ebuhle
commented
3 years ago From https://github.com/kzaret/RQ1v2_PIUVestab/issues/7#issuecomment-813103062:
So they're even-aged because they established following fire, and they're dead because of a subsequent fire?
Yes. It seems that P. uviferum has multiple regeneration strategies: the tree can (if the conditions are right [whatever that means]) establish after intense or catastrophic disturbance, forming even-aged cohorts, or it can establish continuously under a fairly closed canopy with individuals undergoing growth release as canopy gaps are created by the death of older/larger trees; oh yeah, and new stems can form from adventitious roots.
This makes me wonder about the possibility of including some sort of "intervention" in the process (or maybe observation) model to effectively truncate the time series preceding catastrophic disturbance events such as fires. This would obviously be easier if we knew the dates of such events (which we don't in general, right?), although in some cases it is possible to estimate the change-point. (RIP, Rowland S. Howard.)
Thoughts on the wisdom or feasibility of such an approach?
OK, time to fit the elephant.
Let's start at a very high level. The PIUV dendrochronology data set is, fundamentally, a present-day snapshot of the age structure of living (and some dead) individuals in the population at a given site. The goal is to reconstruct the historical time series of recruitment (aka establishment) and relate it to hypothesized environmental drivers.
This problem closely resembles the one that age-structured fisheries stock assessment models are designed to handle. This vast literature has innumerable variations, but one way in which the data typically used in age-structured stock assessments depart from our dendrochronology data is that the samples of age composition are often collected on an annual (or at least recurring) basis. Furthermore, stock assessments typically have other data types available (e.g. time series of total biomass and harvest) to help statistically constrain the model's parameters. In particular, one of those key parameters about which little is known directly is the annual natural (i.e., non-fishery) mortality rate, conventionally denoted M_t. Again, speaking generally and intuitively, information about M_t comes from the interannual fluctuations in age structure along with parallel fluctuations in the overall stock size. Even with these rich time-series data, stock-assessment modelers often find it necessary (or at least expedient) to make ecologically dubious simplifying assumptions about natural mortality, for example that it is constant and/or unrelated to stock size.
To make this slightly more concrete, consider a rather unusual age-structured stock assessment for geoduck in British Columbia. This study system has some striking similarities to our PIUV problem: the density and age structure of a long-lived species are sampled in a one-time snapshot (at all but a handful of sites), and those age-composition samples along with recorded annual harvest are used to reconstruct historical recruitment time series. I mention this paper not because it is a particularly sophisticated or state-of-the-art model (it's basically a form of "virtual population analysis", an old-school method with many known drawbacks) but because it highlights the crucial role of natural mortality. The authors have to resort to the literature for "reasonable" ranges, which they then apply (treated as constant, i.e. M_t = M) to the data to reconstruct historical recruitment. As you can see, even the fairly modest difference between M = 0.016 vs. M = 0.036 produces rather dramatic differences in estimated historical recruitment, never mind the unrealistic assumption of time- and age-invariant mortality.
So the question is how to deal with natural mortality in the case of PIUV. We do have the advantage (?) of having aged dead individuals (which would be like aging dead geoduck valves), but without knowing the dates of death or rates of post-death decay it's not entirely clear how we would use this information. Moreover, I'd imagine the natural mortality rate has varied considerably by age and through time due to, e.g., fire. Then there's the issue of accounting for harvest (if any), a crucial input to stock assessments that (AFAIK) we do not have.
I don't have any clever solutions for this problem, but I wanted to raise and contextualize it so that we can figure out how to approach it. I'll note, again, that this issue is not unique to the fancy modeling approach we're contemplating now; it would apply equally to any methodology for reconstructing historical recruitment from contemporary age structure.
Thoughts?