Is group structure appropriate?

[jmae]

My issue is this:

I ran a 4-pass removal (recapture parameters fixed at zero) experiment in ~60 independent, discrete habitat units to estimate abundance of juvenile salmon. I have modeled these data using two approaches; first, I assembled all the habitat units into one capture history file, and specified the unique habitat unit ID as a grouping factor. Then, I ran the same models (time-varying and constant p, c fixed at zero) on just one habitat unit. I compared the parameter estimates of that habitat unit from the models with and without group structure, and N and p are very close, but not the same. Any insight into why this is, and whether it is appropriate for me to group my data this way? Any help is much appreciated.

Thank you!

Jesse

MS Research Assistant
University of Alaska Fairbanks
School of Fisheries and Ocean Sciences
907-474-5403

[jlaake]

You didn't say what model you used for the run with all habitats in a single file. Saying that you specified habitat as a grouping factor does not mean that it was used in the model for p. However I believe the default for N is ~group. Was the model p~group*time, p~group+time, p~group or what and N~group? What exactly are you asking? If you are asking, can I ignore habitat as a factor then the way to do that is to fit models with and without habitat(group) for p and see which is the better model based on AIC. You'll always want to fit N~group(Habitat) due to the potential differences in abundance by habitat.

--jeff

[jmae]

Hey again,

Sorry to be so late in providing a substantial clarification of my question. Had to do some thinking about how to best describe what it is I'm doing. Hope this helps.

Project background:

• Objective: estimate density of juvenile coho and sockeye salmon by freshwater habitat type

• Two study areas (~ 7rkm long) each divided into 100-m long reaches, within a random sample of reaches, one habitat unit of each type was sampled (eddy drop zone [i.e., backwater], pool, riffle, run)

• Fish sampling: each habitat unit was blocked off from the main channel of the river using fine-mesh beach seines (i.e., closed population) and four passes of removal electrofishing were conducted

• My data are capture histories [1000, 0100, 0010, 0001] for each habitat unit; for example:

ch freq hu_id effort
1000 40 edz001 430
0100 34 edz001 414
0010 13 edz001 429
0001 8 edz001 405
1000 121 edz002 953
0100 77 edz002 1002
0010 50 edz002 965
0001 28 edz002 971 …

• So I essentially have closed-population capture data where the recapture parameter is fixed at zero. I’m investigating whether sampling occasion (time) or effort (seconds of electrofishing on a given occasion) or both additively or interactively affect capture probability, so there are five models:
p(.)c(0)N(.)
p(time)c(0)N(.)
p(effort)c(0)N(.)
p(time+effort)c(0)N(.)
p(time*effort)c(0)N(.)

Questions:

• Is it possible to specify “hu_id” as a design covariate (i.e., grouping factor) for estimation of capture probabilities and abundance? This gives me one abundance estimate for each habitat unit, and three estimates for p (time-varying, p3=p4) – same as when I analyzed each habitat unit capture history separately. What’s different? And why?

• If I were to specify “hu_id” as a design covariate, how would I denote this in RMark? I think I’ve got it, but am not sure:

p(group)c(0)N(group)
p(group+time)c(0)N(group)
p(group+effort)c(0)N(group)
p(group+time+effort)c(0)N(group)
p(group+time*effort)c(0)N(group)

I’ve had problems executing the latter two models in RMark; not sure why…

• Because my objective is to use these abundances to calculate density (abundance/habitat unit area), I need to know whether or not I can then treat them (HU abundances) as individual replicates. For example, can I divide the abundances in edz001 and edz002 by their respective habitat unit areas to get density, then average these two values together to come up with an average density for eddy drop zones?

• I’m also having a difficult time figuring out model averaging in this scenario: when analyzed individually, each habitat unit will likely vary in which model is “best”. This affects how much weight is given to the parameter estimates under that model. When habitat units are pooled/grouped then analyzed, there is only one “best” model for all the habitat units in that set. This doesn’t seem to make sense.

[jlaake]

• Is it possible to specify “hu_id” as a design covariate (i.e., grouping factor) for estimation of capture probabilities and abundance? This gives me one abundance estimate for each habitat unit, and three estimates for p (time-varying, p3=p4) – same as when I analyzed each habitat unit capture history separately. What’s different? And why?

Yes. The results for the pooled analysis will be the same as the seprate analysis if you specify p(time*group)c(0)N(group) for the pooled analysis. There isn't anything different except that with the pooled analysis you can then fit simpler models (p(time), p(time+group) if they are appropriate.

• If I were to specify “hu_id” as a design covariate, how would I denote this in RMark? I think I’ve got it, but am not sure:

p(group)c(0)N(group)
p(group+time)c(0)N(group)
p(group+effort)c(0)N(group)
p(group+time+effort)c(0)N(group)
p(group+time*effort)c(0)N(group)

you need to specify groups="hu_id" in process.data and then use the formula above with one exception noted below.

I’ve had problems executing the latter two models in RMark; not sure why…

You can't fit both a time and effort covariate in the same model. Within a time there is no variation in effort unless it varied across groups but you also have that affect in the model. Think about what you are doing here.

• Because my objective is to use these abundances to calculate density (abundance/habitat unit area), I need to know whether or not I can then treat them (HU abundances) as individual replicates. For example, can I divide the abundances in edz001 and edz002 by their respective habitat unit areas to get density, then average these two values together to come up with an average density for eddy drop zones?

You can except that unless you fit them independently (separately or pooled with group*time), the abundance estimates will have a covariance and would have to be dealt with in computing the variance of the mean.

• I’m also having a difficult time figuring out model averaging in this scenario: when analyzed individually, each habitat unit will likely vary in which model is “best”. This affects how much weight is given to the parameter estimates under that model. When habitat units are pooled/grouped then analyzed, there is only one “best” model for all the habitat units in that set. This doesn’t seem to make sense.

Don't analyze them individually.

--jeff