Modeling thermal effect on growth of chinese shrimp, Penaeus chinensis (Osbeck)

E[OLOfiltRL mOO|LLInfi ELSEVIER

Ecological Modelling 80 (1995) 187-196

Modeling thermal effect on growth of chinese shrimp, Penaeus chinensis (Osbeck) Sha Miao a,,, Shunchi Tu b a Department of Aquaculture, National Taiwan Ocean University, Keelung 202, Taiwan, ROC b Department of Mathematics Division, National Taiwan Ocean University, Keelung 202, Taiwan, ROC

Received 4 August 1993;accepted 16 February 1994

Abstract

A couple of experiments were conducted to estimate the optimal temperature effect on growth of Chinese shrimp (Penaeus chinensis). The equation describing growth-temperature relationship derived from the first experiment

with temperature ranging from 16° to 31°C was found linear as the following: G = -0.005667 + 0.001103 T, where G and T are daily growth rate and temperature, respectively. The second experiment indicated that the daily growth rate was a quadratic function of temperature at the limits of 27° and 35°C. The equation was G = -0.339587 + 0.023476 T - 0.000375 T 2. The optimal temperature in terms of maximum growth was 31.26°C. Keywords: Growth, animal; Quadratic equation; Shrimp; Temperature

1. Introduction

Chinese shrimp (Penaeus chinensis O.) is the most important species cultured in China, comprising approximately 80% of the total production (Liu, 1990). The natural distribution of P. chinensis is limited to the Asian coast from the mouth of the Pearl River in China (near Hong

* Corresponding author.

Kong) to Bohai Bay in the northern Yellow Sea (Liu, 1990; Yang, 1990). P. chinensis becomes lethargic when temperature is below 13°C and may die slowly at 3° to 4°C (Yang, 1990). In China, temperatures from 20 ° to 30°C are considered as optimal for P. chinensis (Wang, 1984; Yang, 1990; Zhang, 1990). In Korea, the optimal range is between 20 ° and 25°C (Kim, 1990; Rho, 1990). Japanese reports indicate that the optimal temperature was 24 ° or 25°C (Oka, 1964) and the growth rate may decline rapidly at temperatures

0304-3800/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0304-3800(94)00048-M

188

s. Miao, S. Tu /Ecological Modelling 80 (1995) 187-196

over 25°C (Oka, 1970). The disagreement can be clarified on two counts: upgrading system analysis and selecting an appropriate index to evaluate growth. To enhance the precision of system analysis, an applicable statistical model of orthogonal polynomial contrasts was employed (Gill, 1978; Petersen, 1985). On the other hand, comparing relative growth rate instead of absolute growth rate may avoid possible biases in growth analysis (Causton, 1983). The objective of this study was to model the temperature effect on daily growth rate of P. chinensis, and to determine the optimal temperature for growth.

2. Materials and methods

When the fixed treatments of a set are quantitative, one may characterize the form of response (linear or some degree of curvilinear) of the primary variable Y to the level of treatment imposed. Polynomial curves are convenient approximations for nonlinear relationships and are particularly easy to use in orthogonal form if the levels of treatments are equally spaced and replication is balanced (Gill, 1978; Petersen, 1985). Based on the cited optimal temperatures and available facilities, four constant temperatures of 16°, 21 °, 26°, and 31°C were selected in experiment 1. Due to no previous statistics available for replication estimate and considering the aquarium availability, we used five aquaria (replicates) for each thermal treatment. Part of Penaeus chinensis from a single batch of hatching provided by Tainan Marine Laboratory were evenly and randomly assigned to the 20 aquaria. The remaining shrimp were kept indoors in a holding tank under environmental condition. Each aquarium was of the same sizes: 60, 30, and 36 cm in length, width, and height, respectively, and stocked with a density of five shrimp per 0.18 m 2. In addition to the experimental error being more effectively reduced by increasing replication than by increasing samples per replicate (Gill, 1978), this low stocking density was to minimize the negative effect possibly caused by a higher density (Wickins, 1976; Delistraty et al., 1977; McSweeny, 1977;

