[TMG] said by S. Wright
supat at supat.eu.org
supat at supat.eu.org
Sat Dec 12 14:40:24 ICT 2009
DEGREE O F DETERMINATION BY HEREDITY
It is of interest to determine the portion of the total variability due to
substrain differentiation. But at once we encounter the difficulty that the
character does not occur in grades from which the variance can be cal-
culated directly. The most significant classification is merely the dichot-
omy 3-toed or 4-toed.
It is already clear that this dichotomy cannot correspond to alternative
phases of a single factor. It is the result of a physiological threshold in a
character affected by many factors. It is therefore reasonable to assume
that there is a scale of factor combinations to which each factor makes
a fairly constant contribution and that variabilities may be compared on
such a scale. As the unit of measurement it is convenient to take the
standard deviation within a substrain ( U , = 1). The deviation of the mean
(m) of each substrain from the threshold for polydactyly can be found from
a table of probability integrals on the assumption that the distribution
within each group is normal on such a scale as described. Thus for the
deviation of the mean of the group, m=prf-l(q-+) where q is the pro-
portion above the threshold and prf-' is the inverse probability integral,
whereprf x = . The variance of such means can now be found
by the usual formula
where m is the weighted average of the means, m =- (- :f). I the set of
f
substrains are thought of as a random sample from a large number, cor-
rection should be made for the uncertainty of the grand average ( i ) by ii
h
multiplying by - where h is the number of substrains (assumed to
h-1
be of approximately the same size). If, on the other hand, the groups be
thought of, not as a sample, but as including all subdivisions of the
population, no such correction should be made.
In the present case the question a t issue is the proportion of the variance
of the actual population due to the differentiation of its substrains, rather
than proportion in a hypothetical population made up of an indefinite
number of such substrains. This correction is accordingly not made in the
final estimate. It may be noted that it is even less justified in cases ana-
lyzed later, such as subdivision by age of mother and month of birth.
Another correction is for the variance of means due merely to accidents
of sampling within the substrains. The formula for the variance of means
of groups consisting of f individuals is -
f
(- -
-
h
The value - may be
n
taken, if the groups are approximately the same size. In the present case
this correction is not very important (!-= .0106).
The variance of the total population is the sum of the variances within
groups and of group means:
UT2 =(T*2+um2 = 1+um2.
The proportion of the total variance due to substrain differentiation is
2
Um
thus ___ * This does not differ appreciably, in most cases, from PEAR-
1+ a m 2
SON'S formula for squared biserial eta, but does not involve the assumption
that the total distribution is normal.
For the 21 substrains of table 3 the above formula gives 19.2 percent
if no corrections are made, 18.5 percent if correction is made for average
size of subgroup and 19.3 percent if both corrections are made. The second
of these may be taken as the best estimate of the proportion of the vari-
ance of the actual population due to differentiation of its substrains.
This differentiation of substrains with respect to polydactyly contrasts
with the relative uniformity of the same substrains in most other respects
(WRIGHT EATON
and 1929). The family is characterized for example by a
tricolor pattern. The percentage of white varies in individuals from 5 per-
cent to 100 percent but the substrains derived from the same mating in
the 12th generation vary only from 60 to 73 percent and wholly a t ran-
dom. The parent offspring correlation of only +.024 k .013 with respect
to amount of white confirms the view that in this respect no appreciable
portion of the variability since the 12th generation is genetic.
SUMMARY
The recurrence of an atavistic little toe is not uncommon in strains of
guinea pigs. Among 23 inbred families, 12 never produced 4-toed young,
5 produced a few sporadics, while the remaining 6 produced percentages
ranging from 2 to 19 (1906 to 1915). A branch of one of these, derived from
a single mating in the 12th generation of brothey-sister mating produced
31 percent a t Beltsville, Maryland. Subdivisions of this ranged from 9 per-
cent to 69 percent. A large random-bred group derived from a single
mating of this family in the 22nd generation, produced 42 percent (in
Chicago).
