173

.A REVIEW OF INDEPENDENT AND LINKED SEGREGATION IN THE NORWAY RAT

Br ROY R O B I N S O N

St. Stephens Road jVurser3,, Eating, Lol~don, Enghv~d

(Received March 14, 1959)

O f the known nmtant genes of the rat, Rallus norvegicus, twenty-eight have been studied :in published accounts of investigations on the possible existence of genetic linkage. ;Numbered among these are a few genes which are Iethals of varying severity, or confer a crippling semi-viability upon the individual, which have involved time-consuming

iprocedures for their analysis, primarily by the method devised by Castle (1939). In connection with the twenty-eight genes which have been smdied, information is avail- .able for 136 (34(}';) of the 406 possible different combinations. The figure of 406 combi-

nations includes sex, since for the purpose of linkage analysis, maleness may be treated (as due to a dominant gene (symbolised here as ~ ; see TaMe 1 for explanation ofgene i:'svmbols employed in this paper). The fewness of the studied combinations is probably =a consequence of several contingencies. Full consideration has not always been given

:ito possible loose linkage (producing the situation where, if two genes display linkage, one is dropped fi'om further study; a dubious action unless the genes are closely linked) and the impIication of partial sex linkage has not been explored. Finally, it is apparent

that negative results, or results duplicating previous tests, are not invariably considered worthy of publication.

However, at present, four groups of!inked genes have been detected. One group is composed of six loci and another of five (possibly six), while the other two have merely two each. For one group adequate data have disclosed that a sex difference in crossing- over may occur. A t\u-ther system may consist of three genes which are extremely

loosely linked, but the evidence at present is unconvincing. Extremely close linkage is apparent between the two genes c .--r, while the linkage between the gent pairs a n - - C u : ,

O/ la --s , and Cuj - -Sh is less than 10 ,/o. It may also be remarked that mutant he has not been firmly established. I f the above considerations ave taken into account the numher of effective different combinations IMls to 276. The percentage examined rises to -'1.9~, although the examination may be inadequate in some instances.

Much of the information relating to genetic linkage is scattered among numerous papers and, except for a cursory summary by Castle (1952), no at tempt has been made hitherto to review the material. Nor, indeed, woulcl a simple collation be of special interest, l-Iowever, with the formulation of statistical :m.etlmds enabling data to be

p~oled fiom various sources, although consisting of diverse mating types and linkage phases, a critical collation of data with the aid ofsuch methods enables greater reliability to be attached to statements of supposedly independent inberitance. This review surveys and statistically comhines all cases of simultaneous segregation of two or 1"I1Ol'1~.

174 Linkage in rals

genes in the literature known to the author. ALl endeavour has been made to include all the pertinent dttta.

In spite of a few discordant early determinations of the dipIoid chromosome number of the rat, recent exarninations have produced general agreement of-t2 as fl~e normal' complement in germinal tissue (see Makino (195 I) for an exhaustive list of re[Erences). It is to be presumed that the nlutant genes of the rat will ultimately be assigned to twen tv-cm e . a u tosonlal .grcmps,- with the distinct possibility ofa scx-I inked asse ~nl),,ge.S~o

PROCEDURE

The statistical technique adopted is essentiaIly the .~ystcm o[ scoring data introduced by Fisher (194-6). This is a special case of a more general methocl of" simultaneous estimation of genetic parameters as discussed, for example, by Rao (I959_). Details of the technique specifically utilized in this paper are described in the previous su,'vey of genetic segregation in the rabbit (Robinson 1956). In the present material a number of the segregations are distorted by differential viability or partial penetrance of the mutant alleles. An indication of the extent to which the rations mutants are affected in this respect is given by Table I. Analysis of segregations with obvious inviabitity or impenetrance present additional complexities, but partial penetrance is tackled by the elegant method described by Parsons (1957) for two-point data, while partial viability requires the precise formulation of the class expectations in terms of the recombination fraction and viability coefficients, as, for example, in Robinson (!958).

It is also possible for small inviability or impenetrance interactions between genes to further distort the observed segregations, and the usuM precaution of baIancing the linkage phases of the genotypes is excluded in the present case. However, in an attempt to allow in part for this, an index of phase balance has been chosen as the percentage oF the total amount of information contributed by the two dominant genes (regardless of which is the mutant) in coupling. Therefore, 50% indicates perfect balance between pleases. Heteroo'eneity between categories and sources of data may be assessed from the attribute possessed by each sample segregation of a X ~- for one

degree of freedom.

THE DATA

IndepeMenl loci

Prima facie evidence is presented in Table 9 for the independent segregation of 116 pMrs o_rgene combinations for which breeding data has been published. The tabula- tion consists of'the estimated recombination fiaction, with a standard error based upon p-=0'5, and the index of phase balance possessed by the pooled data, together with two entries (score and information) useful for incorporating future results without the inconvenience of searching through old records. It would be worthwhile For new material to be accum.ulated whenever ikasible either to increase the precision of quasi- independence or to reveal a Iinkage. In the latter event, o['com'se, alI the segregations

T a b l e 1.

ROY ROBINSON 175

:~f~lanls of the rat, with symbols employed i,~ this paper and commenls zq~oll disadvanlages fiom lhe star qf linkage almlysis

Symbol Designation Characteristic C o m m e n t

at non-agouti coat colour

a n anaemia haematodystrophy lethal

b brown coat colour

e albinism coat colour

Ca cataract eye anomaly semt-penet rant

Cul curly--1 coat texture

Cua cur ly--2 coat texture

cw cowlick coat texture semi-penet rant

d dilute coat colour

f fawn coat eolour

h hooded white spotting semi-penet rant

H~ antigen Ha blood antigen

he haema tomas vascular system senti-viable

H~t matigen H~ blood antigen

hr hairless alopecia semi-viable

in indsorless dentition

j jaundice enzyme system

k kinky coat tcxtflre semi-vlable

lg Gv6nebcvg's lethal skeleton lethal

n naked alopecia

p pink eyed coo t colour

at- red eyed coat colmu'

s silvering coal c~tour scm[-vinMe

Sh shaggy coa~ texture

s r shaker behavlour sterile

s t s tub skelclon semi-vialflc

w waltzing behavlour semi-penetrant

w o wobl>Iy bchaviour

c? male sex

176 Linkage in rats

wil} requi re vescoring at the es t imated value o fp . T h a t m a n y of the genes are merely

mdependenr , in a formal sense of not d i sp lay ing an obvious l inkage, m a y be assessed

from consul tat ion o[" the closest l inkage compat ib le wi th the da t a p rov ided by Fig. 1.

