Measurement, mathematics, and mechanisms of mammalian growth : a thesis presented in partial fulment of the requirements for the degree of Doctor of Philosophy at Massey University

private study only. The thesis may not be reproduced elsewhere without

the permission of the Author.

MEASUREMENT , MATHEMAT I CS , AND MECHAN I SMS OF MAMMAL IAN GROWTH

A thes i s presented i n parti a l ful fi l ment of the req u i rements for the

Degree of Doc tor of Phi l osophy at Massey Uni vers i ty

Ross Graham C l ark

1978

i

VOLUME ONE

Time g o e s , y o u s a y? A h , n o�

A l a s , T i m e s t a y s , we g o .

H . A. Dobson

The Paradox o f Time, stanza 1 .

Abstract of a thes i s presented i n parti al ful fi l ment

of the requi rements of the Degree of Doctor of Phi l osophy

M EASUREMENT , .MATHH1ATICS, AND MECHAN I SMS OF MAMMALIAN GROWTH

by ROSS GRAHAM CLARK

Longi tu d i nal growth exper i ments u s i ng rats , l ambs , and hei fers were anal ysed by esta bl i s h i ng l i near rel ati onshi ps between ages , l i ve wei ghts and body l engths i n i nd i vi dual anima l s . Vari ou s ana l yti cal methods were i nvesti ga ted . Stati sti cal and b i o l og i ca l reasons forced

the l ogari thmi c transformati on of wei ghts and l engths , a three parameter l ogari thmi c metameter was used i f means and standard

dev i a t i ons were correl ated on a two parameter l ogari thmic metameter . Age was transformed to g i ve l i near rel ations h i ps . Changes to the experimental des i gn and analys i s of growth experiments were suggested .

Effects were demonstrated i n i nd i vi dual animal s that were

previ ou s l y onl y shown for grouped data and the techni ques• sens i ti v i ty produced novel fi nd i ngs . Rats were ovari ectomi sed at three ages and/or treated wi th oestrogen and s l aughtered at four ages . The rat ova ry i nh i bi ted growth pre-pu bertal l y , and the response to ovariectomy or oestrogen was nega t i ve l y rel ated to the pre-treatment growth ra te .

iii

Compensatory growth occurred fol l owi ng wean i ng i n rats and fol l owi ng bi rth i n rumi nants . E s t i mated i ni t i a l wei ghts expl a i ned more of the var i ati on i n subsequent growth rates than d i d o�served wei ghts . I n rats pre-weani ng growth l i nes di verged ( compensat i on bei ng negl i gi bl e) , bi rth and weani ng wei ghts bei ng posi ti vely corre l ated , post-wean i ng growth rate was strongl y-nega t i vely correl ated wi th weani ng wei ght . Estimated bi rth and fi na l wei ghts , and weani ng and fi nal wei ghts , were unrel ated ; compensati on bei ng nearl y compl ete .

Two sets of pre-weani ng l amb live wei ghts ( col l ected by others ) were , for i nd i v i dual anima l s , l i near i sed . Pre-wean i ng compensati on

occurred , as i t d i d i n two i ndependent sets of wei ghi ngs from monozygoti c twin hei fers ( a l so col l ected by other s ) . Compensatory growth , between and w i thi n sets of twi n , occurred rapidl y to weani ng , then sl owed . The effi c iency of i denti ca l twi ns for experimentati on , u s i ng these methods , was shown , as were the d i sadvan tages of u s i ng average dai l y gai ns .

The l i near relationships di d not expl a i n al l the systematic variation , short- and l ong-term osci l l at i ons i n growth rate occurred . Long-term osci l l ati ons were rel ated to l i ve wei ght rather than to age . Neo-nata l testosterone treatment of femal e rats transposed and advanced the pattern of growth . Both sex a nd stra i n affected the pattern of growth . The pos s i bl e u se of these techni ques in animal breedi ng was di scussed .

The l ogar i thms of l engths and wei ghts , assumed by many bi ol ogi sts to be l i nearly rel a ted ( a l l ometry ) , s howed curvi l i near rel at i onshi ps .

