# FISH AGE AND GROWTH CASE STUDY

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## Figure 4: Back calculated mean length for age of each fish.

Figure 1 is the Peterson length frequency histogram and it shows the lengths present in the sample of dace caught at Fortesque on the River Exe. The five arrows shown on the Peterson length frequency histogram indicate the age groups. It can be concluded that the younger a fish is, the faster the rate of growth and that the fish increase in length as they get older (Table 1, Figure 4). This means that the rate of growth decreases as the fish gets older. A technique is used to back-calculate, where a set of measurements made on a fish at one time to infer its length at an earlier time or times is used. The dimensions of marks in some hard parts of the fish (fish scales) together with its current body length are used to estimate the fishes length at the time of formation of each individual mark (Francis, 1989).

The log length against the log weight (Figure 3) shows that as the length of each fish increase so does the weight, and vice versa.

Figure 5: Ford-Walford plot used to calculate values of Lâˆž and K. The dashed line shows the 45Â° line and the solid line is the line of best fit.

Figure 6: Validation graph to test the reliability of the value Lâˆž.

By using the Ford-Walford plot (Figure 5) you can calculate the values of Lâˆž and K. Lâˆž is the maximum size or asymptotic length that the fish can reach regardless of age (Weatherley et al. 1987) and can be calculated using the following the following equation: Lâˆž =(intercept)/(1-slope). K is the growth coefficient and represents the mean values for growth and is calculated using the following equation: K = - (LN(slope)). On the graph (Figure 5) Lâˆž can be seen as the point at which the 45Â° line intercepts with the line of best fit. We calculated Lâˆž to be 286.32 and K was calculated to be 0.265, meaning that to reach the maximum length, the fish must grow at an average rate of 0.265mm per year.

Loge is calculated by using the equation: Loge = ln(Lâˆž-Lt). Lt is the back calculated length. If the Loge plots as a straight line (Figure 6) then the value for Lâˆž is accurate.

1

64.2

0.0394

67.09

2

120.9

-0.0762

117.99

3

161.6

-0.1458

157.05

4

182.7

0.1519

187.04

5

202.1

0.3659

210.05

6

229.8

-0.1483

227.71

7

242.5

-0.1162

241.26

## Â

Table 2: Estimation of to for each age group, the to value, and the calculated Von Bertalanffy growth.

Figure 7: Von Bertalanffy growth curve.

To represents the age at which the fish is equal to zero length in the von Bertalanffy equation (Cowx et al. 2007). We calculated the average value for To to be 0.0101 (Table 2). This means that at zero length, the dace caught at Fortesque were 0.0101 years old. The von Bertalanffy growth equation is as follows: To = t + [(1/k)*(loge((Lâˆž-Lt)/Lâˆž))] (Table 2, Figure 7).

1

64.2

64.6

61.6

2

120.9

106.8

105.2

3

161.6

144.1

138.6

4

182.7

168.9

174.2

5

202.1

186

188.5

6

229.8

197.4

205.5

7

242.5

203

8

9

## Â

Table 3: Back calculated data for Dace in the Exe catchment.

Figure 8: Back calculated growth curve for the Dace caught at Fortesque, River Creedy, Trews Wier, and Stoke Canon.

286.3192

0.264639

0.010105203

226.0046

0.334384

-0.037690196

255.9514

0.270311

-0.002893553

## Stoke Canon

239.3956

0.345105

-0.058109089

Table 4: Values for Lâˆž, K, and the average To value calculated for the dace caught at the four sites.

Both the back calculated data and von Bertalanffy (Table 3, Table 5) show that the Dace caught at Fortesque have the greatest length for age values and the older Dace from the River Creedy have the smallest length for age. The Dace from Stoke Cannon are similar to those at Fortesque, in that they initially have a rapid growth rate up until the age of 6 years, but then the growth rate decreases substantially (Figure 8, Figure 9). The Dace at River Creedy and Trews Weir have a similar growth rate. The oldest fish were the ones at Stoke Cannon that reached an age of 9 years old compared to the fish at the other sites, where they only reached ages of 6 and 7 years old.

1

67

66

61

2

118

112

107

3

157

144

142

4

187

167

169

5

210

184

190

6

228

196

205

7

241

205

8

9

## Â

Table 5: Von Bertaanffy growth curve data for Dace in the Exe catchment.

Figure 9: Von Bertalanffy growth curves for the samples of Dace caught at Fortesque, Creedy, Trews Weir, and Stoke Canon.

## Discussion

When it comes to the growth of dace and roach there a number of different factors that could affect the rate in which they grow and their overall size. These factors include the availability of food, water temperature, their genetic make-up, inter and intraspecific competition, and pollution (Cowx & Harvey, 2007). At the lower part of the catchment it drains rock mainly of the impermeable, but softer, Permian New Red Sandstone series. The formation of this underlying rock has a significant effect on the rivers physical and chemical characteristics. Whereas, the upper Exe catchment is mainly impermeable Devonian Old Red Sandstone, Millstone Grit, and Culm Measures.

The main factor that could be affecting the variation in size could be the pollution produce from the Mills situation upstream from Stoke Cannon on the River Culm. The only fish that would not be affected by the Mills would be those at Fortesque as although Creedy and Trew's Weir are on the River Exe, they still lie downstream from the Mill's. The reason the pollution has an impact is because it causes 'sewage fungus' which can colonise all submerged surfaces and affects the normal river biota. At the site of sewage fungus the organic carbon content is high and the dissolved oxygen concentration is low (Curtis, 1969). This is because of the higher demand for oxygen from bacteria and fungus which then deprives it from other areas.