Darwin's famous book,  is not an easy book for the reader. Especially, the central part of his doctrine addressing the problem of how a small difference between varieties of a single species may become larger and larger and become a large difference between two distinct species or between two genera etc. is often confusing. Darwin brings in the "principle of divergence" in order to answer this central question, but the problem is: what is the status of this principle of divergence? Is it an independent principle from that of natural selection? How does it work, and how, exactly, does Darwin explain the diversification of organic beings? In this paper, I will give a logical analysis of Darwin's whole reasoning on this problem, based on the text of  as well as as of 

Uchii, Soshichi

English

PhilSci Archive

1Darwin's Principle of DivergenceSoshichi Uchii, Kyoto University[Paper presented at the 5th Quadrennial International Fellows Conference (inRytro, Poland),May 26-30, 2004,Center for Philosophy of Science, University of Pittsburgh]1. The Principle of Divergence as a Missing LinkToday I am going to talk about Darwin’s Principle of Divergence.1 Yes,most Darwin scholars now agree that this principle was a missinglink between 1844 Essay and the Origin. The development ofDarwin's theory, in this regard, was well traced by Dov Ospovat(1981), based on the unpublished manuscripts in the "Black Box" atCambridge University Library.2. The Big Species Book, and Wallace’s Ternate PaperIn the meantime, R. C. Stauffer edited and published in 1975 theportion of the Big Species Book containing the crucial part whereDarwin discusses Natural Selection together with the Principle ofDivergence. It seems that Darwin was working hard for completinghis discussion of the principle of divergence, when he received thepaper by Wallace—the so-called “Ternate Paper”---, which was readas the "joint paper" at Linnean Society in July 1858. That's one of thereasons why several scholars suspect Darwin of some misconduct,as regards the "joint paper" and the completion of his idea of thePrinciple of Divergence. However, if you read carefully bothWallace's paper and Darwin's texts, it is quite clear that Darwinowes nothing to Wallace, as regards the Principle of Divergence.                                                 1 This presentation is a summary of my paper Uchii (1993) published in Japanese.Thanks are due to the Center for Philosophy of Science, University of Pittsburgh, forenabling me to develop this research in the winter of 1991 as a visiting fellow there.2However, there still remains some obscurity as regards the exactdate of the arrival of Wallace's paper. Darwin's description in thisregard is not reliable; he seems to be saying, intentionally, a wrongdate. And the crucial document (Wallace's letter and its envelope onwhich we would find the stamp of the arrival date) was either lostor destroyed (see, e.g. Brooks 1984).3. The Principle of Divergence in the Big Species BookSetting aside these circumstances, the content of the Principle ofDivergence is stated as follows, in the Big Species Book:...in any country, a far greater number of individuals descendedfrom the same parents can be supported, when greatly       modified in different ways, in habits constitution & structure, soas to fill as many places, as possible, in the polity of nature, thanwhen not at all or only slightly modified.  (Stauffer 1975, 228)But how does this work? The role of the Principle of Divergence issuggested by Darwin as follows:The complex action of these several principles, namely, naturalselection, divergence & extinction, may be best ...         illustrated by the following Diagram, ...  (Stauffer 1975, 238)All right, the question now is: Is the Principle of Divergence distinct       from that of Natural Selection?; what is the relationship betweenthese two principles?  We will come back to these questions later.But one thing is certain, even at this stage. Darwin is arguing that,with the Principle of Divergence, we can explain how the largedifferences between a species and another, between a genus andanother, between an order and another, can be brought about---howsuch an hierarchy is formed by evolution, via natural selection.2                                                 2 Throughout this paper, I will ignore Darwin’s analogy with artificial selection, and34. Darwin’s Original ExpositionThis principle of course appears again in the Origin (ch. 4), but       it seems to me that Darwin's discussion there became more abstract,longer though, and it is one of the hardest parts for understanding.But his original discussion in the Big Species Book is sometimes moreconcrete, specific, and Darwin raises several specific questions,many of which are deleted in the Origin. Thus the Diagram (I) hementioned in the Big Species Book can be understood with this image:We have 12 species of the same genus, A, ..., and M.  A is the mostmoisture-loving plant and M the least moisture-loving plant (seeFigure 1).Figure 1Thus each species has a different character, peculiar to it anddistinguishing it from any other species in the group. And Darwin'squestion is: what is going to happen if several of them continue tovary, competing with others? Variations are provided within eachspecies; and there may well be the "places" in the polity of nature,which each varying species can occupy, provided that it can developa character suitable for that occupation.                                                                                                                                                another analogy with physiological division of labors (Darwin 1859, 115-6).  