quantifying nutrient requirements of fishl

8/11/2019 Quantifying Nutrient Requirements of Fishl

1/6

Quantifying

Nutrient Requirements

of

Fishl

IsRAHtN.{ H.

ZnrrouN,

DUINIE

E. Ur-lREv,

WIr-r-Ierr,t

T.

MacE.e

Department of Animal Husbandry, Michigan State University, East

Lansing, Mich.48824,

USA

J o H u

L . G t l r

Department

of

Dairy

Science,

Michigan State University,

East Lansing,

Mich.48824,

US A

aNo WsnNen

G.

BEncEN

Department

of Animal

Husbandry,

Michigan State

University, East

Lansing, Mich.48824,

USA

ZetrouN,

L H., D. E. Ur-r-ney,W.

T. Me.cEE,

.

L.

GrLt- , .cNo

W. G.

BBncr.N. 1976.

Quanti fying

nutrient requirements

offish.

J.

Fish.

Res. Board

Can.

33: 167-172.

Four replicates

of50

rainbow

trout(Salmo

gairdneri)frngerlings each

were

assigned

o each

of

seven

dietary

protein

levels from 30 Io 60% in 57o

ncrements. Percentage weight

gains

for

10

wk were related to dietary protein levels using an analysis ofvariance and multiple comparisons

of

the means,

a broken line analysis, and a

polynomial

regression analysis. When

correctly

used, one

ofthese techniques should

lead to

a

reasonable conclusion concerning

dietary

protein

requirements.

However, the

polynomial

regression analysis has the

advantage of being

continu-

ous, like

the relation ofgrowth

to

dose, and should be

more accurate than

the other methods

when

the intervals

between experimental

dietary

nutrient

concentrations

are

wide.

The

polynomial

regression

analysis also

provides

the

basis

for

making economic decisions

relative to

protein

requirements

or maximum

economic

returns.

Zer rouN,I .

H. , D. E. Ul ln rv,

W.

T. M,, rcep, ,

.

L. Grr- l , .qNo W. G.

BencrN. 1976.

Quanti fying

nutrient

requirements

offish. J.

Fish. Res. Board Can. 33: 167-1'72.

De s

groupes,

contenant chacun 50

alevins de la

grosseur

du doigt

de truite arc-en-ciel

S

almo

gairdneri),

ont 6t6 expos6s dans

quatre

essais

r6p6t6s ir chacun de sept

niveaux de

proteines

alimentaires allant de 30 d 60%, par gradins de 5Va.Les gains pond6raux en pourcentage ont 6t6

trait6s

par

analyse de

variance

et comparaisons multiples

de

moyennes,

ainsi

que par

analyse

de

ligne

bris6e

et

analyse

de r6gression

polynomiale.

Lorsque utilis6e correctement,

I'une

ou

I'autre

de

ces m6thodes devrait

permettre

d'en arriver

d une

conclusion

raisonnable

quant

au x

exigences

en

prot6ines

alimentaires.

Cependant, I'analyse de

r6gression

polynomiale

a

I'avantage

d'Otre continue, tout comme

la

relation entre

la

croissance

et

la

dose, et devrait

Btre

plus pr6cise

que

les autres

m6thodes

lorsque les extrmes de concentration des

substances

nutritives

du

r6gime

exp6rimental sont espac6s. De

plus,

I'analyse de r6gression

polynomiale

peut

servir

de base d des

d6cisions 6conomiques ayant

trait aux

prot6ines

requises

pour

des

profits

maximums.

Received

une , 1975

Accepted

October2l, 1975

EsrIlraerEs

of

quantitative

nutrient requirements

are influenced

not

only by the criteria used but by

the

statistical

methods

chosen

to

evaluate

criterion

response

to differing

dietary

nutrient

concentra-

tions.

In

studies of

protein

or

amino

acid

require-

ments

of fish,

confusion is evident regarding

the

appropriate

method

to use

(Delong

et al. 1958,

1962;

Halver

1960,

1965;

Halver

et

al. 1964;

Chance

et al. 1964;

Cowey

et aL.

1972;

Zeitow

et al.

1973. 1974).

