Wang 1985 Aquacultural-Engineering

7/28/2019 Wang 1985 Aquacultural-Engineering

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A q u a c u l t u r a l E n g i n e e r i n g 4 (1985) 21-32

W e ig h t a n d W i d th R e l a ti on s h ip o f F r e s h w a t e r P r a w n(M acr obr achi um osenber g i i )*

Jaw-Kai W angAgriculture Engineering Department, University of Hawaii, Honolulu,Hawaii 96822, USA

A B S T R A C TI t has been show n tha t the re i s no s ign i fi can t d i f f e r enc e (P < O . 05 ) in thewe igh t = f (w id th ) and orb i t l eng th = f (w id th ) r e la tionsh ips o f com merc i -a l ly p r o d u c e d m a l e a n d f e m a l e Macrobrachium rosenbergii in Hawaii. Ar eg r es si on e q u a t i o n o f t h e f o r m Y = ( A * X * * B ) * e ha s b e e n s h o w n t oadeq ua te ly de sc r ibe the above r e la t ionsh ips . In par t icu lar

W e ig h t = 0 . 0 1 2 7 8 * ( w i d t h ) * * 2 . 5 1 8 9 , R **2 -- 0 . 9 7 8O r b i t l e ng t h = O . 1 8 2 8 * ( w i d t h ) * * O . 7 7 6 8 5, R * * 2 = 0 . 9 9 6

T h i s re l at io n s h ip a l lo w s t h e d e v e l o p m e n t o f a s im p l e m e c h a n i c a l p r a w ns ize sor ter .

INTRODUCTION

Freshwater prawns M a c r o b r a c h i u m r o s e n b e r g i i are commercially pro-duced in Hawaii. In 1983, there were 20 farms with a total of 238 acresunde r wate r, prod ucing 270 000 lbs of prawns with a farmgate value ofUS$1-35 million (State of Hawaii, 1983).

There are a number of factors which have immediate effects on theprofitability of commercial prawn production. Yield and labor costare among these. Shang (19 81) has estimate d that for a 40-ha farm andat $9 .3 7k g -1 ($4.251b-1), a per-hectare yield of 17 47 kg ye ar -1 isrequired in order to break even. A more recent but informal estimation* Journal Series No. 2852, the Hawaii Institute of Tropical Agriculture and HumanResources. 21Aquacu l tura l Eng ineer ing 0144-8609/85/$03.30 Elsevier Applied SciencePublishers Ltd, England, 1985. Printed in Great Britain


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22 J . -K. Wanghas put the break even point for medium to large Hawaii prawn farms(25-100 acres) at about 1400 kg ha-1 year 1 (1250 lb acre 1) at the1984 average farmgate price of $11 kg x ($5 lb-l). Since the 1983 stateaverage annual yield is less than 1400 kg ha-a, an increase in yield isobviously needed to maintain the overall profitability of the industry.

Traditionally, commercial prawn p roduct ion in Hawaii has been donein two stages, hatchery and grow-out. In the hatchery stage, the prawnsare hatched and grown to post-larvae under intensive culture. The post-larvae are then used to stock the grow-out ponds.In order to increase their yields, some farmers (Rietow, 1982) havebegun to introduce a nursery stage in the production cycle so that thepost-larvae are first grown to the juvenile stage in a nursery pond (ortank) and then used to stock the grow-out ponds.

Gibson and Wang (1977) first suggested the advantages of having anursery stage in the production cycle, and Kneale and Wang (1979)demonstrated that high density nurseries can be designed to have highsurvival rates. More recently, Shang (1982) and Malecha (1984) havealso shown the benefits o f including a nursery stage in prawn product ion.

It is important in prawn production to remove market size prawnsfrom the grow-out pond. Frequent and efficient harvest is anotherkey to high yield.

