we are not sure why “c2007” and “c1” remain constant for each survival estimate but “a” changes. We are of the understanding that “c” represents cohort and “a” equals age. Is this correct? And if so, is this saying that all adults in every year are assumed to be 1 year old in 2007 (regardless of when they were first captured) thus all belong to the first (2007) cohort? And that all adults captured in 2008 are assumed to be 2 years old etc.? We are just a little unnerved because we cannot see year/time to confirm that this is correct. Plus what does the o stand for? Thanks!
1:S gAFA c2007 c1 a1 o
2:S gAFA c2007 c1 a2 o
3:S gAFA c2007 c1 a3 o
4:S gAFA c2007 c1 a4 o
5:S gAFA c2007 c1 a5 o

Real Function Parameters of { S(~time:plot + Sex + JA)Gamma''(~1)Gamma'()p(~session:time + plot + c)c()N(~-1 + group:session) }
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
------------------------- -------------- -------------- -------------- --------------
1:S gAFA c2007 c1 a1 o 0.1063943 0.0410214 0.0486242 0.2171353
2:S gAFA c2007 c1 a2 o 0.7762381 0.1074579 0.5078214 0.9210329
3:S gAFA c2007 c1 a3 o 0.7462118 0.0698258 0.5880334 0.8582922
4:S gAFA c2007 c1 a4 o 0.6120294 0.0988473 0.4109417 0.7810465
5:S gAFA c2007 c1 a5 o 0.7289065 0.0901320 0.5237490 0.8679663
6:S gEFA c2007 c1 a1 o 0.3638548 0.0725178 0.2363601 0.5138455
7:S gEFA c2007 c1 a2 o 0.8436678 0.0718982 0.6496102 0.9401515
8:S gEFA c2007 c1 a3 o 0.6544835 0.0587703 0.5323101 0.7591804
9:S gEFA c2007 c1 a4 o 0.8372448 0.0617125 0.6792263 0.9259116
10:S gEFA c2007 c1 a5 o 0.4713719 0.0714109 0.3370785 0.6099412
11:S gLFA c2007 c1 a1 o 0.4257992 0.0674037 0.3016703 0.5600423
12:S gLFA c2007 c1 a2 o 0.5787313 0.0880492 0.4036477 0.7360277
13:S gLFA c2007 c1 a3 o 0.3182770 0.0785518 0.1867485 0.4869718
14:S gLFA c2007 c1 a4 o 0.4349384 0.1481215 0.1910806 0.7149490
15:S gLFA c2007 c1 a5 o 0.4862026 0.1392278 0.2409311 0.7383043
16:S gPFA c2007 c1 a1 o 0.3069713 0.0565234 0.2083212 0.4271327
17:S gPFA c2007 c1 a2 o 0.9036354 0.0536932 0.7368648 0.9691367
18:S gPFA c2007 c1 a3 o 0.3061908 0.0724123 0.1845107 0.4625959
19:S gPFA c2007 c1 a4 o 0.6405191 0.1260755 0.3785805 0.8390009
...
51:S gAFJ c2007 c1 a0 o 0.0499502 0.0208275 0.0217595 0.1105370
52:S gAFJ c2008 c2 a0 o 0.6050382 0.1534968 0.3031222 0.8436287
53:S gAFJ c2009 c3 a0 o 0.5649154 0.0893264 0.3890777 0.7258089
54:S gAFJ c2010 c4 a0 o 0.4105909 0.1092635 0.2233160 0.6279423
55:S gAFJ c2011 c5 a0 o 0.5428217 0.1164519 0.3212525 0.7486522
56:S gEFJ c2007 c1 a0 o 0.2016448 0.0534733 0.1163879 0.3262924
57:S gEFJ c2008 c2 a0 o 0.7044130 0.1192463 0.4368137 0.8798390
58:S gEFJ c2009 c3 a0 o 0.4554762 0.0631714 0.3367545 0.5794838
59:S gEFJ c2010 c4 a0 o 0.6943415 0.1034255 0.4663857 0.8551590
60:S gEFJ c2011 c5 a0 o 0.2825167 0.0617286 0.1781559 0.4169923
61:S gLFJ c2007 c1 a0 o 0.2466824 0.0513557 0.1600242 0.3601477
62:S gLFJ c2008 c2 a0 o 0.3775861 0.0937038 0.2173313 0.5699564
63:S gLFJ c2009 c3 a0 o 0.1709265 0.0545313 0.0884025 0.3047345
64:S gLFJ c2010 c4 a0 o 0.2536755 0.1186224 0.0905321 0.5371680
65:S gLFJ c2011 c5 a0 o 0.2947182 0.1183973 0.1203627 0.5606607
66:S gPFJ c2007 c1 a0 o 0.1635988 0.0390662 0.1005371 0.2550018
67:S gPFJ c2008 c2 a0 o 0.8054815 0.1005086 0.5408094 0.9357295
68:S gPFJ c2009 c3 a0 o 0.1630971 0.0469939 0.0902846 0.2767660
69:S gPFJ c2010 c4 a0 o 0.4403464 0.1397535 0.2056670 0.7051060
70:S gPFJ c2011 c5 a0 o 0.2829377 0.0849638 0.1479533 0.4727453
...

[jlaake]

It is best to ignore those values in the output because once I implemented simplification to the PIMS there is no longer any correspondence between those labels and the estimates. What you want to do is use summary(model)$reals. If you use summary(model,se=TRUE)$reals then it will associate the design data with the real parameter values.

--jeff