41 3~ 41 / 40

4Y l a 4g . ~ H S ~ 4.~,

[-- 41 ] ] ! 33' J 39 ~ $~" gl

[ +zl ~ - $6 4~" ~.4 i 4~ ~1 gi r

I t

I ] 45 39 4~ 38

I

I 44 r I r ~9

I "

4-3 r ] 37 41

3q P.I I

" i 1 ~:; ~B 38 41

r f t I

s 5 6

J FxG, I. Extent of quasi-independent linkage tests. The entry within each cell is the closest linkage

compatible with the observed data; obtained by subtracting 1.96(s) from 0.5" and expressed as a crosso'ver percentagc.

Wi th 1 t6 observed recombina t ions it may be expected tha t six of the es t imates would

tMt outs ide the 5~/o l imits For r andom assortment by chance alone. Actua l ly , two are

below the lower l imi t while two are beyond the upper . These are discussed in the

succeeding section. I~i view of the theories on the re la t ionship between chronlosome '

map- leng th and the r ecombina t ion value, some of which suggest the occur rence of

ROY ROBINSON 1 77

recombinants i~ excess of 50%, the detection o[" recombination fractions exceeding the

apper limit is of practical concern. It is qf interest with experimental data of this sort, that the observations could be

subject to two forms of observational bias : (1) an observer may terminate his collection i 01"data at a point where free segregation is supported; and (2) should the observations . yield a significan~ (or nearly significant) deviation at some stage of provisional abandon- ment, the experiment may be continued to ascertain if the deviation is maintained. '. The first bias is likely to be at a subconscious level while the second is conscious. \'Vith

either, the total variation would appear to be smaller than that expected by chance; the larger deviations being eliminated. The present compendium of quasi-independent

segregations lends itseIf to an examination for over-homogeneity of the observations. The total ,~- of 83-5I for the 116 pairs ofgene comparisons is outside the 5% admissible

:range (88--148) about the mean X"-for this number of degrees of fieedom, using the

A3 approximation of Rao (1952, p. 222). This value of t h e X ,-~ includes the four excessively large. X~-s,~" which are discussed in the following section. I t would seem

. that one or the other of the biases may have been operating in the collection of the

present data. A number of statements have been made in the literature that certain genes are

inherited independently, but without giving the supporting evidence. Wildm-, et al., (1932) say that a number of crosses show that h r is not linked to e. K.ing and Castle (1935) refer to experiments by Castle that a, c and h are independent of each other. King and Castle (1937) comment that no suggestion of linkage was found between "w and d, ;hr or k . Castle and King (1940) quote Prof . J .W. MacAr thur tha t j recombines

f i ee ly with a, c and h. Castle (t953) states that no linkage is apparent between s and

a~ Cus~ 1~ or w o .

The data of Castle (1939) on the segregation o f a n and wo are included with those in the paper by Castle, King and Daniels (1941). The small amount of information given

by Burhoe (i947) has prompted the suggestion that tlle antioens H a and HM reside

in different chromosomes, but no systematic test appears to have been perfm-med. A personal communication fi'om Dr. E. Roberts slates that the segregation of c and h r in

his (1926) paper is in repulsion phase.

POSSIBLE LINKAGE

Aside fi'om the definitely established linkages, the results of tests between a number of other genes deserve closer scruti~y. In general, the data of the present section are suggestive rather than conclusive and may repay further investigation.

The gene pair e - - C u , display a significant recombination fraction of 0"4063:k0-044-2 (,~}=4-50) a.ccording to the data o[ 'Bhmn and G,-egory (1937). Inspection of the individual litter records by these attthors revealed, however, that one particular female was responsible for about half the observed deviation and that her litters were unusually

small. I t is implied that this may account for the association, rai.her ~han chromosomal

linkage < �9 .

178

Loci

a - - b

a - C ,a

a - Cu~

a C u ~

f i t - - C W

a - d

a - h

a - n . .

a - h r

j

a - k

a - r

a - - s t

A w o

a n - w o

b - c

b h

b - k

c - C u 2

C - - C W

c h

c h r

c - j

c - SIx

C - - SX"

C - - W O

C a .- C u ~

C a - C u ~

Linkage in rals

T a l ~ l e 2 . @,lsi-i;Me/~endent loci

p s S I

0.50 0.0,t- . - 0.8890

0.51 0.03 7-7778

0.47 0.06 -- 8

0.49 O.f13 -- 12

0.47 I].fJ5 -- 1 fl

O.~Ia 0.04 -. 1(~

0-5 ] O.02 3 0

0,:19 0-0 l - - 70"5908

0.48 0"05 -- 6

0'55 0.04. 24

0-50 0.02 18

0.52 0.04. 12

0-50 0.O2 4,88~0

0.50 0.02 28

0-47 0.07 4.8889

0-45 0-06 - 16

0.51 0"09 0.7778

0.4.9 0.04 -- 6

0.42 0.14 -- 4

(1.51 0.05 3.1111

0.46 i 0.03 --44.

0-41 * 0-04 .'18

0.55 0.04 26

0"49 0-02 -- 16-8889

0'51 0'03 13.7778

0.50 0.05 0

0-46 0"05 - - 18

0'47 0-04. -- 8

0"43 0.06 - 2 4

0.46 0.04 - - 24,6667

0,49 0-04 -- 2

O.-18 0.02 --~52

13 h a s c

ba l ance References

514'6667

1609.1850

312

896

292

588

2220

564.1.7005

364

588

2372

672

2324"4.578

3136

182-6667

328

138.6667

644

51-5556

362.6667

1080

512

516

1693-6295

1256.8905

,t72

4.28

695,6592

330.6667

665-3334

756

2256

0

97

GO

100

0

0

1 0 0

100

0

100

100

54

75

0

86

0

0

0

0

100

0

95

0

?

lO0

0

0

51

5O

0

,1.3

,1I, '1.3, 54, 59

27

;1.3

[

2I

54

4.1, 42, :1.3, 54, 59

6

6

55

22

43, 48

42, 54

21

29

59

29

43

43

43

I

21

4 i , 4.3, 54., 59 .

