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[
Forthcoming in
The Journal of the History of Biology
]


The “Evolutionary Synthesis” of George Udny Yule


James
G.
Tabery

Department of Hi
story and Philosophy of Science


University of Pittsburgh

Pittsburgh, PA 15260, U.S.A.

E
-
mail:
jgt1@pitt.edu





Abstract:
This article discusses the work of George Udny Yule in relation to the evolutionary
synthesis and the biometric
-
Mendelian debate. It has generally been claimed that (i.) in 1902,
Yule put forth the first account
showing that the
competing biometric and Mendelian programs
could be synthesiz
ed. Furthermore, (ii.) the scientific figures who

should have been most
interested in this thesis (the biometricians
W. F. Raphael Weldon and Karl Pearson, and the
Mendelian

Will
iam Bateson) were too blinded by personal animosity towards each other to
appreciate Yule’s p
roposal. This essay p
rovides a

detailed account of (i.), maintaining that
Yule’s 1902 propo
sal is better understood as

a

reduction, not a synthesis of the two pro
grams.
The results of this analysis are then used to evaluate (ii.), where I will instead argue that Bateson
and the biometricians

had good reason
s

to avoid endorsing
Yule’s account.


Keywords:

biometric
-
Mendelian debate, evol
utionary synt
hesis,

George

Udny Yule, Karl
Pearson,
law of ancestral heredity,
Ronald A. Fisher,
reduction,
William Bateson










2


Introduction

The biometric
-
Mendelian debate has left a permanent imprint on the history of biology.
On one side, the famously brash
team of Karl P
earson and W. F. Raphael

Weldon led the
biometricians in their statistical study of evolution as a gradual process due to continuous
variation. In opposition was the staunch William Bateson, who utilized his studies of
hybridization experiments to justify

a discontinuous theory of variation. While the theoretical
dispute between the two sides is well known, it is the methodological disagreement that is most
famous. Bateson and the biometricians disputed not only each other’s theoretical claims but also
the

very methods each used to gather evidence for those claims. Bateson sought
causal
explanations

for the process of inheritance by employing experiment
al hybridizations
.
1

In
contrast, Pearson and Weldon chided any attempts to seek out the causal mechanisms
responsible
for inheritance before enough statistical information was gathered. They, instead, searched for
statistical

correlations

between phenomena. Much of Pearson’s
Grammar of Science

is devoted
specifically to defending the proper development of scie
ntific investigation.
2

While he was not,
in principle, opposed to causal explanations, these endeavors were only acceptable after statistics
first identified the correct correlations to investigate.
3


The division that emerged between the two scientific pr
ograms becomes most remarkable
when the coinciding personal histories of
Batson and Weldon are re
counted
. Bateson and
Weldon were educated together at St. John’s College, Cambridge
, under the guidance of

biologist
Francis Balfour.

Both men joined Balfour i
n embryological
, morphological,

and
phylogenetic studies of primitive animals, which straddled the line between vertebrate and
invertebrate life.
Bateson, from early in his
academic career, became interested in the existence
and importance of discontinuous

variation. These investigations were first presented in the form

3

of a study of segmentation patterns in the worm
Balanglossus
.
4

Bateson then set out for Central
Asia

to collect and describe cases of discontinuous variation in the wild. In contrast, Weldon

turned to
wards

mathematics as a tool to investigate biology
.

He was impressed by the
mathematical tools found in Galton’s
Natural Inheritance
, and so he set out on his own
investigations of correlations found in the crustacean
Crangon vulgaris
.
5

Bateson a
nd Weldon

remained close friends through
most of
the 1880’s, but Weldon became increasingly critical of
Bateson’s speculations concerning the
significance

of discontinuous v
ariation in evolution
.
6







Bateson utilized the data he
had
accumulated in C
entral Asia

to compose his massive
Materials for the Study of Variation Treated with Especial Regard to Discontinuity in the Origin
of Species
.
7

As the title suggests, Bateson heavily emphasized the importance of discontinuous
variati
on in relation to
spec
iation.
The

conflict
between Bateson and Weldon
first turned public

when Weldon reviewed
Bateson’s book
and criticized the interpretation of Bateson’s data as
confirming discont
inuous variation
.
8

The polar
izing

sides were displayed again on the pages of
Na
ture

with a series of letters debating the significance of discontinuous variation in the
evolution of the plant
Cinerari
.
9

Finally, in the late 1890’s, Francis Galton organized the
Evolution Committee for the Royal Society. Ever the diplomat, Galton hop
ed the committee
might cultivate both sides’ theoretical and methodological approaches to evolution and so asked
Pearson, Weldon, and Bateson to join the group. Unfortunately, Galton’s dream was not to be.
Differences proved too diverse, and by January 1
900, Galton, Pearson and Weldon resigned from
the committee

and left it to Bateson’s rule
.
10


It was in this environment that Mendel’s principles of inheritance reappeared just months
later. Bateson, preaching discontinuous evolution but without a complete

understanding of the
causal process responsible for discontinuity, saw in Mendel’s principles a solution to his

4

dilemma: Mendel’s heritable factors could be utilized to justify the theory of discontinuous
variation. Bateson immediately set out to publish

a variety of presentations of his discontinuity
theory based on the principles of inheritance laid
out by Mendel 35 years earlier
.
11


Naturally, the biometricians felt a potential threat from Bateson’s Mendelian Messiah,
and so in 1902, Weldon reviewed the

work of Mendel and its application by Bateson in the
biometricians’ journal
Biometrika
.
12

Weldon began by admitting that the Mendelian theory of
inheritance was one of importance and worthy of inspection. Weldon was especially fond of the
extensive data
acquired by Mendel, a methodological criterion that the biometricians demanded
in any rigorous investigation. But Weldon was not willing to admit that Mendel’s principles
could be universally applied to all forms of inheritance, as Bateson was arguing. T
he bulk of
Weldon’s review was the identification of the many research programs underway that did not
consider heredity to be due entirely to the factors passed from parent to progeny but instead took
into consideration the progeny’s ancestral line to dete
rmine e
xpected traits. Weldon concluded
,

The fundamental mistake which vitiates all work based upon Mendel’s method is the neglect of
ancestry, and the attempt to regard the whole effect upon offspring, produced by a particular
parent, as due to the exist
ence in the parent of particular structural characters; while the
contradictory results obtained by those who have observed the offspring of parents apparently
identical in certain characters show clearly enough that not only the parents themselves, but th
eir
race, that is their ancestry, must be taken into account before the result of

pairing them can be
predicted
.

13


Weldon was referring to the biometric law of ancestral heredity first presented in its
complete form by Galton in 1897. Galton claimed, bas
ed largely on his analysis of a breeding
record of Basset hounds, that a particular individual can be thought of as having inherited

5

ancestral contributions from generations in an exponentially decreasing fashion. “The two
parents contribute between them
on the average one
-
half, or (0.5) of the total heritage of the
offspring; the four grandparents, one
-
quarter, or (0.5)
2
; the eight great
-
grandparents, one
-
eighth
or (0.5)
3
, and so on. Thus the sum of the ancestral contributions is expressed by the series
(0.5)+(0.5)
2
+(0.5)
3
, etc., which, being equal to 1, acc
ounts for the whole heritage.”
14

For the
biometricians, the ancestral law of heredity was the rule governing their statistical conceptions of
heredity. Weldon was willing to acknowledge that Mendel’s
principles might be, at best, only a
special case of the more general ancestral law.


