Statement (I) is true: Under the von Bertalanffy growth model, long-lived fishes (K-strategists, such as sturgeons and deep-sea rockfishes) have low growth coefficients ($K$) and grow slowly over decades to approach their asymptotic length ($L_\infty$). Statement (II) is false: In life-history theory (and Beverton-Holt invariants), longevity is inversely related to natural mortality rate ($M$). Long-lived species have low natural mortality rates (low $M$), whereas short-lived species (like anchovies or squids) exhibit very high natural mortality rates ($M$).

Option analysis:

• Both true: Incorrect because Statement II is false.
• Both false: Incorrect because Statement I is true.
• Statement (I) is true but Statement (II) is false: Correct assessment.
• Statement (I) is false: Incorrect because Statement I is true.

The relationship between age ($t$) and length ($L_t$) in fishes is described by the von Bertalanffy Growth Function (VBGF):

This equation generates an asymptotic curve where length increases with age and approaches an upper theoretical boundary (the asymptotic length, $L_\infty$) at older ages.

Option analysis:

• Fishing effort and yield: Gives a parabolic (dome-shaped) Schaefer curve.
• Age and length of fish: Correct, follows VBGF asymptotic growth trajectory.
• Fishing effort and CPUE: Linear declining relationship in the Schaefer model.
• Cushing's fish stock recruitment relationship: Power function curve, not an asymptotic plateau.