Shareef Siddeek wrote:
>
> Sophisticated length based models have been developed for hard to age
> fish and invertebrate stocks. Because, the animals cannot be aged the
> underlying principle in incorporating various sub-models has been that
> of assuming length dependent vital parameters (e.g., natural mortality,
> maturity, etc.). Are we correct in assuming these vital parameters
> length dependent?

This is an important question, I think.  In my opinion, the answer is
'sometimes (most of the time?), yes.'  There is a substantial literature
on this issue.  Some good general ecological works include:

Stein et al.  1988.  Size-structured interactions in lake communities.
  Pages 161-179 in S. R. Carpenter, ed.  Complex interactions in lake
  communities.  Spriger-Verlag, New York.

Sauer, J. R., and N. A. Slade.  1987.  Size-based demography of
  vertebrates.  Annual Reviews in Ecology and Systematics 18:71-90.

LaBarbera, M.  1989.  Analyzing body size as a factor in ecology and
  evolution.  Annual Reviews in Ecology and Systematics 20:97-117.

Also, for mortality, see:

Sogard, S. M.  1997.  Size-selective mortality in the juvenile stage
  of teleost fishes: a review.  Bulletin of Marine Science 60:1129-1157.

Logan, D. T.  1985.  Environmental variation and striped bass
  population dynamics: a size-dependent mortality model.  Estuaries
  8:28-38.

In general, we might expect body size to mediate life history parameters
in organisms that have indeterminate growth, show a wide range in
body size, show size-selective predation (e.g., via gape limitation
of animals that swallow food whole), are affected by size-selective
predators, and etc.  These features apply to many (most?) fishes.

Age-structured models arise naturally as solutions to various problems,
and the context of the question implies acceptance, comfort and
familiarity with them.  I think it is important to recognize that
size-based models are not always simply convenient substitutes for
age-based models when ages cannot be determined.  In some cases, those
age-based models are, in fact, the "solutions" to governing equations
that are based on body size.  The familiar von Bertalanffy, Gompertz,
logistic, and Richards growth functions are all such examples.  For
example, we may be so familiar with the integrated form of the von
Bertalanffy growth function, which expresses body size as a function
of an exponential in age, that it is easy to overlook the fact that
its governing equation is a differential equation expressing growth
rate as a linear decreasing function of body size.

The question can be generalized to ask whether our assessment models
reflect our understanding of ecological interactions.  Given the
apparent ubiquity of size-based interactions among fishes, their prey,
and often size-selective predation by their top predator (Homo
sapiens), I think the inclusion of size-based assessments is
entirely appropriate and natural.


--
/s/ Steve Gutreuter                             U.S. Geological Survey
                           Upper Midwest Environmental Sciences Center
                                                  2630 Fanta Reed Road
http://www.umesc.usgs.gov                 La Crosse, WI 54603-1223 USA

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