This matter

is

of

considerable

Regu

e 4juin 1975

Acceptde 2l octobre

975

significance due to the substantial

growth

of fish

culture

(Bardach

etal.1972;

Huet

1973)

and the

observation

that nutritional deficiency

diseases

are

common

wherever intensive flsh culture

is

prac-

ticed

(Halver

1972).

The

qualitative

nutrient

re -

quirements

of

various

fish

species

have been

previously

reviewed

(Halver

1969,

1970, 1972;

Phil ips

1969; Cowey

and Sargent 1972). When

estimating

nutrient

requirements

to

achieve

bio-

logical

potential,

the consequences

of using

various

statistical

techniques should be considered, and

several of these techniques

will be discussed.

Weight gain is

a common

parameter

used in

evaluating different dietary levels of an essential

nutrient

and in estimating the

quantitative

require-

ments

of that nutrient

for fish.

While

weight

gain

'Michigan

Agricultural

Experiment

Article

No. 6929.

Printed n

Canada

I3861)

Imprim6

au Canada

(J3861)

Station

Journal

167

Forpersonaluseonly.


2/6

r68

J. FISH.

RES. BOARD

CAN.,

VOL.

33(I) , 1976

Tanrr

1. Surnmary

of various responses

f rainbow

trout

(Salmo gairdneri)

fingerlings to different

levels

of dietary

protein

concentration

derived

rom

Zeitoun

et al 1973).

Dietary

protein

concentration

(%,)

SEMg

0

5

0

s

0

5

0

Initial

weight

(s')

Final

weight

g)

Weight

eain

(:Z)^

Weight

gain (f)b

Protein

etention

g)

6 .5

14.2.

1 1 9 . 3

119.3 '

t . z -

6 . 8 o

7 7 O d

1 5 0 . 7 d

I

5 0 .7d

1 . 6 0

6 . 2 .

1 8 . 5

197

3{

197 3

2 . 0 .

6 . 3 '

19.2d

204 s

204.5

2 7 f

6 . 4 '

79.6d

208.9

208.9'

2 . 2 f

6 . 3 ,

7 2 d

0 . 1 5

t9 .4d

20.5t

0 .39

2 0 8 . 1

1 8 4 . l f

7

l

2 0 8 . 1

1 8 4 . 1

7 . l

2 . 2 d

2 . 3 f

0 . 0 6

uDuncan's

multiple

range

est

was

used

o compare

he means.

bTukey's

Honestly

SignificantDifference

HSD)

test was

used o compare

he

means.

'd' 'rMeans

n the

same ine

followed

by different

superscripts

re significantly

P


3/6

ZEITOUNET AL.:

QUANTIFYING

NUTRIENT

REQUIREMENTS

Tantn 2. Mean

square errors

(MSE)

of different

regression ines for

percentage

weight

gain

of rainbow trout

fingerlings.

Range of dietary

protein

levels

ested

f)

Regression

equation

169

MSE

3V40.7

30-40. .

30-40.9^

30-41

0

30-60b

Y :

- 1 2 0 . 9 + 7 . 9 1 X

Y :

- 1 1 8 . 6 + 7 . 8 4 X

Y

:

-116 .3+7 . ' 7 ' 7X

Y :

- 1 1 4 . 0 + 7 . 7 0 X

Y

:

-

39796

24.58X-0.2476X2

310 .63

310.47

310 .46

310.

60

278.20

uFirst

order

polynomial.

Valuesaboveeach

breakpoint

equated o

the

break-

point

value.

Breakpoint

valuesaboveand

below hose isted

were ested,

nd

as

the

breakpoint

deviated

urther from

40.9,

the

mean

square

error increased.

bSecond

order

polynomial.

30

35

40

45 50

55 60

olrfory

Piotlin

Concanfrolion,

6

Ftc. 1. Effect of Duncan's and Tukey's tests on the

point

of interception

of the horizontal line and the

percentage

weight

gain

of rainbow trout

(Salmo

gairdneri)

fingerlings.

Yp is

the average

percentage

when

Duncan's

test was used

to

compare the means

and Yr is

the average

percentagegain

when Tukey's

test

was

applied.

the

two

methods

is different,

and one

can

expect to

obtain different

results

in some

sets

of

data.