These areof course referred to in my original paper Uchii (1993).4With such specific images, it may become easier to grasp thesignificance of Darwin's questions, such as:I believe all the species of the same genus have         descended from a common parent; & we may call the averageamount of difference between the species, x; but if we look atthe contemporaneous varieties of any one species, the amountof difference between them is comparatively extremely slight &may be called a. How thus can be the slight difference a may beaugmented into the greater difference x; which must be on ourtheory be continually occurring in nature, if varieties areconverted into good species? ...  (Stauffer 1975, 243)But it may be objected that as natural selection, extinction &divergence must have been going on since the dawn of Life,why have we not an infinite number of species, almost as manyspecies as individuals? (Stauffer 1975, 246)Darwin gave his own answers to these questions. Now, what do youthink his answers are? Unless you read Darwin's text with this sortof reasoning and questioning back in your mind, you are wastingyour time!  (I will refrain from getting into Darwin’s answers, sincethis is not the main point here.)And here is a picture (Figure 2, depicted by myself based onDarwin’s exposition) of Darwin's idea, as regards "how smalldifferences become larger, and how a species diverges and graduallyforms a genus or genera"; and this was the whole point of Darwin'sdiscussion.5Figure 2In the top picture, the original situation is shown.  Suppose a million yearshave elapsed (the principles of natural selection, of divergence, and ofextinction going on, but the physical conditions of the area are notnecessarily changing), and the middle picture shows the situation at thisstage. The A group and the M group now flourish; they diverged and haveacquired different characters.  Suppose, again, another million years have6elapsed, and the bottom picture shows the changed situation.  The A groupflourishes and further diversified, but notice the descendants from A2perished.  The M group became now three distinct species.Now, if a naturalist sees the final stage, what is he/she going to do by wayof classification of these plants?  Darwin conjectures, the naturalist will see,in all probability, three distinct genera (A’s group, M’s group, and the rest)each consisting of several different species.  Thus large differences betweenspecies, between genera are produced.Although we still have not analyzed the role of the Principle ofDivergence in this process, we can intuitively see how Darwinconceived the process of diversification, from the Figure 2. 5. The Principle of Divergence at Work in Galapagos?By the way, if you think that the principle of divergence is merely atheoretical curiosity, read Jonathan Weiner's book, The Beak of theFinch (1994). A number of scholars are doing research on DarwinFinches in the Galapagos Islands. Weiner nicely depicts the activitiesof Peter and Rosemary Grant, and their groups; and in their research,one of the crucial issues is the Principle of Divergence, presumablyactually at work among the finches there. But again, in order toappreciate their work, we’ve got to know the role of the Principle ofDivergence in Darwin’s whole theory.  So let us turn now toDarwin’s statements as regards this principle in the Origin of Species.6. The Principle of Divergence in the OriginDarwin's Origin of Species is not an easy book even for a specialist.My own example may not be a good example, but let me say thismuch: I had to work hard (several years) in order to understand thesignificance of the principle of divergence, which appear in the lastpart of chapter 4.  For, what Darwin says of this principle seems7sometimes inconsistent, or at least misleading, and many readers,especially those who read the text carefully and for the first time, aswas actually the case with myself, may easily be confused.The principle is introduced as follows:the more diversified the descendants from any one speciesbecome in structure, constitution, and habits, by so much willthey be better enabled to seize on many and widely diversifiedplaces in the polity of nature, and so be enabled to increase innumbers. (Origin, 1st ed., 112)And, Darwin introduces a large diagram, adapted from the BigSpecies Book, in order to illustrate how this principle can be used forexplaining the genesis of a new genus (containing several species)from a single species. As we have seen, this was already discussed inhis Big Species Book, but I believe Darwin's "polished" description inthe Origin is worse than the original version. I will show this in moredetail.7. Three Principles AppearIn chapter 4, again three Principles appear: (1) the Principle ofNatural Selection, (2) the Principle of Divergence, and (3) thePrinciple of Extinction. But you've got to be careful; which areindependent, and which are derivative? I am going to say that Darwinwas quite misleading as regards this question, especially as to thePrinciple of Divergence. No one will doubt that the Principle ofNatural Selection is a fundamental principle, not derivable from theother two. Thus the question boils down to: Is (2) or (3) derivablefrom (1), or is it an independent principle?Let us see what Darwin says.8Now let us see how this principle of great benefit being derivedfrom divergence of character, combined with the principles ofnatural selection and of extinction, will tend to act. (Origin, 116)Here, Darwin may seem to be suggesting that (1) alone is notsufficient, and therefore we need two other principles. But is (2) on apar with (3)? A little reflection shows that this is not so, becauseExtinction (3) is nothing but a direct corollary of (1). Naturalselection, in forming new species (which is more advantageous thansome of the older species or varieties), inevitably causes extinctionof some other species or varieties; thus the Principle of Extinction isnot an independent principle. Then, what about Divergence, (2)?8. Darwin says, many times, Divergence follows from NaturalSelectionOn this．．．． crucial question, Darwin says two contradictory things. Atsome places, he suggests that Divergence follows from NaturalSelection. For example,Owing to the divergent tendency of natural selection, the extreme         amount of difference in character between species a14 and z14will be much greater than that between the most different of theoriginal eleven species. (Origin, 123, my italics)Wow, does natural selection have already the divergent tendency?Then, why do we need Divergence as an extra principle? Comparethe following passage where he refers to Extinction.Within the same large group, the later and more highlyperfected sub-groups, from branching out and seizing on manynew places in the polity of Nature, will constantly tend to9supplant and destroy the earlier and less improved sub-groups.