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 offbase 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 interspecific (and interfamilial and interordinal) 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: 625646 (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) 8899250 R.R.#1, Musquodoboit Harbour, Fax (902) 8899251 Nova Scotia B0J 2L0, CANADA Home (902) 8893555
Science Serving the Fisheries http://home.istar.ca/~gadus
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