BnorpN

LrNe Axlrysrs

Baker

et al.

(1.971)

used

the

broken

line

analysis

to estimate he requirements

of tryptophan

for

baby

pigs.

Thiq

procedure

was developedby

H. W.

Norton,

University

of

Illinois, Urbana, 1972,

personal

com-

munication, and assumes

a

positive

linear relatron

between

growth (Y)

and the dietary level of the

essentialnutrient (X) at or below the minimum re-

quirement.

At the

minimum

requirement

level

(R),

the ascending

ine

which represents he relation be-

tween

growth

and diet

nutrient concentration

breaks

instantly

to

horizontal.

Assuming that the

breakpoint

representsR, then Y

values for X at and

greater

than

R are

estimates

of

the same response.

A1l

values

of

X

greater

than the breakpoint are

equated

o

the

breakpoint

R for

purposes

of comput-

inga regressionine,

Y

=

a* bX.

Several

egressions

are attempted using

different breakpoints.

Concur-

rently, the deviation

sum of

squares or

each

regres-

sion

is estimated.The

regression ine that

gives

the

least mean

square

error

(MSE)

is considered he

best

fitted line

to

represent

the linearity between dose

levels and responsesand

which is the least

squares

estimate

of the

requirement.

Using the

growth

data of

rainbow

trout

fingerlings

from Table 1

for

this

analysis,

and

using arbitrary

values

of X at O.lVo

dietary

protein

intervals, the

regression

ine

that

fit the

percentage

weight

gain

with

a

breakpoint

at

40.9Vo

protein

in

the

diet

gave

the

least MSE if compared to

other

lines

(Table

2) .

Que.one,uc

RtcnpssroN

on Sr.coNo Onosn

Porvvo-

UIAI- RECNISSION ANALYSIS

The second

order

polynomial

regression

analysis s

represented y the equation Y : Bo * B.X * B X'.

This

curve is characterized

by having

a

unique

maxi-

mum

point

(Y-*)

along

its

range.

The

value

of

X- *

that correspo nds o

Y-.* is defined as the

maximum

concentration of the

dietary nutrient that

produces

optimum

growth,

and

beyond

which

growth

is

de-

pressed.

The

advantage

of

this

procedure

is that it

often

provides

a

better empirical

fit

to

the

growth

responses

of

living organisms which

do not exhibit

an abrupt change

rom linearity

as

postulated

n

the

previous

wo analyses.

Cowey et al.

(t972)estimated

the

protein

require-

ments of

the

plaice

(Pleuronectes latessa)

by apply-

ing the

quadratic

regressionanalysis.

The minimum

dietary protein level was defined as the level that pro-

duced the highest

point

on

the

curve. To apply the

Forpersonaluseonly.


4/6

170

J.

FISH,

RES. BOARD

CAN..

VOL.

33(I\ . 1976

same

concept

o rainbow

trout fingerling

growth

data

(Table

1),

a

quadratic

equation

was

calculated

(Y

:

-397.96

+

24.58X

-

0.2476X

which

showed

that

the maximum

response

of these fish

was

achieved

at

50Vo

dietary

protein (Fig.

2).

In

addition, the

profile

of

the data,

which

exhibited

a substantial

growth

depression at both extremes of dietary protein con-

centration,

favored

the use

of this

analysis.The cal-

culated

MSE

of the

curve

was noticeably

lower

(278.20)

than

those

estimated

by the broken

line

procedure

(Table

2) .

Although

this

curve would

best represent

he rela-

tion

of

$owth

to

dose, t

does not reflect

the

practi-

cally insignificant

differences

in

percentage

gain

below

and beyond

the maximum

point,

nor

does it

consider

he

ability

of the animal

to adapt

to a range

of dietary

protein

levels between

a deficiency

on the

left

side

of the

curve

and toxicity

on the right.

That

is,

there

are minimum

and maximum

levels

of

intake

within

which

the

animal is

able to

store, excrete,

or

adapt to the level of nutrient supplied without

sub-

stantial

changes

n metabolic

processes.

A

statistical

approach

could be

adapted

o determine

the level of

nutrients

in

the diet that

can

yield

a response

hat is

within

a certain

confidence

range.

of Y^ .