It is assumed that the presence or absence of the little toe depends on
whether the combination of factors exceeds or falls below a threshold. On
a scale of uniform factor effects, 18 percent of the variance of the Belts-
ville stock was genetic, due to substrain differences (squared biserial eta
.18, also parent-offspring correlation .18). There was no demonstrable
genetic variability within substrains. Genetic variability was also negligi-
ble in the Chicago stock (parent-offspring correlation .03, after correction
for other factors).
Litter-mates were determined 62 percent by common factors in the
Beltsville stock (correlation +.62). This includes the genetic factors and
54 percent of the non-genetic ones. In exact agreement is the correlation
of .54 between litter-mates in the Chicago stock.
The non-genetic factors common to litter-mates are equally divided be-
tween ones also common to non-litter-mates from the same mating (cor-
relation .27) and ones common only to litter-mates (Chicago stock). These
results lead to the following analysis of variability.
There is frequent asymmetry. The correlation between left and right
was .78 in the Beltsville data and .73 in the Chicago data. That between
single feet of litter-mates was .59 in the Chicago data. These results in
combination with the preceding lead to the following analyses of the fac-
tors responsible for digit numbers on a single foot.
Part of the variance assigned to the individual in the analysis of indi-
vidual variability is spurious due to non-additive effects. The analysis of
the variance of single feet is more satisfactory.
No direct evidence was obtained of the nature of the non-genetic factors
affecting whole sibships. Presumably long-continuing conditions of the
mother are involved.
The most important factor affecting whole litters is age of the mother.
This determined 13 percent of the total variance in the Beltsville stock and
(less reliably) 25 percent in the Chicago stock. Immature females produce
much higher percentages of 4-toed young than mature females. The effect
is primarily neither one of parity nor of weight of mother. Indeed the
heavier females of a given age produce slightly more polydactyls than the
lighter ones. A physiological competition for some substance between
growing mother and embryo seems the most plausible suggestion.
A seasonal cycle, high percentage of polydactyls in late fall, winter and
early spring, low the rest of the year, accounted for 3 percent of the total
variance in the Beltsville stock. That this was not an effect of season per se
was indicated by a reversal in the Chicago stock. The seasonal effect and
relation to rate of growth and death rate, indicate that unfavorable con-
ditions tend to increase the percentage of polydactyls. The 4-toed indi-
viduals are not, however, a t all handicapped in prenatal growth or chances
of live birth and only slightly in postnatal growth and viability.
No direct evidence has been obtained of the nature of the individual
factors. The extremely local action of important factors is indicated by the
frequent asymmetry. I n this the left foot is slightly more likely than the
right to develop a little toe. There is no relation to sex.
A recognition and evaluation of the importance of non-genetic factors
in determining the presence or absence of the little toe is a necessary
foundation for analysis of the genetic differences between different stocks.
LITERATURE CITED
CASTLE, E., 1906 The origin of a polydactylous race of guinea pigs. Pub. Carnegie Instn.
W.
Washington, No. 49: 29 pp.
1911 Heredity in relation to evolution and animal breeding. New York.
KELLEY, L., 1923 Statistical method. New York: The MacMillan Co. 390 p.
T.
PICTET, 1932 Formation de la polydactylie et son mode d'htreditt. Z.I.A.V. 63: 1-42.
A.,
STOCKARD, R., 1927 Extra toes in the guinea pig-an atavistic condition, and its genetic
C.
significance. Anat. Rec. 35: 24.
1930 The presence of a factorial basis for characters lost in evolution: the atavistic reappear-
ance of digits in mammals. Amer. J. Anat. 45: 345-377.
C. G.
STOCKARD, R. and PAPANICOLAU, N., 1920 Variation of structural expression in the in-
heritance of polydactyly. Anat. Rec. 18: 1262-63.
WRIGHT, SEWALL, An intensive study of the inheritance of color and of other coat characters
1916
in guinea pigs, with especial reference to graded variations. Pub. Camegie Instn. Wash-
ington, No. 241: 59-160.
1922 The effects of inbreeding and crossbreeding in guinea pigs. 1 . Differentiation among
1
inbred families. US.Dept. Agric. Bull. No. 1090: 37-63.
1926 Effects of age of parents on characteristics of the guinea pig. Amer. Nat. 60: 552-559.
1931 On the genetics of number of digits of the guinea pig. Anat. Rec. 51: 115.
WRIGHT, SEWALL EATON N., 1929 The persistence of differentiation among inbred families
and 0.
of guinea pigs. US. Dept. Agric. Technical Bull. No. 103: 46 pp.
