# 8.7 INDIVIDUAL GROWTH IN LENGTH AND WEIGHT

(3.4)

GROUP I

The parameters of the von Bertalanffy length growth equation of the stock of European anglerfish (Div. VIIIc and IXa of ICES), Lophius budegassa, were estimated as (Duarte et al., 1997):

Asymptotic length = 101.69 cm
Coefficient of growth in length = 0.08 year-1
Theoretical age, when the length is zero = -0.2 year

1. Calculate the theoretical length corresponding to the age 3.84 years.

2. Calculate the length at the beginning of the ages 1 to 12 years.

3. Calculate, for each of the above mentioned ages, the central length.

4. Represent, graphically, the Bertalanffy curve of growth in length for this stock.

GROUP II

Using the growth parameters given in Group I:

1. Calculate the length that corresponds to each age interval between 1 and 12 years as being the simple arithmetic mean of the length at the beginning and at the end of each class.

2. Calculate the mean length in each age for the same interval from 1 to 12 years accordingly to the von Bertalanffy model.

3. Compare the lengths obtained in 1) with those obtained in 2) and with the central values in each age of the interval, calculated in Group I-3.

GROUP III

The data presented in the following table represents the mean length (cm) by age (years) obtained from direct age reading of individuals of the stock of European anglerfish, Lophius budegassa, (Div. VIIIc and IXa).

 t Lt (cm) T Lt (cm) 1 9.2 7 44.4 2 16.5 8 49.0 3 22.9 9 52.3 4 28.8 10 55.0 5 34.7 11 60.8 6 38.6 12 63.4

Based on this data the parameters of the growth equation were estimated according to the Gompertz model as being:

Gompertz: L = 73.7 cm; k = 0.22 year-1; t* = - 2.76 year
(t* is the age corresponding to L = 1 cm)

1. Represent, graphically, the observed values.

2. Calculate, for the interval 1-12 years, the values of the length at the beginning of each age, according to the Bertalanffy growth model and draw the corresponding growth curve.

3. Calculate, for the interval 1-12 years, the values of the length at the beginning of each age, according to the Gompertz growth model and draw the corresponding growth curve. Determine the inflection point of the curve.

4. Say which growth model you consider more appropriate for this case and justify your answer.

GROUP IV

The data presented on the following table concern the stock of European anglerfish Lophius budegassa (Div. VIIIc and IXa).

Table of individual weights by length class, taken from the samples of European anglerfish, Lophius budegassa collected by IEO and IPIMAR in 1994.

 Li (cm) Wmeani (g) n Li (cm) Wmeani (g) n 20- 129 3 50- 1685 28 22- 163 2 52- 1896 30 24- 219 4 54- 2107 24 26- 265 14 56- 2345 41 28- 320 8 58- 2569 41 30- 397 10 60- 2848 32 32- 486 9 62- 3126 35 34- 545 57 64- 3407 28 36- 664 60 66- 3700 19 38- 773 61 68- 4056 23 40- 890 58 70- 4411 17 42- 1027 64 72- 4764 13 44- 1122 56 74- 5203 8 46- 1334 50 76- 5587 4 48- 1503 37 78- 5982 3

The mean of the observed weights and the number (n) of individuals, are indicated for each length class.

Based on this data, the parameters of the weight-length relation were estimated for this stock as:

a = 0.021
b = 2.88

1. Calculate the theoretical weight for each length class.

2. On a graph, plot the observed and the theoretical weights against the length classes.

3. Suppose you want to use the weight-length relation, with b = 3 (the constant estimated for this relation being a = 0.013). Calculate, for this case, the theoretical weights for each length class. Compare these values with the theoretical weights estimated in 1).

4. Using the results obtained up to now, write the Bertalanffy growth equation, in weight, for this stock.