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 "Sizebased models=agebased ones a growth in size curve, or Agebased models =sizebased ones +a growth in size curve." should actually read "Sizebased models=agebased ones +a growth in size curve, or Agebased models =sizebased 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 sizebased models in place of age based models", I would still say, as shown in my last message, that sizebased models are equivalent to agebased 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 sizebased 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 sizebased model. The fact that one can do without a growth curve for some sizebased 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 agebased models must be divided, in the sizebased 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 sizebased 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 sizebased models are the same as agebased ones." > >For a species that cannot be aged, there is no question about using sizebased >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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