Armstrong et al., 1978; Smith et al., 1978; Provenzano, 1985a,b). The room temperatures were controlled at 1 4 + I°C. To prevent the shrimp from jumping out, each aquarium was covered by a net. Illumination consisted of two fluorescent light fixtures with two 40-W tubes, each regulated to a light period from 08:00 to 20:00 h. The aquaria were filled with filtered sea water from the National Taiwan Ocean University supply system originating from the nearby coast. Under the static system, the aerated aquaria were cleaned by replacing one third of the aquarium water on a weekly basis. Salinity, pH, and dissolved oxygen were measured every 3 days. Experiment 1 started after an acclimatization of 10 days and lasted for 30 days. An orthogonal polynomial model (Gill, 1978; Petersen, 1985) calculated by the SAS software system ( S A S / S T A T , 1990) was applied to describe the experimental system as follows: G =/30 +/31T +/32 T2 +/33 T3 where T = temperature; G = daily growth rate on a 30-day basis; /30 = intercept on G axis; and /31, /32, and/33 = the regression coefficients. Variable G in the growth model represents a daily growth rate equal to I n ( W 3 o / W o ) / t . 14130 and W0 denote the observed fresh weights of P. chinensis on day 30 and day zero for a given aquarium Within a duration (t) of 30 days, respectively. Since experiment 1 did not show a temperature optimum for growth, experiment 2 was conducted immediately following the completion of the first experiment at three selected temperatures (27 °, 31 °, and 35°C). The replication in experiment 2 was determined to be five aquaria for each thermal treatment providing MSE = 0.00005147 (Table 2)with statistical power of 0.94 at a = 0.05 (Tiku, 1967; Gill, 1978). The room temperatures were now controlled at 25 + l°C. A growth model in terms of temperature for experiment 2 was as follows: G =/30 +/31T

+/32T2"

The initial fresh weights of P. chinensis ranged from 0.23 to 0.46 g with a mean of 0.327 g and a standard deviation of 0.0556 g. In experiment 2, however, the initial fresh weights ranged from

s. Miao, S. Tu / Ecological Modelling 80 (1995) 187-196 1.19 g t o 1.88 g w i t h a m e a n o f 1.504 g a n d a s t a n d a r d d e v i a t i o n o f 0.1890 g. T h e c o e f f i c i e n t s o f v a r i a t i o n in t e r m s o f initial w e i g h t f o r e x p e r i -

189

ments 1 and 2 were relatively small (17% and 12%, respectively) and therefore were acceptable f r o m b i o l o g i c a l c o n c e r n (Gill, 1978). E a c h d a i l y

Table 1 The statistics on daily growth rate and survival influenced by varied temperatures on a 30-day basis in experiments 1 and 2 Experiment No.

Temperature (°C)

Measured variable a

Statistics on five aquaria (replicates) Minimum Maximum Mean

1

16

G S G S G S G S

0.0059626 0.80 0.0098308 0.80 0.0181972 1.00 0.0198793 1.00

0.0213697 1.00 0.0262122 1.00 0.0364347 1.00 0.0370942 1.00

0.0123049 0.96 0.0156641 0.96 0.0256660 1.00 0.0273488 1.00

0.0064557 0.08944 0.0071567 0.08944 0.0069841 0 0.0080118 0

G S G S G S

0.0118927 0.80 0.0223044 1.00 0.0201395 1.00

0.0282752 1.00 0.0340141 1.00 0.0245568 1.00

0.0205617 0.96 0.0273617 1.00 0.0221475 1.00

0.0059501 0.08944 0.0049156 0 0.0018726 0

21 26 31 2

27 31 35

Standard deviation

a G is daily growth rate computed by G = ln(W30/Wo)/t, where W0 and W30 are total body weights of Chinese shrimp for any given aquarium on days zero and 30, respectively, and t = 30 days. S is survival rate computed by N30/No, where N o is the number of shrimp being stocked in each aquarium on day 0 and N30 is the number of shrimp survived on day 30.

Table 2 Analysis of variance on daily growth rate influenced by temperatures in experiments 1 and 2 Experiment No.

Source of variation

df

Sum of squares

Mean square

F-ratio

P>F

1

Total Temperature (T) Error

19 3 16

0.00164286 0.00081941 0.00082345

0.00027314 0.00005147

5.31

0.0099

Total Temperature (T) Error

14 2 12

0.00037887 0.00012657 0.00025229

0.00006329 0.00002102

3.01

0.0872

2

Table 3 Analysis of variance on survival influenced by temperatures in experiments 1 and 2 Experiment No.

Source of variation

df

Sum of squares

Mean square

F-ratio

P>F

1

Total Temperature (T) Error

19 3 16

0.0720 0.0080 0.0640

0.00267 0.0040

0.67

0.5847

Total Temperature (T) Error

14 2 12

0.03733 0.00533 0.03200

0.002667 0.002667

1.00

0.3966

2

190

S. Miao, S. Tu /Ecological Modelling 80 (1995) 187-196

Table 4 Sequential test of polynomial temperature effect on daily growth rate for experiments 1 and 2 Experiment No.