A techni que of carcass ana l ys i s was devel oped and appl i ed . Ovar i ectomy i ncreased rat body we i ght and l ength but d i d not produce obes i ty ( a ssayed by percentage composi ti on and by a l l ometry) . Oestrog€n stimu l ated fat depos i ti on but i nh ib i ted linear growth . Body we i ght 's response to oestrogen was adaptive , bone growth 's non-adaptive . Simi l arly

there was a l arge pre-pubertal sex d i fference in body l ength but a smal l _• difference i n body wei ght . Thi s separation of the mechani sms

control ling bone growth and body wei ght i ncrease was di scu ssed . Part

·Of the i ncreased s i ze of ovar i ectomi sed rats was attri buted to i ncreased sk i n s i ze ( and al tered composi ti on ) and decreased tai l l ength , giving decrea sed heat l oss , and i mproved energy u ti l i sati on for growth .

Body growth occurs i n two over l appi ng phases , of cel l hypertrophy and cel l hyperpl a s i a , represented by different growth equations , and

control l ed by d i fferent mechani sms . A pos s i bl e mechani sm control l i ng cell hypertrophy , a nd directi ng compensatory growth , based on carti l age growth , woul d expl a i n some of the effects descri bed . The endocri nol ogy of the mechani sm , and oestrogen 's i nteracti on wi th i t , were di scu ssed .

ACKNOWLEDGEMENTS

I wi sh to express grateful appreci ation to my chief s upervi sor , Dr . M . F . Tarttel i n , for propos i ng the general a rea of researc h and for his w i l l i ng assi stance gi ven duri ng the course of my work .

I al so wi sh to express my thanks to Professor R . E . Munford , my second supervi sor) i n whose department thi s study was carri ed out , for his encouragement , g u i dance , and unfa i l i ng i nterest i n the vari ous a s pects of the work . I am especi al l y i ndebted to his enthu s i a s ti c ini ti ati on of my i nteres t i n computi ng and s tati sti cs and for hi s p rovi d i ng fi nanc i a l support for my work . I am al so i ndebted to D r . R . M . Greenway , my thi rd supervi sor , and the other members of the Department of Physi ol ogy and Anatomy .

V

I deri ved con s i derab l e benefi t from di scussi ons , on the anal ys i s of growth curves , wi th D r . R . W . Purchas o f the Sheep Husbandry Depart­

men t . The readi ness wi th whi ch D r . M . F . Tarttel i n , Ms . Li z Sommerv i l l e , P rofessor R . E . Munford , Professor D . S . F l ux , and D r . L . R . Wal l ace gave thei r ori g i nal data i s gratefu l l y acknowl edged . I wi sh to thank the workers , especi a l l y Mr . E . Ormsby , of the Sma l l Ani ma l Producti on Un i t for a s s i sti ng wi th the care of the experimental anima l s .

Mrs . F . S . Wicherts pati e ntly typed the majori ty of the text and hel ped i n many other way� duri ng the work's fi nal preparat i on . Thanks a re due to the staff of the Massey Uni vers i ty Pri ntery for reduc i ng and p rinti ng the fi gures .

The staff and workers at the Computer Uni t a t Massey, e s pecial l y M r . Col i n Read and Mrs . Nol a S i mpson , were al ways wi l l i ng to a s s i s t wi th my computi ng . Thanks mus t a l so go to Mr . Barry H i tchcock for mi rac­

u l ously mai nta i n i ng the I BM ¹⁶²⁰ computer .

To Dr . M . F . Tarttel i n and Professor R . E . Munford , for readi ng a nd cri t i c i s i ng dra fts of the work , and to Ms . L i z Sommervi l l e , Mr . D . Baker-Gabb , and Ms . Gi l l i an Fi ndl ay , for proof- reading , acknowl edgement is a l so due .

F i nal l y I wi sh to thank my fri ends and flatmates, espec i al l y for the i r perseverance wi th my nocturnal hab i ts . To Gi l l ian , tha n kyou .

Th i s work wa s carr i ed out dur i ng the tenure of a Uni vers i ty Grants Commi ttee Post-Graduate Schol arshi p .

TABLE OF CONTENTS

PREFACE

PAGE 1

CHAPTER ONE : T ITLE PAGE

THE L I NEAR I SAT I ON OF BODY W E I GHT-AGE CURVES IN THE

LABORATORY RAT : SOME APPL ICATIONS AND IMPL I CATI ONS ²

I NTRODUCTI ON ³

a} METHODOLOGY 3

b) APPL ICATI ONS 4

MATER IALS AND METHODS 5

B I OMETR I CAL CONS IDERAT I ONS ⁵

RESULTS AND D I SCUSS ION 12.

