Yongshun Xiao wrote:
> "Size-based models=age-based ones +a growth in size curve, or
> Age-based models =size-based ones -a growth in size curve."
> 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.
Yongshun is mathematically correct to say
"Age-based models =size-based ones - a growth in size curve,"
> but in reality when we want to use age based model, we do not formulate
> size-based model first and then deduct the growth curve. One should not
> blindly hold on to mathematical equality without considering biological
> reality. It is mathematically correct to say, if you take 4 from 2, you end up
> with -2, but when you catch 4 fish in a stock containing only 2 fish you will
> end up with 2 fish taken from another stock, if it exists. This is a minor
> comment, but make sense in explaining the next part.
If natural mortality is a function of age, generally it will behave as a step
function, changing at each step of age. Therefore, for a range of length within
an age group, it will have the same value. On the other hand, if natural
mortality is to change as a function of length, then it will change continuously
within an age group, unless the length function is kept as a step function of
age. In that case, natural mortality is assumed to be a function of age.
Therefore, I imagine a difference in the outcome between the two biological
concepts, although one can mathematically transform one to another to get what