Source of variation

df

Sum of squares

Mean square

F-ratio

1

Temperature Linear Deviation from linear

3 1 2

0.00082 0.00076 0.00006

0.00027 0.00076 0.00003

5.31 15.20 0.60

0.0099 < 0.0025 N.S. b

2

Temperature Linear Quadratic

2 1 1

0.00013 0.0000063 0.00012

0.00006 0.0000063 0.00012

3.01 0.30 5.71

0.0872 N.S. b < 0.05

a

P>F

MSE = 0.00005147, with 16 df, is the divisor for F ratios in experiment 1, MSE = 0.00002102, with 12 df, is the divisor for F ratios in experiment 2. b Not significant. a

r a t i o n o f 15% o f b o d y weight was d i v i d e d into two e q u a l p a r t s which w e r e given at 09:00 a n d 15:00 h. A c o m m e r c i a l s h r i m p p e l l e t diet with a c r u d e p r o t e i n c o n t e n t n o less t h a n 38% ( m a n u f a c t u r e d by P r e s i d e n t E n t e r p r i s e s Corp., T a i w a n ) was u s e d for this f e e d i n g s c h e d u l e a n d was k e p t refrigerated.

3. Results T h e statistics on daily g r o w t h r a t e a n d survival i n f l u e n c e d by t e m p e r a t u r e s r a n g i n g f r o m 16 ° to 31°C in e x p e r i m e n t 1 a r e s u m m a r i z e d in T a b l e 1. T h e F v a l u e of 5.31 with P = 0.0099 i n d i c a t e s a highly significant t e m p e r a t u r e effect ( T a b l e 2), while a small 0.67 F - r a t i o with P = 0.5847 den o t e s no t e m p e r a t u r e effect on survival ( T a b l e 3). T h e coefficient o f d e t e r m i n a t i o n in t e r m s of growth f r o m e x p e r i m e n t 1, rl2, was 0.50, calcul a t e d by dividing 0.00081941 by 0.00164286 (the sums o f s q u a r e s shown in T a b l e 2). F u r t h e r analysis s h o w e d that, with P < 0.0025, t e m p e r a t u r e

r a n g i n g f r o m 16 ° to 31°C h a d a significant l i n e a r effect on t h e daily growth r a t e ( T a b l e 4). C o n s e quently, t h e daily g r o w t h r a t e m a y be d e s c r i b e d by a l i n e a r e q u a t i o n ( T a b l e 5) G = - 0 . 0 0 5 6 6 7 + 0.001103 T, w h e r e G is the e s t i m a t e d daily growth r a t e at a given t e m p e r a t u r e T within t h e limits o f 16 ° a n d 31°C. I n c o n t r a s t to t h e significant t e s t e d p a r a m e t e r o f l i n e a r i t y (0.001103) with P = 0.0010, t h e e s t i m a t e d i n t e r c e p t ( - 0 . 0 0 5 6 6 7 ) was statistically n o n s i g n i f i c a n t with P = 0.4133 ( T a b l e 5). T a b l e 1 also s u m m a r i z e s the statistics o n daily g r o w t h r a t e a n d survival u n d e r t h e test t e m p e r a t u r e s r a n g i n g f r o m 27 ° to 35°C in e x p e r i m e n t 2. T a b l e 2 indicates t h a t t h e t e m p e r a t u r e effect o n growth was significant at a = 0.10 with r 2 = 0.33 (dividing 0.00012657 by 0.00037887), while T a b l e 3 suggests t h a t no significant d i f f e r e n c e s o f survival existed a m o n g t h e t e s t e d t e m p e r a t u r e s ( F = 1.00 with P = 0.3966). F u r t h e r analysis i n d i c a t e d t h a t t h e daily g r o w t h r a t e was a q u a d r a t i c function (significant with P < 0.05) of t e m p e r a t u r e

Table 5 Parameter estimates and significance tests of polynomial temperature effect on daily growth rate for experiments 1 and 2 Experiment No.

Variable

df

Parameter estimate

Standard error

t-test for H0: parameter = 0

P > [tl

1

Intercept Linear

1 1

-0.005667 0.001103

0.00676715 0.00028015

-0.837 3.936

0.4133 0.0010

2

Intercept Linear Quadratic

1 1 1

-0.339587 0.023476 -0.000375

0.14959670 0.00973860 0.00015697

-2.270 2.411 -2.392

0.0424 0.0329 0.0340

s. Miao, S. Tu / Ecological Modelling 80 (1995) 187-196 b e t w e e n 2 7 ° a n d 3 5 ° C ( T a b l e 4), a n d t h e e q u a t i o n

where

was

temperatures

G

191

is t h e e s t i m a t e d

daily growth

5). A l l t h r e e t e s t e d p a r a m e t e r s G = -0.339587

+ 0.023476 T-

0 . 0 0 0 3 7 5 T 2,

different

rate

at

( T ) r a n g i n g f r o m 27 ° t o 3 5 ° C ( T a b l e

from

zero

at

were significantly

a = 0.05

(Table

5). A n

Table 6 Statistics of water quality involving dissolved oxygen (D.O., mg/1) and pH at varied temperatures on a 30-day basis for experiment 1 Days of measurement 0

3

6

9

12

15

18

21

24

27

30

Statistics of five aquaria Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD

Temperature 21°C

16°C

26°C

31°C

D.O.

pH

D.O.

pH

D.O.