1} BODY WE IGHT 12

2) PUBERTY AND GROWTH ¹⁵

3) OVAR I ECTOMY , ULTIMATE WEI GHT AND

RATE OF WEI GHT GAI N ¹⁶

4) WEAN I NG WE IGHT , WE IGHT GAI N AND ULTIMATE WE I GHT ²⁰

GENERAL D I SCUSS ION ^{2 1}

tHAPTER TWO : TITLE PAGE

LAMB LIVE WE I GHTS: NORMAL ISAT I ON . L I NEAR I SATI ON,

AND COMPENSATORY GROWTH ²⁴

I NTRODUCT I ON ²⁵

MATER IALS AND METHODS ²⁵

B I OMETR ICAL CONS IDERATI ONS ²⁶

a} NORMAL I SAT I ON ²⁶

b ) L I NEAR I SATI ON O F THE PRE-WEAN ING W E I GHT-AGE

CURVES OF IND IV I DUAL LAMBS ²⁸

c ) B I RTH WE IGHT OR CONSTANT FOR DEMONSTRATING

COMPENSATORY GROWTH? ³⁰

RESULtS AND D I SCUSS I ON ³³

. CHAPTER THREE : TITLE PAGE

LAMB L IV E WE IGHTS AND COVAR IANCE:

AN EXPER I MENT ANALYSED . I NTRODUCT I ON

·B I OMETR ICAL CONSIDERATI ONS RESULTS AND D I SCUSS I ON

CHAPTER FOUR: T I TLE PAGE

THE REGRESS ION OF L IV E WEIGHT AND AGE IN CATTLE I MONOZYGOUS TWIN HEI FERS AT RUAKURA

INTRODUCTION THE DATA

B I OMETRICAL CONS I DERATI ONS RESULTS AND D ISCUSS ION

COMPENSATORY GROWTH SELECTION FOR BODY S I ZE TW IN EFF I C I ENCY

CHAPTER FIVE: TITLE PAGE

THE REGRESSION OF L IV E WE IGHT AND AGE IN CATTLE I I MONOZYGOUS TWIN HEI FERS AT MASSEY

I NTRODUCTI ON THE DATA

B I OMETR I CAL CONS IDERAT I ONS

COMPAR ISON OF TRANSFORMED AND UNTRANSFORMED REGRESS I ONS RESULTS AND D I SCUSSION

RELAT I ONSH I PS BETW EEN THE ESTIMATED SLOPES

37 38 40 43

49 50 51 53

55 58 62

64 65 66 68

70

AND CONSTANTS ⁷²

COMPAR I SON OF JERSEYS AND NON -JERSEYS ⁷² COMPAR ISONS BETWEEN Y EARS ( IGNORING TWINS) ⁷⁴ BETWEEN SET AND W I TH IN SET MEAN SQUARES

(WITH IN YEARS ) ⁷⁶

vii

DISCUSS ION

LIVE W E I GHT-AGE GROWTH CURVES COMPENSATORY GROWTH

78 81

CHAPTER S I X : TITLE PAGE

FURTHER ANALYSES OF RAT L IV E WEI GHTS IrHRODUCTI ON

88 89 SECT ION ONE :

SECTION TWO :

THE ZUCKER LOG-RECI PROCAL EQUATI ON COMPARED TO THE BRODY ASYMPTOTIC EQUATI ON

THE "L I NEAR" RELAT I ONSH I P BETHEEN THE LOGARITHM OF RAT L IVE WE IGHT AND THE RECI PROCAL OF AGE : THE PRESENCE OF SYSTEMATIC OSC I LLATI ONS

90

ABOUT THE F I TTED L I NE ⁹⁵

INTRODUCTION 9 6

THE DATA ⁹⁸

B I OMETR I CAL CONSIDERATI ONS 99

DUR B I N -WATSON TEST FOR I NDEPENDENCE

OF RESIDUALS 100

RESULTS AND D I SCUSS I ON

DATA FROM THE MASSEY COLONY ^{. 102}

STRA I N D I FFERENCES I N PATTERNS OF GROWTH? ¹⁰⁸ THE EFFECT OF NEO-NATAL TESTOSTERO NE ON THE

PATTERN OF LIVE WEI GHT GRmHH IN FEMALE RATS ¹¹⁶ I NDIV I DUAL AND MASS CURVES ^{. 119} A B I OLOGICAL EXPLANATI ON FOR THE SW I NGS