Bateson was quick to respond. In his famous
Mendel’s Principles of Heredity, a Defense
,
Bateson,

with a religious fervor, lashed

out at the
criticisms put forth by Weldo
n
.
15

What Bateson
feared most was the possibility that Weldon might upend Bateson’s efforts at cultivating the
nascent field of experimental hybridization known by 1902 as “Mendelism”, the field t
hat would
eventually become

genetics.
He wrote, “
It was ther
efore with a regret approaching to
indignation that I read Professor Weldon’s criticism. Were such a piece from the hand of a
junior it might safely be neglected; but coming from Professor Weldon there was the danger
-
almost the certainty
-
that the small ba
nd of younger men who are thinking of research in this field
would take it they had learnt the gist of Mendel, would imagine his teaching exposed by
Professor Weldon, and lo
ok elsewhere for lines of work
.

16


But after Bateson’s initial attack on Weldon, he

immediately tu
rned

to voice his
recognition concerning the importance of statistical applications to biol
ogy, as long as they were

combined with experi
mental research. Bateson admitted
, “The study of variation and heredity,
in our ignorance of the causat
ion of those phenomena,
must

be built of statistical data, as Mendel
knew long ago; but as he also perceived, the ground must be pre
pared by specific experiment.”
17


6

The Mendelian even went on to praise the biometricians Pearson and Galton after lambasting
their respected counterpart Weldon: “With sorrow I find such an article sent out to the world by a
Journal bearing, in any association, the revered name of Francis Galton, or under the high
sponsorship of Karl Pearson. I yield to no one in admiratio
n of t
he genius of these men.”
18



British statistician

George Udny Yule
(1871

1951)
was shocked by Bateson’s attack on
Weldon. A close friend of Pearson, Yule would w
rite soon after to him
,

The man seems to have
clean lost his head from the way he talks about
Mendel: ‘wet dish clouts’ are rather good
treatment for such style. He does not seem to realise that high falutin’ of that kind only tends to
make one the more critical.

19

Yule was more than just a close friend of Pearson; he was also
a
biometrician
.
But d
espite his own biometric biases,
Yule attempted to address the increasing
tension betwe
en Bateson and the team of Pearson and Weldon

and hoped to quell the fires on
both sides of the debate in his 1902 article “Mendel’s Laws and Their Probable Relations to

Intra
-
Racial Heredity.” A trained engineer and physicist, Yule
had
quickly turned to statistics
and became a demonstrator at University College London in 1893 at only 22. This early post
was a direct result of the elder Karl Pearson, who knew Yule as a
student. Yule found in Pearson
a stimulating mentor and began a life
-
long study of statistics hampered only by “the
war to end
all wars” and persistent heart trouble

late in life. Yule’s practical

applications of statistics to
economics and sociological
aspects of pauperism were extensive, but he became most famous for
his work on correlation and association
with Pearson and for his classic

Introduction to the
Theory of Statistics
, which saw fourteen edi
tions in Yule’s lifetime alone
.
20



7

Yule in the Histor
y of Biology

In the history of biology it is Yule’s 1902 paper on Mendel’s laws that has ensured him a
footnote in any history of the evolutionary synthesis.

What exactly was synthesized during this
period remains a hotly debated issue.
21

The matter is so c
omplex in large part because there are a
variety of different ways in which one might identify a synthesis. F
or example, Dudley Shapere

has claimed that there are at least three components of the evolutionary synthesis: the removal of
objections to the co
mpatibility of the Darwinian theory of evolution and the Mendelian picture of
genetics, and the demonstration that these two theories can, in fact, support one another;
second,
the rethinking of these previous enterprises in terms of population level model
s
; and
third,
the
realization that other fields (such as paleontology, systematics, botany, zoology, and
embryology) do not stand in opposition to the first two features.
22

Shapere’s distinctions are a
useful starting place; however, it is in need of furthe
r clarification. This is not a criticism of
Shapere, for he readily concluded his discussion with the sentence, “However, this picture of the
synthesis is almost certainly incomplete and oversimplified
and subject to revision.”
23

I will
specifically address

his first component: the removal of objections to the compatibility of
Darwinian evo
lution and Mendelian genetics
. This point needs clarification because it is itself
composed of several different elements. First,
the biometric studies of continuous varia
tion and
the Mendelian studies of discontinuous variation had to be shown to be compatible. And second,
there needed to be the realization that the biometric law of ancestral heredity did not stand in
opposition to the Mendelian principles of inheritance.

These clarifications of the relationship
between biometry and Mendelism both had to be addressed before the more general
compatibility of Darwinian evo
lution and Mendelian genetics could be deciphered.
It is here that
we can now understand and situate Yule
’s place in the history of the evolutionary synthesis. He


8

addressed the two elements that I mentioned above by showing how

the processes of continuous
and discontinuous variation were not incompatible and
by
demonstrating mathematically a
relationship betw
een the ancestral law of heredity and the
principles of Mendelian inheritance
.

But the history of biology tells us that Yule’s peace offering fell on deaf ears. The story
goes: Bateson and the biometricians were so engulfed in their own personal disdain

for each
other, that they were unable to recognize the potential unification of the two theories as presented
by Yule. And so it was to be
nearly
two decades before
R. A. Fisher put forth the popularized
attempt

to display the theoreti
cal relationship

be
tween biometry
, Darwin,

and Mendel. This
version of the history seems to have originated with several of th
e biologists, who directly
contributed to this
period
. For

instance, Sewall Wright, a figure generally regarded as an
architect of the evolutionary s
ynthesis,

claimed in 1978,

The acrimonious debate that ensued
[between the biometricians and the Mendelians] probably delayed experimental population
genetics for several decades in England
, that is, until Mather

began his studies of what he called
polyge
nic heredity.
24

This was in spite of papers by the biometrician, Yule, in 1902 and 1906,
showing that there was no irreconcilable difference between Galton’s purely statistical law,
essentially a multiple regression equation, and a physiological law suc
h a
s Mendel’s
.

25


Likewise, the influential

Ernst Mayr, offered

Yule a similar homage:


There was one
outstanding exception at that period, the biometrician Yule. As Provine points out, Yule
recognized not only ‘that Mendelism and biometry were compatible bu
t also even more crucial,
that Mendelism and Darwin’s idea of continuous evolution were compatible.’ Yule, alas, was
too far ahead of his time to be appreciated and it required many more years of tortuous argument
before others arrived at

the same conclus
ion
.

26


9

This traditional tale has been internalized by historians of biology. For example, the most
detailed account of Yule’s work comes from Mayr’s literary source

William Provine. In
The
Origins of Population Genetics

Provine paid

special attention to
the role of

personal conflicts in
the rise of population genetics and argued
, “Yule’s approach of synthesizing Mendelism and
biometry in the study of Darwinian evolution was submerged by the conflict. His was the
approach of population genetics. Conflict
s among his contemporaries prevented its development
at this time
.”
27

And also, “Yule’s excellent [1902] paper had little effect upon the widening gap
between the Mendelians and the biometricians. Not until R.A. Fisher’s first genetical paper in
1918 was t
here an important attempt in England to follo
w the lead suggested by Yule.”
28

We find a similar discussion of Y
ule from Raphael Falk who stated

in 1991, based on Yule’s
application of the m
ultiple factor hypothesis,


A similar argument had been put forward
already
in 1902 by George Yule, who pointed out that the conflict between biometrical and Mendelian
concepts of variation of quantitative characters was resolved if one assumed that many factors
may cooperate in determining one character. Instrumental red
uctionism was not incompatible
with conceptual holism. But to no avail. Neither the advocates of continuous variation in
evolution nor those of discontinuous variation were ready for the kind of explanation that
resolved the con
flict more than a decade l
ater
.

29


One other take on the reaction to Yule’s work has been simply to claim tha
t it was ignored.
The h
i
storian Daniel Kevles claimed
, “The suggestion, as early as 1902, of the British statistician
G. Udny Yule that Galton’s law and Mendelism actually c
omplemented rather than contradicted
each other was a
pparently ignored by Pearson.”
30

As we will see below in the analysis of
Pearson’s extensive reaction to Yule’s pr
oposal, this statement is

inaccurate. As a result, I will

10

leave Kevles’ perspective out of

the subsequent “received view”, since he is the only

historian to
make this

claim.