53

22

25

21

29

59

27

27

R o Y ] ~ O B I N S O N

Tablc 2. Odmsi-i~dependeJ~l loci (contd.)

179

Loci p s S I Phase ba l ancc

References

Ca - e w 0-4.8 0-07 -- 4 '4444

Ca - d 0"43 0"08 - - 12

Ca - h 0'62 0 '09 16

Ca - j 0-53 0 '05 12

Ca - k 0"53 0 '13 2

Ca - p 0 '48 0-04 - - 2 0

Ca - S h . 0"51 0"05 4

C a - s r 0"51 0"09 0 '6667

C a - w o 0"50 0.7,4 0

C u 1 - C u 2 0-54 0"07 6"8

C u , - e w 0"46 0-04 - - 2 0

Cu~ - d 0-50 0.03 0

C a z - h 0"59 O" 10 t0"4.772

Cuj - HA 0.49 0.07 = 2

Cu~ - H~, 0.48 0-07 - - 6

Cn I - h r 0"49 0 '05 - - 2

Cu~ - j 0.49 0"02 - -20

C% --- k 0.58* 0.03 67.5370

Cu~ - p 0"57 0.05 22

C u I s r 0-43 0"05 24.'6667

C % - w o 0.51 0.07 2

Cu 2 - c w (I-4 ~ 0"05 -- 8

C u e d 0"5't 0"06 14

C, ua - h 0.47 0"05 113

Cue - H,~ 0"4 ~ 0.06 -- 8

Cu.. - H~, 0"5'1 0.05 12

C u , - h r 0 '49 0"05 -- 6

C u e - j 0-4(; 0.04 - - 24.

C u a - I( 0"66 0 '09 20"6t~67

Cu~ - p 0.48 0"04 Ig

C u a - s r 0.53 0 '05 14

Cu~ - w o 0 '50 0"0'1 0

208

160

135

408

60

832

368

132

48

190.6567

512

124.8

I04-8990

236

236

340

2095

862-4268

340

353.3245

196

400

332

'15(;

336

34-,t.

,112

624

126"66W

74g

4.36

560

100

100

35

31

100

}00

0

100

100

0

100

100

100

100

I00

100

9

100

I00

100

?

I00

100

0

100

I00

I00

?

100

100

100

0

21

27

27

27

27

27

25

21

27

39

21

43

43

6

6

43

22

3 7 , 4 3

4.3

21

29

21

1

I

6

6

1

22

i

]

21

29

180

' F a b l e 2.

Loci p .r

c w - - d 0.46 0.07

c w - h 0.55 0.05)

c w j 0,4 {; 0,07

c w - k 0,46 0"135

c w - p 0.59 0"06

c w - Sh 0.50 0.04-

e w - s r 0.40 0 '03

c w - w o 0-53 0.06

d - f 0.45 0.07

d - h 0.4.7 0.02

d - H,~ 0-47 0-06

d .- H v 0.54. 0.08

d - h r 0 " 5 1 0 " 0 2

d - j 0.62* 0.06

d - k 0.50 0-05

d - r 0"51 0-02

d - Sh 0,52 0-06

d - s r 0 '31" 0"08

d - w o 0'51 0 '04

h - H a 0.50 0-06

h - H ~ 0.50 " 0.05

h - h r 0"50 0"02

h - j 0-47 0.03

h - k 0.57 0.04

h - r 0.50 0-02

h - s r 0'4-7 0"04

h - w o 0"47 0"03

h -c~ 0 '47 0"06

tlA - h r 0.47 0.04

HA - k 0-50 0 '05

H a - r 0.54 0.07

H~ - h r 0'53 0 '07

Linkage in rals

Ojeasi-i~Mcpotde,t loci ( c o a t d . )

S [

-- 9.7778 224

5(; 1136

-- I f} 273.3265

-- i9-1111 456.8946

26 279

2 679

- - 3 8 . 8 8 8 9 1053.7832

6.7778 24Y5586

10 196

-- 60 2'28O

- . l 0 300

5-7778 161.7778

26.8889 2419.1111

39-5556 279.1 t 11

1.7778 4.76.444-4

I4-2222 2936

6 3O0

- -30 156

8 840

0.8889 295-I l I I

0 496

- - 12 24.24

- - 2 2 860

50.9217 734.2323

- - 4 3888

-- 16.8889 644.0067

- -46 1596

-- 7.3333 278.6667

- - 16 58,t-

- - 2 380

9 0 8 _34

6 236

. [> ] ] ago

ba[ancc

0

0

0

0

0

100

0

0

100

100

100

I00

90

0

0

84

0

0

"}

i 00

0

100

9

I00

61

0

-}

80

I00

0

0

0

Re[erences

21

21

21

2t

2 I

21

2I

21

26

54

6

6

54

22

48

54

25

21

29

6

6

55

22

43, 48

42, 54

21

29

59

6

6

6

6

' R o Y ROB1NSON 18i

Table '2. (h~asi-itldependc~z! loci (contd.)