The

selection

of the

confidence level

is

dependent on

the

researcher

and his

objectives. n

the case

of the rain-

bow

trout fingerlings,

confidence

imits of

95Vo of

all estimated

esponses

f the curve

(?)

were

calcu-

lated

using

hc fol lowing

expression:

Y

+

t . . . L

n

+ ( X - X ) ' V ( b , )

+

( Z - Z ) ' V ( b )

+ 2(X - XltZ _ 71corlb,b,1f

where

MSE is

the mean square

error of the means,

n is

the number

of observations

on Y, X is the treat-

ment level,

X is

the average

of treatments, Z is

the

square

of X,2

is the

average f Z,

andV(b,), V(0,),

llo

l2o l3o t4o t5o

160 r7o

rao r9o

2oo 2to 22o

2fi

W.ight

coin, %

Frc. 3. Relation

between

percentage

weight

gain

and

protein

retention of rainbow

trout

fingerlings.

and cov(brDr) are variances and

covariance

of esti-

mated

parameters

of the

polynomial

curve.

Levels

of confidence

were

plotted (Fig.

2) on either

side of the

quadratic

line,

and

a straight line

parallel

to

the

abscissa and

passing

through the maximum

level

of the lower

line of the confidence limit was

drawn.

Moving left from Y-.., this horizontal line

first crosses he

polynomial

curve at a

point

Xr.

Then,

continuing

to the left, the

horizontal line intersects

the

upper

line

of

the confidence limit at

a

point

Xo.

The value X' is the estimated level of dietary

protein

concentration expected to

produce

a

growth

response

equal to the lower

bound

on the

interval

estimate of

Y-

in

the

initial

study.

The value Xo is the

estimated

level

of

protein

concentration

for which

an upper

bound on predicted growth response is equal to the

lower bound on Y- *. Strictly speaking one cannot

say that the responseat

X

(say

Yr)

is not

statistically

significantly different

from

Y^ ,

because

the dis-

tribution of

(Y* *

-

Y')

is

not

known

exactly and

the sampling

variance

is

a

complex nonlinear func-

tion. But

statistical significance

s

somewhat

irrelevant

for

regressionswith significant

parameters (Williams

1959).

What

is

relevant

s

a difference hat

has

prac-

tical importance.

When economics dictates, dietary

levels

of

protein

ranging between

Xo

and

Xr

may be

taken

as a

rough

estimate

of the concentration which

minimizes cost while maintaining adequate

growth

response. f

estimatesof

cost

per

unit dose

(C)

and

economic ncome per unit of yield (I) are available,

one can

base

a decision on those rather than

the

somewhat arbitrary range,

&

to X'.

Savings

from

reduced

dose are C(X- -

-

X ),

where the

economic

dose

(X )

is

to

be

determined. Loss

in

return is

IAY-, , where

yield

expressed at the

economic dose

is

(1

-

A)Y---. If

one maximizes net return

with

respect o A,

then

Xu

=

X- *

-

{A[X'9- *

(bo/b )l]'/'

and

A

-

(c/2r),[x,^^*

-

(bo/

b )]/Y,^^*.

Letting

C- *

=

CX- * and

I*

:

IY- *,

one obtains

X

=

X* -[1

-

C^ /2I^^*)

+ c- /2I- -X ^,*) (b, /b ) l

as the

estimated economic dose.

Whereas

it is

possible

2. 4

'6

I A

220

zto

200

t20

lo

roo

t90

8 l @

.E

tzo

_

160

I

r5o

t4 0

t30

30

35 40

xo xr

45

r@r

55 60

DialoryProll in

Concantrol ion,. [

Frc. 2.

The

second order

polynomial

relation

(solid

curved

line)

of

percentage

weight

gain

and dietary

protein

concentration

for rainbow

trout fingerlings,

with

0.95 confidence

limits

(dashed

curved

lines).

O Estimated mean of Y (Y); Observedmean of

Y.

Forpersonaluseonly.


5/6

ZEITOUN

ET

AL.:

QUANTIFYING

NUTRIENT

REQUIREMENTS

t7 l

to set fiducial limits

on

X* *

(Finney

1964),

which

is economically irrelevant,

the

complexity

of

X makes

computation

of limits intractable.