I N THE RESI DUALS ¹²¹

CONCLUSIONS ¹²⁴

CHAPTER SEVEN: T ITLE PAGE

11L INEAR11 RELATI ONSH I PS BETHEEN AGES , BODY WE I GHTS , AND BODY LENGTHS , AND SYSTEMATI C DEPARTURES FROM

. THESE RELAT I ONSH I PS , I N LABORATORY RATS 127

INTRODUCTION 1 28

EXPER I MENTAL P

F

^OCEDURES 130

B I OMETR I CAL CONSIDERAT IONS 1 3 1

RESULTS AND D I SCUSS ION 134

RELATIONSH I PS TO AGE 134

LOG L I VE WE I GHT

vs

LOG CONCEPTION AGE 136 THE RELAT I ONSH I PS OF L I NEAR D IMENS IONS

TO CONCEPTION AGE 147

ALLOMETRY 150

SEX D IFFERENCES IN GROWTH 153

BIRTH , WEANING, AND ULT IMATE WE I GHTS :

COMPENSATORY GROWTH 157

EVIDENCE FOR FOUR DAY CYCLES OF 30DY GROWTH

I N THE RAT . .

162

CONCLUS I ONS 171

CHAPTER E I GHT : TITL E PAGE

SOME EFFECTS OF OVARI ECTOMY AND OESTROGEN TREATMENT ON THE BODY COMPOS ITION AND THE ALLOMETR I C RELATI ONSH I PS BETWEE N BODY CONSTITUENTS OF THE RAT

I NTRODUCTION

MATERIALS AND METHODS B I OMETRICAL CONSI DERATIONS

PERCENTAGE COMPOSITION ALLOMETRY

RESULTS

BODY WE I GHT NOSE-ANAL LENGTH tONSTITUENT WE IGHTS EFFECT OF TREATMENT

180 181 184 185 187 189

193 193 193 195

ix

RESULTS ( cont . )

E FFECT OF AGE AT SLAUGHTER 196

I NTERACTI ONS 196

ALLOMETRY 201

PERCENTAGE COMPOSITION 202

. SKI N 204

CARCASS 205

WHOLE BODY 205

EFFECT OF AGE ON PERCENTAGE COMPOS ITION 206 SKI N COMPONENTS AS A PERCENTAGE OF THE IR

RESPECTI VE WHOLE BODY COMPONENTS 207

HEAT LOSS 207

CONCLUS IONS 209

ADDENDUM

A METHOD FOR CHEMICALLY ANALYS I NG THE

CHEMICAL COMPOS ITION OF ANIMAL TI SSUE 216

I NTRODUCTI ON 216

SECTION ONE

THE PRIMARY PROCESS I NG OF TI SSUES 216

D I SCUSS ION 217

SECTION TWO

ANALYS I S OF CHEMICAL COMPOSI T I ON

L I P IDS 218

ASH 220

PROTE I N 220

D I SCUSS ION 221

CHAPTER N I NE : TITLE PAGE

THE CONTROL OF BODY GROWTH I N MAMMALS 222

I NTRODUCTION 223

MECHAN ISMS REGULAT I NG GROWTH BY HYPERPLAS I A 226 EFFECTS OF NUTRITION ON CELL HYPERPLAS IA

AND COMPENSATORY GROWTH 230

TECHNIQUES FOR I NDUC I NG UNDER-NUTRI T I ON

DURI NG CELL HYPERPLASI A 230

EFFECT OF NUTRITION ON ADI POSE CELL NUMBER 234

COMPENSATORY GROWTH 236

AGE AT ONSET 236

MECHAN I SMS 237

CARTILAGE GROWTH 238

MUSCLE GROWTH 239

GROWTH IN CELL S IZE AND CARTI LAGE 240

HORMONAL CONTROL OF GROWTH 243

THE HYPOTHALAMUS AND GROWTH 244

GROWTH HORMONE AND THE SOMATOMED I NS 249

OESTROGENS AND GROWTH 250

C HAPTER TEN : TITLE PAGE

NOTES 257

NOTE ONE : THE DEFI N I TION OF COMPENSATORY GROWTH 258 NOTE TWO : THE USE OF AVERAGE DAI LY GA I N 259

NOTE THREE : S I GMOI D GROWTH CURVES 263

NOTE FOUR : T I ME SCALES I N LONGITUD I NAL EXPER IMENTS 265 NOTE FIVE : ANALYSES OF VAR IANCE :

