Instraspecies Relationship between Fasting Heat Production ...ported for the same animal, the...

M. L. Thonney, R. W. Touchberry, R. D. Goodrich and J. C. Meiske

.75Body Weight: A Reevaluation of WInstraspecies Relationship between Fasting Heat Production and

1976. 43:692-704. J Anim Sci

http://jas.fass.orgservices, is located on the World Wide Web at:

The online version of this article, along with updated information and

www.asas.org

at Albert R Mann Library on December 11, 2009. jas.fass.orgDownloaded from

http://jas.fass.org

http://www.asas.org/

http://jas.fass.org

INTRASPECIES R E L A T I O N S H I P BETWEEN FAST ING H E A T P R O D U C T I O N A N D B O D Y W E I G H T : A R E E V A L U A T I O N OF W "75

M. L. Thonney I , R. W. Touchberry, R. D. Goodrich and J. C. Meiske

University o f Minnesota, St. Paul 2'3'4 55108

SUMMARY

The use of W "Ts as an estimator of fasting heat production (HP) for male and female rats, chickens, rabbits, dogs, humans, cattle and for ewes was studied using data obtained from the literature. Regression coefficients for models which related HP to body weight (W) were calculated from data for each population of animals. Highly significant (P<.001) equations were obtained for animals in each species-sex subclass, thus nullifying the common assumption that the narrow W ranges within species prevent the determination of meaningful relationships between HP and weight.

Data from various sources within species-sex subclasses did not differ with respect to bl for the model: log HP = b0 + bl (log W). However, source of data did affect b0 for dogs, ewes, women and steers. Weight exponents (bl values) were significantly different for the sexes within the chicken, dog, and human species.

Tests for equality of weight exponents showed that exponents derived for species-sex- source, sex-source within species, and species- source within sex subclasses were not equal (P<.001). Thus, a universal equation which relates HP to W should not be declared the best fitting equation for species-sex subclasses. It is concluded that W .Ts, which was developed from data of species varying widely in W, ig- nores effects other than weight which are pecu- liar to specific populations. Therefore many researchers have inappropriately adjusted biolog-

1 Present address: Department of Animal Science, Cornell University, Ithaca, New York 14853.

2Scientific Journal Series, Paper No. 9158, Minne- sota Agricultural Experiment Station, St. Paul.

S Department of Animal Science. 4Appreciation is expressed to the University of

Minnesota Computer Center for a grant-ln-aid for the conduct of this research and to the Department of Applied Statistics for assistance. The senior author wishes to acknowledge the helpful suggestions of Dr. R. L. Quaas and other colleagues at Cornell University during the revision of this manuscript.

ical data for variation in weight by dividing response criteria by W .75. A more appropriate adjustment would be to include W b or log W as a covariable in the statistical model. (Key Words.. Metabolic Body Size, Weight, Fasting Heat Production, W .75.)

INTRODUCTION

The metabolic body weight of animals is commonly calculated by applying the exponent, .75, to body weight (W). Many researchers assume that W raised to an exponent close to .75 represents the metabolic body weight of all animals, since Kleiber (1961) and Brody (1945) showed that fasting heat production (HP) was related closely to W -Ts and W .73, respectively, when means of groups of mature animals which varied greatly in W were used to evaluate the relationship. In 1964 the European Association for Animal Production adopted W .Ts as a ref- erence base for comparing the metabolism of different species of animals (Kleiber, 1965). The National Research Council has defined metabolic size as W -Ts (N.R.C., 1966). Many researchers appear to have assumed that W .Ts is the unit upon which physiological processes are based and as a consequence, have attempted to adjust data by dividing response variables by W.TS.

The objective of the study described herein was to determine if the exponent which should be applied to weight to predict fasting heat production for a given species-sex subclass should be .75, the exponent which was developed ig- noting sex differences and using means of species varying more than 1,000-fold in average weight.

MATERIALS AND METHODS

Daily fasting heat production and body weight data on individual animals were obtained from the literature for male and female rats, chickens, rabbits, dogs, humans, cattle and for ewes. Means and standard deviations for heat

692 JOURNAL OF ANIMAL SCIENCE, Vol. 43, No. 3 (1976)


http://jas.fass.org

A REEVALUATION OF W "75 693

production (HP) and body weight (W) as well as sources of data for each species and sex are shown in table 1. The references were reviewed to determine if the data were obtained using mature animals in the post-absorptive state in a thermo-neutral environment and to determine if the animals were performing a minimum amount of physical activity. Thus, the data met the definition of fasting heat production. Many of the references which Kleiber (1932, 1961) included in his analyses provided data for the present analysis. Observations on animals of a given species and sex which were reported in different references by workers from the same laboratory were considered to represent one source of data unless the animal activity or data plots showed HP differences among animals from different references. The data on dogs which were summarized by Kunde and Stein- haus (1926) were categorized into the two groups of references which these authors concluded represented high and normal HP values for dogs. The post-absorptive state for cattle and sheep was assumed to have been reached after 2 to 4 days of fasting, although some authors reported data for longer periods of fasting. When more than one observation was reported for the same animal, the average of observations on the mature animal was used. Most cattle data were reported on the basis of 12 hr lying and 12 hr standing or a standard day. Where cattle data were reported on the basis of 24 hr lying, they were adjusted to a standard day by increasing 12 hr of heat production by 10% (Hashizume et al . , 1962).

Regression coefficients were calculated from data which included all observations or from data which included observations within each species-sex-source subclass for the following functional forms of equations:

HP = bo + b l (W) (1)

HP = do(W bt ) (2)

Kleiber (1932, 1961) and Brody (1945) used equation (2) to develop the W.TS (W.73) con- cept. The regression coefficients, do and b 1 for equation (2) were determined by transforming the equation to a linear function with loga- rithms:

log HP = b0 + b l (log W) (3)

where bo = log do. Sholl (1948) has shown that

the back transformation of equation (3) to equation (2) will not result in the same values as when the coefficients in equation (2) are determined directly. However, the objective of the present analysis was to evaluate the past use of equation (3) to determine bl values.