The story of Yule’s neglect is clear from both biologists and historians of biology: in 1902,
Yule attempted the first synthesis of biometry and Mendelian inheritance,
but the two schools of
thought who should have been most interested in their relationship were too blinded by personal
hatred to appreciate the union. The biological community would have to wait until 1918 for
Fisher to put forth his account in the
Transa
ctions of the Royal Society of Edinburgh

for a widely
recognized unification. It is not surprising that this brief story has become the common account
of Yule. Wright and Mayr are both regarded as two of the most influential architec
ts of this
period in
the history of evolutionary biology
; their interpretations are naturally revered.
Meanwhile, Falk and Provine are two exemplary historians of evolutionary biology. Provine’s
The

Origins of Population Genetics
, in particular
, is one of the definitive stud
ies of the
biometric
-
Mendelian debate. In the pages that follow, I will argue that
the picture of Yule
painted by the figures above
begins with a very limited understanding of Yule’s 1902 proposal
and, thus, results in a mistaken conception of why Bateson
and the biometricians did not endorse
Yule’s suggestion.


The turn to Yule in analyzing the biometric
-
Mendelian debate shares a common focal
point with some of the more recent investigations of this history. The motivation comes from
understa
nding the deb
ate not just

from the primary players (Bateson, Pearson, and Weldon), but
from the “second
-
tier” biologists who were associated with either Bateson or the biometricians.
The hope is that, by taking one step back, a clearer picture of the theoretical base o
f the debate
emerges that is not necessarily bogged down in some of the personal disagreements between the
primary individuals. This investigation of the second
-
tier figures can be found in Rachel

11

Ankeny’s investigation of A.D. Darbishire’s supposed conver
s
ion from biometry to Mendelism
,
and in Kyung
-
Man

Kim’s analysis of the emergence of “scientific consensus” in the debate.
31


Fisher’s
Reduction

of the Law of Ancestral Heredity to the Mendelian Principles of
Inheritance



The best place to begin understand
ing Yule’s 1902 discussion is actually with an article
that came 16 years later: R.A. Fisher’s “Correlation between Relatives on the Supposit
ion of
Mendelian Inheritance.”
32

This comparison makes sense for several reasons. First, though the
evolutionary s
ynthesis
is much debated and
has been placed on the shoulders of several
b
iologists, Fisher is generally

regarded as the first to successfully put forth a theory

of the
relationship between biometry, Darwinian evolution, and Mendelian inheritance
. That th
eory
first
emerged in the 1918 article. Secondly, Fisher, like Yule, was
a trained biometrician
and in
close contact with Pearson. This fact meant that both men were familiar with similar statistical
approaches to biology. Finally, Fisher’s theory is co
nsidered to be a direct descendent of Yule’s
earlier suggestion. Fisher himself adm
itted

in the introduction of his article that “the subject had
been pr
eviously opened by Udny Yule.”
33


It is interesting to point out here that Yule may have played more th
an just an indirect
role in pointing Fisher to th
e relationship between biometry

and Mendel. He may have
personally reviewed Fisher’s early theoretical investigations. In 1915, as Fisher was formulating
the relation
ship between biometry

and Mendelian inh
eritance, he was in constant correspondence
with Leonard Darwin, the son of Charles Darwin and President of the Eugenics Education
Society. Much of Fisher’s early (pre
-
1930) correspondence is no longer in existence, but
Darwin’s letters to Fisher have bee
n collected by J.H. Bennett in
Natural Selection, Heredity,
and Eugenics
.
34

In a letter to Fisher, Darwin

discussed

Fisher’s considerations of evolution and

12

select
ion and then suggested
, “if you did intend to write something, whether it would not be best
t
o write out your remarks in their final form, and submit them to Yule, or get us to do so. I
should be bound to get assurances you were on the right track before publishing in our
journal.”
35

I
t is unknown whether or not Fisher heeded this advice.


The mo
s
t important aspect of Fisher’s
work

for our discussion
is
the fact that it is
potentially
misleading to even call it a “synthesis”
. The
now
-
famous
“synthesis” locution used
to describe the wor
k of Fisher (along with other figures such as Haldane, Wright,

and Mayr)
came

twenty
-
four

years after Fisher’s 1918 presentation
,

initiated largely by Julian Huxley and
his
Evolution: the Modern Synthesis
.
36

The title of the work (“The Correlation between Relatives
on the Supposition of Mendelian Inheritance”) best ex
plains Fisher’s theory: if one
first

supposes
Mendelian inheritance, then one can derive the correlation between relatives, resulting in the
ancestral law of heredity.
Sahotra Sarkar has pointed out that it makes more sense to understand
Fisher as providi
ng a
reduction

of biometry’s law of ancestral heredity to Mendelian heredity,
rather than as generating a synthesis of the two.

This is because the two programs, on Fisher’s
model, did not contribute equally to the understanding of inheritance and evolutio
n; rather,
Fisher took the Mendelian principles of inheritance as the explanatory base and then derived the
biometric law of ancestral heredity to show that the statistical law was just a special case of the
physiological law.
37

The two theories were not eq
uals
, as a synthesis

would imply; biometry’s
ancestral law was just a mathematical consequence of Mendel’s principles.


Of course, it might be argued that a reduction is just a special case of a synthesis. On this
line, a “synthesis” is just understood as
a union of two theories, and so a reduction is one way to
unite theories, making it a special case of the more general synthesis. I have no problem with
conceptualizing the connection

between reduction
and synthesis in a
n

instance
-
kind

relationship;

13

howeve
r,
the trouble emerges when Fisher’s work is understood
only

as a synthesis, and when
the reductive aspect is left out.
As we will see below, w
ithout an appreciation for how Fisher
utilizes a reduction to explain the relationship between biometry and Mende
lism, we are ill
-
equipped to evaluate Yule’s own proposal and also to recognize the relationship between the two
biometricians’ work.

In addition to Sarkar’s concern,
I take this to be the more serious deficiency
of using the “synthesis” locution to captur
e the work of these biometricians.


An understanding of the reductive (rather than synthetic) nature of Fisher’s proposal is
best understood when we turn to his own paper of 1918.
In section 17
of this article, Fisher
discussed

the coefficient of correla
tion between generations while taking into consideration the
effects of dominance and t
he environment. He then derived

the results of Mendelian crosses
with the correlation
coefficients included and found
that there wa
s a direct, mathematical
relationship

between suc
cessions of generations. This wa
s
similar to the

identification of
ancestral heredity that Galton derived in 1897. Fisher conclud
ed

his discussion of the
relationship between biometry’s statistical law and Mendel’s physiological principl
es by

pointing
out that he came

upon “the Law of Ancestral Heredity as a necessary consequence of the
f
actorial mode of inheritance.”
38


Yule’s
Reduction

of the Mendelian Principles of Inheritance to the Law of Ancestral
Heredity


It was important to first poin
t out the nature of Fisher’s explanation because, as we will
see, Yule’s explanation of the relationship between Mendel and biometry
bears a striking
similarity to

Fisher’s,
but with one very important difference
. To identify the similarities and the
diff
erence between Yule and Fisher, I will outline the several steps Yule took to arrive at his
comparison between Mendel an
d biometry. His first step wa
s his most important; however, this

14

step
is conspicuously absent from the

historical discussions of his wo
rk

that I cited earlier
. It is
tru
e that Yule eventually discussed

the possibility of a compatible relationship between ancestral
heredity and Mendelian i
nheritance, but he only attempted

to define this
relationship after he
demarcated

the scientific doma
ins of each field of study. The relationship between the biometric
and Mendelian theories cannot be understood until the differences between the theories are first
appreciated.