(Origin , 125-6, my italics)Yes, this is extinction, a by-product of natural selection! Then isDivergence also another by-product? Without giving a clear answerto this lingering question, Darwin now tries to summarize the wholechapter. And this summary magnifies our confusion.9. In the Summary, Darwin again RepeatsHaving said that natural selection accomplishes adaptation, Darwincontinues:But we already see how it [natural selection] entails       extinction; and how largely extinction has acted in the world'shistory, geology plainly declares. Natural selection, also, leads todivergence of character; for more living beings can be supportedon the same area the more they diverge in structure, habits, andconstitution, ... (Origin, 127-8, my italics)In this passage, Darwin treats (2) and (3) as if they are on a par. But       then, why did he spend so much space for discussing the Principleof Divergence? But Darwin repeats the same point in the same page:Natural selection, as has just been remarked, leads to       divergence of character and to much extinction of the less improved       and intermediate forms of life. (Origin, 128, my italics)Again, he re-confirms, when he refers to the problem ofclassification, the same point a page later:but, to the best of my judgment, it is explained throughinheritance and the complex action of natural selection, entailing10extinction and divergence of character , as we have seen illustratedin the diagram. (Origin, 129, my italics)Thus, most readers may believe that Darwin's final position is thatboth (2) and (3) are derivative of (1)!10. But All This is Wrong!However, your impression is all wrong! As I have analyzed some 10years ago, the Principle of Divergence itself is an independentprinciple, not derivable from Natural Selection. And that's whereDarwin's great originality lies, in comparison to Wallace's version ofthe theory of Natural Selection. Darwin himself seems to be misledby his own words; he confounded the Principle of Divergence itself,with the consequences from Divergence together with NaturalSelection. I will show, in the final section, the result of my ownanalysis.11. How the Principle of Divergence WorksWe should analyze Darwin’s Principle of Divergence into twoconstituent elements (this was first presented in my 1993 paper):(D1) Any species, if it can occupy a new place in nature, notutilized so far, it can increase the number of its own member.(D2) By acquiring diversified characters, any species tends to beadaptable to new places in nature.The point of this analysis is to separate the crucial element of thePrinciple of Divergence; this element is (D1) and this is independentfrom the Principle of Natural Selection.  (D1) merely states, as abiological possibility, that if the places (or niches) are increased, thespecies can have more members (a benefit for that species), and thishas nothing to do with Natural Selection.  (D2), on the other hand,11is related with Natural Selection, because adaptation isaccomplished by competition and Natural Selection.  So when weassert (D2), Natural Selection is presupposed.  I can point out thatDarwin’s formulations of the Principle of Divergence—one in theBig Species Book, and another in the Origin---contain these twoelements, without separating (D1) from (D2); and this was the mainsource of much confusion.  In short, (D1) is an independentprinciple, whereas (D2) becomes, given (D1) and other relatedconditions, one of the consequences from the Principle of NaturalSelection.If you can grasp this point, then the rest of my analysis may becomeeasy.  What Darwin wishes to assert is that the difference betweentwo species originated from the same ancestor tends to becomelarger and larger.  And Darwin’s scenario for showing this seems tobe this.(D3) Given a place (niche) of nature and competitors in it,optimal characters are formed.And, of course, this again presupposes Natural Selection. (D3) is aconsequence from (D1), (D2) and the Principle of Natural Selection.Since this process is adaptation and Natural Selection, we can expect(as a matter of probability) that this optimal character (or a set ofcharacters) is quite different from another optimal character foranother place (niche) in nature. Optimization generally increases thedifferences, until it reaches an equilibrium state. That is, the initialdifference between two subspecies tends to be enlarged.  Darwinsometimes includes (D3) into his Principle of Divergence, and that’sanother source of confusion.Here is a diagrammatic representation of my analysis.12Figure 313ReferenceBrooks, J. L. (1984) Just before the Origin , Columbia University         Press.Ospovat, D. (1981) The Development of Darwin's Theory , Cambridge         University Press.Darwin, C. (1859)  On the Origin of Species, 1st ed.  (Oftenabbreviated as Origin)Stauffer, R. C., ed., (1975)  Charles Darwin’s Natural Selection, beingthe second part of his Big Species Book written from 1856 to 1858,Cambridge University Press.Uchii, S (1993), “Darwin and Wallace on the Principle ofDivergence”, Memoir of the Faculty of Letters 32 (1993), 43-103 [inJapanese].Weiner, Jonathan (1994) The Beak of the Finch, Vintage Books(originally from A. A. Knopf). [Chs. 10 and 12 are especiallyilluminating in relation to the principle of divergence.]