Hypotheses which were tested and their cor- responding models are shown in table 2. Under model I the null hypothesis (I) was that all 29 species-sex-source subclasses had equal b l values. Under model I lA the null hypothesis (I lA) was that the data sources within each species- sex subclass had equal bl values. For species- sex subclasses where hypothesis IIA was accepted, a covariance model (liB) was used to test the null hypothesis (liB) that source effects were equal. Under model III the null hypothesis (1II) was that both sexes within each species (except sheep) had equal bl values. Under model IV the null hypothesis (IV) was that all species within each sex had equal bl values. Subclass effects (S) remain in each model since sums of squares and cross products which determine bl values were pooled from within species-sex-source (model I), source (model II), species-source (model III), and sex-source (model IV) sub-classes.

Null hypotheses I, IIA, III and IV were tested by calculating the analysis of variance and determining probabil i ty values for subscripted b effects (differential regressions). A similar analysis was demonstrated by Daniel and Wood (1971). The analysis is essentially the same as that described by Snedecor and Cochran (1967) for the comparison of regression lines among treatments in analysis of covariance. Hypo- thesis l i b is a test of equality of source effects where the effect of different log W values among sources is removed by analysis of covariance (Snedecor and Cochran, 1967). Where more than two sources of data contr ibuted to differences among b0 values, the differences were tested for significance by computing the standard error of differences among source means adjusted by covariance for differences in log W (Steel and Torrie, 1960).

Species-sex weight exponents (model IIB) were compared with weight exponents of 0, .75 and 1.00 by a t-test. These three comparisons were of interest to show 1) if a significant relationship existed between log HP and log W, 2) if the weight exponent should be .75 and 3) if the relationship between HP and W was linear for a given species-sex subclass.

Three functional forms of equations in addi-


http://jas.fass.org

6 9 4 THONNEY ET AL.

<

<

0

< (- r..q

o r.~

0

<

[.-,

L~

o

L~

. 1

<

0

0

+1

0 ~ . .

u~

0

~ ~.~.~ - . ~ ; ~ ~ ~ o ~ ~ . ..~ ,.,.-~ = ' ~ ~ , , ~ ~ ~ ~ ~..~. ~ . .~

<

§ +1 +1 § +1 § +1 +1 +i +1 § +1 § § § § +1 § § § § § § § +1 § § § +1 §

. . . . . . . ~ �9

v

i +

z ~

v


http://jas.fass.org

A REEVALUATION OF W "75

TABLE 2. REGRESSION MODELS AND THE HYPOTHESES TESTED FOR EACH MODEL a

695

Model Hypothesis Statement

I b

IIA c

I IB c

III d

IV e

IIA

IIB

III

IV

log HPOk I = ~ + Sij k + b(log Wijk l) + bi jk( log Wijk l ) + ei jkl

Ho: All bi jk equal to 0.

log HPkl = # + S k + b(log Wkl) + bk(log Wkl) + ekl

Ho: All bk equal to 0 for each ij subclass.

log HPkl = g + S k + b(log Wkl) + ek l

Ho: All Sk equal to 0 for each ij subclass for which hypothesis IIA was accepted.

log HPjk 1 = t.t + Sjk + b(log Wjkl ) + bj(log Wjk l) + e jk l

H o : Both hl equal to 0 for each i subclass.

tog HPik I = l~ + S ik + b(log Wik l) + bi(log W ik l) + eik 1

H o : All b i equal to 0 for each j subclass.

awhere: i = species, j = sex, k = source of data, 1 = animal.

bWhere: log HPijk I = the log of heat production of t h e / t h animal of the kth source from the j sex within the ith

species, /~ = the mean log HP for all subclasses, Sij k = the effect of the kth source from the j th sex within the ith species, b = the weight exponent common to all species-sex-source subclasses, log Wijk. l = the log of body weight of the /th animal of the kth source from the j th sex within the ith

species, bij k = the differential weight exponent of the kth source from the j th sex within the ith species, ei jkl = residual error.

CSubscripts are the same as in model I, except ij are not included since model II applies within species-sex subclasses.

dsubscripts are the same as in model I, except i is not induded since model III applies within species sub- dasses.

esubscripts are the same as in" model I, except j is not included since model IV applies within sex subclasses.

t i o n to equa t ions (1) and (2) were c o m p a r e d wi th in a given source for ewes (Peirce, 1934) , w o m e n (Harr is and Benedic t , 1919) and da i ry cows ( R i t z m a n and Benedic t , 1938 ; R i t z m a n and Colovos, 1943) . T he Peirce ( 1 9 3 4 ) ewes were chosen fo r this d e m o n s t r a t i o n because t h e r e was m u c h less va r i a t ion in t he re la t ionsh ip b e t w e e n HP and W t h a n for t h e m o r e n u m e r o u s da ta o f Lines and Peirce (1931) . T h e add i t iona l f u n c t i o n a l fo rms o f equa t i ons were:

HP = bo + b t (W "75) (4)

H P = b o + b l ( W ) + b 2 ( W 2) (5)

HP = b l ( W -Ts) (6)

SSimilar values were determined when b I was calculated by minimizing the error sum of squares.

where bl values fo r e q u a t i o n (6) were de ter - m ined b y dividing t h e HP o f each an imal b y t he co r r e spond ing value o f W.75 and averaging t he resul t ing b l values s. This m e t h o d is c o m m o n l y used b y researchers to adjus t var iables fo r t h e e f fec t of weight . Values fo r ~2 and Sy.x were d e t e r m i n e d for equa t i ons (2) and (6) by calcula t ing p red ic ted HP values fo r each d a t u m and p roceed ing to calcula te e r ror sums of squares. Here R 2 is de f ined as t he f rac t iona l r e d u c t i o n in t he co r rec ted sum o f squares fo r HP due to f i t t ing t he m o d e l F o r e q u a t i o n (6) th is def ini - t i on m a y resul t in negat ive f~2 values.