THE DIGITS O F GUINEA PIGS
Guinea pigs normally have four digits on the front feet (no thumb) and
three digits on the hind feet (digits I and V absent). This condition is
found in all wild species of the family Caviidae and in the closely allied
family Hydrochoeridae.
A larger number of digits is found in general in the species of other
families of the hystricoid rodents. The reduction in the Caviidae and
Hydrochoeridae is thus in all probability a very ancient character.
It is a frequently stated principle of paleontology (DOLLO'S law) that
lost parts never return. Nevertheless, it is well known that an extra digit,
resembling in every respect (when well-developed) a normal little toe is not
an especially uncommon occurrence in the guinea pig. CASTLE (1936)
found a guinea pig with one imperfectly developed little toe and was able
by selection and inbreeding to build up a race in which this digit was in-
variably present and perfectly developed including bones, muscles and
nail and even a new plantar tubercle on the foot. I have found a similar
little toe in several independent stocks. It has also been described by
STOCKARD (1930) and by PICTET (1932). The appearance of the little toe
in two grades of development is shown in figure 1. Its position and struc-
ture have been the same in all stocks in which it has keen observed. This
type of polydactyly must be sharply distinguished from the duplication
of a digit which has occurred associated with other abnormalities of the
foot (figure 2) in a few cases in stocks which have no special tendency to-
ward the development of the reversionary type.
A series of grades of development of the little toes has been used in the
records but for the purposes of this paper two will suffice : "Good" in which
both little toes are full-sized and so firm that they do not bend back
laterally to the foot on moderate pressure, and "poor" including all lower
grades. Grades of perfection are recognizable within the category "good"
but the above line of cleavage seems to be the most objective one which
can be made.
PREVIOUS GENETIC RESULTS
CASTLE (1906) found that the extra-toed condition was transmissible
both by males and females and that the degree of transmission was closely
related to the grade of development. His original male with only a weak
fourth toe on one foot had 25 percent (9 out of 36) extra-toed young from
related females and 6 percent (2 out of 32) from unrelated ones. Four out
of 9 young from polydactylous females were polydactylous. I n the next 3
generations selected males produced increasing percentages of polydactyls
from the various classes of females but even matings between perfect
polydactyls produced some normals as well as many with imperfect fourth
toes. A close approach to fixation of the perfect fourth toe was reached in
generation 5. Complete fixation was later attained and has continued to
the present in a branch of this strain in my possession. CASTLE noted a
slight excess tendency toward extra toes on the left side (630 left, 589
right).
The breeding results could be accounted for neither on the basis of a
simple recessive, nor of a simple dominant. CASTLE concluded that the
extra toe was probably inherited in a manner intermediate between blend-
ing and alternative inheritance and that there was some sort of latency in
normal guinea pigs. I n a later publication (1911) he noted that "an al-
ternative explanation is possible that the development of the fourth toe
depends upon the inheritance of several independent factors and that the
more of these are present the better will the structure be developed."
STOCKARD PAPANICOLAU concluded that the character is a
and (1920)
Mendelian dominant. In a more recent paper (1930) however, STOCKAR
reaches the conclusion that the mode of inheritance must be more complex.
He has found it occurring occasionally in eight distinct stocks and con-
siders it probable that it is latent in all stocks. The results of matings were
in the main similar to those reported by CASTLE. NormalXnormal pro-
duced 11 percent (22 out of 199) with the extra toe. Conversely when both
parents were four-toed, 25 percent (53 out of 214) of the progeny were
normal. Contrary to CASTLE obtained no normals among 35 young,
he
both of whose parents had perfect fourth toes. I n all cases in which both
parents were of the same grade, this grade was in excess among the prog-
eny. The proportion of four-toed young from matings in which one parent
was four-toed and the other normal varied with the grade of the former and
the source of the latter.
PICTET (1932) has recently reported on experiments with this character.
