魚類の老齢期生長の解析および繁殖終了年齢と寿命の推定

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With special considerations of the senescence, the growth in fish population is analysed in relation to essential components of the life history, that is, ages at end of reproductive span and life span. Based on the biological characteristics of senescence, the growth model is given by a quadratic parabola equation, G(t)=a0+a1(t-tM)+a2(t-tM)2 in t ?? tM, where G(t)is a growth measure at age t;tM, age at end of reproduotive span, i.e. age of intersection between two growth phases of stable and senescent; and a0, a1, and a2 are constants. According to the growth continuity at age tM, constants a0, a1, and a2 can be expressed by the parameters k and t0 of von Bertalanffy's equation for stable growth phase (t ?? tM). a0=1-e-k(tM-t0), a1=ke-k(tM-t0), a2=(-k2/2)e-k(tM-t0). In the senescence, parameters about age can be expressed as follows: Age at end of reproductive span: tM=(1/k)ln |1-ekt0|+t0, Ecological life span: tλ=tM+1/k (A), and Physiological life span: Tλ=tM+(1/k)[1+√2ek(tM-t0)-1] (B). When the senescence finishes at tλ(type II), the life span may be estimated by equation (A), and when it does at Tλ (type II), the life span may be estimated by equation (B). In the case of type II, if t>tλ, the growth is instabilized, and sometimes the growth rate dG(t)/dt becomes minus.
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