RESULTS AND DISCUSSION

Sca t t e r p lo ts and equa t i ons fo r all observa- t ions and for obse rva t ions w i th in sources of da ta are s h o w n in f igures 1, 2 and 3 for t he raw da ta ( e q u a t i o n 1) and for t he log t r a n s f o r m e d


http://jas.fass.org

6 9 6 T H O N N E Y ET AL.

n~

477t

2}+3

HP = )M +~ + 15.87(~D

S ,x- 124+ 99 i ~ . , ~ �9

" . / / : . /

/ .o . " �9 . i f + , ,

.. ." . , ; / " ' "

�9 ~ 1 4 9

~ oo

/ /

. /

r"

~ o u w+IGm, mG

S~+x..o'J+ P~ .w ] JZ l -

�9 i!.':F'" ~.ol P

1+7s t" . / :" . /

1.(9 [ . : ~ ' �9

ALLOBSE~VATION$

.. :. ~ f

o

, . ;~( :~;:~

SS.0

51.0

47.0

4 X O

}l.o

2).0

tg,0

l+.o

R^TS

MALES ............... emtOlCT ~ A L Itglmq. HORST El A+L ~I~4)

Hp - 12.48 + ~k ]2<WI

s -~.m PA.n / /

HP �9 3.54 + 9k~w) . . . + /

s r x. 3.m I~Z- .s)

�9 �9 J " � 9

: ~ . y i , ~ / ~ - " . . . . .

[ ] .>-;~- . . . . m s F t ~ + ; / �9 . . . . .o~s+ E~_L . ~ ,~

(]~ | �9 s - L W ~ z . . ~ y ~ y.,

<~'~r Hp �9 + . 7 7 + m,4~4Wl

.lO .16 .21 +27 .3) .$8 ~PY WEIGHT, KG

LT~ RATS .

I~ He " L784 + . ~9 W) �9 / / /

L~ s ..o~ ~z.,n -*-/ ~-x /

- - - MITCI41E~ AND CAR~4 ( I ~ 1 . . ~ " '

]+58 io9 H p . 1. e~lj + BI~41~g W) . . , / �9

s r -.oe f . ,~ fi~ /~

L ~1 j f

~+ | s . .o. "+ i i l �9 [ ] . . . . . MImHELL AND CAIIMm (1r /

| / . u ,m . ~ .+1 . 6 )

LOG BODY W[IGHT, KG

~t%o cH)c~ms

0 . . . . . ~LE$ ~L5 Hp, 1.41 + ~l, Z~Wl

Sy, x - 16,21 ~2..s3

. . . . . . FO~AtE$ / ~ j 188.0

Hp �9 49. ~ll § ~0. 9I~W)

..... . / / o % j , ~ .

�9 o .

z.~i I

z.z~ [

Z.21 1

z .16f

2.m

L~ t

L~ I-

CHICK~qS @

| . . . . . . ~L(S

Sy.x. r ~2�9 0 0 ~f" @ | @ / ~

. . . . . . . . . . F~LES 1~ IO9 HP - 1. ~S + (~:41o 9 W) /~

s-.+. ~2�9 . o / ~ . . f -~ �9 / / ~ . ~ ..J"

~ �9 - , . 1 " " .

~. 2'.~ ~'.~2 ' ~ I,, ;.3 -~,, 1.~h , , 2.,~ .~ .~ .26 :~ '.++ '.~, '.41 .,5' .% 1,2 [K)OY Ws Gb~, KG L(J~ EQOYWE~GHT, KG

Figure 1. Relationships between fasting heat production (HP) and body weight (W) for all observations and for rats and chickens�9

data ( equat ion 3). When the data were assumed to represent a s ingle popu la t ion (f igure 1), the log transformat ion ( equat ion 3) decreased the variat ion about the regression line. However , wi th in the species and sex subclasses the plots s h o w that the log transformat ion resulted in l i t t le reduct ion in variation (f igures 1, 2 and 3).

The w e i g h t e x p o n e n t s and their standard errors are s h o w n in table 1. If there were no di f ferences among spec ies -sex-source bt values, and if spec ies -sex-source d i f ferences among mean l o g HP values are assumed to ex is t , then sums o f squares and cross products cou ld be p o o l e d from wi th in spec ies -sex-source sub-


http://jas.fass.org


z r t ~

ll~,l

51.0

~ a l s l t s

| . . . . . . ~ a t t s

. . . . F~dALES

�9 i ~ o l �9 =o oltw~

/ �9 .. ; . : ; . .

.~:'~.~ . �9

z.~

z.lr ;

> z.)l

L z t

@ . . . . . ~ t t S

~ ~ .t.?e0 * . ~ . ~

sy I - .e,~o }z- .~o

t.~. I

t 0 ~ B o o r WerGm

m a t e s

~Z'~ [~ . . . . ~UNDE. STEINP~U$. tUSK

. . . . . . ~ T H B Y ANO ~NOIFORD, R U ~ , ~ ' ~ "

I "

415.~

~opy w [ i G m KG

ur~

i i |?

=

/ /

,,,,f EODY W[IG'IT K~

a i r s

�9 - - L i r a s ANO PEIRCt ( l ~ l )

s r / m . n Ii z . ~

w �9 zs~ .~ , lit r ~ w l

/ "

Hp - 61L~ * ZL 8raW, . " .

