Constructs a vector of natural mortality values at age using a fixed length-based allometric decline followed by a linear increase at older ages.
Usage
get_M_length(
min_age = 0L,
max_age = 30L,
age_increase_M = 25L,
m10 = 0.1,
m30 = 0.4,
mc = -1L,
length_mu_ysa
)Arguments
- min_age
Numeric scalar. Minimum model age.
- max_age
Numeric scalar. Maximum model age.
- age_increase_M
Numeric scalar. Age at which the length-based decline ends and M begins its linear increase to
m30.- m10
Numeric scalar. Natural mortality rate at age 10, which scales the length-based curve.
- m30
Numeric scalar. Natural mortality rate at the terminal age.
- mc
Numeric scalar. Length-scaling exponent for the allometric decline. The default model map fixes this parameter at -1.
- length_mu_ysa
Numeric array. Mean length by year, season, and age with dimensions
[n_year, n_season, n_age]. The first-year, first-season length-at-age vector is used as the fixed reference curve.
Value
A numeric vector of length max_age - min_age + 1, containing
natural mortality rates in increasing age order.
Details
From age 0 through age_increase_M, mortality follows
\(M_a = M_{10}(L_a/L_{10})^{m_c}\), using the supplied mean length for
each age and the age-10 length as the reference. It then increases by a
constant natural-scale increment to equal m30 at max_age,
matching the older-age transition in get_M(). The age range must
contain age 10, the reference lengths must be positive and finite, and
age_increase_M must lie between age 10 and max_age. These
requirements are part of the caller's data contract and are not checked
by this low-level RTMB helper.
References
Lorenzen, K. (2000). Allometry of natural mortality as a basis for assessing optimal release size in fish-stocking programmes. Canadian Journal of Fisheries and Aquatic Sciences, 57, 2374–2381. doi:10.1139/f00-215
Lorenzen, K. (1996). The relationship between body weight and natural mortality in juvenile and adult fish: a comparison of natural ecosystems and aquaculture. Journal of Fish Biology, 49, 627–642. doi:10.1111/j.1095-8649.1996.tb00060.x