Loci p s S I P h a s e R e f e r e n c e s b a l a n c e

]

H, ,~ - k 0-4-8 0 .07 - - 4. 24.0 0 6

I t ~ - r 0-4.7 0-07 - - 7.1111 206 .2222 0 6

la r - j 0"52 0"06 6"22'22 2 8 0 ' 8 8 8 9 0 22

h r - k 0 '51 0 ' 0 5 5-5556 ,196 0 48

h r - n 0"4.5 0"04. - . I 2 884. 33 20, 21

h r - p 0 ' 52 0 ' 0 5 6 340 100 43

h r - r 0"50 0"02 -- 6 2'292 100 55

h r - s r 0"150 0"08 16"8889 171 '8522 0 2 I

h r - w o 0"4<I 0"03 - - 6 6 1164 .-' 0 20, 29

j - k 0"53 0"03 37"7778 114"6'6811 0 32

j - S h 0 '4B 0 ' 0 5 - - 8 376 0 25

j - s r 0"4'7 0"06 - - 8 264 0 21

j - w o 0"50 0'04. - - 2 572 0 22

k - p 0"47 0"04- - - 16 512 0 48

k - s r 0"17 0"06 - - I0 288 0 21

k - w o 0"51 0"04" 2 52'1' 0 29

n - w o 0"53 0 ' 0 3 28 1032 39 20, 21

p - s r 0"50 0"05 - - '2 2 2 2 2 4 6 7 ' 5 6 1 4 0 21

p - w o 0"51 0"04 8 760 ? "29

r - c~ 0 ' 5 5 9"09 6 134"6667 100 59

* s ign i f i c an t

,krotc. S t a n d a , ' d c r r o r (s), s co rc (S) a n d i n f b r m a t i o n (1) a r c c o m p u t e d for p .~:0"5.

Castle and King (1940) record a F. repulsion populatJon which yields an estimate [bl-p of 0.6147 d:0.0599 (,~ 5.61) for the interval d j. This vahte of" p represents significant excess recombination, and examination o[" the se~regatlon shows l}lis to be due to an overabtlndat/ce ofindividuals in tim double recessive class. It is not clear in this case how the excess could arise flom f'aclors ot ~er than chance. It must be remem- bcred, however, that super-recombination may be as indicative oF linkage in certain

C i r C t l l l l S t a l l C e S a s under-recombh~ation. Anlong the many tests conducted by Gasi:le, Dem.pster and Shurrager (1955), one

case of doubtthl linkage is reported. A backcross generation with lhe two genes d and s r yielded a significant crossover value ofp=-0.3077q--0.080I (X~-5-77). Thc

182 Litdcagc in "rals

number of olt~pring reared is small (39) and the low value ofp is due to a deticiency in one of the two crossover classes. The Pact that the remaining three classes are of almost exact numerical equality implies that the fi'equencies may be a consequence of random sampling.

The offspring recorded by Feldma.a (1935b) l'or the joint segregation of Cu, and k show a highly signilicant departure fi'om random assortment (,~ =21"24.). The two genes appear to be repelling each other but the effect is presumably due to heavy

m o r t a l i t y o f k k a n i m a I s . Nfitchell (1935) lbund that the viability o f k i s 0.8697 and, on the assumptloa that this value is true for Feldmaz~'s data, reduces the ,~ to 17-.292.

However, King and Castle (1935) found no evidence of either lower viability of k or all association of Cu and k. The combined data have the ,y'{ of 5.29 and the lmtero-

geneity is ,~=11 .93 . There is no method of checking whether Feldman's animals are iess viable than g7 ~o, which is the probable explanation for the anomalous result.

IL: 1941, Castle, King, and Daniels found evidence lbr linkage of the oenes h r and w% p=0-4034.4--0-0458 (X~=4.45). However, subsequent data of Castle (i955) have failed to confirm the linkage, and [lie estimate fiom the pooled data is i ~.4433~0.0291

(,~z=3.74), a sub-significant result? Castle, Dempstev and Shurrager (1955) reported a linkage of0.34694-0.0714 (X~. =4,'59) between the mutants h r - - n . Now, if linkage exists between h r and w% it may be possible to detect linkage between n and w% but the data of Castle el al. (1955) are completely negative, p=0"51164-0.0539. This prechtdes the possibility that n lies between h r and w o but not necessarily that the order is w o - - h r - - n . I~owever, Castle (t955) in an at tempt to pinpoint tile location of the three genes more exactly, obtained results which do not encourage beliefin the existence of linkage. The estimates fi-om the pooled data are p=0.45254-0.0335 for the pair h r - - n and p :0 '52904-0"03I I for the pair n wo ; both of these values are non-signi- ficant deviates from random segregation. The amount of heterogeneity between the various experiments is negHgible for all three combinations, and in the case of two, the phases are somewhat balanced. I t is patent that i1" these genes are borne on a common chromosome, their relative positions are such to produce extremely weak linkages. Additional studies, .especially with a new mutant displaying linkage with both h r and wo, would probably clarify the situation. 5.ieanwhile, it would seem wise to suspend judgment.

ESTA1~ LtSI-IED LINKAGES

If it is agreed to leave in abeyance, until fitrther data are lbrthcoming, tile question of possible iinkage of the genes lax-, n and wo, lbur systems of linked genes are known in tim rat. Two of these are individually composed of five known loci (at least), while the other two merely subsist of single linkages. The computed values of the recom)ination

fractions are conveniently summarised by Table 3. The linkage relationships between the genes constituting the linked groups are displayed by the trigons of Fig. 2. A trigoll '

1 Castle's (I.955) figure of 4.3 crossovers is an arithmetical slip and this Icads tu an m'rot~eously significant .i deviation in his'paper.

RoY RoslNsos 183

i s defined as a tr iangular d iagram in which the observed crossover percentages ca1,. be

both graphical ly and analytically displayed. The top row of the trig on shows the

amount of determined crossingover between adjacent genes and if the genes are arranged

hi the correct serial order the diagonal columns should decrease monotonical ly to the

nadir. This feature, if sufficient crossover values have been determined, would ensure

that the correct sequence has been found. It may also be possible to detect variation of

the amount ofcrossingover along the chromosome, brought into being by liuctuations in

the chiasmata interference interval, or by other factors.

Group I . The first linkage group consists of five genes with the possibility that a sixth

(he) may also reside in the chromosome.

