influence of variation in age-specific survival on lambda

[arpat]

I am investigating the influence of spatiotemporal variation in age-specific survival rates on population growth rate, and I ran into some difficulties with Pradel's model. I read the related chapters in MARK book, papers and online class notes, but I could not come up with a solution.

I apologize for the long post, and will greatly appreciate the patience and ideas of those that are willing to read it:

I have analyzed the spatial and temporal variation in age-specific (pup [1yr], yearling [2yr], adult [>2yr]) survival rates using a CJS model and a long term data from 8 different sites (I used sites as groups). Temporal variation was significant only in pups, and spatial variation was significant in all three age classes. I used the underlying process standard deviation of survival rates over space (or time) as an estimate of the spatial (or temporal) variation in survival rates. The SD was estimated using the variance components procedure in MARK. Estimated process SD over space was 0.08 for pups, 0.11 for yearlings, and 0.04 for adults, and SD over time was 0.20 for pups.

Next, I wanted to do an analysis to understand the effect of observed spatial/temporal variation on population growth rate using Pradel's model. However, as I am using age-specific survival rates, I ran into some difficulties. If I use the original recapture histories in Pradel's models, I will be totally ignoring the age-specific differences in survival rates, and my lambda and gamma will be biased by unaccounted age-specific differences in survival rates.

I decided to look at the population growth of (and recruitment into) adult stage, only. I deleted pup and yearling entries from the recapture histories. For this analysis, I didn't have enough individuals to use 8 different sites, and I pooled them into one group.

I used seniority parameter to assess the relative effects of changes (1) in recruitment into the adult stage and (2) in adult survival on the lambda of adult population. As I have used only resident females in my analysis, recruitment could have only resulted within the site and not from immigration.

recruitment = reproduction within the site -> survival of pups to yearling age -> survival of yearlings to adult age

The most parsimonious model indicated constant survival, constant recapture, and time effect on lambda (hence on gamma). The point estimates of gamma (seniority) ranged 0.52 - 0.79, indicating temporal variation in relative contribution of adult survival and recruitment to lambda. Using the same model structure, I estimated the time specific lambda. Estimates ranged 0.92 - 1.40, showing apparent fluctuation during the study period. As the adult survival was constant through time, the observed temporal variation in gamma and lambda could only be caused by temporal variation in the recruitment into the adult stage.

Now, I know that adult and yearling survival rates are both constant over time, and pup survival rate varies over time. Therefore, temporal variation in lambda can only arise from pup survival, but also from reproduction. If I can assume that reproduction is constant over time, then I think I can say that the observed temporal variation in lambda is caused solely by the temporal variation in pup survival. And I have the estimates of this temporal variation in lambda.

When it comes to spatial variation, it gets more complicated. One thing I can do is to estimate the mean gamma over time. This will tell me the importance of adult survival versus adult recruitment. Using this estimate, I can say " 10% change in adult survival will lead to x% change in lambda" or better use the already estimated SD and say "one SD change in adult survival will lead to y% change in lambda". I think I can use this approach to investigate the influence of the observed spatial variation in adult survival rates on lambda.

However, the problem is that I cannot do the same thing for pup or yearling survival rates, as they are all part of the recruitment rate (reproduction * young survival * yearling survival)

So, this is where I got stuck! I am trying to find a way of investigating the effect of observed spatial variation in pup & yearling survival rates on lambda.

I, again, apologize for such a long post, and thank you for being patient.. I will greatly appreciate comments on possible flaws in my aproach, and ideas on how to tackle this problem.

Arpat