Size sorting is needed both in the nursery operation and duringharvest. In the nursery operation, size sorting is needed to groupjuvenile prawns into appropriate size groups for stocking purposes.During the harvest operation, the undersized prawns need to be returnedto the grow-out pond, and the above market size prawns, dependingupon the market structure, may need to be grouped into two or moresize classes.

PRAWN SIZESize sorting of prawns can be simply defined as the selection andgrouping of prawns by one or more physical characteristics.

Several physical characteristics of a prawn can be used to define itssize. The most frequently used dimensions are weight, orbit length,tail length and width (carapace width). Among these, weight is thecommonly accepted measure of size in the marketplace and is also


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Weigh t and wid th re la tionsh ip or f reshwa ter praw n 23w i d e l y u s e d b y b i o lo g i s t s to m e a s u r e g r o w t h o f t h e a n im a l . T h e r e f o r e ,f o r b o t h n u r s e r y a n d m a r k e t p r a w n s iz e s o r ti n g , w e i g h t s e e m s t o b e t h em o s t a p p r o p r i a t e m e a s u r e t o u s e. U n f o r t u n a t e l y , a v ai la b le a c c u ra t ew e i g h i n g e q u i p m e n t t h a t a r e c a p a b l e o f w o r k i n g a t t h e r e q u i r e d h ig hs p e e d a re g e n e r a l l y e x p e n s i v e . T h e y a ls o r e q u i r e e x a c t s i n g u la t io n a n do f t e n a ls o r e q u i r e e v e n s p a c in g o f i t e m s b e i n g f e d i n t o t h e e q u i p m e n t .T h e o r b i t l e n g t h , d e f i n e d a s t h e d i s t a n c e f r o m t h e p o s t e r i o r e d g e o f t h ee y e o r b i t i n th e c a r a p a c e t o t h e p o s t e r i o r e n d o f t h e t e ls o n , is c o m m o n l yu s e d b y r e s e a r c h e r s w h e n r e p o r t i n g p r a w n s iz e. It is a ls o a g o o d p r e d i c -t o r o f p r a w n w e i g h t . H o w e v e r , it is d i f f ic u l t to d e v e l o p a s i m p l em e c h a n i c a l d e v i c e t o d e t e r m i n e o r b i t l e n g th q u i c k l y a n d e a sily .T h e d i s t a n c e b e t w e e n p a r a ll el p l a n es t a n g e n t t o th e c a r a p a c e o v e r ap r a w n ' s g ills is g e n e r a l l y r e f e r r e d t o a s t h e p r a w n ' s w i d t h . S i n c e t h ew i d t h o f a p r a w n d e f i n e s t h e s m a l le s t c l e a r a n c e b e t w e e n p a ra l le l p l a n e s( b a r s ) t h r o u g h w h i c h t h e p r a w n w i ll p a s s, it l e n d s i ts e l f t o p r a w n s iz ed e t e r m i n a t i o n b y s i m p le m e c h a n i c a l m e a n s ( A r n d t e t a l . , 1 9 8 4 ) .

T h i s p a p e r p r e s e n t s i n f o r m a t i o n o n p r a w n w e i g h t, o r b i t l e n g t h a n dw i d t h t o s h o w t h a t w i d t h c a n b e u s e d a s a b a s is f o r si ze s o rt in g f o r b o t hn u r s e r y a n d m a r k e t s iz e p r a w n s a n d t h a t p r a w n w i d t h is a g o o d p r e -d i c t o r o f b o t h p r a w n w e i g h t a n d o r b i t l en g th .

