Seniority probabilities

[steve v]

Dear Phidot

I am involved in estimating recruiment rates in a population of guillemots (common murres) in the UK. Initially we adopted a multi-state approach, but subsequently have faced a raft of problems, mainly connected with problems of parameter estimation, but also issues of managability when trying to investigate cohort effects (the latter issue not being resolved whether using M-Surge or MARK).

For this reason a simpler approach appears to be to revert to Roger Pradels (1996 & 1997) approach of reversing capture histories and estimating seniority probabilities. However I do recall some debate in the literature between Schwarz/Arnason and Frederiksen/Pradel about the potential biases associated with this method. I therefore wondered if anyone could offer a current view on whether this method is appropriate or not? I ask this particularly in light of the current advancement in multi-state approaches.

Very many thanks in advance

Steve Votier

[cschwarz@stat.sfu.ca]

Both approches are equivalent in that you will get the same answer to the same question. However, sometimes the answers will look different because you are estimating slightly different quantities. For example, suppose you are interested in the proportion of animals that first start to breed at each age . Should this be conditional upon having bred or conditional upon simply being alive? An analogy would be trying to estimate the proportion of women who have a first child at various ages in human populations -- what do you do with people who don't have children? Should they be included or not included in the denominator of the ratio?

As both the AS and FP approaches are equivalent, they make the SAME CRITICAL ASSUMPTION about how animals are selected for initial marking. UNLIKE the ordinary CJS models that condition upon first capture and so the process that captures animals is relatively unimportant, any approach that tries to estimate recuitment MUST assume that animals that are captured for the first time are a random sample from the population of interest with probability of capture equal to the propability of recapture of previously marked animals.

Estimating population size is difficult and is severly affected by heterogenity in catchability; estimating population growth rates (lamda) is less sensitive to heterogeneity (the biases tend to cancel out). I haven't investigated the sensitivity of absolute recruitment vs relative recuitment to heterogeneity in catchability.


Just because you collected data for a CJS model, doesn't imply that reading the histories backwards (as in the Pradel odels) or using the data for a Jolly-Seber approach (as in POPAN models) makes the study valid.

So... before going too far along this road, please have a good look at your study design and think about how animals are initial captured and marked....

Carl Schwarz.

P.S. to toot my horn...
Schwarz C.J. (2001) The Jolly-Seber Model: More Than Just Abundance. Journal of Agricultural, Biological & Environmental Statistics, 6, 195-205.
is where I talk about the equivalence of the AS and PF approaches for several cases.

[Morten Frederiksen]

To follow up on Carl's comments: estimating age-specific recruitment in long-lived organisms with a prolonged pre-breeding phase (such as guillemots/murres) is fraught with conceptual and technical problems. To start with, you need to define exactly what evidence you need to say a bird has recruited. Is presence at the breeding site (breeding ledge for guillemots) sufficient, or should breeding be confirmed by the presence of e.g. an egg? In any case, you need to apply your criterion not just to the first breeding record, but to all subsequent records as well. This follows from the fact, as mentioned by Carl, that both the Arnason-Schwarz and the Pradel models don't condition on first capture. Note also that the Pradel model requires the assumption of equal survival of breeders and non-breeders of the same age to allow calculation of age-specific proportions of breeders.

In my opinion, a multi-state approach is more logical for estimating recruitment, although the technical problems aren't fully resolved yet. Age- and state-specific survival and transition probabilities allow all derived parameters to be estimated unambiguously. A further strength of this approach is that you can define more than two states if needed, and thus model recruitment as a gradual process rather than an immediate transition from unobservable pre-breeder to established breeder. This way you can use data from pre-breeders observed at the colony, instead of discarding them as I assume you're doing at present. We have recently employed such an approach for another seabird data set - results to be published soon.

Morten

[cooch]

In followup to Morten's comments, and at the risk of appearing completely self-serving, you might also want to look at

Cam, E., E.G. Cooch, & J-Y. Monnat. (2005) Earlier recruitment or earlier death? On the assumption of homogenous survival rates in recruitment studies. Ecological Monographs, 75, 419-434

The paper compares a number of different methods (AS, reverse-recapture, multi-state) - specifically addressing the question of bias if the assumptions of 'homegenous survival rates' (i.e., breeders and pre-breeders having the same survival rate) are violated.