pH

D.O.

pH

6.4 6.7 6.56 0.114 6.5 6.7 6.60 0.100 6.5 6.8 6.66 0.152 6.5 6.6 6.58 0.045 6.2 6.5 6.38 0.130 6.4 6.6 6.52 0.084 6.1 6.6 6.48 0.217 6.5 6.7 6.60 0.071 6.6 6.8 6.72 0.084 6.6 6.7 6.62 0.045 6.5 6.7 6.64 0.089

8.30 8.52 8.422 0.0807 8.31 8.42 8.364 0.0483 8.31 8.53 8.430 0.0851 8.49 8.51 8.502 0.0084 8.56 8.61 8.588 0.0192 8.44 8.57 8.476 0.0532 8.43 8.47 8.446 0.0152 8.32 8.35 8.336 0.0114 8.41 8.45 8.430 0.0158 8.41 8.44 8.426 0.0134 8.40 8.43 8.416 0.0114

6.6 6.8 6.70 0.071 6.4 6.9 6.70 0.187 6.9 7.0 6.92 0.045 6.5 6.7 6.56 0.089 6.5 6.7 6.64 0.089 6.5 6.6 6.58 0.045 6.5 6.6 6.56 0.055 6.5 6.6 6.56 0.055 6.7 6.8 6.76 0.055 6.5 6.7 6.60 0.100 6.6 6.8 6.68 0.084

8.38 8.47 8.420 0.0339 8.41 8.48 8.434 0.0336 8.40 8.48 8.436 0.0321 8.49 8.51 8.500 0.0071 8.55 8.64 8.618 0.0383 8.57 8.59 8.582 0.0084 8.43 8.51 8.458 0.0311 8.32 8.35 8.340 0.0122 8.41 8.47 8.424 0.0261 8.40 8.43 8.418 0.0110 8.42 8.44 8.430 0.0100

6.5 6.9 6.68 0.164 6.7 7.0 6.82 0.110 6.8 7.0 6.88 0.084 6.5 6.7 6.58 0.084 6.1 6.8 6.54 0.270 6.2 6.6 6.52 0.179 6.4 7.0 6.80 0.235 6.6 6.8 6.70 0.071 6.5 6.7 6.62 0.084 6.6 6.6 6.60 0.000 6.7 6.8 6.74 0.055

8.36 8.49 8.438 0.0559 8.40 8.44 8.410 0.0173 8.45 8.47 8.454 0.0089 8.50 8.55 8.522 0.0192 8.60 8.66 8.632 0.0217 8.48 8.59 8.560 0.0453 8.47 8.58 8.550 0.0453 8.33 8.34 8.332 0.0045 8.39 8.44 8.418 0.0192 8.39 8.48 8.456 0.0371 8.47 8.48 8.476 0.0055

6.5 6.8 6.68 0.130 6.6 6.9 6.74 0.114 6.5 6.9 6.78 0.164 6.5 7.0 6.66 0.195 6.3 6.9 6.66 0.230 6.4 6.7 6.60 0.122 6.5 6.9 6.72 0.164 6.5 6.7 6.66 0.089 6.4 6.8 6.64 0.182 6.6 6.7 6.62 0.045 6.5 6.8 6.66 0.114

8.43 8.56 8.474 0.0503 8.39 8.50 8.430 0.0436 8.41 8.57 8.470 0.0600 8.37 8.55 8.496 0.0720 8.47 8.64 8.586 0.0702 8.48 8.61 8.56 0.0500 8.52 8.63 8.582 0.0449 8.37 8.51 8.426 0.0518 8.39 8.47 8.436 0.0297 8.41 8.48 8.458 0.0277 8.46 8.51 8.488 0.0217

S. Miao, S. Tu /Ecological Modelling 80 (1995) 187-196

192

optimal temperature T = 31.26°C for the maximum daily growth rate was calculated by differentiating the quadratic function with respect to

T, equating the result to zero, and then solving for T. The predicted maximum daily growth rate of 0.0273363 was estimated by substituting the

Table 7 Statistics of water quality involving dissolved oxygen (D.O., mg/1) and pH at varied temperatures on a 30-day basis for experiment 2 Days of measurement 0

3

6

9

12

15

18

21

24

27

30

Statistics of five aquaria Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD Minimum Maximum Mean SD

Temperature 27oc

31°C

35°C

D.O.

pH

D.O.

pH

D.O.

pH

6.5 7.0 6.70 0.187 6.6 6.9 6.72 0.130 6.8 6.9 6.84 0.055 6.5 6.8 6.62 0.110 6.3 6.8 6.56 0.182 6.3 6.7 6.56 0.167 6.6 6.9 6.76 0.114 6.6 6.9 6.78 0.130 6.4 6.7 6.56 0.114 6.6 6.8 6.66 0.089 6.5 6.7 6.60 0.071

