Fig 1.
Trajectories of various rates of reproductive energy allocation and somatic growth.
Variations in the rates of reproductive energy allocation (a and b) and somatic growth (c and d) with different values of q (a and c) and τ (b and d) using the present function (Eqs 13 and 14). Values of q and τ are shown in the graphs, while values for the other parameters are fixed as = 200, r = 1, τ = 2, and t0 = 0 for (a) and (b); and
= 200, r = 1, q = 0.4, and t0 = 0 for (c) and (d).
Table 1.
Designated titles of the parameters.
Fig 2.
Estimated growth curves using the ‘standard fit’.
(a) Female willowy flounder (Tanakius kitaharae) and (b) female Alaska pollock (Gadus chalcogrammus) are shown.
Fig 3.
Estimated growth curves using ‘shared parameter fits’.
Generalised q-VBGF are fitted using ‘shared parameter fits’ between males and females of (a) the willowy flounder (Tanakius kitaharae) and (b) the Alaska pollock (Gadus chalcogrammus), among males and females of four decadal cohorts of (c) the Antarctic minke whale (Balaenoptera bonaerensis), and among male and female groups with different terminal instars for (d) the snow crab (Chionoecetes opilio) using the generalised q-VBGF. For the snow crab, the solid squares represent the average size at each instar, and the solid squares with a black asterisk on the left side represent the average size at the terminal instar for each group. The blank squares represent the size at age after terminal moulting, and the dotted line represents the fitted growth curve in the period with repeated reproductions, during which no further moulting or somatic growth occurs.
Fig 4.
Estimated growth and reproductive curves using the ‘simultaneous fit’.
Shown are the estimation of somatic growth and reproductive allocation in gonad weight using ‘simultaneous fit’ for male (a and b) and female (d and e) Alaska pollock (Gadus chalcogrammus). The standard errors are compared for each parameter among the ‘standard fit’, ‘simultaneous fit’, and ‘simultaneous fit’ with adjusted number of samples by the generalised q-VBGF for (c) male and (f) female Alaska pollock. The standard errors of t0 show the actual values and the standard errors of ŵ, r, q, and τ show the actual values divided by the estimated parameter values for standardization.
Fig 5.
Relationship between estimated parameter values.
(a) The maturation timing parameter τ and growth indeterminacy exponent q, and (b) τ and q*r (q multiplied by growth exponent r) are shown. The solid curve in (b) is a hyperbola fitted to the plots. Arrows indicate axes for the r/K selection theory (horizontal) and determinate–indeterminate growth continuum (vertical).
Fig 6.
Role of five parameters to depict growth curves, in which growth rates change between pre- and post-maturation.
As an example of the five parameters, those of the generalised q-VBGF are shown. The pair of arrows indicates that each parameter in the box can adjust the growth trajectory in the pointed direction.