Darwin and Wallace on the Principle of Divergence”,

Just before the Origin ,

On the Origin of Species, 1 st ed. (Often abbreviated as Origin) Stauffer,

The Beak of the Finch, Vintage Books (originally from

The Development of Darwin's Theory ,

Darwin's Principle of Divergence

Darwin's famous book, <On the Origin of Species> is not an easy book for the reader. Especially, the central part of his doctrine addressing the problem of how a small difference between varieties of a single species may become larger and larger and become a large difference between two distinct species or between two genera etc. is often confusing. Darwin brings in the "principle of divergence" in order to answer this central question, but the problem is: what is the status of this principle of divergence? Is it an independent principle from that of natural selection? How does it work, and how, exactly, does Darwin explain the diversification of organic beings? In this paper, I will give a logical analysis of Darwin's whole reasoning on this problem, based on the text of <On the Origin of Species> as well as as of <the Big Species Book>

Name not available

Philsci-Archive

1Darwin's Principle of Divergence
Soshichi Uchii, Kyoto University
[Paper presented at the 5th Quadrennial International Fellows Conference (in
Rytro, Poland),
May 26-30, 2004,
Center for Philosophy of Science, University of Pittsburgh]
1. The Principle of Divergence as a Missing Link
Today I am going to talk about Darwin’s Principle of Divergence.1 Yes,
most Darwin scholars now agree that this principle was a missing
link between 1844 Essay and the Origin. The development of
Darwin's theory, in this regard, was well traced by Dov Ospovat
(1981), based on the unpublished manuscripts in the "Black Box" at
Cambridge University Library.
2. The Big Species Book, and Wallace’s Ternate Paper
In the meantime, R. C. Stauffer edited and published in 1975 the
portion of the Big Species Book containing the crucial part where
Darwin discusses Natural Selection together with the Principle of
Divergence. It seems that Darwin was working hard for completing
his discussion of the principle of divergence, when he received the
paper by Wallace—the so-called “Ternate Paper”---, which was read
as the "joint paper" at Linnean Society in July 1858. That's one of the
reasons why several scholars suspect Darwin of some misconduct,
as regards the "joint paper" and the completion of his idea of the
Principle of Divergence. However, if you read carefully both
Wallace's paper and Darwin's texts, it is quite clear that Darwin
owes nothing to Wallace, as regards the Principle of Divergence.
                                                 