The first l inkage in the rat was recorded by Castte and Wr igh t in 1915 and was dis-

cussed in detail by Castle (1916). The two genes in question were p and r, and ahnost

i /, > \

I

14-

44-

/

X

1,'m. 2. Trigons shmving the relative crossover percentages bcl.wccn the genes ol'linkagc groups I and II.

immediately both were lbund t~ be also linked will1 e. This trio of genes has been sub- scquently subjected to intensive study. Ill I937, Castle and Kin 3 reported the linkage

o[ 'w with c and p and, later (1941), with r. Finally, Gr(ineberg (1939) has folnld that

the lethal lg showed linkage with c and p. In regard to Ig, the data of Griineberg's

table 5 has not been used, because o f l h e aberrant ratio for p. No evidence of hetero-

geneity between ctitlkrent segrexations has 3een re, covered for the ,gene pairs c - - w ,

lg--p~ p - - r ur p - - w , where the recombit~ation fraction is derived from more than one

segregation.

The existence of discordance is apparen t between the m a n y studies on the intercept e - - r , acc)lcln~ " " ,,,g to a hetcrogeneity. X:'-'~ of 37-01, fen . . . . /~ 0-00339-1-0-00064. The

disturbing datum is that of Durra (19')0). _ . , where certain anim~.~ls {?ore twt~ classes of a

repulsion doubtc intereross were individually analysed ['vr the presence of crossover

gametes, llt .is impossible to parti t ion Duma's fi~.!"u:ces as required for exact analysis: bttt an averagiug shc~wed no disagreement with Dtmn's own conclusion. Thc valoe of

P~-0'0187_q:0'0083, which was the outcome, is significantly greater than tile mean above. R.ecomputation of the wlmle data without DumFs datum yields a revised mean of

I)=-0-0028-}-0-00064 . with the hcterogeueity reduced to a negligible amotmt

184- LiiKage i~z rais

(X[0-=8.12). It is dilt~cult to account for the extraordinary high value of p frora Dunr~'s anMysis especially since the intercross (hom. which these animals were drawn)

gives no outward sio'u that crossingover had occurred. Marked hcterogeneity is also apparent between studies on the c - - p interval. The

X~ for heterogeneity has the significantly high value of 4.1"37 (P<0-001) for the mean p - . 0-1934-k00030. The heterogelmity is due to two widely discrepant values r)f p tot

segregations from hererozygous females, namely', 0.1599 q 0-0098 (Feldman 1924.) and 0-2193• (Castle and Wachter 1924.). I f these data are eliminated, the

joint estimate [br the remaining segregations is ~0= 0"1856-_]-0"0037 (heterogeueity X~:~-5"99)" It is possible that the two deviations may be due to chance, since taken wgether they roughly cancel, but their divergence is excessive. The high fl'equency from Castle's datum is the greater deviation and it may be noted that this particular

sample provides the obvious evidence for a sex difference in crossingover. The analysis o r w ill relation to othe,- genes is made complex by the imperfect pene-

trance of the characte~'istic behaviour. The degree o[ 'penetrance in the various crosses

varied from 0.23 to 0'53, and as a consequence the estimates for p of this paper differ from those of King and Castle (1937) and Castle and King (1941). The largest dis- c e p a n c v is that for p - - w , Castle and King suggesting a ]a=0.35, with a subsequent

correction to 0-45 (Castle I94.4, 1946), whereas the actualvalue appears to be about 0-52. This fact, iueidentally, assists to clarify the dispute on the precise order of the three genes e, p and w (Whittinghitl 1944, Castle 1946).

The relative sequence ofgenes lot" the linkage system would appear to be p - - e --r--lg - -w, as shown more clearly by the trigon of Fig. 2. However, it may be commented " that e and r are very closeIy linked and both of these genes show similar crossover values :

with the third ge~:e p. I t is true that the calculated values are of the expected magnitude (e - -p<p--r as 0- 185 < 0" 190) but the difference is of the same order of smallness as are the standard errors. I t is possible to hold, therefore, that although the trigon implie s

that the sequence is p - - e - - r , the correct sequence could be c - - r - - p , but on general ' grounds the latter is the less probable arrangement.

I f the haematomas described briefly by Dunning and Curtis (i939) are a recessive :

monogenic trait, it appears highly probable that the gent belongs to this linkage group. :i The data indicate an association of the pa~hological condition with pink eyed dilution.

Group I[. This group has the genes an~ b, Cuj, in~ s and Sh in a linked system which -:

could be more thoroughly explored. In particular, the znore recently discovered gent ' s requires testing against the presumabIy neighbouring gent in, and investigation ot' tIae relationship of Sh with some of the intermediate genes may be a useful undertaking, il.

The tbundatio~aal linkage is that between the mutants b and Cu,, discove,ed by Castle and King in 1935. A third, an~ was found in 1941 by the same investigators to exhibit ZI

linkage with both of these genes. A fourth was added by Castle and King (1944); i: with the discovery that in was linked with an and Cu t. The mutant Sh was obse,ved--: by Castle and Kil:g (1947) to show unmistakable linkage with Cu~. but an exceedingly: i:: loose linkage, with b (X~ =0.07). The latest .gent to be included in the group is s :: which shows linkage with b and CII 1 (Castle 1953). ' '

. L

i,~::: R o Y ROB~NSO~ 185 ~ - ' .

}i:. No indication of heterogeneity was found ~'or the pairs b - - s , a n - - b , or Cu. i - -Sh,

['~."w~ere the estimation os upon more than one segregation. A hint of hereto-

!:..! ge~xeitv, however, is 1-evealed by a .~ =9-52 (P.---9-05) l'o,: the comparison b - - C u p

iii:The off'ending segregation is a double backcl-oss from heterozygous females in which

ii. ~#=0.385 compared widl the mean of 0-'-t52. The heterogeneity, while it should be

~:' noted in passing, did not appeal" to be great enough for the segregation to be rejected fl'om

..-combined estimation. il . Significant heterogeneity is apparen t between die three segregations published on thc :.:~ g'ene pair a n - - C u 1 for p = 0 - 0 4 8 3 ~ ' 0-0092 ('X~=-17-06; P < 0 ' 0 1 ) . The discordant (,

7 segregation here is a double backcross which is characterised by a ]) ~- 0-1029 :~0.0230,

:] in contrast to a p=0.0228-b0-0079 for dle remaining two. The estimate 0.0028 is

.i probably closeJ* to the true value of p as judged bv the almost identical recombination

! fractions (0.15 and 0-14-, respectively) for the intercepts C u l - - i n and a n - - i n . This

:. suggests that the a n and Cu 1 may be closely linked. The smaIler value has been 'entered :: in Table 3. " . . . . . .