,.=.~ ..... f .-

~/~ ~ . _

/.11

i ~ . l l

~ot;$ �9

~ I - - - - - -KUt lO[ , SII I~t~US. LUSK

Srx" .o l ~1 ~ , . ~ | . - ' ~ / " "

. - " | ~ " .

. ' a / .'a . "1 --~p. LKU~,E* :T$, ~1Nbj~/tU . . . . . .

/ s ) . x - . o ~ ~-.TZ

i i ~ i i i

3. U

Z.~

. . . . . . . tints AND Ptlrcc ~I~3U

io~ H p . L 159 * .713 (iotj W ) . , * . "

Sy. - c~ ~ Z . ~ ~ �9 j . . . J

[ ~ - - -pEIRCE 119341 / " . . / -

log H p , 2 137 + .611 ilOg w) [~] ~ / , ~ " ~ o

sy - o,, ~2. ~ / / / - �9

/ / J

LOG 80DYWEIG~L KG

Figure 2. Relationships between fasting heat production (HP) and body weight (W) for rabbits, dogs and e w e s ,

classes to determine a common bz value. How- ever, the view of Kleiber (1961) and Brody (1945) was that when studying basal metabolism, all animals are from the same population and should not be categorized by species and sex. When the data from all species and sexes are assumed to represent a single population, the 99.9% confidence interval for the weight exponent was .752 to .766. Thus, when species-

sex classification of animals is disregarded, the present analysis confirms the hypothesis that the weight exponent which should be used to make comparisons of fasting heat production is close to .75.

The analysis of variance for model I is shown in table 3. The effect (P<.O01) of species-sex- source differential weight exponents ( b i j k ) indicates that no common bl value can ade-


http://jas.fass.org

698 THONNEY ETAL.

�9 - - - - HARRIS AND BO~OICT 119191 HP �9 617, 43 + 15, ~P/I~

SY "x" Iz~z'r 1~2. , ~ y-x ~ " 2244

& - - MCK ITTR ICK 119321 O ~ - I- . . . . . . . . . . | . . .

"~ s~. . , . , , ~ . . , , - ~ ~ . - ~ _ �9 �9

�9 - .

BODy W(IG~T. KG

~ N S

3.3~ ~- . . . . . . . . H~REISANO B~EDICT (191q~ | . . . . . MEN

log HP - 2.4~7 § 379 llog W) I ~ H p �9 2. O/? + .631 (~og W}

~.r, .~.~. . . .~,~, ~ ~ , ~ e ~ ~.. ~ r s,, - . ~ ~..,~ e ~ ' ~ ' ~ .~'.I ....

.... : .

. . . .

@

LOG BOOYWEIGffr KC

|

a/77

~ o

STB~$

H p . ~i/./~ * ILZI(WI ~ ]

;.s . . . . . | ~ , /

. . . . . . . M)|CI4~ L AND ~ I L I O N (1q411, MITC~'~-L U ~k I lg

j , . , - , s . , . | . . . .

. .~- �9149 O- - - - - - -FORe t$ ~ &L {IgZI~, 19t1+ 1~8, I~0, 1931J

n E T

r

,to~

).TS

) . l ]

~. 5r

STEI~S [ ]

~] . . . . BI]~EDICT ANO RriZMAN II r RITZIVbKN A~ID BL~EOlCT (193~

s - . o n ~ z . . ~

IOgHp - .q. 4 m * ~k~lo9 W} ~

. / - j

�9 : .~| j f -

/ / / �9 . . . . . . . . NITC ~ AN~ ~MILION 11~I/ MJTCH~L ~ / A ~ ll@,dO

s~. x" 0~7 ~ . . , ~ | ETA~ Ilg26a, 1r 1~, 1910, 1931~

S x, . o ~ ~ z . . e

IOG ~ODy WEIGHT. xc

c(~vs OAlnV cmvs

. . . . . . . . ~91TZMAN ~ l o BBIF~ICT I I ~ , R r ' ~ N ANO col.ovos ~19~

Hp - 3 1 ~ . I B * 9.~iO(W)

Hp - 1713 2~ * 12.B/lWl

[ ] . . . . FORBES ET A L IIr~2~ . . ' A

He - IpA~.33 * IL7(4WF , ~ .

�9 | " �9

~B �9 ~ - - ~ t ~ cows

By.x" I~LII ~ , ,7~

(IODy WEIGHT KG

Figure 3. Relationships between fasting heat production c o w s .

t m

t0~

x ~

COWs

DAIRY COW5

.............. RIIZR~N AND gEIWEDICT 1193~. RIIZMAN AND COtOVOS 11943}

i

| ~SHIZUME El AL ( 1 ~

s �9 .~ ~L .~ .~.~

�9 . . . . . FLAn AN0 COPPOCK ~ 1 ~ ~ . . . . �9 t " A

s - . ~ # - , ~ ~ . , , . - ' - ' ~ ' ~ " ~ [~ y.x

.~B �9 [ ] . . . . . . JAeANESE BLACK BREED COWS

~ . [~ IO~ HP * 4.524 - , 3~841og WI

. . . . ...~....~_ S~x" .036 flz- .07

6B [ ] A - - B ~ cows

[] s t . . .09t ~ z . . 2 s

LC~ SOOY WE~Gm, KG

(HP) and body weight (W) for humans, steers and

quately represent all populat ions. Therefore, data from different populat ions o f animals should not be pooled to develop a single equa- t ion which predicts fasting metabol i sm for all animals�9

There were no significant differences among

exponents o f weight for different sources of data within a given species-sex subdass . How- ever, there was no significant relationship between HP and W for cows of the Japanese Black Breed and the fasting heat product ion for these cows was m u c h lower than that of the


http://jas.fass.org

A REEVALUATION OF W "75

TABLE 3. ANALYSIS OF VARIANCE FOR HYPOTHESIS I: EQUALITY OF WEIGHT EXPONENTS AMONG SPECIES-SEX-SOURCE SUBCLASSES a

6 9 9

Sum of Mean Effect squares DF square F pb

Species-sex-source subclasses (Silk) 315.8968 28 11.2820 6636.5 <.001

Common exponent (b/Sil k) 3.0177 1 3.0177 1775.1 <.001

Species-sex-source differential exponents (bi jk lb) .2268 28 .0081 4.8 <.001

Error (eijkl) 1.1597 679 .0017

aAssumes the following model (model I): log HPijkl = I~ + Sijk + b(log Wijkl) + bijk(log Wijkl) + eijkl.

bprobability value.