8.45 8.59 8.492 0.0581 8.42 8.51 8.456 0.0358 8.45 8.52 8.464 0.0313 8.43 8.56 8.516 0.0518 8.56 8.64 8.610 0.0308 8.51 8.59 8.550 0.0354 8.46 8.60 8.540 0.0534 8.43 8.44 8.432 0.0045 8.47 8.54 8.508 0.0286 8.49 8.57 8.534 0.0358 8.48 8.58 8.534 0.0385

6.5 6.8 6.60 0.122 6.6 6.8 6.72 0.084 6.5 6.9 6.76 0.195 6.5 6.7 6.62 0.084 6.4 6.9 6.64 0.207 6.6 6.7 6.64 0.055 6.5 6.8 6.66 0.152 6.4 6.8 6.66 0.152 6.4 6.8 6.64 0.152 6.3 6.7 6.54 0.152 6.4 6.7 6.60 0.122

8.46 8.57 8.498 0.0497 8.49 8.63 8.552 0.0634 8.45 8.51 8.482 0.0228 8.37 8.56 8.512 0.0801 8.47 8.64 8.588 0.0687 8.47 8.58 8.508 0.0444 8.53 8.62 8.568 0.0432 8.52 8.62 8.570 0.0453 8.44 8.61 8.510 0.0644 8.46 8.52 8.492 0.0277 8.44 8.60 8.534 0.0598

6.3 6.8 6.60 0.200 6.3 6.7 6.52 0.179 6.5 6.7 6.56 0.089 6.3 6.9 6.58 0.239 6.5 6.8 6.64 0.114 6.2 6.7 6.48 0.192 6.4 6.8 6.58 0.148 6.5 6.7 6.62 0.084 6.4 6.7 6.54 0.152 6.3 6.7 6.48 0.148 6.5 6.6 6.58 0.045

8.46 8.52 8.482 0.0228 8.42 8.53 8.476 0.0397 8.45 8.61 8.532 0.0585 8.47 8.61 8.522 0.0554 8.50 8.63 8.556 0.0483 8.49 8.60 8.568 0.0444 8.44 8.61 8.53 0.0612 8.44 8.57 8.496 0.0527 8.43 8.57 8.496 0.0527 8.42 8.56 8.496 0.0623 8.46 8.58 8.524 0.0483

S. Miao, S. Tu / Ecological Modelfing 80 (1995) 187-196

solved T = 31.26°C into the equation. Figs. 1 and 2 show the trends of daily growth rate under varied thermal conditions. Salinity ranged from 34%0 to 35%0 throughout the 30-day experimental periods. The water statistics on dissolved oxygen (D.O.) and pH of experiments 1 and 2 under the test conditions are summarized in Tables 6 and 7, respectively. In each 30-day experiment, the dissolved oxygen level was maintained within the range of 6.1 to 7.0 mg/l, and 8.30 to 8.66 for the pH (Tables 6 and 7).

0.040

r. 0.030

c

0.025

0.020

0.015

0.010

4. Discussion

/

0.005

. . . .

14

Thermal effects on growth of penaeid species is controversial. Taiwan, Korea and Japan researchers suggest 20°-28°C, 22°-27°C, and 25°28°C thermal optima, respectively, for kuruma shrimp (Penaeus japonicus B.) growth (Main and Fulks, 1990). Reports from the southern provinces of China showed that the redtail shrimp (Penaeus penicillatus A.) had an optimal growth as temperatures ranging from 23° to 30°C; however, it was 20° to 28°C in Taiwan (Main and Fulks, 1990). The present study indicated that the daily growth rate was proportional to temperature over the range of 16° to 31°C (Table 5 and Fig. 1). Wang (1984) found that the higher the temperature within the range of 20° to 30°C, the higher the growth rate. Yang (1990) indicated that the growth rates at 30°C were higher than those obtained at 25°C. A linear relationship between the growth of P. chinensis and temperature increasing from 1° to 25°C was noticed in Kim's report (1990). Such a linear relationship was also shown by Yang (1990) with temperature ranging from 10° to 30°C. However, Zhang (1990) indicated that 25°C was favorable for growing P. chinensis, and it did not grow well in ponds where water temperature exceeded 30°C. On the other hand, the increase in growth rate does not cease until 33°C (Yang, 1990) and apparently slows when temperature is over 33°C (Liao and Chien, 1990). Yet, the growth curve from Yang's report (1990) showed that the growth increment (in millimeters) reached its maximum at 29°C and then

193

1

16

. . . .

I

18

. . . .

I

20

. . . .

[

22

. . . .

]

. . . .