Extra-toed animals appeared in a certain stock which had previously pro-
duced only normals, 3000 in number. The 7 pairs which produced poly-
dactyls a t all, gave a total of 9 polydactyls in 144 young. The following
table gives in condensed form the results obtained in eight later genera-
tions in which both parents trace in part a t least to this foundation stock.
TOTAL 4-TOE PERCENT 4-TOE
Normal X Normal 196 9 4.6
Normal X 4-toe 148 47 31.8
4-toe X 4-toe 173 121 69.9
As in CASTLE'S STOCKARD'S matings of polydactyls with un-
and data,
related normals gave smaller percentages of polydactyls (15 in 101 or
14.9 percent) than matings with related normals. PICTET'S results re-
sembled CASTLE'S the excess of left little toes over right ones (46 left
in
only, 18 right only, 139 both). He could find no heredity of the asym-
metry.
PICTET attempted to reach a definite factorial analysis. His reasoning
may be summarized as follows : normal x normal may give ratios approxi-
mating 15 normal to 1 polydactyl. This requires a dihybrid ratio at least.
But polydactyly cannot be due merely to a combination of two recessives
implied by the 15 :1 ratio, since polydactyl Xpolydactyl may produce nor-
mals. Thus a third gene is required. The specific hypothesis put forward
is that polydactyly depends on the combination of P P with a t least two
positive genes from the series E , e and N , n. The six combinations P P E E N N ,
PPEENn, PPEEnn, PPEeNN, PPeeNN, and PPEeNn are 4-toed while
the other 21 combinations are normal.
He assumes that all of the original matings of normalxnormal which
gave polydactyly were of the type PpEennXPpeeNn yielding 15 normal
to 1 polydactyl as observed. Matings between polydactyls from these
(PPEeNn) would then be expected to yield 5 normals to 11 polydactyls.
The observed F1 ratio, 9 normals to 19 polydactyls, is in agreement. The
ratio of 43 normals to 102 polydactyls from all matings between poly-
dactyls from the next 7 generations is pointed to as additional evidence,
overlooking that most of the polydactyls of these generations would be
homozygous in E or N or both and would give higher percentages.
I n the cases of normalxnormal and normalxpolydactyl, he finds it pos-
sible to yick out formulae for the parents which will account for each type
of ratio observed. It must be taken into account, however, that with 6
different genetic constitutions assigned polydactyls and 21 to normals
there are 126 possible types of matings of normal with polydactyl and 210
between normals. This gives considerable room for choice of formulae to fit
observed cases. Under such conditions the demonstration that a choice of
formula is capable of accounting for observed ratios does not constitute
proof that the formulae are correct.
The whole argument also ignores the fact already demonstrated (WRIGHT
1926) that non-genetic factors play such an important role that normals
and polydactyls may be of the same genetic constitution. It may be con-
cluded that the specific genes P , p , E , e and N , n cannot be taken seriously.
My own experiments began in a preliminary way in Dr. CASTLE'S
laboratory in 1914. The results showed clearly that further advance was
hardly possible without the use of stocks known to be homozygousor
nearly so, that is to say, of closely inbred stocks. Shortly thereafter I had
an opportunity to study the records of such stocks. A considerable number
of inbred lines were started a t the experiment station of the U. S. Bureau
of Animal Industry a t Beltsville, Maryland in 1906 and maintained by
brother-sister mating. Among the 23 which persisted more than a genera-
tion or two, it was found (WRIGHT 1922) that 12 had produced no poly-
dactyls in a total of 8400 young (1906 to 1915) as shown by the records
(which however merely noted the occurrence of polydactyly, not of nor-
mality during this period). Five of the strains had produced a total of 12
polydactyls in 4600 young or 0.26 percent. The remaining 6 strains had
produced polydactyls in percentages ranging from 1.7 percent to 19.0 per-
cent.
TABLE 1
Occurrence of polydactyls in 23 inbred s h i n s .
~
STRAIN 4-TOED TOTAL PERCENT 4-TOED
1,3,9, 13,15,18, 19,20,21,23,32,34 0 8404 0
2, 7, 14, 17,39 12 4626 0.3
24 19 1142 1.7
36 26 1298 2.0
11 25 1151 2.2
38 59 768 7.7
35 181 1343 13.5
31 152 802 19.0
A study of the histories of these families, especially of 35 and 31, led to
the conclusion that "the segregation among the family lines is so sharp
that it is probable that a careful investigation of polydactyly would yield
Mendelian results, though much nongenetic variation must be present."
