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Hello from Australia,
It is only me. Before commenting Shareef's comments, I must apologize for
having not made my point clear and for having left you to draw some of the
conclusions.
I must also apologize for a typo in my previous message, where
"Size-based models=age-based ones -a growth in size curve, or
Age-based models =size-based ones +a growth in size curve."
should actually read
"Size-based models=age-based ones +a growth in size curve, or
Age-based models =size-based ones -a growth in size curve."
But, I was just about to have a pig swill at a nearby bar with some of my
colleagues and you can, of course, imagine my feeling then!
Shareef is correct in saying that my comments did not answer the basic
biological question: whether natural mortality is age or length dependent.
The conclusion that I would wish you to draw from my previous message is
that, if natural mortality is age dependent, then it must be length
dependent, or vice versa.
However, to his comment on "For a species that cannot be aged, there is no
question about using size-based models in place of age based models", I
would still say, as shown in my last message, that size-based models are
equivalent to age-based models. This could be proved in many other ways. For
those who have learnt a bit of calculus, for example, it is just a matter of
changing the variable of integration. Therefore, there is no doubt that if
one uses a size-based model, the growth curve gets in the way. It is not
affected by whether one can age the fish or not. Thefore, one cannot escape
from ageing fish by formulating a size-based model. The fact that one can do
without a growth curve for some size-based models implies that one should
rethink about the model structure.
Just in case some colleagues need an escape from this piece of sobering
news, notice that the mortality Z(t) in age-based models must be divided, in
the size-based model, by the rate of growth in an average individual's
size., or Z(t)/f(L(t)), as in my previous message. One may call the quantity
Z(t)/f(L(t)) the size-based mortality. As mentioend in my previous message,
one can assume f(L(t))=1. However, such an assumption has a nasty
consequence. It means that, for one unit of increase of age t, there is one
unit of increase in size L(t). In other words, if you plot size L(t) versus
age t, you get a 45 degree straight line, the intercept of which is the size
at age t=0. If one is happy with this straight line, then it is fine. But,
the overwhelming evidence points to the contrary. In fact, there are so many
growth curves out there, few of which can be approximated by a straight
line, provided that the range of age is sufficiently large. After all, why
would one use von Bertalanffy growth curve instead of a straight line, for
example?
Hoe all these help.
Best wishes
Yongshun Xiao
SARDI Aquatic Sciences Centre
2 Hamra Avenue, West Beach
Adelaide, SA, Australia 5024
Email [log in to unmask]
Phone + 61 8 8200 2434
Fax + 61 8 8200 2481
========= Shareef Siddeek wrote=====================
-----Original Message-----
From: Shareef Siddeek <[log in to unmask]>
To: [log in to unmask] <[log in to unmask]>
Date: Tuesday, 11 April 2000 20:45
Subject: Re: Stock Assessment models
>
>I was away from my PC for a number of days, which delayed my response to
>interesting replies to my post.
>
>Yongshun Xiao wrote:
>
>> "I would think that the size-based models are the same as age-based
ones."
>
>For a species that cannot be aged, there is no question about using
size-based
>models in place of age based models. However, in your size based model
>specification, you started with an age based Z(t(s)), then integrated in
terms
>of length. What should be the mathematical function of the non predatory
part
>of the natural mortality component (assuming M not a constant) in the
numerator
>of Z(t(s))/f(L(s))? One can assume it to be either M (L) or M(t). Of
course,
>in either case, the entire integrant can be transformed into a function in
>length. But the basic biological question remains unanswered, whether
natural
>mortality is age or length dependent.
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