D A T A D E S C R I P T I O NA t o t a l o f 5 0 3 p r a w n s , o f w h i c h 2 2 1 w e r e j u d g e d t o b e m a l e s a n d 3 9w e r e j u d g e d t o b e f e m a l e s a n d t h e re s t u n d e t e r m i n e d , w e r e r a n d o m l yg a t h e r e d f r o m t h e A m O r i e n t f a rm o v e r a p e r i o d o f t im e d u r i n g 1 9 8 3 .T h e s iz e s o f m a l e p r a w n s v a r ie d f r o m 1 .4 g i n w e i g h t ( W T ) a n d 8 m m inw i d t h ( W D ) t o 1 3 5 -7 g i n W T , a n d t o 3 9 m m i n W D . F o r f e m a l e p r a w n s ,t h e r a n g e w a s f r o m 1 .3 g i n W T a n d 8 m m i n W D t o 8 5 - 2 g i n W T a n d3 1 m m in W D . I n c l u d i n g t h e p r a w n s w i t h i n d e t e r m i n a t e s e x, t h e s iz er a n g e d f r o m 0 . 0 5 g in W T a n d 4 m m in W D t o 1 3 5 g i n W T a n d 4 0 r a min W D . T h e l o n g e s t p r a w n w a s a m a l e p r a w n 1 05 m m i n o r b i t le n g t h( O L E N ) , 3 0 m m in W D a n d 1 2 8 . 7 g in W T . T h e s h o r t e s t p r a w n w a s15 m m in O L E N , 4 m m in W D , 0- 0 5 g in W T , a n d w i t h u n k n o w n s ex .

F i g u r e 1 s h o w s t h e m a l e p r a w n w e i g h t a n d w i d t h d i s t r ib u t i o n , F i g. 2t h e f e m a l e p r a w n w e i g h t a n d w i d t h d i s t r i b u t i o n , a n d F i g . 4 t h e w e i g h ta n d w i d t h d i s t r i b u t i o n o f t h e e n t ir e 5 0 3 d a t a p o i n ts .


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2 4 Z - K . W a n g2.5525PREDICTED WEIGHT= 0.01165 (WIDTH)

140-130-

120-

l l O -

100-

90 -

60 -

70 -

60 -

50 -

40 -

30 -

20 -

F ig . 1 .

+

+ -I-

+ + + +

+ +

*

0 ~ . . . . . . . . . . . . . . . . . . . .7.5 12.5 17.5 22.5 27.5 32.5 37.5

NIDTH. MMWeight versus width for male prawns. (+) Observed; ( - - ) predicted.

P O S T U L A T E D M O D E LS i m p l e p h y s i c a l a r g u m e n t w i ll s h o w t h a t w h e n o n e o f t h e v a r ia b le s , i .e .W T , W D , o r O L E N , is z e r o , t h e o t h e r t w o v a r ia b l es m u s t b e ze r o .

T h e r e f o r e , a m o d e l o f t h e t y p e~ 'i = A i X i B i e i (1 )

w h e r e e i = e i I N D ( O , o ,.2) i s p o s t u l a t e d .


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Weigh t and w id th r e la t ionsh ip or f r e shw ate r prawn 2590 -

80.

70.

60

WE 5 0 -IGHT

40-GM

3 0-

2 0-

10-

F ig . 2 .

PREDICTED HEIGHT= 0.0032 4 (HIOTH) 2.907

.+

++ +

$ + +

6 8 10 12 14 16 18 20 22 24 26 28 30 32HIDTH, MH

W e i gh t v e r s u s w i d t h f o r f e m a l e p r a w n s . ( + ) O b s e r v e d ; ( ) p r e d i c t e d .

F o r t h e r e l a t io n s h i p s b e t w e e n p r a w n W T a n d W D , t h e p o s t u l a t e dm o d e l i s

~ " ( W D ) ff i e i ( 2 )W T ) / = A iw h e r e i = m a l e , f e m a l e o r al l p r a w n s , - 1, 2 a n d 3 , r e s p e c t i v e l y . L e a s t


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2 6 J.-K . WangT A B L E 1

Summ ary o f Least Square Regres sions , WT = f (W D )Ai Bi R 2

i = 1 0 . 0 1 1 6 5 2 . 5 5 2 5 0 .9 8 5i = 2 0 . 0 0 3 2 4 2 . 9 0 7 0 . 9 5 6i = 3 0 . 0 1 2 7 8 2 . 5 1 8 9 0 . 9 8 7

Fig . 3 .