Yule demarcated

the domains by a process of conceptual clarification
. An int
erest in
conceptual clarification was not uncommon for Yule. For instance, in a 1901 letter to Pearson,
Yule demanded Pearson make clear the difference between “regression coefficient” and
“reversion”, writing, “If you have got an article on nomenclature o
n hand I wish you would alter
the word ‘regression coefficient’. The confusion between the original meaning of reversion
towards type and regression coefficient is horrid. The ‘regression’, in [the] sense of reversion, is
measured rather by 1
-
r(
σ
1
/
σ
2
), i.e
. r(
σ
1
/
σ
2
) would be better termed the co
-
regression. Personally,
I should like to call r(
σ
1
/
σ
2
) ‘the deviation ratio’ or some such term and confine the word
‘regression’ to the sense of reversion to type.”
39

Yule applied his process of

conceptual clarificat
ion to the biometric
-
Mendelian debate by
focusing on the term “heredity”.
For th
e general biologist, Yule claimed
, heredity is just a notion
of “like begets like”; “a character may be said to be
inherited

when it always, in one generation
after another, is

one of the characters of the species, of the race, or of the one sex of the race
, as
distinct from the other.”
40

But Yule told

his re
ader that there wa
s a further question of heredity
that also must be answered: even if the type of the race is constant, d
o individual types within the
race beget their likes? “It is to this question that statisticians have confined themselves, and they

15

speak of a character being ‘inherited’ or not according as the answer to the question is yes or
no

they deal solely with wh
at we may term ‘
individual

heredity.’”
41



For Yule, it was the realization that the two scientific programs were concerned with two
different forms of heredity that was most important to
any clarification because this wa
s the first
step that must be taken

to appreciate both bio
metric and Mendelian programs. He wrote, “
The
distinctions between continuity and discontinuity of variation, between inheritance of attributes
and of variables do not seem to me to be of necessary importance for the theory of heredi
ty;
successive discontinuities may be so slight as to be undiscoverable by the most careful and
repeated measurements. The real and important distinction seems to lie between the phenomena
of
heredity

within the race, and the phenomena of
hybridization

th
at occur on crossing

two races
admittedly distinct
.

42

Yule rightly emphasized

the differences between the two theories because,
up until that point, each side was attempting to use the data supporting their own theory to
disprove the conclusions of the oth
er research program. Bateson believed his experimental
crosses undermined the ancestral law of heredity, and the biometricians believed their statistical
results disconfirmed Bateson’s account of Mendelian inheritance. But when the domains of the
two the
ories are demarcated, the results of each theory can be appreciated separately without
opposition.
Yule’s initial

po
int

t
hat biometry
’s study of continuous variation and Bateson’s
study of discontinuous variation

are not incompati
ble

is often what gets ci
ted
by historians
.
43

B
ut it is important to keep clea
r what history has emphasized for

Yule and what he himself
believed to be the important points of his discussion. This will be essential for understanding the
remainder of his
1902 paper
.


Yule first det
ermined that biometry is concerned with heredity within a race (intra
-
racial
heredity), and Mendelism instead is focused on hybridization between races (inter
-
racia
l

16

heredity). Yule’s next move was to discuss what he took

to be the most fundamental fact i
n
biology

the biometric law of an
cestral heredity. He recognized

the potential importance of
Mendelian heredity, but
experimental evidence had not accumulated to justify its generality by

1902.
Moreover, Yule pointed out the fact that Bateson and his col
league Edith Saunders, “like
other observers, found some difficulties and exceptions, notably in the case of
Matthiola

hybrids
and in
the experiments with poultry.”
44

The law of ancestral heredity, contrarily, had been
successfully shown to apply to data fr
om many different sp
ecies at this point. Yule listed

the
application to
Daphnia
,
Aphis
,
Lemma
, coat
-
color in horses and Basset hounds, and

eye
-
color in
man. He concluded
, “the list is not a long one certainly, but the characters and the genera are so
ext
raordinarily diverse that the law must be
one of very great generality.”
45

This “great
generality” which Yule identified in the law of ancestral heredity but which he was not yet
willing to attribute to Mendel’s principles is the first important point to g
lean from his 1902
discussion of ancestral heredity.


The second point that Yule made

which is vital to our discussion
concerns how he
actually defined

the law o
f ancestral heredity

because it was quite different from how his
biometrical colleagues defined

the law
. He admitted

from the very beginning of his di
scussion
of the law that he used

“the term ‘Law of Ancestral Heredity’ in a sense somewhat wider than
that given by Professor Pea
rson.”
46

The ancestral law, as defined by Galton, remember, was a
mathe
matical relationship of heritable contributions from various generations. The parents
contributed half of the heritage to the offspring; the grandparents contribute one
-
quarter; the
great
-
grandparents contribute one
-
eighth, and so on. Both Galton

and Pea
rson believed that this
strict,
mathematical relationship

formulated as such
could accurately account for the hereditary
contribution of any given ancestor
and act as a universal law. But Yule did not believe this

17

universal applic
ation was accurate. He po
inted out that Pearson called

the equation “
The

Law of
Ances
tral Heredity”, but Yule chose

“to drop t
hat signification, as [Yule did
] not think the facts
indicate any fixity of formula ev
en for intra
-
racial heredity.”
47

If Yule did

not admit of Pearson
and
Galton’s form of
the ancestral law, then how did

he conceive it? Yule’s answer wa
s as
follows:

the mean character of the offspring can be calculated with the more exactness, the
more extensive our knowledge of the corresponding characters of the ancestry
, may be termed
the Law of Ancestral Heredity
”.
48

So, for Yule, the ancestral law was not so much a
rigid,
mathematical equation for computing the given contributions from specific generations as it was
a much wider acknowledgement concerning the ability to

better predict the mean of any trait
with more knowledge of the ancestry. This very general definition is quite

different from the law
espoused

by Pearson and the other biometricians.


We have now identified the two important aspects of Yule’s analysis o
f the law of
ancestral here
dity: first, the ancestral law wa
s found across a range of biological species, so it
should be considered one of the most ge
neral of all biological principles
. Second, the law,
formu
lated by Pearson and Galton
, often did

not pro
vide an accurate account of inheritance, so
the law should be defined as no more than a description of an increasing ability to make
predictions based on an increasing knowledge of the ancestral lineage.


With the

law presented, Yule then began

consideri
ng how the ancestral law for intra
-
racial heredity and the Mendelian principles for inter
-
racial heredity might be related. “Little
work has yet been done on the intra
-
racial inheritance of attributes, but the form which the law of
ancestral heredity woul
d take in s
uch a case is fairly obvious.”
49

The
biometrician hoped

to
define how

the distribution of Mendelian

attributes (commonly termed “A” and “a”) might be
predicted on the basis of

the ancestral law. He decided
, “the percentage of A’s and a’s amongs
t

18

the offspring can be calculated with the more exactness, the more extensive our knowledge of the
corresponding characte
rs in the ancestry.”
50

Notice that this is in the exact same form of Yule’s
ancestral law of inheritance except that “the mean characte
r” has now been replaced by “the
percentage of A’s and

a’s.” Yule began with his unique

definition of the very general law of
ancestral heredity and then applied it to the case of Mendelian characters.


Yule first gave a brief definition of how to cons
ider the Mendelian characters behaving
under the predictive power of the ancestral law

of heredity. He next performed a thoug
ht
experiment by asking

what would happen if the “two races A and a are left to themselves to
inter
-
cross freely
as if they were o
ne race.

51

I quote the next paragraph in its entirety because it
is essentially Yule’s attempt to

mathematically determining the relationship between the
Mendelian principles and the biometric ancestral law.