TABLE 4. TESTS OF HYPOTHESIS liB: EQUALITY OF SOURCE EFFECTS (b 0 VALUES) WITHIN SPECIES-SEX SUBCLASSES a

Species-Sex Source b b b I • SE

Male rats ~ .681 • .077 Benedict et al. (1932), Horst et al. (1934) 1.804 Mitchell and Carmen (1926) 1.823

Female rats .718 -+ .076 Horst et aL (1930, 1934) 1.812 Mitchell and Carmen (1926) 1.841

Male dogs .531 -+ .047 Boothby and Sandiford, Rubner c 2.213 t Kunde, Steinhaus, Lusk c 2.096 t

Female dogs .740 • .087 Boothby and Sandiford, Rubner c 1.935 t Kunde, Steinhaus, Lusk c 1.851 t

Ewes .634 • .146 Lines and Peirce (1931) 2.041 z Marston (1948) 1.981 vz Peirce (1934) 2.103 vz

Women .370 • .033 Harris and Benedict (1919) 2.482 t McKittrick (1936) 2.485 u Tilt (1930) 2.452 TM

Steers .460 +- .093 Blaxter and Wainman (1961) 2.647 x Benedict and Ritzman (1927), Ritzman and Benedict (1938) 2.733Y Forbes et al. (1926a, 1927, 1928, 1930, 1931) 2.656 x Mitchell and Hamilton (1941), Mitchell et al. (1940) 2.588 w

Dairy cows .597 + .087 Flat and Coppoek (1963) 2.287 Forbes et al. (1926b) 2.269 Hashizume et al. (1962) 2.285 Ritzman and Benedict (1938), Ritzman and Colovos (1943) 2.284

aAssumes the following model (model liB) for each species-sex subclass: log HPkl = # + S k + b I (log Wkl) +

ekl.

bb 0 = ~u + S k.

CCited by Kunde and Steinhaus (1926).

t 'Ucoeffieients with one superscript the same within a species-sex subclass are different (P<.001).

VCoeffieients with v as superscript within a species-sex subclass are different (P<.01).

w'x'Ycoeffieients with different superscripts within a species-sex subclass are different (P<.055).

ZCoeffieients with z as superscript within a species-sex snbelaas are different (P<.075).


http://jas.fass.org

700 THONNEY ET AL.

other beef or dairy cows (table 1 and figure 3). Therefore the cows of the Japanese Black Breed were not used to compare sexes of cattle or species of females.

A comparison of the intercepts (b0 values) adjusted for differences in log W among sources is shown in table 4. The dogs of Boothby and Sandiford and of Rubner (cited by Kunde and Steinhaus, 1926) had higher HP than the three groups of dogs from Kunde, Steinhaus and Lusk (cited by Kunde and Steinhaus, 1926) which agrees with the analysis of Kunde and Steinhaus (1926). The low HP for ewes reported by Marston (1948) may be due to Mars- ton's adjustment for increased HP caused by standing, while Lines and Peirce (1931) and Peirce (1934) did not adjust for standing. Peirce (1934) reported that the ewes observed by Lines and Peirce (1931) were sometimes measured in the lying as well as the standing position while the data from Peirce (1934) were from ewes measured in the standing position only. Therefore, the higher HP for ewes reported by Peirce (1934) shown in table 2 is explained by the fact that they were more ac- tive. The HP of women measured in Florida (Tilt, 1930) was lower (P~.001) than that of women measured in Wyoming (McKittrick, 1936) or the District of Columbia (Harris and Benedict, 1919). Therefore climate may-have had an effect on fasting heat production. No readily available explanation can be given for the differences in HP for the steers. Dairy and beef cows were pooled into one population

since the regression coefficients for these two groups of cows did not differ significantly.

A comparison of weight exponents for sexes within species is shown in table 5. Weight exponents were higher for males than females in the chicken (P<.I 5) and human (P~.001) species. When bl is low an increase in W results in a smaller increase in HP than when b l is high. Keys e t al. (1973) found that total HP decreased over a 19-year period in men which had replaced an average of 1.13 kg of their original body tissue with fat and gained additional weight as fat. Therefore, the significantly lower bl value for women than men may be due to more adipose tissue in the W of heavier women than in heavier men (McGilvery, 1970). The same reason may account for the tendency for the lower bl value for steers compared to cows although no logical explanation is apparent for the difference (P<.05) in weight exponents between male and female dogs.

The two analyses of variance for model IV are shown in table 6. For both males and females the species differential weight exponents (bi) were not equal (P<.001).