]

24

26

TEMPERATURE

( ° C)

,

,

~

1

i

28

. . . .

i

30

q

i

$ ~

32

Fig. 1. Daily growth rate (G) of Penaeus chinensis at varied temperatures in experiment 1. • represents the daily growth rate observed from individual aquaria ubjected to a given temperature.

declined over 30°C. Experiment 2 related the growth and temperature ranging from 27° to 35°C by a quadratic equation (Table 5). Moreover, the proportion of total sum of squares of Y attributable to linear regression on X is termed the coefficient of determination, r 2, which may be thought of as a measure of the strength of straight-line relationship. Depending upon the nature of the curvilinearity, one can obtain r2s of various sizes. Thus, it is not valid to conclude that if r 2= 0.00, there is "no relationship" between X and Y; rather, the conclusion should be that there is "no linear relationship" between X and Y (McCall, 1975; Gill, 1978; Zar, 1984). The coefficients of determination estimated from experiments 1 and 2 were r ( = 0.50 and r~ = 0.33, respectively. Comparing these two r2s indicated that the degree of linear relationship between temperature and growth is greater in experiment 1. Further analysis from Table 4 made a strong suggestion that such a relationship observed in experiment 1 is linear (with F = 15.20) instead of curvilinear (with F = 0.6). The scatter diagram shown in Fig. 1 agreed with the existing linearity. However, the sample scatterplot ob-

S. Miao, S. Tu / Ecological Modelling 80 (1995) 187-196

194 0 •036 0 •034 0.032 0.030 0 •028 0.026C 0.024 0 •022

i

0.020 0 •018

"

C9

0. 0 1 6 0.014 0. 0 1 2

0. 0 1 0

. . . . 25

I 27

. . . .

i 29

. . . .

~ 31

. . . .

I 33

. . . .

I 35

. . . .

I 37

TEMPERATURE (°C) Fig. 2. Daily growth rate (G) of Penaeus chinensis at varied temperatures in experiment 2. • represents the daily growth rate observed from individual aquaria ubjected to a given temperature.

served in Fig. 2 revealed a strong curvilinearity which resulted in a lower coefficient of r ] = 0.33. Table 4 further pointed out that the relationship between growth and temperature ranged from 27° to 35°C is quadratic (with F = 5.71) instead of linear (with F = 0.30). As a result, the optimal temperature in terms of maximum daily growth rate of 0.0273363 was 31.26°C (Fig. 2). The daily growth rate (G) considered here was defined as G=

W,

or, equivalently, dW - -

=GW,

dt where G is an instantaneous growth rate and W is body weight (Causton, 1983). This differential equation implies that the absolute growth at any instant of time ( d W / d t ) is proportional to body weight already attained. The solution of the linear differential equation, d W / d t = GW, is Hit = Wo exp(Gt), where ~ is weight at time t, and W0 is initial weight. Thus, by taking natural loga-

rithms on both sides, we get G = ln(Wt/Wo)/t. The absolute growth rate not only can be expressed by (Wt - W0)/(a unit time), but also can be shown as d W / d t = GW (Causton, 1983). As a result, the absolute growth rate is not very helpful to the growth analyst (Causton, 1983). For instance, chinook salmon has a higher absolute growth rate than fathead minnow at the same stage of development, and most of the differences in absolute growth rate between the two fish are due to the size difference, rather than to any difference in the constant of proportionality (G) (Causton, 1983). Therefore, one can never evaluate the growth performance among different species or at different life stages within the same species by just comparing their absolute growth rate (Causton, 1983). Consequently, we may attribute the controversy of thermal effect on growth of P. chinensis to applying absolute growth rate. P. chinensis, a eurythermal species mainly distributed in the Yellow Sea, is originated in the sub-tropical South China Sea (Wang and Ma, 1990). The annual thermal ranges of Bohai Bay, Yellow Sea, East China Sea, and South China Sea were 2°-24°C, 6°-26°C, 14°-28°C, and 18°29°C, respectively (Li, 1984). There is a difference between the experimental optimum of 31.26°C and 29°C, the upper limit of the highest annual thermal range found in South China Sea. Nevertheless, it is frequently discovered that organisms in nature are not actually living at the optimal range (as determined experimentally) of a particular physical factor (Odum, 1983). The marine hydroid (Cordylophora caspia P.) is apparently an example of a euryhaline organism that does not actually live in waters of an optimal salinity for its growth. Kinne (1956) studied this species under laboratory conditions of controlled salinity and temperature and found that a salinity of 16 parts per thousand resulted in the best growth. Yet the organism was never found at this salinity in nature, but always at a much lower salinity; obviously some condition, perhaps a biotic one, present in its natural habitat but not in the laboratory cultures, is limiting (Odum, 1983). Probably, no situation in nature can be really understood from either field observation or experimentation

