Question

L(infinity) to 0.2335 31.48 -1.86 VGBF 2 1 4 6 8 10 12 L

Describe this Von Bertalanffy growth curve (age Vs. length of fish); what does it show and interpret results

Answer 1

The Von Bertalanffy Growth Equation:

Von Bertalanffy derived this equation in 1938. It is the most widely used growth curve and is especially important in fisheries studies.

dL/dt = k(L(infinity) - L)

L(t) = L(infinity)(1-e^-k(t-t0))

L(infinity) is maximum length of the animal. It is the assumptote of model average length at age. It has meaning in fish populations where mortality is low enough to allow fish to reach an age at which the mean length(virtually) ceases to increase.

L(infinity)=31.48 =>This represents the maximum average length of the fish in its lifetime.

k measures the exponential rate of approach to the asymtotic size. Second the value e^-k is the fixed fraction by which the annual growth increment is multiplied each year.

k >0 => the quantity e^-k is a decimal. Thus, each growth increment growth increment indicating that growth slows as the fish gets older.

k = 0.2335 => rate constant with units of reciprocal time.

The estimation and interpretation of t0 is further complicated by the fact that the value of to is generally an extrapolation.

t0 is the time at length=0, not the length at time=0. This is a common misconception. As such, it should always be negative, as fish have length at hatch(i.e. length at time t=0 is positive)

t0 = -1.86 => you truly mean that the length at time t=0 is negative, then there's a problem. One solution is to add data for size at birth using values from the literature and fix the size at time t=0 at birth.

The negative birth length problem could arise from more than one case. The true growth pattern of the species is not perfectly matched by the abstraction of the VBGR.

Negative t(0) meaning that very young fish grow faster.

L(infinity), k and t(0) are highly related k depends upon values of the L(infinity) and t(0). k larger for the correlation of age and the length of fish.