FOR REPLI CATED L I NES I N A CROSS CLASS I FICATI ON

NOTE S I X : COMPUTATION O F ORTHOGONAL COEFF ICI ENTS FOR THE SUBD I V I S I ON OF MEAN SQUARES FOLLOW I NG AN ANALYS IS OF VAR IANCE FOR

267

UNEQUAL SUB-CLASSES 272

NOTE SEVEN : DO RATS PLATEAU IN L I V E WEI GHT? 274 NOTE E I GHT : THE BIOLOGI CAL I NTERPRETATION OF THE

TRANSFORMAT I ONS USED FOR L IVE WE I GHTS 279

REFERENCES CITED 282

APPEND I CE S : VOLUME TWO

xi

L I ST OF F I GURES

F IGURE PAGE

l . la The rel a ti onshi ps between means and s tandard devi ati ons for body wei ghts , on a ri thmeti c and l ogari thmi c metameters , for femal e rats ovari ectomi sed a t 4 weeks and wei ghed

until 15 weeks of age 7

1 . lb Pl ots of body wei ght aga i ns t age for one fema l e rat on untransformed and transformed (l og body weight vs the reci procal of age) metameters --

7 1 . 2a , b , c , & d .

P l ots of l og body wei ght aga i nst the reci procal of age

for rats sham operated and ovari ectomi sed at 3 ages 1 1 1 . 3a The pre-ovari ectomy rate of body wei ght g�i n v s the change

in rate of body wei ght ga i n fol l owi ng ovari ectomy at week 7. 17 1 . 3b The rates of body wei ght ga i n of ovari ectomi sed rats vs

the change i n thei r rates of body wei ght ga i n

fol l owi ng E B treatment 17

1 . 4a , b , c , & d ^•

P l ots of s l o pes and constants , from the l i near equati ons rel ati ng l og body wei ght to the reci procal of age ,

a ga i nst weani ng wei ghts, for rats from the U.C.L.A.

and Massey col oni es . 19

2 . la & b

Rel a ti onshi ps between means and s tandard devi ati ons , on ari thmeti c , two and three parameter l og metameters , for Border Leicester - C hev i ot x Suffol k l ambs , wei ghed weekly

from bi rth to weani ng, Data of Wal l ace ( 1948 ). 27 2 . 2a & b

The l i near rel ati onshi ps between l og l i ve wei ght and l og age (weeks + 1 . 0 ) for a s i ngl e , a pa i r of twi ns and a set

of tri pl et l ambs , Data of Wallace ( 1948 ) . 29 2 . 3a & b

The l i near rel ati onshi ps between the s l opes , from the l i near equati ons rel ati ng l og l i ve wei gh t to l og age , and the

mea sured and cal cu l a ted bi rth wei ghts , Lamb s of Wal l ace ( 1948) 3 1 2 . 3c The rel ations h i p between s l opes and constants , from the

l i near equa ti ons rel a ti ng l og ( l i ve wei ght + 7 l bs ) to

l og age , Data of Wal l ace ( 1948 ) 32

2 .4a & b

Rel ations h i p s between means and standard devi ations , on ari thmeti c and two and three parameter l og metameters , for i ntact fema l e rats wei ghed weekl y from 4·to 15 weeks of age ,

Data from Chapter One , Ma ssey col ony. 35

xiii

F I GURE PAGE

3.1a & b

Rel ationshi ps between means and s tandard dev i ati ons , on a ri thmeti c , two and three parameter l og metameters , for

l ambs wei ghed weekly unti l weani ng ,

Data of Tarttel i n and Munford ( 1974- 5 ) 39

3 . 2 The l i near rel a ti onshi ps between l og l i ve wei ght and l og age (weeks. + 1 . 0 ) for the 3 l ambs wi th the sma l l est corre-

l at i on coeffi c i ents , Data of Tarttel i n & Munford ( 1974-5 ) 41

4� 1 Rel ationshi ps between mean s and s tandard devi ati ons for l i ve wei ghts a t 8 ages , on ari thmeti c and two and three parameter l og metameters , for Rua kura monozygoti c twi n

hei fers , Data of Hancock ( 1951 ) 52

4 . 2a & b

Rel a ti onshi ps between l og age and l og l i ve wei ght , on two and three parameter l og metameters , for two sets of monozygoti c twi n hei fers weighed from 4 to 88 weeks of age ,