Consider then the successive generations of pos
terity of the dominant forms, starting, say,
with 300 of which 100 are pure. The 100 pure individuals will give rise to dominant
forms in the proportion of 50 pure to 50 hybrids; the 200 hybrids may, as segregation
takes place, be considered as 100 pure d
ominants and 100 pure recessives, the former
giving rise to 50 pure dominants and 50 hybrids, the latter to 50 hybrid dominants and 50
pure recessives. The 300 parent dominants, therefore, give rise to offspring in the
proportion of 250 dominant forms to
50 recessive, i.e., the chance of a dominant parent
producing a dominant form as offsprin
g is 5/6
.
52

I diagram below (Figure 1) the rather co
nfusing description Yule phrased

above
.





19



200 (hybrid)


segregation

:


1
st

gen.
:

100 (pure dominant)


100 (pure dominant)


100 (pure recessive)



2
nd

gen.:
50 (pure dom.
)
50 (hybrid)

50 (pure dom.) 50 (h
ybrid
)


50 (hybrid)
50 (pure rec.)




Figure 1: Diagram

of Yule’s thought experiment for

intra
-
rac
ial

crossing



Before I turn to the conclusions Yule draws from his thought experiment, it is important to take a
moment to examine t
he actual details of Figure 1. This is because, o
n close inspection
,

it
becomes clear that the biometrician

misunderstood the
nature of Mendelian inheritance at several
points
, making the his

proposed connection between the ancestral law and the Mendelian
principles particularly problematic
.
53

For instance, Yule

treated

individuals as gametes

in the
statement, “the 200 hybrids may
, as segregation takes place, be considered as 100 pure dominant
and 100 pure recessive”. This leads to the initial division in Figure 1 of the 200 hybrids into the
100 pure dominant and
the
100 pure recessive of the 1
st

generation. We see here
conflation

o
n
Yule’s part between the level

of individual organisms and the
level of the
gametes they produce
.

Additionally, Yule clearly was confused about what the Mendelians meant by the “pure”
homozygous state (both the dominant and the recessive). This is appare
nt both when he claimed
that the 100 pure dominant produced 50 pure dominant and 50 hybrid, and when he supposed
that the 100 pure recessive produced 50 pure recessive and 50 hybrid.

This confusion on Yule’s
part is particularly odd because just two pages
earlier in his paper he pointed out, “these
‘extracted’ recessives

to use Bateson’s convenient terminology

breed pure, i.e. never give
ris
e again to the dominant form.”
54

A final point of confusion comes not from the quote above
but from a broader trend in
Yule’s essay, which has implications
for Yule’s thought

20

experiment

t
his was

the habit of Yule to move back and forth between the somatic, trait
-
based
notion of A and a (namely, A is pure dominant, Aa is hybrid dominant, and a is pure recessive)
and the gam
etic,

allelic
-
based notion of A and a

(or, AA is pure dominant, Aa is hybrid
dominant, and aa is pure recessive).

This shifting makes it difficult for the historian to determine
which state Yule believed he was investigating in his discussions.
In the anal
ysis that follows I
turn to what Yule
thought

he could conclude from his thought experiment

and leave his mistakes
behind. This is

because it was these
inferred
conclusions that generated
for Yule
the relationship
he proposed between biometry and Mendelism
. And subsequently, it was this relationship that
received the responses from the biometricians

and Bateson. Nevertheless, it wa
s worthwhile
identifying these mistakes in Yule’s analysis if only to keep in mind the fact that the relationship
Yule proposed
was a faulty one.

Yule utilized the numbers from what I have called the “second generation” to assess the
implications of his thought experiment.
The highlighted forms
of Figure 1
are the numbers Yule

used to establish his value of 5/6, with the one reces
sive form in italics.
This value of 5/6 is
just
what the biometrician
believed
he
needed

to then make consistent predictions about future
progeny. Based on the

distribution above, Yule claimed

that “quite generally one
-
half of the
pure dominants and one
-
q
uarter of the hybrids of any generation give rise to pure dominants as
offspring, while the remaining half of the pure dominants and one
-
half of the impure give rise to
hybrid forms.

55

Yule proceeded with the following calculations (the numbered equations

are
his own
; T
n

denoted the total number of dominants in the n
th

generation, p
n

is pure, and i
n

is
impure or a hybrid
):

(5
) p
n+1

= 1/2 p
n

+ 1/4 i
n

(6
) i
n+1

= 1/2 p
n
+ 1/2 i
n

= 1/2 T
n


21

If these two equations are added together, then

(7
) T
n+1

= T
n



1/4 i
n

Or by equation (6
) above

(8
) T
n+1

= T
n



1/8 T
n
-
1

This equation can be divided on both sides by T
n

to provide

the equation

(9
) C
n

= (T
n+1
)/ T
n

C
n

here is just the chance of a dominant form of the n
th

generation producing dominant offspring,
so the final eq
uation becomes

(10
) C
n

= 1


1/(8C
n
-
1
)

Yule already calculated the correlation coefficient of C
1

to be 5/6. This number could

then be
plugged in for successive generations to determine what the probability of a particular generation
exhibiting the dominan
t trait
was
if a gi
ven form was dominant. Yule did

the math himself for
five generations and provides the following results:

C
1

= .83333, C
2

= .85000, C
3

= .85294, C
4

= .85345, C
5

= .85354

Yu
le concluded
, “The figures illustrate as nicely as could be desi
red the two chief properties of
Ancestral Heredity

(i.) the chance of an A producing an A is increased if the ancestry be also
A’s. (ii.) it is not of much use to take into account more than the first few generations of
ancestry, for the chance C rapidly
approaches a limiting value.

Mendel’s Laws, so far from being
in any way inconsistent with the Law of Ancestral Heredity, lead then directly to a special case
of that law

.
56

Yule then went on to consider the relationship between Mendel’s principles and
his

version of the ancestral law

in cases where either dominance or predetermination (i.e., the
somatic attributes are rigidly fixed by the gametes) failed, where he ultimately came to the same
conclusion as above: his very general notion of the law of ancest
ral heredity was
the
general rule

22

for understanding inheritance, while the Mendelian principles, where applicable, could
generally
be considered
“a special case of that

law.

57


For Yule, application of Mendel’s ratio to the an
cestral law just resulted in

unique
formulation
s

of the more general biometric law.
Yule took his version of the law of ancestral
heredity to be the explanatory base because it provided the most generalized account of
inheritance in 1902, in contrast to the limited applicability of th
e Mendelian principles. With that
base set, he then demonstrated that the Mendelian principles could
often
be mathematically
deduced from the ancestral law. Like Fisher, Yule provided a reductive account of the
relationship between the Mendelian rules for
inheritance and the law of ancestral inheritance:
one theory stood as the explanatory base, while the other was a special case of that more general
theory. However, their reductions have one important difference between them, and it is to that
difference t
hat I now turn.


Co
mparing the Reductions of Fisher and
Yule

Yule attempted

to reconfigure the Mendelian
principles
in terms of the ancestral law. But
this is the very opposite
of the
move that Fisher made! Fisher believed the Mendelian principles
of in
heritance provided the basic theory of inheritance upon which all other accounts should be
based, and so he showed that the
mathematics utilized in the
biometric law of anc
estral heredity
could be reduced

to

the mathematics utilized to analyze
a randomly m
ating population made up
of Mendelian unit
-
characters.
But Yule

took
the
reduction in exactly the opposite direction.
His
unique characterization of

the law of ancestral heredity wa
s supposed to be the standard theory
by which all other theories of inher
ita
nce were measured, and so he used

it to judge the results of
Mendelian characters being passed down an ancestry. For Fisher, the ancestral law was a special

23

case of the Mendelian principles. For Yule, the Mendelian principles were a special case of the
ancestral law.

With just the term “synthesis”, the historian is limited to identifying
only
the fact
that both Yule and Fisher proposed a relationship between the ancestral law and the Mendelian
principles.