Discussion

An examination

of

the

consequences

of

using

the

three described statistical

procedures reveals

that growth

maxima may

be

identified

in a

range

of dietary

protein

concentration

from

40 to 50%.

llowever,

selection of the upper

figure

assumes

that

the maximum

percent

weight

gain deflned

by application

of the

second order

polynomial

regression

represents a

response which is

different

biologically from the lower values

defined by

use

of

the

polynomial

limits.

Statistically,

the

limits

of

response

expected with

sOEo

(X-u*)

dietary

protein include the mean response expected with

44Vo

(Xr)

dietary

protein.

Economically,

this

difference in dietary

protein

can be very

impor-

tant,

particularly

if the saving is

greater

than

the

fall

in returns

(Carpenter

L97l).

Dietary

protein

is

generally

one of the most

expensive compo-

nents

of

artificial

fish

diets, and if increasing

increments

of dietary

protein

concentration

do

not

result in concomitant increase in value,

the

economic

successof fish

culture

is

in

jeopardy.

The

selection

of

Xo

to

X1 on the

polynomial

regression

as the

minimum

range

of

protein re-

quirement

is

an

economic decision; and

while

this

decision

may

be economically conservative,

the

selection of X-o- is more

physiologically

con-

servative.

Using local

prices

of

dietary

protein

and

fish, average initial weight of the

fish,

and

estimated

efficiency of

feed

conversion,

it was

possible

to

estimate the ratio, C-o,/2I,,,u ,

which

equals

0.

1534.2

Then,

the

estimated

economic

protein

requirement is

X

-

50(1- 0.L534)

+

(0 .1534 /

50)

( -397.96/

-0 .25)

=

47 .2%.

For

the

current data,

this

result

is

above Xt

-

44Vo.

However, if

the cost

of dietary

protein rises

above the figure

assumed in these

calculations, or

if the selling price of fish declines, then the esti-

mate

of

the economic

protein

requirements

(o r

economic

dose, X,) would

be

lower. Decreased

efficiency

of conversion of dietary

protein

to

gain

'Protein

was

derived

from Purina Trout Chow

(40%

minimum

crude

protein),

at

a

price

of

$9.85/

22.7

kg

or

$1.08/kg

of

protein.

Local

prices

of

farm-reared

rainbow

trout averaged approximately

$2.64/kg.

Estimated

efiiciency of

feed

conversion

to

gain

was 1.5. Cost

of

protein

per

kilogram

gain

at

the

m a x i m u m

( X - , *

:

5 O % )

:

( 1 . 5 ) ( 0 . 5 ) ( $ 1 . 0 8 )

0.81;

gain

at

maximum

rate

(average

nitial

weight)

lY^- /100)

-

l l

=

(0 .2)1212/100) 1 l

=

0.224ke;

maximum

cost

(C, , )

-

(0.81)(0.224)

=

0.1,874;

I- -

-

(2.64) 0.224)

:

0.5914.

will have the

same effect.

Estimation

by Xn is to

be

preferred, but when

economic considerations

are strong,

and

information

on costs

and income

are

difficult

to obtain,

one may

choose

as a

simple

substitute

the

range between

Xe

and

X1.

Certainly an increase in the number of observa-

tions used

to

determine

the

polynomial curve

would

narrow

the confidence

limits

and tend to

shift the range

of Xn

to Xr

to the right. Whether

this

shift is important

must be

answered

by

the

researcher

himself.

If the

criterion

of response

were badly chosen

(in

representing

the effect

of

increasing

dietary nutrient

levels),

such a shift

may be very

important.

Weight

gain has

been

criticized

(Phillips

et al.

1957; Allison

1959; Maynard

and

Loosli 1969)

for inaccuracy

as

a

measure of

growth,

since

gain

in

weight

may

result from

deposition

of fat rather

than

from true

growth.

The

potential for

growth

may be

considered

identical

with

maximum

pro-

tein

retention,

and

when

values for the latter

(Table

1)

were

regressed

against

percent

weight

gain (Fig.

