Step 1: Understanding the Concept:
Fish life-history strategies are often categorized along a continuum. K-strategists (long-lived, slow-growing) and r-strategists (short-lived, fast-growing) have distinct growth and mortality parameters that are mathematically linked.
Detailed Explanation:
Analysis of Statement (I): According to the von Bertalanffy Growth Function (VBGF), the parameter $K$ represents the curvature or the rate at which a fish approaches its maximum length ($L_{\infty}$). Long-lived species (like sharks or sturgeons) typically have very low $K$ values, meaning they grow slowly and take many years to reach their asymptotic length. Thus, Statement (I) is correct.
Analysis of Statement (II): Natural mortality ($M$) is closely related to longevity ($T_{max}$). Biologically, a species that lives a long time must, by definition, have a low rate of death from natural causes (predation, disease, old age) per unit of time. If a fish had a high natural mortality rate, it would rarely reach an old age. Empirical formulas, such as Pauly's $M$ equation or Hoenig's model, demonstrate that $M$ is inversely proportional to longevity. Therefore, fishes with high longevity have low natural mortality rates. Thus, Statement (II) is false.
Step 2: Final Answer:
Statement (I) is true while Statement (II) is false.