Brood survival, Lukacs et al (2004)

[bmattsson]

I am trying to estimate apparent survival of fledgling Louisiana Waterthrushes that were individually color-banded as nestlings. I am concerned that individual fledglings within a brood are not independent, and so I would like to use the model for estimating brood survival as described by Lucaks et al (2004) in Condor. There is a module in MARK called "Young survival from marked adults," but I cannot find any documentation for this module, nor does it seem to do what Lukacks et al (2004) did. Any help is appreciated.

[gwhite]

The MARK model you mention is not the Lukacs et al. model. I should take out the link to the model, because it should not be used. You can get SAS code from Paul Lukacs to run his brood survival model.
Gary

[Paul Lukacs]

If the chicks are individually marked, then the Lukacs et al model is not appropriate. Well more correctly, the model would be extremely ineffecient. The Lukacs et al model applies when only the adult is marked.

You might consider using a CJS model to get point estimates and then bootstrapping on broods to get your variance estimate.

[bmattsson]

Thanks for the quick response. I like the idea of bootstrapping over the point estimates for apparent survival. I would still be interested in using the Lukacs model for comparison purposes, so please let me know how I could acquire the code.

[egc]

Thanks for the quick response. I like the idea of bootstrapping over the point estimates for apparent survival. I would still be interested in using the Lukacs model for comparison purposes, so please let me know how I could acquire the code.

You might also want to have a look at

Flint,P.L., Pollock,K.H., Thomas,D. & Sedinger,J.S. (1995) Estimating prefledging survival: allowing for brood mixing and dependence among brood mates. Journal of Wildlife Management, 59, 448-455.

Pre-MARK, but it addresses some relevant statistcal issues. Also,

Williams,T.D., Cooch,E.G., Jefferies,R.L. & Cooke,F. (1993) Environmental degradation, food limitation and reproductive output: juvenile survival in lesser snow geese. Journal of Animal Ecology, 62, 766-777.

use a faux Mayfield estimator to address similar issues (although the method could be much-improved using newer, more robust approaches to nest survival-type problems - second author, pers. comm.)

Bot papers deal with chick (gosling) survival, when all goslings in a brood are marked, and where there is non-independence (potentially) among brood-mates.

[luke.eberhart]

Hi team,

I'm estimating daily chick survival of snowy plovers. The details of my analysis and help I've received from Jeff so far are here.

Chicks in my system are individually marked, which allows me to use resightings (in addition to recaptures) to estimate daily chick survival as opposed to simple brood survival. However, the survival of a chick could be dependent on the survival of other members of its brood because they forage often in close proximity to one another (these guys are precocial) and if, for example, and predator finds them, the predator would most likely predate them all at once. Thus I would like to figure out some way to acknowledge the non-independence of chicks within the same brood.

To address this problem, one idea I had was to use "brood ID" as a random effect. However, I'm not sure if this is possible in RMark, which is what I'm using for building the models.

The reason I'm posting in this thread is because bmattsson brought up a similar situation:

...I am concerned that individual fledglings within a brood are not independent...

With this reply from Paul:

You might consider using a CJS model to get point estimates and then bootstrapping on broods to get your variance estimate.

It sounds like bootstrapping by broods could be an good alternative.

Questions:

1) Is it possible to use random effects in a CJS implemented in RMark?

2) How do I bootstrap by broods to estimate variance? (Preferably instructions for implementing in RMark, but if it is not possible, I could transfer the models over to MARK and run the bootstrapping from there).

3) More of a technical stats question: Would these two routes address the same problem of chicks in the same brood being non-independent? If so, which one is better or more appropriate?

Thanks in advance for your time and support!

Cheers,
Luke

[jlaake]

1) Is it possible to use random effects in a CJS implemented in RMark?

The CJSRandom model in MARK is supported by RMark but it only has individual random effect and I don't think you could implement a brood effect.

2) How do I bootstrap by broods to estimate variance? (Preferably instructions for implementing in RMark, but if it is not possible, I could transfer the models over to MARK and run the bootstrapping from there).

This is relatively straightforward as long as you have your data setup correctly. Let's say you have a broodID field for each capture history. You split the data by broodID, resample the broodIDs with replacement, put data back together and run the model, collect the results and repeat. Below is an example that I created with the dipper data as if it was of broods of 2.

Code: Select all

data(dipper)
# create a dummy broodID field
dipper$broodID=rep(1:(294/2),each=2)
# split dipper data into a list by ID
dipper.list=split(dipper,dipper$broodID)
nboot=2
results=matrix(NA,nrow=nboot,ncol=2)
for (i in 1:nboot)
{
   bs.sample=sample(1:length(dipper.list),replace=TRUE)
   newdata=do.call("rbind",dipper.list[bs.sample])
   results[i,]=coef(mark(newdata,output=FALSE,delete=TRUE))$estimate
}
results


3) More of a technical stats question: Would these two routes address the same problem of chicks in the same brood being non-independent? If so, which one is better or more appropriate?

So bootstrap should work but dependence will also muck up model selection as well so the bootstrap should also fit each model and select best model separately for each bootstrap. You'll have to decide what you'll want to store for results. But the concept of broods and independence fits in well with the c-hat adjustment and you can estimate c-hat as simply number of birds/ number of broods = the average brood size assuming that each chick in a brood is completely independent. You can think of it this way. If n is the number of birds then you can think of your variance as something like sigma/n but if all chicks in a brood are completely dependent then really you only have b (number of broods) independent samples. Thus your variance should be something like sigma/b. chat=n/b will adjust from sigma/n to sigma/b. That may overestimate the adjustment because the chicks in a brood will not be completely dependent but would provide a check on the bootstrap approach. I don't know how you can accomplish the random effect approach with MARK at this point. You can try my R package marked. With it you can structure any type of random effect like a brood effect. But to be honest I programmed it up with ADMB but have not used or tested it as much as I should.