1 This presentation is a summary of my paper Uchii (1993) published in Japanese.
Thanks are due to the Center for Philosophy of Science, University of Pittsburgh, for
enabling me to develop this research in the winter of 1991 as a visiting fellow there.
2However, there still remains some obscurity as regards the exact
date of the arrival of Wallace's paper. Darwin's description in this
regard is not reliable; he seems to be saying, intentionally, a wrong
date. And the crucial document (Wallace's letter and its envelope on
which we would find the stamp of the arrival date) was either lost
or destroyed (see, e.g. Brooks 1984).
3. The Principle of Divergence in the Big Species Book
Setting aside these circumstances, the content of the Principle of
Divergence is stated as follows, in the Big Species Book:
...in any country, a far greater number of individuals descended
from the same parents can be supported, when greatly       
modified in different ways, in habits constitution & structure, so
as to fill as many places, as possible, in the polity of nature, than
when not at all or only slightly modified.  (Stauffer 1975, 228)
But how does this work? The role of the Principle of Divergence is
suggested by Darwin as follows:
The complex action of these several principles, namely, natural
selection, divergence & extinction, may be best ...         
illustrated by the following Diagram, ...  (Stauffer 1975, 238)
All right, the question now is: Is the Principle of Divergence distinct       
from that of Natural Selection?; what is the relationship between
these two principles?  We will come back to these questions later.
But one thing is certain, even at this stage. Darwin is arguing that,
with the Principle of Divergence, we can explain how the large
differences between a species and another, between a genus and
another, between an order and another, can be brought about---how
such an hierarchy is formed by evolution, via natural selection.2
                                                 
2 Throughout this paper, I will ignore Darwin’s analogy with artificial selection, and
34. Darwin’s Original Exposition
This principle of course appears again in the Origin (ch. 4), but       
it seems to me that Darwin's discussion there became more abstract,
longer though, and it is one of the hardest parts for understanding.
But his original discussion in the Big Species Book is sometimes more
concrete, specific, and Darwin raises several specific questions,
many of which are deleted in the Origin. Thus the Diagram (I) he
mentioned in the Big Species Book can be understood with this image:
We have 12 species of the same genus, A, ..., and M.  A is the most
moisture-loving plant and M the least moisture-loving plant (see
Figure 1).
Figure 1
Thus each species has a different character, peculiar to it and
distinguishing it from any other species in the group. And Darwin's
question is: what is going to happen if several of them continue to
vary, competing with others? Variations are provided within each
species; and there may well be the "places" in the polity of nature,
which each varying species can occupy, provided that it can develop
a character suitable for that occupation.
                                                                                                                                                
another analogy with physiological division of labors (Darwin 1859, 115-6).  These are
of course referred to in my original paper Uchii (1993).
4With such specific images, it may become easier to grasp the
significance of Darwin's questions, such as:
I believe all the species of the same genus have         
descended from a common parent; & we may call the average
amount of difference between the species, x; but if we look at
the contemporaneous varieties of any one species, the amount
of difference between them is comparatively extremely slight &
may be called a. How thus can be the slight difference a may be
augmented into the greater difference x; which must be on our
theory be continually occurring in nature, if varieties are
converted into good species? ...  (Stauffer 1975, 243)
But it may be objected that as natural selection, extinction &
divergence must have been going on since the dawn of Life,
why have we not an infinite number of species, almost as many
species as individuals? (Stauffer 1975, 246)
Darwin gave his own answers to these questions. Now, what do you
think his answers are? Unless you read Darwin's text with this sort
of reasoning and questioning back in your mind, you are wasting
your time!  (I will refrain from getting into Darwin’s answers, since
this is not the main point here.)
And here is a picture (Figure 2, depicted by myself based on
Darwin’s exposition) of Darwin's idea, as regards "how small
differences become larger, and how a species diverges and gradually
forms a genus or genera"; and this was the whole point of Darwin's
discussion.
5Figure 2
In the top picture, the original situation is shown.  Suppose a million years
have elapsed (the principles of natural selection, of divergence, and of
extinction going on, but the physical conditions of the area are not
necessarily changing), and the middle picture shows the situation at this
stage. The A group and the M group now flourish; they diverged and have
acquired different characters.  Suppose, again, another million years have
6elapsed, and the bottom picture shows the changed situation.  The A group
flourishes and further diversified, but notice the descendants from A2
perished.  The M group became now three distinct species.
Now, if a naturalist sees the final stage, what is he/she going to do by way
of classification of these plants?  Darwin conjectures, the naturalist will see,
in all probability, three distinct genera (A’s group, M’s group, and the rest)
each consisting of several different species.  Thus large differences between
species, between genera are produced.
Although we still have not analyzed the role of the Principle of
Divergence in this process, we can intuitively see how Darwin
conceived the process of diversification, from the Figure 2.
 