3

),

the correlation

coelncient

was

0.93. It is

apparent

that

for rainbow

trout finger-

Iings, weight

gain

was

a

good

measure

of

true

growth. Analysis of

variance

and

multiple com-

parison

of

treatment

means,

broken line anal-

ysis,

and

second

order

polynomial

regression

analysis may

lead to

similar conclusions

concern-

ing

dietary

protein

requirements.

Flowever, the

polynomial approach has the advantage of being

continuous,

like the

relation

of

growth

to dose,

and

should

be more

accurate than

the other

methods if the intervals

between

experimental

dietary

nutrient

concentrations

are

wide. Also,

the

polynomial

method

is well

adapted to

eco-

nomic analysis

if

information

is available

on

costs and

returns. One

should

remember,

how-

ever, that the

polynomial is

only

a smooth, sym-

metric approximation

to the real

relation of

gain

and intake and may

be

in some cases

better than

others.

Acknowledgments

We thank

Drs P.

L Tack

and

E.

R.

Miller

fo r

reviewing he

manuscript.

ArrrsoN,

J.

B. 1959. heefficiency

f utilization f

dietary

proteins, .97-116.

n A. A. Albanese

ed.]

Protein

and

amino

acidnutrition.

AcademicPress, nc.,

New

York. N.Y.

BexE.n,D. H.,

N.

K.

AII-rN, J.

Boovceenor, G.

GrqBsn,

.qNnH. W.

NoxroN. 1971.

Quantitative

s-

pects

of

D- andL-tryptophan

utilization

by

the

young

pig.

J.

Anim.

Sci.33: 246.

Bnnrncn, J.

E.,

J.

H.

Rvruen, eNo W.

O. Mcl-enNev.

1972.Aquaculture: he farming and husbandry of

freshwater

and marine organisms.

Wiley-Inter-

science, ew York,

N.Y.

868

.

Forpersonaluseonly.


6/6

172

J.

FISH. RES,

BOARD

CAN,, VOL. 33( I ) , 1976

Ce.reeNren,

K.

J. 1971.Problems

n

formulatingsimple

recommended

llowances

f amino

acids

or

animals

and

man.Br.

J. Nutr.

30:

73-83.

CneNcE,

R.

8.,

E. T.

Mrnrz.,cNo

J. E.

Helvrn.

1964.

Nutrition

of

salmonoid

fishes:

XII.

Isoleucine,

leucine,

valine

and

phenylalanine

equirements

f

chinooksalmon nd nterrelations etweensoleucine

and

eucineor

growth.

. Nutr .

83:

177-185.

Cowrv,

C.

B. ,

J . A. Popp,

. W. AonoN, lNo

A. Br_ l rn .

1972.

Studieson the

nutrition

of

marine

latfish.

The

protein

equirement

f

plaice Pl

eu

one

es

plat

es sa).

Br.

J. Nutr. 28:447456.

Cowey,

C.

B.,

elro

J. R.

SencrNr.

1972. ishnutrit ion.

Adv.

Mar. Biol.

0:

383492.

DeLoNc,

D.

C., J. E. Huvpn,

AND

E. T.

Mrnrz.

1958.

Nutrition

of

salmonoid

ishes:

VI.

Protein

require-

ments

of chinook

salmon

at two

water emperatures.

J. Nutr.

65:589-599.

1962.Nutrition

of

salmonoid

ishes:X.

Quantita-

tive

threonine

equirements

f

chinooksalmon t

two

water emperatures.. Nutr. 76: 17.4-178.

FrNNry,

D. J.

1964.

tatist ical

ethod

n biological ssay.

HafnerPublishing

o.,New

York, N.Y. 668

.

FtsnEn,

H., D.

JoHNsoN

R.,AND

G. A. LEvErr- 1e,.

957.

The phenylalanine

nd

tyrosine

requirement

f the

growing

chick

with

special eference

o

the

utilization

of

the D-isomer

of

phenylalanine.

J. Nutr.

62:

349-355.

GnrurNcen,

P.,

H. M.

Scorr, nNo

R.

M.

FoRBEs.

955.

The

effectofprotein

level

on the

tryptophan equire-

ment

fthe

growing

hick.