5.0-

4.5-

4 , O-

3.5-

3.0-

2.5-

2.0-

1.5-

1.0-

0 . 5 -

0 . 0 -

fi i I 0/ / / I I 0 0

i 1 "i i I /

/ / / / 1 1 / 1 1 1

/ / 0i i

i i I

4 .0

2 , 0 2 , 2 2 , 4 2 . 6 2 , 8 3 . 0 3 . 2 3 . 4 3 . 6LOG(WIDTH in r am)W eight versus w idth for prawns , l og - lo g p lo t . M ale : (+ ) observed; (

pred ic t ed . Fem ale : ( o ) observed; ( - - - ) p red ic t ed .


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Weight and w id th re la t ionship or f r eshwa ter prawn 27square regressions yielded the results given in Table 1. The table showsthat the postulated model is reasonable.

At this point, a question can be raised about whether or not theregression eq uati ons with i = 1 and 2, can be considered identical or, inother w,ords, wh ether or no t there is any real difference between therelationship of WT versus WD for male and female M a c r o b r a c h i u mr o s e n b e r g i i .

The covariance analysis procedure outlined by Wine (1964) was usedto answer this question.

Taking logarithms to the base e in eqn (2) converts the model intothe linear form. The transformed data of male and female prawns areplotted on Fig. 3. The regression lines are produced using eqn (3) andlnA; and Bi values from Table 2.

ln(WT) i = l n A i + B i ln(WD)i + l n e i (3)The transformed model can be handled according to the standard pro-cedures outlined by Wine (1964) or Dunn and Clark (1974). First thehypothes is B1 = B2 = B is used to see if the re is any reason to suspectthat the slopes of the lines are different. If the hypothes is is not rejected,the male and female prawn data are th en p ooled to calculate B, andusing the same slope, lnAi is then calculated. Finally, the hypothesi sA 1 = A 2 = A is tested. If this hypothesis is not rejected, it is thenconclude d that there is no statistically significant difference betweenmale and female prawns in their size relationship WT = f(WD).

The first hypot hes is to be tested is Bt = B 2 = B . The calculations areperfor med using data fr om Table 2.

3.8115 + 2.9947S 2 = = 0.02659(221-- 2) + (39 -- 2)

' 1 1 '\S~B,-B~)=0"02659 ,o.av,z[-GXgg~+2.17,42}y :0.01524S(B, - B2) = 0- 12345

B1 -- B2t - - 1.8599S ( B , - - B 2 )

Since t(o.o2s,2s6)= 1.96 and the critical region is 1.96 < t < - 1.96,the h ypothesi s B I = B2 = B was not rejected.


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28 J . - K . W a n gT A B L E 2

Log Weight and Width Regression of Male and FemalePrawn Data

M a l e , i = 1 F e m a l e , i = 2n i 221 39l n A i -4 .8589 -5 .7378B i 2-6721 2.9017SSwT, i = NOn WTi -- In WTi)2 64.5528 21-4692SSreg, i 60 '7413 18'4745SSres, i 3.8115 2.9947SSwD,i = NOn WDi - In WDi)2 8.5072 2.1942In WT = (~ In( W T ) i ) /n i 3.9690 3.3038In WDi = (~ In ( W D ) i )/ n i 3.3757 3.1408

The second hypothesis to be tes ted i s A I = A 2 = A , o r l n A l = l n A 2 =lnA.The weight and width data of the male and female prawn s are first

pooled and, using a calculated B, l n A i is calculated.(8 .5072) (2 .6721) + (2 .9017) (2 .1942)B = = 2. 55 05(8.5072 + 2.9017)

al = lnA1 = ln(WT)l - - (B ) ln(WD)l = - - 4. 45 74a2 = lnA2 = ln(WT)2-- (B) In(WD)2 = --4-6350

(64 .5528) + (21 .4692) - - (2 .55055) (8 .5072 + 2 .1942)S ~ a l - a 9 = 221 + 39 -- 3

= 0.2285S(a _~2 = 0. 478 0

- -4 .4574 + 4 .6350t = 0.4780Since t(o.o25,277)--1.960, the

rejected.