5. The Principle of Divergence at Work in Galapagos?
By the way, if you think that the principle of divergence is merely a
theoretical curiosity, read Jonathan Weiner's book, The Beak of the
Finch (1994). A number of scholars are doing research on Darwin
Finches in the Galapagos Islands. Weiner nicely depicts the activities
of Peter and Rosemary Grant, and their groups; and in their research,
one of the crucial issues is the Principle of Divergence, presumably
actually at work among the finches there. But again, in order to
appreciate their work, we’ve got to know the role of the Principle of
Divergence in Darwin’s whole theory.  So let us turn now to
Darwin’s statements as regards this principle in the Origin of Species.
6. The Principle of Divergence in the Origin
Darwin's Origin of Species is not an easy book even for a specialist.
My own example may not be a good example, but let me say this
much: I had to work hard (several years) in order to understand the
significance of the principle of divergence, which appear in the last
part of chapter 4.  For, what Darwin says of this principle seems
7sometimes inconsistent, or at least misleading, and many readers,
especially those who read the text carefully and for the first time, as
was actually the case with myself, may easily be confused.
The principle is introduced as follows:
the more diversified the descendants from any one species
become in structure, constitution, and habits, by so much will
they be better enabled to seize on many and widely diversified
places in the polity of nature, and so be enabled to increase in
numbers. (Origin, 1st ed., 112)
And, Darwin introduces a large diagram, adapted from the Big
Species Book, in order to illustrate how this principle can be used for
explaining the genesis of a new genus (containing several species)
from a single species. As we have seen, this was already discussed in
his Big Species Book, but I believe Darwin's "polished" description in
the Origin is worse than the original version. I will show this in more
detail.
7. Three Principles Appear
In chapter 4, again three Principles appear: (1) the Principle of
Natural Selection, (2) the Principle of Divergence, and (3) the
Principle of Extinction. But you've got to be careful; which are
independent, and which are derivative? I am going to say that Darwin
was quite misleading as regards this question, especially as to the
Principle of Divergence. No one will doubt that the Principle of
Natural Selection is a fundamental principle, not derivable from the
other two. Thus the question boils down to: Is (2) or (3) derivable
from (1), or is it an independent principle?
Let us see what Darwin says.
8Now let us see how this principle of great benefit being derived
from divergence of character, combined with the principles of
natural selection and of extinction, will tend to act. (Origin, 116)
Here, Darwin may seem to be suggesting that (1) alone is not
sufficient, and therefore we need two other principles. But is (2) on a
par with (3)? A little reflection shows that this is not so, because
Extinction (3) is nothing but a direct corollary of (1). Natural
selection, in forming new species (which is more advantageous than
some of the older species or varieties), inevitably causes extinction
of some other species or varieties; thus the Principle of Extinction is
not an independent principle. Then, what about Divergence, (2)?
8. Darwin says, many times, Divergence follows from Natural
Selection
On this
．．．．
 crucial question, Darwin says two contradictory things. At
some places, he suggests that Divergence follows from Natural
Selection. For example,
Owing to the divergent tendency of natural selection, the extreme         
amount of difference in character between species a14 and z14
will be much greater than that between the most different of the
original eleven species. (Origin, 123, my italics)
Wow, does natural selection have already the divergent tendency?
Then, why do we need Divergence as an extra principle? Compare
the following passage where he refers to Extinction.
Within the same large group, the later and more highly
perfected sub-groups, from branching out and seizing on many
new places in the polity of Nature, will constantly tend to
9supplant and destroy the earlier and less improved sub-groups.
(Origin , 125-6, my italics)
Yes, this is extinction, a by-product of natural selection! Then is
Divergence also another by-product? Without giving a clear answer
to this lingering question, Darwin now tries to summarize the whole
chapter. And this summary magnifies our confusion.
9. In the Summary, Darwin again Repeats
Having said that natural selection accomplishes adaptation, Darwin
continues:
But we already see how it [natural selection] entails       
extinction; and how largely extinction has acted in the world's
history, geology plainly declares. Natural selection, also, leads to
