Question

Which one among the following is not true in relation to Von Bertalanffy plot?

• A. Estimates growth parameters are $K$ and $t_0$
• B. The plot is parabolic
• C. The time interval is need not to be constant
• D. Provides reasonable estimate of $K$ if $L_{\infty}$ input is reasonable

Hint:

Linearization of the growth model relies on a straight-line plot ($y = mx + c$). Hence, a linearized plot cannot be parabolic.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The Von Bertalanffy Growth Function (VBGF) is a mathematical model used to describe the length-at-age growth of fish.
The classic VBGF equation is:
\[ L_t = L_{\infty} [1 - e^{-K(t - t_0)}] \] where $L_t$ is length at age $t$, $L_{\infty}$ is asymptotic length, $K$ is the growth coefficient, and $t_0$ is the theoretical age at length zero.

Step 2: Detailed Explanation:
To estimate the growth parameters $K$ and $t_0$, the VBGF equation can be linearized into the Von Bertalanffy plot.
By rearranging and taking the natural logarithm of both sides:
\[ -\ln\left(1 - \frac{L_t}{L_{\infty}}\right) = K \cdot t - K \cdot t_0 \] Plotting the term \( y = -\ln\left(1 - \frac{L_t}{L_{\infty}}\right) \) against age \( x = t \) yields a straight line with a slope equal to $K$ and a y-intercept of $-K \cdot t_0$.
Because the plot is a straight line, it is linear and not parabolic.
Unlike the Gulland and Holt plot, the Von Bertalanffy plot does not require constant time intervals between samples, and it provides a reliable estimate of $K$ if a reasonable estimate of $L_{\infty}$ is used.

Step 3: Final Answer:
Therefore, the statement that the Von Bertalanffy plot is parabolic is incorrect.