S. Miao, S. Tu / Ecological Modelling 80 (1995) 187-196

alone, since each approach has obvious limitations (Odum, 1983). Consequently, field observation and analysis should always be combined with laboratory experimentation. Wickins (1976) reported that shrimps are stressed when dissolved oxygen level falls below 2.0 mg/l. The required oxygen level for the best growth of Penaeus chinensis was higher than 4 ppm (Main and Fulks, 1990). Meanwhile, the pH ranged from 8.0 to 9.0 was considered to be the best growing (Main and Fulks, 1990). The observed D.O. and pH met both requirements under the test conditions throughout the two experiments (Tables 6 and 7). Mortality was observed in few aquaria with no more than one death per aquarium in both experiments (Table 1). However, further analyses showed that there were no temperature effects on survival for both experiments (Table 3). The model, Wt= W0 exp(Gt), is a sufficient approximation if short intervals of time are considered and the main advantage for this model is the simplicity of the calculation for production and yield (Everhard and Youngs, 1981). Obviously, the daily growth rate, G, is a function of environmental temperature based on our studies. As a result, with provided temperature forecast of climatic report, we may predict the daily growth rate, thus, the yield (W~) at a given production period (t). A desired marketable size (Wt) associated with a production period (t) would further help in evaluating profitability under economic concern. However, a local daily temperature forecast may be given as an expected mean with a standard deviation due to temperature variation existing in our natural environment. Such variation among daily temperature for a given area will result in the variation among daily growth rate, and among yield and size with a mean (Wt) and a standard deviation (Sw) at a given period (t). Therefore, the coefficient of variation in terms of yield or size ( S w , / Wt) may be examined by different locations. The lower the coefficient of variation, the less risk (the more successful) where the farming business would be located (Odum, 1983; Shang, 1990). This coefficient of variation may serve as one of important indices to locate aquaculture industry in a proper geographic area

195

for national development concern. In addition, the growth is not only affected by temperature but also could be a function of farming management such as stocking density (Miao, 1990, 1992; Miao and Tu, 1993), water quality (Provenzano, 1985a,b), nutrient requirements (National Research Council, 1981, 1983), feeding management (Miao and Tu, 1994), etc. The better we understand these subsystems (how factors affecting growth in qualitative and quantitative ways), the more control we may have on our aquaculture industry. Success in raising and caring for an animal is directly related to the amount of knowledge one has concerning the way the animal functions in its environment. Temperature is part of a crustacean's natural environment. The present study clarified those disagreements of thermal effect on growth of P. chinensis by providing growth models based on temperatures ranging from 16° to 35°C. In summary, the daily growth rate of Chinese shrimp will increase linearly as temperature increases from 16° to 31°C. However, the effect of temperature ranging from 27° to 35°C on daily growth was of a quadratic pattern. Consequently, the optimal temperature for growth was 31.26°C.

Acknowledgements The research on which this report is based was financed by a grant from the National Science Council of the Republic of China under project number NSC 80-0409-B-019-08. Thanks are extended to Dr. Min-Nan Lin who assisted in providing fry.

References Armstrong, D., Chippendale, D., Knight, A.W. and Colt, J.E., 1978. Interaction of ionized and unionized ammonia on short term survival and growth of prawn larvea, Macrobrachium rosenbergii. Biol. Bull., 154: 15-31. Causton, D.R., 1983. A biologist's basic mathematics. In: A.J. Willis and M.A. Sleigh (Editors), A Series of Student Texts in Contemporary Biology. Edward Arnold Ltd., London, UK, pp. 1-216. Delistraty, D.A., Carlberg, J.M., Van Olst, J.C. and Ford,