This is exactly what we found in the perspectives

on
Yule offered by Mayr, Provine,
and Wright

earlier.
58

But the important difference between Yule and Fisher identified above
emerges only when their models are reevaluated as reductions.




The events that occurred between 1902 and 1918 in the investigati
ons of inheritance give
evidence for why
Yule wo
uld have taken
his
reduction in one direction, and Fisher would have
taken it in the exact opposite direction just 16 years later. In 1902, as I mentioned above,
Mendel’s principles lacked an extensive amoun
t of experimental evidence
to justify

their
generality in

nature
.

Mendel’s paper from 1865 reappeared only two years earlier, and, by the
tone of Bateson’s
Defense
, it is clear that

there was a very limited number

of biologists interested
in taking the tim
e to experiment with the hybridizations that would study Mendel’s principles.
Between 1902 and 1918, though, the biological community saw major shifts in its theoretical and
methodological emphases. In 1903, Wilhelm Johannsen released the results of his
studies on
pure
-
line experiments using lines of the bean
Phaseolus vulgaris
. Johannsen utilized the
biometrical methodologies but came to the conclusion that a heritable character could
continuously evolve to only a certain degree before it became static
and required a discontinuous
var
iation to begin changing again
.
59

Later attempts to derive biometric results from Mendelian
principles came from American biologist Edward East and Swedish biologist Hermann Nilsson
-
Ehle, who provided Mendelian interpretation
s of what appea
red to be continuous variation
.
60

Also during this period Bateson was able to begin gathering around himself both the personnel,
such as R.C. Punnett along with a variety of female colleagues at Newnham College, and the

24

financial resources fr
om several donors, to construct the growing field of genetics.
61

The most
notable work in this fifteen
-
year span came from Thomas Morgan and his colleagues at
Columbia where they studied
the
chro
mosomes

of
Drosophila
. After 1909, Morgan based his
entire ch
romosome theory upon the Mendelian principles of inheritance. Fisher, but not Yule,
had the gift of an extra 16 years worth of experimental hindsight to reevaluate which theory of
inheritance held up to rigorous investigational scrutiny
, and so which theo
ry deserved to be the
reducer and which would be the reduced
.


Pearson and Bateson React to Yule’s Proposal


As I discussed abov
e, the received view in the history of biology has claimed

that Yule’s
synthesis

was overlooked by the biometricians and by Bate
son because they were blinded by
their personal ani
mosity for each other. I will now
argue that, based upon
the understanding of
Yule’s 1902 discussion of the relationship between the ancestral law of heredity and the
principles of Mendelian inheritance

a
s a reduction
, both the biometricians and Bateson

had good
reasons to avoid endorsing

Yule’s thesis.
By “good reasons”, I simply want to contrast the
theoretical issues I discuss below with the more traditional focus on the acrimonious nature of
the debate

between the two research groups as the source for disagreeing with Yule’s reduction.
This is not to say that the irrational, personal matters of Pearson and Bateson played no role in
assessing Yule’s work; rather, this is an attempt at situating their res
ponses along a more rational
axis

an avenue that has been neglected when discussing Yule’s 1902 paper. The biometric
-
Mendelian debate certainly was an acrimonious one, but Pearson’s and Bateson’s responses to
Yule’s reduction only make complete sense when
the form of Yule’s reduction, with a very

25

generalized notion of the law of ancestral heredity at the base and the Mendelian principles
reduced to it, is understood.



Yule began discussing with Pearson his interest in the relationship between biometry an
d
Mendelian inheritance as early as the summer of 1901. Yule was quite excited about his ideas at
this early stage, writing to Pearson, “There is very little of the ‘physico’ in my theory and I only
deal with simple blended inheritance. On the other hand,
it seems to knock the bottom out of our
present views and that is why I am really very anxious to get the first part ready for you as soon
as I can.”
62

This enthusiasm, though, quickly subsided as Yule became overwhelmed by the
enormity of dealing with such

a large issue. He admitted to Pearson in mid
-
August, “As you say,
I have got rather a big subject and the more I go with it, the more I feel I want time to go with
details and test it fairly before publishing. I had no idea when I started…that it would wo
rk out
so big.”
63


Pearson encouraged Yule’s work but also warned him not to overexert himself, as the
research was not in competition wit
h any other such investigations, saying, “
I want to send you a
line because I am a bit worried about you tonight. You l
ooked a little overdone and I fear you are
worrying too much over your heredity problems. I don’t think you should rush the paper…Other
investigations don’t seem likely to be about [it], so don’t hesitate to leave the thing for a month
or two.

64

As it turn
ed out, Yule would not have the time to take off from his project.
J
ust
months later, Bateson
publish
ed

his vitriolic
Defense
.
65

Yule’s project was la
rge, but he worked
up the model for the biometric
-
Mendelian relationship and sent it for publication. Inter
estingly,
t
hough the work was obviously of interest to both Mendelians and biometricians, Yule avoided
sending the work to
Biometrika
, under Pearson and Weldon’s command, or to the
Proceedings of
the Royal Society of London
, under Bateson’s control.
Instea
d, Yule chose the
neutral
journal

26

The

New Phytologis
t

founded i
n that same year by the ecologist

Arthur Tansley
.

Why did

Yule
select such a young journal devoted solely to the study of the botanical sciences? One reason, as
I mentioned just above, was the
fact that it was not mired in either side of the dispute between
the biometricians and the Mendelians. Anothe
r reason can be found in the

Editorial, which
introduced

the first issue of
the

journal by
explaining part of the motivation for
The

New
Phytologis
t

as follows
, “
It must be within the experience of most of us that observations are
constantly being made and views suggested, which at present never see the light because their
authors are engaged on other work, and lack the time or perhaps the inclinatio
n to follow them
up…[T]here are special cases in which it is desirable, and authors may find the new journal a
convenient medium for announcing discoveries or theories which seem to call fo
r immediate
publication
.

66

Two features are mentioned above

about
t
his blossoming journal that made it a
perfect venue for Yule’s proposal. First, Yule was a statistician, not a biologist of any sort. As a
result, the time Yule devoted to the issues surrounding inheritance was extremely limited in
comparison to the other
biometrical investigations he performed. In fact, Yule would only
discuss the relationship between the ancestral law and the Mendelian principles one more time
after his 1902 essay in a short, three
-
page discussion presented at t
he 1906 Conference on
Genet
ics
.
67

This made Tansley’s
The New Phytologist

an excellent format
,

since Yule’s
reflections on the biometric
-
Mendelian debate was a perfect example of a scientist’s observations
“being made and views suggested, which at present never see the light because
their authors are
engaged on other work.”
68

And second
, the fact th
at the

journal
was intended
to be “a convenient
medium for announcing discoveries or theories which seem to call for immediate publication”
made
The New Phytologist

a very suitable site for
Yule to quickly address the impending storm
created by Weldon’s criticism and Bateson’s response.
69

In light of the fact that Tansley was not

27

involved in the biometric
-
Mendelian debate to any extent and that Tansley’s journal was a good
fit for the nature o
f Yule’s 1902 proposal, it is not surprising that Yule sent his attempted
mediation of the dispute to
The New Phytologist
.