Data of Hancock ( 1951 ) 54

4 . 3 The rel ati onsh i p between s l opes and constants , from the l i near equati ons rel ati ng l og ( l i ve wei ght + 60 l bs ) to

l og age , Data of Hancock ( 1951 ) 56

5 .la & b

Rel a ti onshi ps between means and s tandard devi ati ons , on ari thmeti c and two parameter l og metameters , for

the Ma ssey monozygoti c Jersey twi n hei fers , wei ghed from

1 to 92 weeks of age and born i n 1966 67 5.2a & b

Rel a ti onshi ps between sl opes and constants , from the l i near equa ti ons rel ati ng l og l i ve wei ght to l og tan age

(weeks/2 ) , for Massey Twi n hei fers , born i n 1966 & 1968 7 1 5.3 The rel ationshi p between s l opes and constants , from the

l i near equati ons rel ati ng l og l i ve wei ght to l og tan age

(weeks/2 ) , for Massey Twi n hei fers , born from 1964-8 . 73

6 . 1 Log-rec i proca l (Zucker) and asymptoti c ( Brody) growth equati ons compared ; pl ots of res i dua l s about the fi tted

l i nes� age , mal e rats , data of Bl i ss ( 1970 ) . 91 6 . 2a & b

The resi dua l s a bout the l og-reci procal l i nes fi tted to

i nd i vi dual i ntact o i l i njected fema l e rats � age 1 01

F I GURE PAGE 6 . 3a & b

6 . 4a 6 . 4 b 6 . 5a 6 . 5b 6 . 6a 6 . 6 b 6 . 7a 6 . 7b 6 . 8

6 . 9

The resi dua l s a bout the l og-reci procal l i nes fi tted to i ndivi dual neo-natal l y ovari ectomi sed femal e ra ts ,

Data of Sommervi l l e and Tarttel i n , Massey col ony 103 The resi dua l s a bout the l og rec i procal l i nes fi tted

to i nd i vi dual fema l e rats vs l og l i ve wei g h t , Data o f Tarttel i n et al . (1975 ) , U . C . L . A. col ony Oi l i njected control s

Testosterone propi onate ( 10ug ) Day 2

11 11

( 30ug ) ¹¹

11 11

( 90ug ) ¹¹

11 11

( 270u g ) ¹¹

11 11

( 270ug ) ¹¹ Oi l i njec ted control s

Tes tosterone propi onate ( 270ug ) Day 2

•

( outl i er excl uded ) ( pl us weani ng wei ght)

11 11 11

Res i dua l s about the l og - rec i procal l i ne fi tted to the mas s curve of mal e rats vs l og l i ve wei ght ,

Data of Zucker et a l . ( 1941b)

Res i dual s a bout the l og-rec i proca l l i nes fi tted to the mass curves for mal e and fema l e ra ts , vs l og l i ve weight , Data of Acheson et a l . ( 1959 ) --

105 105 106 106 107 107 1 1 0 1 10

1 1 2

1 14 6 . 10a & b

The res i dua l s about the l og-reci procal l i nes fi tted to ind i v i dual femal e rats vs l og l i ve wei gh t ,

Data o f Tarttel i n a n d Clark , Massey col ony 1 1 5 6 . 1 1a & b

Untransformed and transformed growth curves of neo­

natal l y ovar i ectomi sed femal e rats ,

Data of Sommervi l l e and Tarttel i n , Massey col ony 1 17 6 . 12a �; b

7 . 1a 7 . 1b

7 . 2a 7 . 2b 7 . 3a 7 . 3b 7 . 4a 7 . 4b

The resi d ua l s a bout the i ndi vi dual and mass curves , v s l og l i ve wei g ht , for neo-nata l l y ovari ectomi sed

femal e rats , Sommervi l l e and Tarttel i n , Ma ssey col ony 118

Body wei ght growth i n mal e and femal e rats , wei ghed da i l y from 16 to 38 days of age , Data of Acheson et al .