196

S. Miao, S. Tu / Ecological Modelling 80 (1995) 187-196

R.F., 1977. Ammonia toxicity in cultured larvae of the American lobster, Homarus americanus. Proc. World Maricult. Soc., 8: 647-672. Everhard, W.H. and Youngs, W.D., 1981. Principles of Fishery Science, 2nd ed. Cornell University Press, Ithaca, NY, 349 pp. Gill, J.L, 1978. Design and Analysis of Experiments in the Animal and Medical Sciences, Vol I. Iowa State University Press, Ames, IA, 409 pp. Kim, J.H., 1990. The culture of Penaeus chinensis and P. japonicus in Korea. In: K.L. Main and W. Fulks (Editors), Proceedings of an Asian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 64-69. Kinne, O., 1956. Uber den Einfluss des Salzgehaltes und der Temperatur auf Wachstum, Form und Vermehrung bei dem Hydroidpolypen Cordylophora caspia (Pallas), Thecata, Clavidae. Zool. Jahrb., 66: 565-638. Li, K., 1984. Climatic Atlas of Chinese Offshore Areas and Northwest Pacific, Vol II. Ocean Press, China, 339 pp. (in Chinese). Liao, I.C. and Chien, Y.H., 1990. Evaluation and comparison of culture practices for Penaeus japonicus, P. penicillatus and P. chinensis in Taiwan. In: K.L. Main and W. Fulks (Editors), Proceedings of an ASian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 49-63. Liu, J.Y., 1990. Present status and future prospects for shrimp mariculture in China. In: K.L. Main and W. Fulks (Editors), Proceedings of an Asian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 16-28. Main, K,L. and Fulks, W. (Editors), 1990. The Culture of Cold-Tolerant Shrimp. Proceedings of an Asian-U.S. Workshop on Shrimp Culture, Honolulu, HI, 1989. The Oceanic Institute, Hawaii. McCall, R.B., 1975. Fundamental Statistics for Psychology, 2nd edition. Harcourt Brace Jovanovich, Inc., New York, 406 pp. McSweeny, E.S., 1977. Intensive culture systems. In: J.A. Hanson and H.L. Goodwin (Editors), Shrimp and Prawn Farming in the Western Hemisphere. Dowden, Hutchinson and Ross, Stroudsburg, PA, pp. 255-266. Miao, S., 1990. Growth and production control of golden shiner Notemigonus crysoleueas (Mitchill) by manipulating temperature and density. Bull. Inst. Zool. Acad. Sin., 29: 223-243. Miao, S., 1992. Growth and survival models of redtail shrimp Penaeus penicillatus (Alock) according to manipulating stocking density. Bull. Inst. Zool. Acad. Sin., 31: 1-8. Miao, S. and Tu, S., 1993. Modeling effect of thermal amplitude and stocking density on the growth of redtail shrimp Penaeus penicillatus (Alock). Bull. Inst. Zool. Acad. Sin., 32: 253-264. Miao, S. and Tu, S., 1994. Modeling effect of daily ration and feeding frequency on growth of redtail shrimp Penaeus penicillatus (Alock) at controlled temperatures. Ecol. Model., 70: 305-321. National Research Council, 1981. Nutrient Requirements of Domestic Animals Series: Nutrient Requirements of Cold-

water Fishes. National Academy Press, Washington, DC, 63 pp. National Research Council, 1983. Nutrient Requirements of Domestic Animals Series: Nutrient Requirements of Warmwater Fishes and Shellfishes. National Academy Press, Washington, DC, 102 pp. Odum, E.P., 1983. Basic Ecology. Saunders College Publishing, Philadelphia, PA, 613 pp. Oka, M., 1964. Studies on the bioloby of Penaeus orientalis. Bull. Fish. Reser. Univ. Nagasaki, 17: 55-67. Oka, M., 1970. The larval rearing and culture of Penaeus orientalis. Aquaculture, 2: 34-40. Petersen, R.G., 1985. Design and Analysis of Experiments. Marcel Dekker, New York, 429 pp. Provenzano, A.J. Jr., 1985a. Commercial culture of decapod crustaceans. In: A.J. Provenzano Jr. (Editor), Economic Aspects: Fisheries and Culture. Academic Press, Orlando, FL, pp. 269-314. Provenzano, A.J. Jr., 1985b. Culture of crustaceans: general principles. In: A.J. Provenzano Jr. (Editor), Economic Aspects: Fisheries and Culture. Academic Press, Orlando, FL, pp. 249-268. Rho, Y.G., 1990. Present status of fleshy prawn (Penaeus chinensis) seed in Korea. In: K.L. Main and W. Fulks (Editors), Proceedings of an Asian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 29-35. SAS/STAT, 1990. SAS Institute Inc., SAS/STAT User's Guide, version 6, fourth edition, Vol. 1. SAS institute, Cary, NC, 943 pp. Shang, Y.C., 1990. Aquaculture Economic Analysis: An Introduction. The World Aquaculture Society, Baton Rouge, LA, 211 pp. Smith, H.T., Schreck, C.B. and Maughan, O.E., 1978. Effect of population density and feeding rate on the fathead minnow (Pimephales promelas). J. Fish. Biol., 12: 449-455. Tiku, M.L., 1967. Tables of the power of the F-test. J. Am. Stat. Assoc., 62: 525-539. Wang, K., 1984. Effects of temperature on growth of Chinese Penaeid shrimp. J. Trans. Oceanol. Limnol., 4: 42-45. Wang, K. and Ma, S., 1990. Advances in larval rearing techniques for Penaeus chinensis in China. In: K.L. Main and W. Fulks (Editors), Proceedings of an Asian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 42-48. Wickins, J.F., 1976. Prawn biology and culture. Oceanogr. Mar. Biol. Annu. Rev., 14: 435-507. Yang, C.H., 1990. Effects of some environmental factors on the growth of the Chinese shrimp, Penaeus chinensis. In: K.L. Main and W. Fulks (Editors), Proceedings of an Asian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 92-96. Zar, J.H,, 1984. Biostatistical Analysis, 2rid edition. PrenticeHall, Englewood Cliffs, NJ, 718 pp. Zhang, N., 1990. On the growth of cultured Penaeus chinensis (Osbeck). In: K.L. Main and W. Fulks (Editors), Proceedings of an Asian-U.S. Workshop on Shrimp Culture. The Oceanic Institute, Hawaii, pp. 97-102.