Pearson replied directly to Yule’s published account just two months later in
Biometrika
.
70

Pearson, interestingly, b
egan by emphasizing that he agreed

with the major point
of Yule’s discussion. “With much of his paper, I agree, for example, with his insistence on the
point that the laws of intra
-
racial heredity are not incompatible with Mendelian princip
les
holding for

hybridization.”
71

So Pearson
did

recognize Yule’s point about the potential
compatibility between biometry and Mendelism
. However
, the biometrician quickly turned

to
discuss a point of dissent because, “Mr. Yule does not seem to me to have clearly expresse
d my
personal position with regard to t
he law of ancestral heredity.”
72

Remember that Yule chose to
redefine the ancestral law in a very general format because he claimed the strict mathematical
structure of Pearson and Galton could not stand up to experim
ental

data. Pearson, however,
argued

his own, “memoir of 1898 [discussing the law of ancestral heredity] adopted the simpler
hypothesis that the correlation coefficients decrease in geometrical progression,
it did not involve
the fixity of the numerical c
onstants of heredity
which Mr. Yule tells us has not stood the test of
time. This simpler hypothesis…still seems to
me to stand the test of time.”
73

Pearson was
claiming that he agreed

with Yule in so far as there would

be no strict application of univers
al
constants to the

ancestral law, but he disagreed

with Yu
le in concluding that this meant there wa
s
no geometrical progression

at all to the law. Pearson stood firm on his belief that the correlation
coefficients
did

decrease in a geometrical progressio
n. Since Pearson was unwilling to give up
the mathematical nature of the ancestral law, then he surely would have been unreceptive to the

28

very general form of the law put forth by Yule, which only allowed for better prediction with
better knowledge of the

ancestral line.


Pearson, one year later, published his own account of the possible relationship between
the law of ancestral heredity and the principles of Mendelian inheritance in his famous series of
articles on the mathematical contributions to th
e theory of evolution titled, “On a Generalised
Theory of Alternative Inheritance, with Specia
l Reference to Mendel’s Laws.”
74

It is worth
mentioning here that there is no written account of Weldon’s response to Yule’s article;
however, the 1904 essay by Pe
arson was the result of months of work with Weldon on the topic
of a possible relationship between biometry and Mendelism, so we can essentially take Pearson’s
discussion to al
so be representative of Weldon
.
75

Pearson, in fact, dedicated

the article to
Wel
don stating, “I owe the incentive of this memoir to Professor W.F.R. Weldon, who had
already worked at some of the simpler special cases and who placed his res
ults entirely at my
disposal.”
76


Pearson

judged the validity of what he termed

the Mendelians’
pu
re gamete theory
: “the
gamete remains pure, and the gametes of two groups, while they may link up to form a complete
zygote, do not thereby absolutely
fuse and lose their identity.”
77

This was in contrast to the
concept of blending inheritance defended by
the biometrician
s. Pearson argued

that the
Mendelian theory may be worked together with the biometricians’ statistical methodology, but if
the mathematical results of the coordination do not coincide with the data gathered by the
biometricians, then “we a
re bound to discard it, and seek for its modification or replacement.
The present study is an attempt to see how far one generalised pure gamete theory leads to
results in accordance with the law of regression and the known nature of the distribution

of
o
ffspring in populations.”
78



29


Pearson began

by ass
uming what he took

to be the Mendelian notion of comp
lete
dominance. He then derived

the parental and grand
-
parental correlation coefficients that result
ed

from the statistical analysis of the pure gamete t
heory breeding randomly in a population. The
biom
etrician did

not find the two research programs, in principle,

to be incompatible, and so he
wa
s able to calculate the parental coefficient to be 1/3 and the grand
-
parental coef
ficient to be
1/6. Pearson a
dded
,


Now these results are of very singular importance. A very general theory
of the pure gamete type leads to linearity of the regression curve, a result amply verified by
observations on inheritance in populations…Further, the value of the correlation

reached is
numerically identical with the value obtained by Francis Galton in his original investigations on
the inheritance of stature! The generalized theory of the pure gamete is thus shown, whatever
the number of couplets taken, to lead to precisely
the chief results already obtained by those who
have
studied heredity statistically
.

79

But Pearson’s initial applause of t
he two programs’
compatibility wa
s quickly replaced by doubt, for the values obtained by Galton in 1885 were
greatly “refined” by the
biometricians in subsequent years. The parental coefficient, rather than
being equal to 1/3 as it was in 1885, was, in 1903, identified as being closer to 1/2. And,
similarly, the grand
-
parental coefficient was not 1/6 but instead 1/4. Pearson’s general
iz
ed
theory of the pure gamete led

directly to the biometric notion o
f regression, but the values were

too strict to account for the biometrician’s observed phenom
ena. Pearson sarcastically added
, “It
is most unfortunate for this general theory of the pur
e gamete, that it throws the Mendelian back
into the position

of the biometrician of 1885.”
80


The debate between Pearson and Yule turned on the form of the law of ancestral
heredity.
81

In contrast to the biometrician’s methodological disagreement with Bates
on
concerning the proper way to study biology, Pearson and Yule’s dispute was not subject to this

30

problem, as both men approached biology with statistical investigations.

They were both
biometricians.
Yule and Pearson simply disagreed over whether correlat
ion coefficients
decreasing in a geometric progression could be included in the ancestral law, or whether the law
only pointed to increased predictive capabilities with increased knowledge of the ancestral line.



Turning now to Bateson, Yule and the Men
delian

corresponded frequently and
even
worked together later in the 1920s when Yu
le performed statistical analyse
s for Bateson
.
82

But
there is little to show of any personal relationship between the men in the first decade of the
twentieth cen
tury. Neverth
eless, Bateson did

discuss the relationship between the ancestral law
of heredity and the Mendelian principles of inheritance at several points in these early years, and
there are several indications as to why Bateson would not have endorsed Yule’s suggest
ion.

For
instance, Bateson discussed

the relationship between the Mendelian principles and the statistical
methods of the biometricians in his 1909 publication
Mendel’s Principles of Heredity
. In the
ve
ry first chapter, Bateson argued
, “Galton’s method fa
iled for want of analysis. His formula
should in all probability be looked upon rather as an occasional consequence of the actual laws
of heredity than in any pr
oper sense one of those laws.”
83

The Mendelian was
admitting that the
statistic
al law of ances
tral heredity might

occasionally match data, but only because Mendelian
mechanisms occasionally produce
d

such results. So sometimes the law of

ancestral heredity just
happened

to be one special case of the Mendelian princi
ples. This obviously contradicted

the
relationship between the two theories as proposed by Yule. Yule began with the law of ancest
ral
heredity at the
base an
d then reduced

the results of Mendelian crossing to f
ind the Mendelian
principles offer

a
special case of the more general biometric

law. Bateson would certainly have
avoided such a proposal, as this was essentially the same suggestion Weldon made in his 1902
review of Mendel’s work. This same suggestion by Weldon elicited Bateson’s fear that interested

31

biologists would neglect the st
udy of Mendelian inheritance because the results were merely a
special cas
e of ancestral heredity. This wa
s not a case of personal hatred caus
ing scientific
blindness; this wa
s a case of a scientist steering clear of a suggestion that would have reduced h
is
research program to a mere footnote of biometrical statistics.


Bateson also
identified a second
reason for disagreeing with a proposal such as Yule’s.
Remember that Yule began his discussion by demarcating the scientific realms of the

two
programs. B
iometry studied

intra
-
racial heredity, and e
xperimental hybridizations studied

inter
-
racial heredity. One prob
lem with this conceptual distinction

came

from
the fact that Yule never
defined what he took

to be a “race”.
Without this definition, there wa
s
no way to accurately tell
what was inter
-
racial and what wa
s intra
-
racial. Bateson put great emphasis upon the role of
discontinuous variations in the process of evolution, but he did not believe that the emergence of
such variations necessarily placed th
e bearer of such a variation into another race. Speaking
direct
ly to this issue, Bateson claimed
, “in spite of their recent origin, such new combinations
have just the same genetic properties and powers of transmission that are possessed by the types
of l
ong
-
selected breed
s.” Bateson therefore concluded
, “The suggestion hazarded by several
writers that a distinction may be drawn between inter
-
racial and intra
-
racial heredi
ty has no
foundation in fact.”
84

Remember that
Yule took his most important contribut
ion to the discussion
of the relationship between the ancestral law and the Mendelian principles to be the
initial
distinction between their domains of investigation based on his conceptual analysis of
“heredity”. If this distinction is disregarded, as Bat
eson argued it should be, then Yule’s
subsequent assessment of the relationship between biometry’s study of intra
-
racial heredity and
Mendelism’s study of inter
-
racial heredity necessarily
falls apart.



