Estimate trend as slope of N's or average of lambdas?

[sixtystrat]

I am estimating the population trend for a decreasing population and was wondering if it made more sense to average the lambdas over time or to fit a line to the population estimates year by year. I am using estimators whereby N is a derived parameter so I cannot directly model N as a time trend. Also, the estimator does not estimate lambda directly so I have to calculate that as Nt/(Nt-1). The problem that I see with averaging the lambdas and determining the CI is that when the population is small, a change in just a few animals can have a big effect on lambda. However, the effect would not be as great if those points were all part of a general regression line. Which is more appropriate if I wanted to evaluate whether the decline was not due to sampling error? Thanks,
Joe

[egc]

I am estimating the population trend for a decreasing population and was wondering if it made more sense to average the lambdas over time or to fit a line to the population estimates year by year. I am using estimators whereby N is a derived parameter so I cannot directly model N as a time trend. Also, the estimator does not estimate lambda directly so I have to calculate that as Nt/(Nt-1). The problem that I see with averaging the lambdas and determining the CI is that when the population is small, a change in just a few animals can have a big effect on lambda. However, the effect would not be as great if those points were all part of a general regression line. Which is more appropriate if I wanted to evaluate whether the decline was not due to sampling error? Thanks,
Joe

This can be handled (more or less) using a random effects approach with a trend. However, that hasn't been documented (yet) in 'the book'.

In the interim, I would suggest you consider simply estimating realized stochastic growth rate - if its <0 (on the log scale), the population has been declining. Have a look at the following thread:

http://www.phidot.org/forum/viewtopic.p ... torder=asc

The occasional weird lambda probably won't affect the estimate much (although some care is needed with Pradel models, since the first and last estimates can be somewhat strange...).

[sixtystrat]

Thanks Evan. My problem is that I was estimating growth based on live captures (POPAN) and within-year hair sampling (Robust Design) and neither estimate lambda directly (POPAN will of course but I was trying to avoid the confounding effects of estimating both phi and lambda directly). Anyhow, it looks like my best course is to take the geometric means of my derived lambdas and estimate teh 95% CIs with the delta method (which is what I did originally).
Cheers,
Joe

[Bill Kendall]

If you are just dealing with one state (i.e., no temporary emigrants), MARK can estimate lambda with robust design data. Look at the Pradel model set of modules in MARK and you will see options for the RD. Gary essentially "robustified" the Pradel model, by replacing each p(t) with a p*(t) = 1 - (1-pt1)(1-pt2)... We have not written it up for publication, and I'm not sure if we say anything about it in the RD chapter, but it's there.

[sixtystrat]

Thanks Bill, that's good to know.