The data in table 4 show that, even within a species-sex subclass, wide variations sometimes exist among b0 values. Furthermore, the analyses in tables 5 and 6 show that one should not pool data to develop a common weight exponent for a species or sex. Thus, even for mature animals measured under conditions of fasting metabolism, the .75 exponent should not be considered as a physiological constant which

TABLE 5. TESTS OF HYPOTHESIS Ilh EQUALITY OF WEIGHT EXPONENTS BETWEEN SEXES WITHIN SPECIES a

Difference between b I values

Species (males - females) b pc

Rats -.037 >.15 Chickens .392 <. 15 Rabbits .033 >. 15 Dogs -.209 <.05 Humans .261 <.001 Cattle -.152 d >.15

aAssumes the following model (model III) for each species: log HPjk I = # + Sjk + b(log Wjk 1) + bj(log Wjk 1) +

ejkl.

bDifference between b I values shown in table 4 or table 1. C . . Probabdlty value for the bj effect given th~ null hypothesis that bj = 0.

dDifference between b I value for steers (table 4) and b I value for dairy cows plus beef cows (.612 + .104).


http://jas.fass.org


r ,1

Z

Z O

<

Z

Z O

a:

r,. O >

<

[-

>

�9

r ,1

Z <

>

�9

M < Z

.d

M <

0 0

~., v v

g 4 ~

e'-,

a =

o v

O 00

0 0

' O Ox

O (',1 "~" O Z ~

O

V

t"- 00

O4 ~ "

o. o

u'~ Ox

O ",O ,,~ 00 ",O "~"

C

0 e ~

. &

+

tx~

e~

+

+

b7 +

II

>

0

0

,.o 2s

+a

s e ~

e~

applies to all species and sexes�9 A m o n g species and between sexes within species, variations in the relationship between HP and W m a y be caused by hormone , b o d y compos i t ion or other differences. The wide range in weight among species for the data which were used to derive the .75 weight exponent resulted in a close rela- t ionship between HP and W and masked differences in that relationship among species and be-

1850(

1665 (

1480(

1295.O

111OO

9250

7400

.~ 5550

3700

1 8 5 . 0

EWES / - ~ Pewee O ) . w . ~:'>"

~ P a ~ 82 �9 21 8 ~ w ~ ~ ~ " ~ ~ - . . . . .

" ] {5 y Hp ~s 38 * 469]~, 3950 [w 2

. / /

ig'. s , 0 . ~ 5R

O'~o 130 2 6 0 39.0 5 2 0 65.0

BODY WEIGHT, KG

2s6o0) W O M E N Harris and Bened,ct (1919)

0 1280, ( ~ * * * *

/ / . / ' / / / / NP : 3 9 2 2 9 , 2 4 47 ~ 1280 ~ 2

5 ~ 2 ( - J - s .2~ao k ~: ~o

. . . . . . EQUATION [~ 256.( 75!

O'C0!o 22' . . . . !O 66 ~ . . . . . . . . O'.0

BODY WEIGHT," K G

0905.0 DAIRY C O W S Ritzman and 8enedl~t (19381 Ritzman and Co~ovos 0943)

107145.

9524.0 HP 314O83 ' 9,0~V, " ~

HP ,77ol,w ~11 , ~ ~ ~ . s ~ 78171 ~ 58 *

O 5952.5 ~ ~ ~ ~-/ ............. EQUAqON 441

...... r~->~" " . . . . . . . . . . . . . ~'~, 4 7 6 2 0

. . . ~ " 7 ~ s 8a437 ~2 57

33715 . . . . . . . EQUA;ION [51 HP o30~1. ~2e6r 047Bow21

....... / i / - s~ 723m ~2 m

/ ~e 7~ ~2twT~ ]tgo.s f/ / '

0 " 0 , 0 '29!0 258 ~ . . . . '0 516!0 64510

BODY WEIGHT, KG

Figure 4. Examples of functional forms of equations which predict heat production from body weight.


http://jas.fass.org

702 T H O N N E Y ET A L .

T A B L E 7. P R O B A B I L I T I E S O F T H E O C C U R R E N C E O F T H E O B S E R V E D b 1 V A L U E S F O R E A C H O F T H R E E N U L L H Y P O T H E S E S a

Species Sex P(bl/Ho: 3t = 0) P(b I/Ho:/31 = .75) P(bl/Ho: /3a = 1)

Rats Male < .OO1 > .15 < .001 Female < .OO1 > .15 < .005

Chickens Male < .O01 > .15 > .15 Female < .001 > .15 < .O1

Rabbits Male < .001 < .05 < .01 Female < .001 < .075 < .001

Dogs Male < .001 < .001 < .001 Female < .001 > .15 < .01

Ewes < .001 > .15 < .02 Humans

Male < .O01 < .005 < .001 Female < .001 < .001 < .001

Cattle Male b < .001 < .01 < .001 Female < .001 < .10 < .001

abl values are shown in table �9 1 0 4 .

bsteers.

4 or table 1 except that the b I value for dairy cows plus beef cows was .612 +-

tween sexes. The data in table 7 show that highly signifi-

cant (P<.O01) equat ions were obtained for each subclass o f animals. Therefore , a def ini te rela- t ionship be tween log HP and log W exists, even within the relatively narrow W ranges o f species-sex subclasses. In seven of the 13 data sets, the probabi l i ty that b l was equal to .75 was low. Thus, these data provide fur ther evi- dence that .75 is no t the correct exponen t for W for several species and that a constant exponent for W should not be used for all species and sexes.

The value o f b l was close to 1.00 only for male chickens (table 7). Therefore , for many species-sex subclasses the relat ionship be tween HP and W is nonl inear when equat ion (2) is used. One of the assumptions which is made when equat ion (2) describes the relat ionship is that the in tercept is zero. This assumption is logical f rom a biological v iewpoint since animals which weigh nothing should produce no heat. The weight of rats relative to the weight o f catt le is close to zero. However , the weight o f rats or animals of any o ther species is certainly not zero.