32

Conclusion

This essay investigated the work of Georg
e Udny Yule in relation to
both
the
evolutionary synthesis and the biometric
-
Mendelian debate. I have argued that
it is misleading to
claim that Yule
put forth the first proposa
l for an evolutionary synthesis. I
nst
ead, Yule’s work is
better understood as
a

reduction with a much
-
generalized form of the law of ancestral heredity at
the base.
Understanding both Fisher and Yule’s work as a reduction rather than as a synthesis
allows for a clearer appreciation of how the two biometricians’ theories were related
, and where
they importantly differed. Specifically, Fisher attempted to reduce the biometric law of ancestral
heredity to the Mendelian principles of heredity, while Yule attempted the reduction in the
opposite direction. I also claimed that it was unders
tandable that Yule would have proposed such
a relationship in 1902 and Fisher would have gone in the opposite direction in 1918 when we
considered the important trends in the biological sciences that occurred in those 16 years
separating the two works.

Wi
th this
reductive
form of the propose
d relationship understood,
I attempted to
demonstrate the variety of reasons why both the biometricians and the Mendelians would not
endorse Yule’s

hypothesis. Pearson, wedded to the stricter mathematical form of the an
cestral
law, found Yule’s more general form to be an oversimplification. In contrast, Bateson disagreed
with the idea that the Mendelian principles were merely a special case of the more general
ancestral law and that the distinction between inter
-
racial
and intra
-
racial here
dity was not
grounded in fact.
In

hindsight, we might
commend Yule’s motivation

for attempting to find a
way to unite biometry and Mendelism
, as many historians have done; he sought to mediate a
divide that truly did need mediation. Un
fortunately, his proposal brought with it a number of

33

elements which neither the biometricians nor the Mendelians could have endorsed

in the form
that Yule presented it
.



Acknowledgments

Many thanks to Paul Griffiths, James Lennox, David Miller, Margare
t Morrison, Robert Olby,
Jeffery Schwartz, and three anonymous referees for providing useful comments and suggestions
on earlier drafts of this work. They all contributed much to the final version of this paper;
however, the mistakes remain my own. I also
benefited from discussions with participants at the
46
th

Annual Midwest JUNTO for the History of Science. Finally, Robert Cox of the American
Philosophical Association, Elizabeth Stratton of the John Innes Centre, John Wells of Cambridge
University, and Ju
lie Archer and Susan Stead of the University College London Library were
kind enough to make archival material available to me from across the state of Pennsylvania and,
in some cases,
from
across the Atlantic Ocean.




















34

Endnotes




1

Bateson
,

1894


2

Pearson
,

1900


3

The first, admittedly descriptive, account of the biometric
-
Mendelian debate came from
Froggatt and Nevin, 1971. This was soon followed by Provine’s classic study
The Origins of
Population Genetics

(Provin
e, 1971). The debate was then taken up by sociologists of science as
evidence for the social nature of the scientific process (Farrall, 1975; MacKenzie, 1981;
MacKenzie and Barnes, 1974; and MacKenzie and Barnes, 1979). For a critique of this social
interp
retation, see Roll
-
Hansen, 1980. The debate has also been used as a case to better
understand the figures involved in the dispute. For example, Cock, 1973; Darden, 1977; and
Olby, 1988 use the debate to assess the influence of Bateson, and Norton, 1973 and

1975; and
Morrison, 2002 use the history to evaluate the biometricians.

4

Bateson
,

1886


5

Galton
, 1889;

Weldon
,

1890 and 1892



6

Olby
,

1988


7

Bateson
,

1894


8

Weldon
,

1894


9

Bateson
, 1895;

Thiselton
-
Dyer
, 1895;

Weldon
,

1895


10

Froggatt and Nevin
,

1975


11

Bateson
,

1901, 1902a, 1902b


12

Weldon, 1902


13

Weldon
,

1902, 252


14

Galton
,

1897, 402


35







15

Bateson
,

1902d


16

Bateson
,

1902d, vi


17

Bateson
,

1902d, x


18

Bateson
,

1902d, xii


19

Yule to Pearson, 14 June 1902, Pearson Papers, University College London
, Addn. 905,
London, England.

20

Kendall
,

1971


21

A sample of the var
ious interpretations of

the evolutionary synthesis can be found in
The
Evolutionary Synthesis
, edited by Ernst Mayr and William Provine (1980).

22

Shapere
,

1980, 398


23

Shapere
,

1980, 398


24

Mather
,

1941


25

Wright, 1978, 5


26

Mayr
,

1973, 149


27

Provine
,
1971, 89


28

Provine
,

1978, 82


29

Falk
,

1991, 474


30

Kevles
,

1981, 196


31

Ankeny
, 2000;

Kim
,

1994


32

Fisher
,

1918



33

Fisher
,

1918, 401


34

Bennett
,

1983



36






35

Bennett
,

1983, 65


36

Huxley
,

194
2


37

Sarkar
,

1999, 106


38

Fisher
,

1918, 421


39

Yule to Pearson, 10 September 1901
, Pearson Papers, Addn. 905


40
Yule
,

1902, 196

(
Yule utilized italics to emphasize words in his discussion quite often. All
italicized words in quotes in this paper are from
the original.)

41

Yule
,

1902, 196


42
Yule
,

1902, 199


43
Falk, 1991;

Provine
,

1971



44

Yule,
1902, 193


45

Yule
,

1902, 201


46

Yule
,

1902, 204


47

Yule
,

1902, 204


48

Yule
,

1902, 202


49

Yule
,

1902, 202


50

Yule
,

1902, 202


51

Yule
,

1902, 225


52

Yule
,

1902, 225


53

T
hanks to Bob Olby and an anonymous referee for helping me dissect the mistakes in Yule’s
thought experiment.

54

Yule
,

1902, 223


55

Yule
,

1902, 226



37






56

Yule
,

1902, 226

227


57

Yule
,

1902, 227


58

Mayr
, 1973;

Provine
, 1971;

and Wright
,

1978


59

Johannsen
,

1903


60

East
,

1910
;

Nilsson
-
Ehle
,

1909


61
For a discussion of Bateson’s rather unique employment of female colleagues during these
formative years of genetics, see Richmond, 2001.

62

Yule to Pearson, 28 July 1901, Pearson Papers, Addn. 905.

63

Yule to Pearson, 18
August 1901, Pearson Papers, Addn. 905.


64

Pearson to Yule, 29 September 1901. Pearson Papers, Addn. 905.


65

Bateson
,

1902c


66

Editorial
,

1902, 2


67

Yule
,

1906


68

Editorial
,

1902, 2


69

Editorial
, 1902, 2;

Weldon
, 1902;

Bateson
,

1902c


70

Pearson
,

1903


71

Pe
arson
,

1903
, 212



72

Pearson
,

1903, 228



73

Pearson
,

1903, 229


74

Pearson
,

1904


75

Froggatt and Nevin
,

1971, 20


76

Pearson
,

1904, 53


77

Pearson
,

1904, 53



38






78

Pearson
,

1904, 55


79

Pearson
,

1904, 64


80

Pearson
,

1904, 65


81

Pearson and Yule debated the form of

the ancestral law and its implications for hybridization
experiments in two more publications: Yule (1906), claimed that Pearson’s 1904 interpreted the
pure gamete theory too strictly, and Pearson (1907), argued that Yule’s 1906 again misconstrued
Pearson
’s concept of the law of ancestral heredity.

82

S
ee, for example, Bateson
,

1923


83

Bateson
,

1909, 6


84

Bateson
,

1909, 49

























39






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