( 1 959 )

Log l i ve wei ght� l og concepti on age 135

Resi dual s -v s l og concepti on age 135

Growth curves of rats wei ghed from b i rth to 49 days of age , Data of Tarttel i n & Cl ark , Massey col ony

Mal es L i ve wei ght vs Age , Untransformed 137

11 Log l i ve wei ght vs Log concepti on age 137 Fema l es L i ve wei ght vs Age , Untransformed 138

11 Log l i ve wei ght vs Log concepti on age 138 Androgeni sed Li ve wei ght vs Age , Untransformed 139

11 Log l i ve wei ght vs Log concept i on age 139

F I GURE

7 . 5a 7 . 5b 7 .6a 7 .6 b 7 . 7a 7 . 7b

7 .8a 7 . 8 b

7 . 9a 7 . 9 b

7 . 1 0a 7 . l Ob 7 . 1 1a 7 . ll b

7 . 1 2a 7 . 1 2 b

7 . 1 3a 7 . 13 b

7 . 14a 7 . 14b

7. 15a 7 . 1 5 b

Res i dua l s a bout the l og-l og l i nes fi tted t o i nd i v i dual rats , Data of Tarttel i n & Cl ark , Mas sey col ony

vs Age Mal e rats

vs ¹¹ Femal e rats

vs Log l i ve wei ght Mal e rats vs ^{11 11 11} Fema l e rats

vs Log l i ve wei ght Androgeni sed fema l e rats

vs Age ^{11 11 11}

Tail growth i n mal e and fema l e rats measured da i ly from 16 to 38 days of age , Data of Acheson et al . ( 1959 ) Log tai l l ength vs Log concepti on age

Res i dual s about the l og-l og l i nes �age

Body l ength growth i n mal e and femal e rats measured d ai ly from 16 to 38 days of age ,

Data of Acheson et al . ( 1959 )

Log body l ength v s l og concepti on age Resi dual s a bout the l og- l og l i nes � age Al l ometri c rel ati onshi ps between body l engths a nd wei ghts for mal e and femal e rats ,

Da ta of Acheson et a l . ( 1959 )

Log body wei ght vs Log total body l ength

11 11 11 vs Log body l ength

11 11 11

vs Log tai l l ength Log body l ength vs ^{11 11 11}

and

Post-weani ng rate of body wei ght ga i n vs Day 28 l i ve wei ght (both estimated from the fi tted-rag-rec i procal li nes ) , Data of Tarttel i n & C l a rk , Massey col ony

Femal e rats Mal e rats

Ul t i mate wei gh t vs Day 28 l i ve wei ght ( both estimated from the l og -reci procal l i nes fi tted to i nd i v i dual rats ) , Data of Tartte l i n & C l a rk , Massey col ony

Femal e rats Ma l e rats

The effect of b i rth wei gh t on the subsequent growth i n l i ve wei ght of fema l e rats , Data of Tarttel i n & Cl ark Estimated bi rth wei ght vs Estimated u l timate wei ght

1 1 1 1 11

vs Estima ted Day 28 wei ght Res i dual s a bout the l i nes rel a ti ng l og l engths to l og l og concepti on age vs l og concepti on age ,

Data of Acheson et a l . ( 1959 ) Mal e tai l l ength

Femal e total l ength

XV

PAGE

142 142 143 143 144 144

146 146

148 148

151 151

152 152

155 1.55

156 156

159 1 59

161 161

F I GURE

7 . 16a 7 . 16 b

7 . 17a 7.17b 7 . 17c 7 . 17d 7 . 18a 7.18b 7 . 18c 7 . 18d 7.19a 7 . 19b 7 . 19c 7 . 19d

8 . 1

8 . 2

8 . 3

8 . 4

1 0 . 1a 1 0 . 1b 1 0 . 1c

1 0 . 2a 1 0 . 2b 1 0 . 2c

Res i dual s a bout the l og-reci procal l i nes for femal e rats measured from 21 to 38 days of age ,

Data of Acheson et a l . ( 1959 ) Body wei ght

Body l ength Resi dual s vs Age

1 1 -��- 11

Residual s a bou t the l og-reci proca l l i nes fi tted the da i ly li ve wei ghts of rats �bi rth age , Data of Tartte l i n & Clark , Massey col ony Mal e rat Rat No . 40