= 0.3715hypo thes i s A1- - A2=A was no t


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W eigh t and w id t h re l at i o n sh ip o f re shw a te r p rawn 29T h e e n t i re d a t a s et o f 5 0 3 d a t a p o i n t s w a s t h e n p o o l e d t o d e v e lo p

t h e r e s u l t a n t r e g r e s s i o n e q u a t i o nW/-T = 0 . 0 1 2 7 8 ( W D ) 2" sis9 ( 4 )R 2 = 0. 97 8

F i g u r e 4 s h o w s t h e a c tu a l a n d p r e d i c te d w e i g h t a n d w i d t h r e la t io n -s h i p f o r p r a w n s .

F o l l o w i n g i d e n t ic a l p r o c e d u r e s , r e g re s si o n e q u a t i o n s o f t h e t y p e o fe q n ( 1 ) w e r e a ls o d e v e l o p e d f o r o r b i t l e n g t h a n d w i d t h , a n d w e i g h t a n do r b i t l e n g t h ( s e e T a b l e 3 ) .

140-~130--

1 2 0 2

1 1 0 -

loo29o-~

N 2E 80~IG ZH 70-2T

8M 250-~

3 0 -

2 0 - -2

10-2

F i g . 4 .

a @

00

t

+ 0# +

0

+0 +

+4 -+O

O

[]4-

0 ~ ~ . m ~ ~-0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0

N I D T H , M MW e i g h t v e r su s w i d t h f o r p r a w n s . O b s e rv e d : ( + ) m a l e ; ( o ) f e m a l e ; ( ~ ) u n -k n o w n . ( - - ) P r e d i c te d . P r e d i c te d w e i g h t = 0 . 0 1 2 7 8 ( w i d t h ) 2"s1~9


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30 J . -K. WangT A B L E 3

Su mm ary o f Regression Equa t ions , Al l Prawns ( I7 = A X B )1 7 X A B R 2 N o t e

WeightWeightOrbi t length

W idth 0-01278 2-5189 0 .978Orb i t l eng th 0 .000032 3 .2615 0 .978W id th 6 .1828 0 .77685 0 -996

Fig. 4Fig. 5Fig. 6

140-

130-

1 2 0 -

1 1 0 -

1002

9 0 ~HE 8 0 -IGH 70-"T 6 0 -GM 5 0 -

40 -

30 .

20 -

10-

F i g . 5 .() unk now n. (

+n %++

ooo

0 10 20 30 40 50 60 70 90 90 100 110ORB IT LENGTH. MM

Weight versus orbi t leng th for prawn s. Observed: (+ ) m ale; (o) fem ale;) Pre dicted . Predicted we ight = 0-000032 (orb i t len gth) 3a61s.


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Weigh t and w id th r e la tionsh ip or f r e shw ate r prawn 31I I 0 -

i00-

80-

80-

8BB 70-ITLE 80-NGTH, 50-MM

40-

30.

20.

I0 .

I l

I l l

Bl Ooo /

B

OO

O

I S , :3 + *

O

Oi l

: ~ a a4 .I-

n o[ ]

0 5 I 0 1 5 2 0 2 5 3 0 3 5 4 0N I O T H . M M

Fig. 6. Orbit length versus w idth for prawns. O bserved: (+) m ale; () female;(m) unkn ow n. ( - - ) Predicted. Orbi t length = 6 .1828 (w idth) 'v%Ss.