. The basis of the co,~struetion of l inkage maps is the tl ' iangutalion o f triads of genes,

a,~d this process for the present group produces the trigon of Fig. 2. There is a small inconsistency of values in the first d iagonal from the right where the monotonic descent

�9 of p is hahed for the corrtparisons p - - C u and an - -b . Since the linkage intensity in the

in diagonal (14~ is greatm7 than in the relevant ~egion of" the formm (45%),

' and hence mo~ e reliable in the sense oflessened genetic interf'erence, the inconsistency is

doubtless due to chance. It is a remindm', however, the interference is a p tobable f'actor to be reckoned with in the ~at, a l though the phenomenon has yet to be directly

demonstrated in this species.

Groe,p I I I . The third linkage gFoup may be represe,~ted by the observed linkage of

: genes k and st. The computed recombinat ion value of table 3 difl'ers slightly f'rom that derived by Castle and King (194/1.) since these authors did not allow adequately for the

: effect on estimation offl resulting from the poor- segregation o f s t . The linkagc of" k ancI

' a ' (1939) o f c o p i n g w i t h l e t h a I g e n e s . However, due to st was t 'ound by Ca~tle s method

the severe inviabilitv of s ts L a propo~tiou of the S t s t animals wme undetected and

misclassified as StSt. This is equivalent Io partial penet~'aucc e~fst, a~d the seg egat ion

was analysed., on this basis. The propor t ion o[ penetrance is ~,.:~q~ and the crossover

value is 0-2585.-J-0.0522, lc_,wm than Castle aud King 's dmivation of0.3-'lI. Grmq~ I I 7. This g ,oup is represented by the single linkage between a and t', which

was determined by a double backcross populat ion in coupling (Ca.stie anti King 1949)- ,S'c.v d{{/i~ic'Itce'.~. Those studies on the [nfhtence of sex of the dihete,-ozygous parent on

the amoun t o~-L'ecombi,~alio,~ are summarised by Table ~1. Oi~l). lot two linkage inter-

(:~:l)ts (nan:ely, c - - p and b - -Cux) have experime~tal data pFovJded significant evidence

that crossi~govm cmctus more f lequently in the fi=male tha~ in the male. t-lc,wever,

it would appea r that, in general, the I'cmate sex will give higher ~ecombinatio~, values

than will the male. For" the nine comparisons of the table, seven disclose laigher values

when the data are obtained fiom f~male diheterozygotes. M.oreover, it is to be expected iu the karyologica] nbservations of Bryclel~ (1932), which showed that the I'~'cquency of

2

186 Linkage in rats

chiasmata lbrmation was higher in females than in males, that genetical crossingover

will occur more frequently in the l'emale.

..lge diJfi, rence. Castle and Wachter (1924.) have investigateci the possible effect - f age :

~f tile diheterozygous parent upo~ the recomlfination value fbr the pair of linked genes

c - - p , over the age range ol'31o 18-20 months. The ex tens ive tabu la t im~of recombina .

tion Iiactions made for the two sexes separately fail to bring ottt a consistent trend.

C, astle ( 1919) states that a similar study for the genes p - - r has led. to negative coo.clusiotls.

However, the decrease in fi 'equency of chiasmata Ibrmation with age, as [bund by

8ryden (1933), would imply that an age difference may in fact exist. I t is not to be

presumed, however, that sllclx differences may be great enough for easy cletection or

appty to all regions ~ffa bivalent.

Table 3. ,5'ummaJy oJcstablishcd linkageJ

Linkage group Loci p References

I e--lg 0'1066 ::L0"0522 40

e--p 0"1856 --0"0037 9, tO, 23, 30, 36

r 0-00279 ~0.00064 9, 10, 30.. 34, 42, 59

c--w 0.4250 !0-0153 23, 4-1.

he--p 0"2923 • 35

Ig--p 0"2210 --0'0162 40

p - - r 0"I90t =0"0105 9, t0

p--w 0.5202 • 23, 4.4

r - -w 0.3684 --0"0589 28

II an--b 0'4522 ~0'0233 23

an--Cu: 0"0228 --' 0"0079 23, 24

an- - in 0"1373 • 24

h--eu~ 0'4516 ~0.0102 23, 43

b--s 0"0760 zk0'0115 19

b--Sh 0-5120 • ' 25

Cu;--in 0"1487 =0"0269 24

Cul--s 0"4375 =I=0'0259 19

Cu~--Sh 0'0391 • 25

III k--s t 0.2585 ' • 24

IV a - - f 0"4466 • 28

*not significant

RoY ROBINSON

T a b l e 4. Sex differemes ir~ recombirzalioll values

187

Linkage group . Loci Sex p Rcfcren'ccs

t c - -p 3 0.1853 --' 0.0111 36

~! 0'1599 4-0.0098 36

0,0254- •

0.1845 4-0.004-0 30

? 0"2193 =- 0,0058 30

0.0348 4-0'00555*

iI

C---It" d 0.00181 ~ 0-00064. 30

~-r ~ 0'00532 4-0"00168 30

0-00351 •

l g - -p ~ 0.2451 ~ 0" 0601 40

'.r 0.2472 =-0.0345 40

0.0021 •

p - - r c~ 0.1700 -'0-0162 10

0"2085 =-0,0!52 t0

0.0385 =-0-0222

a n - - b ~ 0'4.-t-56 zk0"0255 23

}. 0-4892 :k0"0570 23

0'0'136 --0,062-'I

an - -Cu j ,:7 0"0222 ___0"0086 23

0'0282 2 0'0214 23

0"0060 4-0"0230

b - - C u I g 0'463I --0"013-t. 23:-I3

~ 0"1.086 .-0"0200 23, 43

0"05-t'5:1:0"0241"