.

Nutr.

59:67-76.

Helven,

J.

E.

1957.

Nutrit ion

of

salmonoidishes:

IL

Water-soluble itamin

requirements

f

chinook

sal-

mon.

J. Nutr.

62:225-243.

1960.Vitamin and amino acid requirements f

salmon.

roc.

Fifth nt.

Congr.Nutr.

191:

2.

Abstr.)

1965.

Tryptophan

requirements

of chinook,

sockeye.and

ilver

almon.

ed.

proc.

Fed.Am.

Soc.

Exp.

Biol.24:229.

Abstr.)

1969.

itamin

equirements,

209-232.ln

O.W.

Neuhaus

nd

J. E. Halver

[ed.]

Fish in r esearcn.

Academic

ress,

nc. ,

New

york,

N.y.

1970. utr i t ion

n

marine

quiculture,

.75-102.

1n

W.

J. McNeil

[ed.]

Marine

aquiculture.

Oregon

State

UniversityPress,

Corvallis,

Oreg.

1972.

The vitamins,

p.

29-103.1nJ. E. Halver

[ed.]

Fish

nutrition.

Academic

Press, nc.,

New York,

N.Y.

Her-vpn, J. E., L.

S. Bares,

AND E. T. Meptrz.

1964.

Protein equirements

or

sockeye almon nd ainbow

trout.

Fed.

Proc.,Fed. Am.

Soc.Exp. Biol.

23: 17'18.

(Abstr.)

Huer,

M. 1973.Textbook

of

fish culture. Fishing

News

Books,

td. ,

London,

36

.

LAGLER,

.

F., J. E. Bnnoecu,

euo

R. R.

Mrr-lpn.

1962.

Ichthyology.

ohn Wiley

and Sons,

nc.,

New

York,

N .Y . 545

.

MnvNeno,

L. A., e.No

. K. Looslr.

1969.

Animal

nutri-

t ion.

McGraw-Hil l ook

Co.,New York, N.Y.

613

.

Mlrcnrr-r,

H. H.1962.

Comparative

utritionof man

and

domestic nimals.

Vol.

l. AcademicPress, nc.,

New

York,N.Y.701

.

MonnrsoN,

W. D., T.

S.

Hl.vrt-roN,

ANDH. M.

Scorr.

1956.Utilization of D-tryptophan

by the chick.

J.

Nutr. 60:47-63.

PnrlLIrs,

A.

M.

Jn. 1969.Nutrition,

digestion ndenergy,

p.391-432.1n

W. S.

Hoar

andD.

J.

Randall

ed.]

Fish

physiology.

ol. 1.Academic

ress,

nc. ,

New York,

N . Y .

PHILltrs,

A. M. Jn.,D.

R. BnocxwAy,

F. E. Lovpr-ncn,

AND

H.

A. Pooolrer.

1957.A

chemical

omparison

of hatcheryand

wild brook

rout. Prog.Fish

Cult. 19:

19-25.

SNeoecon,G. W. 1956.Statisticalmethods. owa

State

University

ress, me s, owa.

534

.

Srn.pr-, . G. D., eNo

J.

H.

Tonnlp. 1960. r inciples

nd

procedures

f statistics.

McGraw-HillBookCo.,

New

York, N.Y.

481

.

Wllltarls, E. J. 1959.Regression nalysis. ohn Wiley

and

Sons,

nc . ,

NewYork,

N.Y.214p.

ZrrrouN,

L

H.,

J. E. Her-vrn,

D. E.

ULLREy,

ND

P. L

Tecr. 1973. nfluence

of salinity

on

protein

equire-

mentsof

rainbow

rotl(Salmo gairdneri)

ingerlings.

J. Fish.

Res.

BoardCan.

30:1867-1873.

ZerrouN,

L

H., D. E.

ULLREv,

.

E. Halvrn, P.

.

Tecr,

AND

W.

T.

MecEe. 1974. nfluenceof salinity on

protein

equirements

f coho salmon

Oncorhynchus

k isutch)smol ts .

J .

F ish.

Res. Board Can.31:

I 145-1 48.

Forpersonaluseonly.

quantifying nutrient requirements of fishl

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