The data in figure 4 show that , when equa- t ion (2) is used, the relat ionship be tween HP

and W is forced to be nonl inear (bl < 1.00) since the line must pass through the origin and through the range o f the data. Fur thermore , 22 and Sy.x values among equat ions (1), (2) and (4) were not significantly different . For cows, the addi t ion of W 2 (equat ion 5) improved ~2 and decreased the Sy.x value. However, l i t t le benefi t is seen when equat ion (5) is applied to the data for ewes and women. These results sug- gest that , in most cases, a l inear equa t ion with an intercept adequate ly predicts HP f rom weight.

Many researclaers a t t empt to remove the effect o f W by dividing variables by W.75. The lines for equat ion (6) in figure 4 show the result o f such an adjustment�9 In all cases equa t ion (6) underpredicts HP at l ight W and overpre- dicts HP at heavy weights. The result is especial- ly not iceable for the data on w o m e n where the negative ~2 value indicates that the mean HP, alone, would predict HP more precisely than equat ion (6). The problem is more p ronounced for women because the dif ference be tween b 1 and .75 is greater than is the difference between bl and .75 for ewes and cows.

Many researchers have assumed that o ther response variables have the same relat ionship to W as does heat product ion . Tanner (1949) and


http://jas.fass.org


Dinkel et al. ( 1 9 6 5 ) have s h o w n t h a t t he e f fec t o f a c o n t i n u o u s i n d e p e n d e n t var iable (such as W.75) o n a response cr i te r ion is n o t r em oved b y dividing each value of t h a t c r i t e r ion b y the cor- r e spond ing value of the i n d e p e n d e n t variable unless t he l ine which relates t he response cri ter- ion to the i n d e p e n d e n t var iable is l inear and passes t h r o u g h the origin. Since the m a g n i t u d e o f b l depends on the da ta wh ich are ana lyzed , t he line wh ich relates fas t ing hea t p r o d u c t i o n to W.75 m a y ne i t he r be l inear n o r pass t h r o u g h the origin. The re fo re , even if o t h e r variables were re la ted to W in t he same way as HP, i t is i napp rop r i a t e to adjus t da ta for va r ia t ion in W b y dividing b y W.7s . E q u a t i o n (6) in f igure 4 is a d e m o n s t r a t i o n o f such an i n a p p r o p r i a t e ad- j u s t m e n t . The app rop r i a t e a d j u s t m e n t wou ld be to include W or some o t h e r f u n c t i o n a l f o r m of W in the e x p e r i m e n t a l model .

The weigh t e x p o n e n t s in th is paper are ap- p ropr i a t e w h e n a m o d e l wi th a f u n c t i o n a l f o r m as in e q u a t i o n (2) is used to p red ic t hea t produc t ion . However , an i n t e r c e p t will be i nc luded in mos t mode l s wh ich are used to p red ic t variables o t h e r t h a n hea t p r o d u c t i o n . There fo re , W will serve adequa t e ly as a covar iable in m o s t ex- pe r imen ta l models . I f response variables appea r to be re la ted to W in a curv i l inear m anne r , W 2 may be added to the mode l or log W m a y be used as t he covariable. I f a single e x p o n e n t o f W is desired to descr ibe a curve, n o n l i n e a r m e t h - ods (Daniel and Wood, 1971) m a y be used to e s t ima te t h a t e x p o n e n t .

LITERATURE CITED

Benedict, F. G., K. Horst and L. B. Mendel. 1932. The heat production of unusually large rats during prolonged fasting. J. Nutr, 5: 581.

Benedict, F. G. and E. G. Ritzman. 1927. The metabolism of the fasting steer. Carnegie Inst. of Wash. Pub. 377.

Blaxter, K. L. and F. W. Wainman. 1961. Environmen- tal temperature and the energy metabolism and heat emission of steers. J. Agr. Sci. 56:81.

Brody, S. 1945. Bioenergetics and Growth. Reinhold Publ. Corp. New York.

Daniel, C. and F. S. Wood. 1971. Fitting Equations to Data. Wiley-Interscience, John Wiley & Sons, Inc., New York.

Dinkel, C. A., L. L. Wilson, H. J. Tuma and J. A. Min- yard. 1965. Ratios and percents as measures of car- cass traits. J. Anim. Sci. 24:425.

Flatt, W. P. and C. E. Coppock. 1963. The fasting metabolism of dry, non-pregnant adult dairy cows. J. Dairy Sci. 46:638 (Abstr.).

Forbes, E. B., W. W. Braman, M. Kriss, J. A. Fries, D. C. Cochrane, C. D. Jeffries, R. W. Swift, R. B. French and J. V. Maucher. 1926a. The influence of

the environmental temperature on the heat production of cattle. J. Agr. Res. 33:579.

Forbes, E. B., W. W. Braman, M. Kriss, C. D. Jeffries, R. W. S~vift, R. B. French, R. C. Miller and C. V. Smythe. 1928. The energy metabolism of cattle in relation to the plane of nutrition. J. Agr. Res. 37: 253.

Forbes, E. B., W. W. Braman, M. Kriss, R. W. Swift, R. B. French, C. V. Smythe, P. S. Williams and H. H. Williams. 1930. Further studies of the energy metabolism of cattle in relation to the plane of nutrition. J. Agr. IRes. 40:37.

Forbes, E. B., W. W. Braman, M. Kriss, R. W. Swift, R. C. Miller, R. B. French, T. V. Letonoff and G. R. Sharpless. 1931. The fasting metabolism of cattle as a base value of heat production in the determination of the net energy of feeding stuffs. J. Agr. Res. 43:1003.

Forbes, E. B., J. A. Fries, W. W. Braman and M. Kriss. 1926b. The fasting katabolism of dry cows. J. Agr. Res. 33:591.

Forbes, E. B., M. Kriss and W. W. Braman. 1927. The computed as compared with the directly observed fasting katabolism of cattle as a measure of the maintenance requirement of energy. J. Agr. Res. 34:167.