Cu~--Sh c1 0-0319 4-0"0158 25

? 0"0,176 _+_0"0210 25

0'0157 -.'--O'O263

~ignifican t barely significant

~ and individual diJ/e, re'nccs. No c o n s i s t e n t e v i d e n c e was f o u n d by Cas t l e (1919)

c l iv idua l F~. m a l e s w e r e g i v i n g a n e x t r e m e l y h i g h or low f r e q u e n c y o f c r o s s i n g o v e r

i n t e r c e p t p - - r . A f i n t h e r s t u d y by Cas t l e a n d W a c h t e r (1924) f'or t he c - - p '

188 Lbzkagr ilz rals

did llot yield poshive conclusions, aRhough one male was credited with a very high

fiequmacy. However, the peculiarity was not transmitted to his sons, which collectively

gave a1~ estimated recombinat ion percentage ,mr dilli:rent fiom that expected. Fe ldman

(1924-) has rather cursoriiy considered the possible effects o[ the i,:dividual, or parentage,

upon the cross(wet vMue between the genes e - - p but ~ailed to uncover any positive

tet~dency. There is teason to believe that the a.mount oI 'crossingover is an adapt ive l'eattu'e Ibr a

species and, ms such, under the influence ofheredit.y, h m a t c diflizrences may, tb.erefi~re,

exist which could be only detected by inter-strain comparisons. [t is possible that the.

difl'e,-ences will be smalI and detection will require large numbers of progeny which can

only be realized liom several ntales of the same inbred strain. The heri table differences which are being mooted at this juncture are visualised as part of the "no rmaI variation"

and distinct l'rom a major alteratlot~ of chromosome morphology (such as aR inversion)

which could produce a gross difference.

PARTIAL SEX LINKAGE

It is still true, as Darl ington, Haldanc and KolIer (1932) have pointed out in their appeaI, that few of the mutan t genes of the rat have been specifically tested for partial

sex linkage. This omission should not be allowed to continue, since the observations

of KolIer and Darlh~gton (11934) suggest that the XY bivalent possess a mutua l pair ing

region, in addition to the differentiated segments. The linkage, however, m a y be loose

and not self-evident without deliberate search.

AFF~N~'rY

I t may be wondered if the affinity phenomenon may make some express i( m upon the data

as a whole. Two tentative tests were made upon the possibility. The signs of the scores tabulated in Table 2 shouId not diverge f romequal i ty in the absence of a systematic

bias. The actual frequencies are 50q-, 6 1 - - a n d 5 indefinite, and the deviation is

insignificant (X~ := I '04). A comparison of signs for each genc separateP>' aIso revealed �9

no consistently suggesti,,;e trend. The absolute scores relative to the amount ofinforma-

t i o n m a y bemore in~brmat ive but the results are negative. The scores are @775 a n d

--1041, with. Eotal information of 87214, alld the difference in the two scores yields A X~ of0-8i . The only poss ibl.e gene which could be showing an affinity etTect in the sense

o f a succession ofunusua l abso[ute scores is d, which at tracted attention in the seetiml. on possible li~lf~age: hut the summed scores for the segregation of this germ are -I 1:t.7 a ~ d

--132, w{th [:--14528 and X~ =0021 fi;r.the diflklence. The amount of heterogeneity.

is ,V,~s : - 15.48 which is insignifiqant. The anmunt of heterogeneity is an impor tant item:

since the phase of a pair of 'genes may not correspond to that o f t h e two centromcres."

(see Wallace 1957) and divergent scores could cancel for a simple summation. However, these tests appear to be insensitive tbr the detection ot" affinity, unless thai:

phenomenon is very pronounced- in which event it might have aroused commeng!i

previously. For a ~ n i t y to be readiIy detected by the aid of segregating genes, these/

must be situated close to the afl'ined ccntromeres. A negation of aff-~nity would imply"

R O Y ROBINSON l 8 9

'.either that the genes are distant from tile eentromeres or that tile centromeres are not

:aflined. The unambiguous detection of affinity wouId requh'e suitabl) p repared

�9 breeding programmes and tile perception of individual animals showing affinit},', as

i discussed general ly b), Michie (1955) and in detail by Wallace (1957) for a par t icular

case. The present tests would perhaps be more instrumental in detecting loose linkages

-if these were f iequem in the data ; but, if anything, the results indicate the converse.

CI-IIASMATA FREOIJENCIES

Bryden (1932) has seriously at tempted to determine the distribution ofchiasmata among

the 2I bivalents of the rat. The fi'equencies o fch iasmata were found by count ing the

number cIearly observed on bivalents t'rom numerous nuclei. This may int roduce two

;biases, (1) the same bivalent may recur more often than r andom inclusion Would require;

and (2) the fi 'equency ofchiasmata on the smaller, indistinct, bivalents may not be given

due weight. The two biases are probably not independent . ! Difficulties of finding

regular associations of 21 bivalents per nucleus precluded detailed enumerat ion o f

chiasmata for the whole complex. It is likely that the smaller bivalents would form

fewer chiasmata than the average and the distribution it biased to that extent. The

percentages o f T a b I e 5 may, therefore, be even more leptokurtie than the figures suggest.

The fi-equencies o f ehiasmata are at their m a x i m um during diplotene, decreasing progressively through diakinesis and metaphase due to terminalisation. T h e best

estimate available of the mean frequency per bivalent is that for diplotene in males, and i s l ' 9 1 ~ 0 . 0 4 c h i a s m a t a . T h e r a t i o o f m e a n s f o r e a c h s e x a t m e t a p h a s e i s l ' 5 7 : 1 - 9 8 : : : 1 : 1-27 and, if this ratio holds for diplotene, the mean for females would l{e ai~proxi-

matetv 2-424-0.05. The 95% fiducial limits for males are 1-83--1"99 and for females

2"32--2.52. On the assumption that each chiasma roughly corresponds to 50 centi-

morgans, the average length of" chromosome m a p may be of tlle ordei- o f 96 units

(92- -100) got" males and 121 units (116--126) for females. It is recognised, of course,

that these tentative estimations m a y have to be revised in the light of'fllture observations

or more sophisticated ~heory. Bryclen (1039"1_. _, was able to show that tile earlier work of Pincus (t ( , .097'~, o~'~ rat chro-

moso.mes was in excellent agreement with his own observations. A subsequent paper by the same author has given data which indicate that the number ofchiasma ta decreases

with age of the individual for the male sex (Table 5). This decrease is correlated with a

general dectine ill spermatogermsis and meiotic activit); i]/ the tubules ol" the testes from

older animals. A fall in genetic crossingover may, as a consequence, be expected with

iacreasiag age. However, this IM1 does not appear to have been observed by Castle and

\'Vaeh~er (1924.) l-or tile chrom.osome intercept e - - p .