C O N C L U S I O NI t h a s b e e n s h o w n t h a t t h e r e i s n o s t a t i s ti c a l l y s i g n i fi c a n t d i f f e r e n c eb e t w e e n m a l e a n d f e m a l e Macrobrachium rosenbergii r a i s e d c o m -m e r c i a l l y i n H a w a i i r e g a r d i n g t h e i r w e i g h t v e r s u s w i d t h , o r b i t l e n g t hv e r s u s w i d t h , a n d w e i g h t v e r s u s o r b i t l e n g t h r e l a ti o n s h ip s .


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32 J.-K. WangI t is c o n c l u d e d t h a t e q n ( 1 ) i s a n a d e q u a t e m o d e l a n d b y u si n g t h is

m o d e l , p r a w n w e i g h t a nd o r b i t l e n g th c a n b e p r e d i c t e d b y p r a w n w i d th .B a s e d u p o n t h e a b o v e , a m e c h a n i c a l s o r t e r u s in g a p a i r o f d i v e rg e n t

r o l l e r s h a s b e e n d e v e l o p e d . T h e s o r t e r h a s b e e n u s e d t o s o r t b o t hm a r k e t s iz e as w e l l a s n u r s e r y p r a w n s ( A r n d t et al., 1 9 8 4 ) .

A C K N O W L E D G E M E N TM e a s u r e m e n t s o f p r a w n s iz es w e r e t a k e n b y M r L o r e n D . G a u t z ,f o r m e r R e s e a r c h A s s o c i a te , A g r ic u l t u ra l E n g i n ee r in g D e p a r t m e n t ,U n i v e r s it y o f H a w a i i, H o n o l u l u , H a w a i i. T h e w o r k w a s s u p p o r t e d b yg r an t s fr o m t h e S e a G r a n t C o l le g e P r o g r a m , N O A A , a n d th e D e p a r t m e n to f L a n d a n d N a t u r a l R e s o u r c e s , S t a te o f H a w a i i ( c o n t r a c t n o . 1 5 6 3 0 ) .

R E F E R E N C E SArn dt, G. D ., Gautz, g. D. & Wang, J .-K. (1 984 ). M echanical size grading o f post-

harvest prawns. 15th Annual World Mariculture Society Meeting, Vancouver,Canada , 03 /18-22 /84 .Dunn, O. J . & Clark, V. A. (1974). Applied Statistics: Analysis of Variance andRegression, Joh n W iley and Sons, New York, cha pter 13.

Gibso n, R . T. & W ang , J ,-K. (1 977 ). An alternative prawn prod uction systemsdesign in Hawaii. Sea Grant Technical Report, UNIHI-SEAGRANT-TR-77-05,University of Haw aii.Kneale, D. C. & W ang, J .-K. (1 979 ). A labor ato ry investigation of Macrobrachiumrosenbergii nursery production. Proc. World Marieulture Society, 10, 359-68.

M alecha, S. (198 4). The effec t of pre-harvest s ize grad ing and sto ck rotation inpond cultured freshwater prawns Macrobrachium rosenbergii. 15th AnnualWorld Mariculture Society Meeting, Vancouver, Canada, 03/18-22/84.Rietow, A. (1982). One approach to farm const ruct ion. Proc. Third Annual BigIsland Aquaculture Conference, Hilo. Hawai i , 05/14-16/82, pp. 33-5.

State of H aw aii (1983 ). Unpublished farm survey, Department of Land and NaturalResources. Aquaculture Development Program.Shang, Y. C. (1981). Freshwater (Macrobrachium rosenbergii) production in Hawaii ,practices and economics. Sea Grant Miscellaneous Report, UNIHI-SEAGRANT-MR-81-07, University o f Haw aii.Shang, Y. C. (198 2). Som e potential p on d management strategies of freshwater

prawn farming in Hawaii . Proc. Third Annual Big Island Aquaculture Confer-ence, Hilo, Hawai i , 05/14-16/82, pp. 84-7.Wine, R. L. (19641). Statistics for Scientists and Engineers, Prentice-Hall, NewJerse y, section 14.10.

Wang 1985 Aquacultural-Engineering

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