Harris, J. A. and F. G. Benedict. 1919. A biometricai study of basal metabolism in man. Carnegie Inst. of Wash. Pub. 279.

Hashizume, T., Y. Kaisbio, S. Ambo, H. Morimoto, T. Masubuchi, M. Abe, S. Horii, K. Tanaka, T. Ha- mada and S. Takahashi. 1962. Metabolism of matter and energy in cattle. IlL On the maintenance requirement of energy and protein for Japanese Black Breed and Holstein Breed cows in Japan. Bull. Nat'l. Inst. Agr. Sci. (Japan) Series G 21:213 (Nogyo Gijutso Kenkyujo, Tokyo).

Horst, K., L. B. Mendel and F. G. Benedict. 1930. The metabolism of the albino rat during prolonged fasting at two different environmental temperatures. J. Nutr. 3:177.

Horst, K., L. B. Mendel and F. G. Benedict. 1934. The influence of previous diet, growth and age upon the basal metabolism of the rat. J. Nutr. 8:139.

Kaisho, Y., T. Hashizume, S. Ambo, G. Abe, T. Masu- buchi, M. Abe, H. Motimoto, S. Horii, Y. Kurata, M. lshihara and H. Tsuchiya. 1955. Metabolism of matter and energy in cattle. I. Respiration appara- tus and its tests. Bull. Natl. Inst, Agr. Sci. (Japan) Series G 11:157 (Nogyo Gijutso Kenkyujo, Tokyo).

Keys, A., H. L. Taylor and F. Grande. 1973. Basal metabolism and age of adult man. Metabolism 22: 579.

Kleiber, M. 1932. Body size and metabolism. Hilgardia 6:315.

Kleiber, M. 1961. The Fire of Life. John Wiley and Sons, Inc., New York.

Kleiber, M. 1965. Metabolic body size. Third Sympos- ium on Energy Metabolism of Farm Animals. E.A.A.P. Pub. 11.

Kleiber, M., H. Goss and H. R. Guilbert. 1936. Phos- phorus deficiency metabolism and food utilization in beef heifers. J. Nutr. 12:121.

Kunde, M. M. and A. H. Steinhaus. 1926, Studies on metabolism. IV. The basal metabolic rate of normal dogs. Amer. J. Physiol. 78:127.


http://jas.fass.org

7 0 4 THONNEY ET AL.

Lee, R. C. 1939. Basal metabol ism of the adult rabbit and prerequisites for its measurement . J. Nutr. 18: 473.

Lines, E. W. and A. W. Peirce. 1931. The basal (standard) metabol ism of the Australian Merino sheep. Australian Commonwea l th Sci. and Ind. Res. Bull. 55.

Marston, H. R. 1948. Energy transactions in the sheep. I. The basal heat product ion and heat increment. Australian J. Sci. Res. 1:93.

McGilvery, R. W. 1970. Biochemistry: A Funct ional Approach. W. B. Saunders Company, Philadelphia. p. 313.

McKittrick, E. J. 1936. Basal metabol ism of Wyoming university women. J. Nutr. 11:319.

Mitchell, H. H. and G. G. Carman. 1926. Effect of ex- cessive amounts of vitamin B on the basal metabolism of rats of different ages. Amer. J. Physiol. 76:385.

Mitchell, H. H. and W. T. Haines. 1927. The basal metabol ism of mature chickens and the net-energy value of corn. J. Agr. Res. 34:927.

Mitchell, H. H. and T. S. Hamilton. 1941. The utilization by calves of the energy contained in balanced rations composed of combinat ions of different feeds. J. Nutr. 22: 541.

Mitchell, H. H., T. S. Hamilton and W. T. Haines. 1940. The utilization by calves of energy in rations containing different percentages of protein and

glucose in supplements . J. Agr. Res. 61:847. N.R.C. 1966. Nutrient requirements of domest ic ani-

mals. Biological interrelationships and glossary of energy terms. Pub. 1411. National Academy of Sci- ences -- National Research Council.

Peirce, A. W. 1934. The basal (standard) metabol ism of the Australian Merino sheep. II. Factors affect- ing basal metabolism. Australian Commonwea l th Sci. and Ind. Res. Bull. 84.

Ritzman, E. G. and F. G. Benedic.t. 1938. Nutrit ional Physiology of the Adul t Ruminant . Carnegie Inst. o f Wash. Pub. 494.

Ritzman, E. G. and N. F. Colovos. 1943. Physiological requirements and utilization o f protein and energy by growing dairy cattle. N. H. Agr. Exp. Sta. Tech. Bull. 80.

Sholl, D. 1948. The quanti tat ive investigation of the vertebrate brain and the applicability of allometric formulae to its s tudy. Proc. Royal Soc. 135:243.

Snedecor, G. W. and W. G. Cochran. 1967. Statistical Methods. (6th Ed.), Iowa State Univ. Press, Ames.

Steel, R. D. G. and J. H. Torrie. 1960. Principles and Procedures of Statistics. McGraw-Hill Book Co., New York.

Tanner, J. M. 1949. Fallacy of per-weight and per- surface area standards, and their relation to spur- ious correlation. J. Appl. Physiol. 2:1.

Tilt, J. 1930. The basal metabol ism of young college women in Florida. J. Biol. Chem. 86:635.


http://jas.fass.org

Citations

http://jas.fass.org#otherarticlesHighWire-hosted articles: This article has been cited by 2


http://jas.fass.org#otherarticles

http://jas.fass.org

Instraspecies Relationship between Fasting Heat Production ...ported for the same animal, the...

Documents

Transcript of Instraspecies Relationship between Fasting Heat Production ...ported for the same animal, the...