The preceding calcuiatioHs would impl}, that reconlbhmtion will occm less f iequent ly

in males than in females, r the average. This need not apply, of c:om'se, to all chro-

n~osornes or uniformly to all regions of a part icular chromosome. The predicted average

lctlgth o l ' cbromosome Fnr both sexes is i~ full harmony~ with the existence of malay' loose linkages, and could aecomm.odate (ibr the longer chromosomes) seveJ-al quasi-

i teependenl linked groups of genes. These considerations should make us cautious

190 Lbzkage itz rats

for the too-ready acceptance ~f i ndependency of genes, especia l ly while the numbers

known and s tudied are few. In two suhsequent reports, Bryden (1936, 1937) has t abu la t ed the distr i l )ut ion of

eh ia sma ta among the bivalents as controls for the effect of envi ronmenta l factors upon "

the movement of the chromosomes. These 1bur groups of de te rmina t ions are consistent

hetween themselves but differ s igni l icant ly from those given in 1%2. The mean per

b ivalent is 2.042L0-03, and the difference (0'13) in terms ~)1" its s tandard error (0"047)

is 2-81 (P<0.01) . Few detai ls are given o1 the degree of met iculous c.cJllectiol: o[" these

ligures, a l though it appears that the bivalents were santpled at random with testes

ma te r i a l from the same strain of rats as examined previously . The mean length oi'

chromosome ia crossingover units tbr the male would be 102, with the 95% range o["

100-105. The cor responding values for li:males are a mean of 130, with a range cJl"

127-133.

Tab le 5. The dislribalion (~f chiasmata at diplolel~e (males), ie.r di/fererlce (metaphase) and declb2e with age (metaphase)

% chiasmata ". N o . r . . . . . " - - - - 4~ i"vIean

Distribution bivalcnts 1 2 3 chiasma~a R eI'erences

Diplotene (maIe) 320 25 55 16 9 1.91 2

Diplotene {male) 1200 30 42 21 7 2.04 4, 5

Metaphase (sex) male 320 47 49 5 0 1.57 2

female 80 30 50 13 8 1.98 2

Metaphase {male, ag'e) 2 monlhs 900 32 42 20 6 1.62 3

8 ,, 900 31 44 2l 4 1.57 3

I7 ,, 900 40 39 17 3 1.40 3

Dtscussio:',

I t only remains to under l ine the high des i rab i l i ty of r epor t ing in full the results o f

l inkage tests with newly discovered mutan ts of the rat . A general discussion of this.

aspect tOot . the p rob lem of l inkage detect ion has a l r e ady been given in the review of

studies on the r abb i t (Robinson 1956), to which reference may be made. The ftmda-)

menta l p r inc ip le is that beyond a cer tain sample size of p rogeny the detect ion of ever-i

weaker l i n k a g e i s subject to sharp increases in the a m o u a t o fe f lb r t required. Tha t is,-:

tile p rob lem o f d e t e c t i o a of l inkage encounters the onset of d imin ish ing returns. There):

a p p e a r to be two approaches by which this onset can be countered to some extent.:il

First ly, by a r r ang ing that the testing of a new m u t a n t also involves the simultaneous:

segregat ion otomany e• genes, and secondly, by the format ion of stocks to preserve

known mutan ts which are in a state of constant segregat ion.

R O Y ROBINSON t91

A simple auto-perpetuat ing stock of this nature could be one where ;all the recessive

alleles are located in one sex. The breeding policy is equivalent to a testcross for an)

particular gene pair and, furthermore, the multiple recessive animals would be readily available in the event of a new mutat ion. Assuming that no serious interactions (ot

epistasis or inviahility) occur between the genes, the limit to the number which can be maintained is imposed by, the need tbr replacement of breeding animals. I f there are

n genes, there will be 2" phenotypes in each generation and the probability of occurrence

of any one will be 2 - ' . I f k be the proport ion required for replacement, then 2 - " >~k

must follow. In general, the limit would be set by the number of females and the exigency of finding mates of similar age, indicating that the number of genes which

could be "he ld" is few. However, in polygamous breeding this limit could be exceeded

if the male is the multipl~, homozylgous sex. Unrelated wild-type females could be iotroduced to these males in order to maintain the supply' of multiply heterozygous

females. The segregating families would be produced by the latter and k would be

determined by the amount o f male replacement. In rabbits, tl'ais system would be most

workable; in other laboratory rodents, probably less so.

The system of breeding outlined is advanced to encourage the preservation of known

mutants and to collect segregation data of known linkage phase. I t does not supplant,

but directs at tention to, the ingenious, but more elaborate, scheme developed by Carter

and Falconer (195I) for the mouse. A suitable modification of this, and tee formation

of suitable stocks, for other laboratory species wmdd soon lead to rapid linkage detection with economic deployment of animals.

SUMMARY

The published data on possible genetic linkage are reviewed and statistically cdmbined to provide estimates of (a) the closest linkage compatiMe with ,iae apparent r andom

assortment or (by the recombinat ion fractim~ where r a n d o m assortment is contradicted.

Various aspects of l inkage detectio~ and linkage analysis are discussed.

I am indebted to Professor L. C. Dunn and Dr. E. Rober ts for items of information

and to Miss Iv)' C. Robertson fo, valuable hibliographical assistance.

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192 Linkage in rals

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