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Re: Stock Assessment models


Trevor Kenchington <[log in to unmask]>


[log in to unmask]


Thu, 6 Apr 2000 19:51:53 +0000





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Shareef Siddeek wrote:

> As a side observation, in the tropical fisheries, scientists have
> estimated the average instantaneous natural mortality for a variety of
> fish and invertebrate stocks using an established multiple regression
> equation relating natural mortality to growth parameters and
> environmental temperature. Although the multiple regression has been
> established using strictly fish data, scientists have liberally used
> this equation for invertebrate stocks as well. One reason for using this
> equation more liberally is that natural mortality is a hard to determine
> parameter for a heavily exploited stock. By applying this equation to
> any marine animal one implicitly assumes that natural mortality is
> primarily governed by growth and environment not by any other genetic
> functions. Is this assumption correct?

Excellent point Shareef.

Dan Pauly's equations (assuming those are the ones you mean) have come
in for their share of criticism but they do seem to work -- for
teleosts. I applied one of the two versions to blue greandier/hoki
(Australian continental slope species) and got a value around M=0.25,
which matched rather well with our observed maximum age (in a sample of
a few hundred aged individuals from a virgin population) that was
somewhere in the 25 to 30 years range**.

However, I could not beleive it when I first saw those equations applied
to squid. Dan used estimates of natural mortality rates from teleosts to
fit his regressions and to assume that a cephalopod (or a shark or a
cetacean) would have the same relationship between length, growth
coefficient and mortality rate is, frankly, bizarre. The physiologies
and life histories of the different phylla, or even of different
classes, make any such extrapolation far too uncertain to be reliable.

To see just how off-base this misapplication of the equations really is,
consider what length measurement one might use: I don't recall whether
Dan used fork or total lengths of teleosts (and perhaps he used a
combination -- fork lengths are usually not that different from total
ones). However, before applying his equations to squid, one would need
to choose either total length (including the tentacles) or just the
mantle lengths (which are what is normally measured). With lobsters, you
could use total length (including antennae and claws), body length
(rostrum to telson) or just the carapace length (measured either from
the rostrum or an eye socket). Each type of measurement would lead to a
quite different estimate of "natural mortality rate" and yet there is
_no_ basis for preferring one measurement over another.

I would be wary of using Dan's equations even with a teleost of
"unusual" shape, such as a Macrurid rattail. The physiology that
underlies the inter-specific (and inter-familial and inter-ordinal)
relationship is much more likely to be related to body weight than to
length. Hence any species with extreme prolongations at one end or the
other is likely to be an outlier from Dan's regression lines.

Trevor Kenchington

**The blue grenadier study was published in Aus.J.Mar.Freshw.Res. 38:
625-646 (1987) -- for anyone who wants to check whether my memory is
still holding up after a dozen years.

Trevor J. Kenchington PhD [log in to unmask]
Gadus Associates, Office(902) 889-9250
R.R.#1, Musquodoboit Harbour, Fax (902) 889-9251
Nova Scotia B0J 2L0, CANADA Home (902) 889-3555

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