divergence of character; for more living beings can be supported
on the same area the more they diverge in structure, habits, and
constitution, ... (Origin, 127-8, my italics)
In this passage, Darwin treats (2) and (3) as if they are on a par. But       
then, why did he spend so much space for discussing the Principle
of Divergence? But Darwin repeats the same point in the same page:
Natural selection, as has just been remarked, leads to       
divergence of character and to much extinction of the less improved       
and intermediate forms of life. (Origin, 128, my italics)
Again, he re-confirms, when he refers to the problem of
classification, the same point a page later:
but, to the best of my judgment, it is explained through
inheritance and the complex action of natural selection, entailing
10
extinction and divergence of character , as we have seen illustrated
in the diagram. (Origin, 129, my italics)
Thus, most readers may believe that Darwin's final position is that
both (2) and (3) are derivative of (1)!
10. But All This is Wrong!
However, your impression is all wrong! As I have analyzed some 10
years ago, the Principle of Divergence itself is an independent
principle, not derivable from Natural Selection. And that's where
Darwin's great originality lies, in comparison to Wallace's version of
the theory of Natural Selection. Darwin himself seems to be misled
by his own words; he confounded the Principle of Divergence itself,
with the consequences from Divergence together with Natural
Selection. I will show, in the final section, the result of my own
analysis.
11. How the Principle of Divergence Works
We should analyze Darwin’s Principle of Divergence into two
constituent elements (this was first presented in my 1993 paper):
(D1) Any species, if it can occupy a new place in nature, not
utilized so far, it can increase the number of its own member.
(D2) By acquiring diversified characters, any species tends to be
adaptable to new places in nature.
The point of this analysis is to separate the crucial element of the
Principle of Divergence; this element is (D1) and this is independent
from the Principle of Natural Selection.  (D1) merely states, as a
biological possibility, that if the places (or niches) are increased, the
species can have more members (a benefit for that species), and this
has nothing to do with Natural Selection.  (D2), on the other hand,
11
is related with Natural Selection, because adaptation is
accomplished by competition and Natural Selection.  So when we
assert (D2), Natural Selection is presupposed.  I can point out that
Darwin’s formulations of the Principle of Divergence—one in the
Big Species Book, and another in the Origin---contain these two
elements, without separating (D1) from (D2); and this was the main
source of much confusion.  In short, (D1) is an independent
principle, whereas (D2) becomes, given (D1) and other related
conditions, one of the consequences from the Principle of Natural
Selection.
If you can grasp this point, then the rest of my analysis may become
easy.  What Darwin wishes to assert is that the difference between
two species originated from the same ancestor tends to become
larger and larger.  And Darwin’s scenario for showing this seems to
be this.
(D3) Given a place (niche) of nature and competitors in it,
optimal characters are formed.
And, of course, this again presupposes Natural Selection. (D3) is a
consequence from (D1), (D2) and the Principle of Natural Selection.
Since this process is adaptation and Natural Selection, we can expect
(as a matter of probability) that this optimal character (or a set of
characters) is quite different from another optimal character for
another place (niche) in nature. Optimization generally increases the
differences, until it reaches an equilibrium state. That is, the initial
difference between two subspecies tends to be enlarged.  Darwin
sometimes includes (D3) into his Principle of Divergence, and that’s
another source of confusion.
Here is a diagrammatic representation of my analysis.
12
Figure 3
13
Reference
Brooks, J. L. (1984) Just before the Origin , Columbia University         
Press.
Ospovat, D. (1981) The Development of Darwin's Theory , Cambridge         
University Press.
Darwin, C. (1859)  On the Origin of Species, 1st ed.  (Often
abbreviated as Origin)
Stauffer, R. C., ed., (1975)  Charles Darwin’s Natural Selection, being
the second part of his Big Species Book written from 1856 to 1858,
Cambridge University Press.
Uchii, S (1993), “Darwin and Wallace on the Principle of
Divergence”, Memoir of the Faculty of Letters 32 (1993), 43-103 [in
Japanese].
Weiner, Jonathan (1994) The Beak of the Finch, Vintage Books
(originally from A. A. Knopf). [Chs. 10 and 12 are especially
illuminating in relation to the principle of divergence.]


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Darwin's Principle of Divergence

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