11 11 11 11

11 11 11 11 43

11 11 11 11 41

42 Femal e rat ^{1 1 11} .33

11 11 11 11 3 5

11 11 11 11

11 11 11 11 49

50 Androgeni sed ^{11 11} 30

11 11 11

11 11 11 31

11 11 11 29

32

Al l ometric reg ressi ons of l og wet wei ghts upon l og nose-anal l engths for i ntact + EB treated and ovari ectomi sed rats

Al l ometric regres s i ons of l og ski n consti tuent wei ghts upon l og nose-anal l engths for i ntact + EB treated and for ovari ectomi sed rats

to

Al l ometri c regre s s i ons of l og carcass consti tuent wei ghts upon l og nose-a nal l engths for i ntact + EB treated and for ovari ectomi sed rats

Al l ometric regress i ons of l og whol e body consti tuent wei ghts upon l og nose-anal l engths for i ntact

+ EB treated and for ovari ectomi sed rats

Untransformed pl ots of l i ve wei ght v s age , Lack of 'pl atea u i ng• i n 3 ma ture rat

�

^{Data of} Tarttel i n ( 1970 ) , U . C .L . A . col ony

Rat No . 14 Rat No . 3 Rat No . 1

Transformed pl ots of l i ve wei ght vs age , Ra t No . 14

Rat No . 3 Rat No . 1

PAGE

163 163

165 165 166 166

167 167 168 168

169 169 170 170

197

198

1 99 200

275 275 275

276 276 276

PREFACE

Thi s thes i s does not begi n i n the c us tomary manner , wi th a large revi ew of the rel evant l i terature . The c h i ef reason for thi s departure from c us tom bei ng the pauc i ty of l i terature rel evant to the areas covered by Cha pters One to Seven . Some parts of thi s thes i s had been , or were abo ut to be , publ i shed . Thus the present format refl ects an attempt at mi nimi s i ng the amo unt of re-drafti ng of thi s publ i shed materi al . I n add i ti on the thes i s evo l ved i n a somewhat unus ua l manner , thi s al so determi ned i ts form . The i ni ti al scope of the thesi s was to i nvesti gate the effects of sex steri ods on body growth , body composi ti on , and the di stri buti on of body fat i n the l aboratory rat . But the chi ef meas ure of body growth used , l i ve wei ght , wa s fo und to be i nadeq uately anal ysed

1

i n the c urrent l i terat ure . Thi s l ed to a n extens i ve study of the

s tati sti cal methods that coul d be appl i ed to l i ve wei ght data a nd to the eventual c ho i ce of what appears to be the mos t frui tful l i ne of analys i s . The stati s ti cal method s devel oped for analys i ng rat l i ve wei ghts were a l so appl i ed to the l i ve wei ghts of domesti c a n i ma l s ( sheep and cattl e ) .

S i nce wha t was , i ni ti a l l y , a smal l part of the thes i s grew , i nto perhaps the mos t i mportant part , a re- structuri ng of the work was obv i o us l y necessa ry .

The s tud i es i n Chapters One to Seven wi l l be presented i n ro ug h l y the order that they were compl eted . This method of presentation does tend to g i ve repeti tion as the same data i s sometimes ana l ysed a nd re-analysed i n separa te chapters . E ssenti a l l y the same stati sti cal techni ques are al so used and descri bed i n more than one chapter . So some parts of the c hapters coul d have been combi ned b ut the l i nes of reasoni ng may have then become confused . Al so a reader i nterested i n the growth of a s i ng l e

s pec i e s wi l l , under the present format , genera l ly fi nd the i nformat i on rel evant concentrated i n one chapte r , or secti on , rather than scattered throug h the text. Al tho ugh thi s l ay-out enta i l s some restatement of methods the general reader wi l l note that d i fferent stati sti cal probl ems occ ur i n the . vari o us s pecies a nd da ta sets and that their sol uti on makes the whol e rel evant to the parti c ul a r . The reader , i t i s hoped , wi l l benefi t from seei ng the methods descri bed i n the order that they were deve l o ped , a nd appl i ed , as the l og i cal progre s s i on of the work sho ul d

become c l earer.