M'(t) = transition matrix for immature fish;

    M"(t) = transition matrix for mature fish;

    m(t) = maturation matrix at time t,

where m(t) is a diagonal matrix with diagonal elements equal to the maturation rates by region for time step t and all other elements = 0. In most cases I suspect that at any time t, the elements of m(t) will be assumed identical, implying that the maturation process is the same over all regions.

To simplify, assume that immature fish do not migrate during the modeling period, and thus M'(t) = I (the identity matrix). If we further assume that mature and immature fish have the same survival and harvest matrices (in practical terms this probably means assuming they have the same size, vulnerability to gear, feeding behavior, etc), we can write the SSM as:

    n'(t) = [I - m(t)] S(t) n'(t-1)

    n"(t) = M"(t) [S(t) n"(t) + m(t) S(t) n'(t)]

    c(t) = H(t) [n'(t) + n"(t)]
   
In considering how to model the maturation process, I see three key parameters: (1) what is the total maturation rate for the given year--15% ? 75% ?; (2) when is the peak maturation date--the date on which the most immature fish become mature fish--Julian day 156?, 275?; and (3) over what time range does the maturation process continue--two weeks?, two months?.

If one assumes that the maturation process is independent of region (ie for any given time t, the diagonal elements of m(t) are identical) and fixes one or two of the parameters mentioned above (based on other biological information), it seems that the maturation process could be modeled with only one or two additional parameters to estimate.

Is this feasible?

Other ideas?