REPLY Age of material in a stock (SD6428)

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Posted by  <richard.dudley at attglobal.net>

Yes....  I neglected to mention _why_ I am interested in this question: How
can we determine the mean time material remains in a stock?

In my particular case I am working on a fishery model.  Many fishery models
are cohort models, but some are single stock biomass models.  While cohort
models tend to be more widely used in fisheries analysis, in some ways
single stock biomass models are more like the real world.  When fishing
takes place we are really dipping into multi-cohort mass of fish.  Also, we
often don't have sufficient data to look at cohorts by numbers and weight.  

So I'm interested in how could we better use single stock biomass models as
the basis for looking at larger fishery issues with system dynamics models.
Inflow to biomass in the single stock models is typically a constant
fraction of the biomass... although in a system dynamics model we could have
that fraction change for various reasons.

One issue is that the inflow to a stock of fish biomass can be considered as
being from two components: additions due to growth of biomass already
present, and additions due to recruitment-- that is, the addition of new
biomass in the form of new fish -- what fisheries people might call
recruitment biomass.

In a cohort model it's fairly likely that there is a relationship between
the numbers of older fish and the amount of recruitment biomass.  In the
biomass model this is less likely to be clear.  Traditional one stock
biomass models do not address this question.  In those models additions to
biomass are usually a constant fraction of biomass.  But we can partition
this fraction into two components.  (Basically I am continuing work on a
paper I presented at the New York meeting in 2003).

==> So I am interested in the relationship between the mean age of the
biomass and  the addition of new biomass due to recruitment.  There are two
feedback  issues here.  Most importantly, I think, is the fact that as the
age of biomass decreases the proportion of new biomass due to recruitment
will increase.  That is, biomass with a mean age of say 2 years will be
influenced more by an influx of new biomass and a biomass of the same size
with a mean age of say 7 years. This is particularly important if there are
fluctuations in the recruitment component of the inflow.  This is important
in fisheries because as the stock declines natural fluctuations in
recruitment additions will have a larger and larger effect.  

There is also another affect whereby the same biomass of older fish may
produce more young than that biomass made up of younger fish.  However this
is probably less of an issue than the first. 
 

Richard
Posted by  <richard.dudley at attglobal.net>
posting date  Sat, 21 Apr 2007 14:04:05 +0700