Since 1916 the number of digits on the hind foot and the grade of extra
toe if present was made a matter of routine recording for every animal
born in the colony of the Bureau of Animal Industry. The positive nota-
tion of normality doubtless increased the reliability. A large branch of
family 35, descended from a single mating in the 12th generation of
brother-sister mating, was made the object of intensive study with regard
to non-genetic factors. Important effects of age of parents (presumably of
dam) and of season of birth were demonstrated and it was shown that
these constituted only a part of the total non-genetic variability (WRIGHT
1926). In the same paper the results of crosses between certain of the
strains (2,13,32,35) and Professor CASTLE'S strain of perfect polydactyls
[D] were reported briefly as indicating "segregation of two or three major
genetic factors, the results being clearly different in crosses with different
3-toed stocks."
The present paper will present more fully than before and on the basis
of additional data, the analysis of the variability within the inbred strain
No. 35. It is hoped to present in detail in later papers the results of the
crosses between inbred strains referred to above, the results of linkage tests
and the results in a strain (I) in which pollex and hallux appear as well as
little toe.
DIFFERENTIATION OF SUBSTRAINS OF FAMILY 35
The branching lines of descent from the foundation mating of family 35
are shown in figure 3 and table 1. Four branches (B, C, E and G) started
in the second generation. Three of these produced low percentages of 4-
toed young, while one (C, D) produced none a t all among 335 young in a
history extending through the 12th generation. One of the other branches
of the 2nd generation (E) split off a branch (F) in the third generation
which never produced polydactyls. These early differences may easily have
been the result of segregation of factors heterozygous in the original pair.
Of greater interest are the records of the later branches, all descended
from a single mating in the 12th generation of brother-sister mating. Under
such mating, some combination of genes should have become nearly fixed
by the 12th generation, assuming of course the absence of new mutations
or selection for heterozygosis. The theoretical rate of decrease of hetero-
zygosis is 19.1 percent per generation, under which, 92 percent of the
genes, not similarly homozygous in the foundation pair of guinea pigs,
should have become homozygous. The percentage of unfixed genes should
be approximately halved with each additional 3 generations of brother-
sister ancestry.
All of the 2 1 substrains, descended from the single mating in the 12th
generation, indeed nearly all of the matings, have produced polydactyls.
The mere occurrence of both 3-toed and 4-toed young would indicate con-
tinued heterozygosis on such an interpretation as that of PICTET. does
It
not necessarily do so, however, if non-genetic factors play a role. The dif-
ference in percentage among the strains (9 percent to 69 percent) are, how-
ever, indicative of real genetic differentiation.
Cpmparison of the observed frequencies of 3-toed and 4-toed young in
the 21 substrains with those calculated from the percentages in the grand
total (31.07 percent 4-toed) yields a X2 of 247. The probability that such
a value of X2 could arise by random sampling (20 degrees of freedom) is
indefinitely small. There may, however, be some other factor than heredity
tending to cause correlated occurrence within a substrain. It is shown later
that there is an important correlation between litter-mates which is not
genetic in origin. But even if litter-mates were invariably identical with
respect to number of digits, so that number of litters instead of number of
individuals should be used in calculating X2, the value of the latter would
still be as great as 101 (247 divided by 2.44 the mean size of litter) and
this still has no appreciable chance of arising by random sampling. There
seems to be no other factor which brings about correlated occurrence to
an important extent and as X2could be reduced to 50 and have a chance
of only about .0002 of origin by random sampling, there can be no doubt
of the reality of the genetic differentiation among the substrains.
On comparing each substrain with that from which it was derived, it
will be seen that there has been some tendency toward persistence. The
correlation between successive substrains is +.47. There are a t least half
a dozen cases, however, of changes of percentages which appear important.
Their interpretation as due to segregation is rather unlikely, in view of the
many generations of brother-sister mating back of some of the most
striking ones. The most plausible explanation seems to be the occasional
occurrence of minor mutations followed by segregation.
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