Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory
Evolutionary trees (caulograms) and phylogenetic cladograms for both morphological and molecular analyses of certain species in the moss genus Didymodon (Pottiaceae, Bryophyta) were compared. A new two-step macrosystematic (macroevolutionary systematics) method of calculating statistical support f...
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Zander, R.H. 2021-02-19T11:21:08Z 2021-02-19T11:21:08Z 2016 Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory / R.H. Zander // Український ботанічний журнал. — 2016. — Т. 73, № 4. — С. 319-332. — Бібліогр.: 41 назв. — англ. 0372-4123 DOI: http://dx.doi.org/10.15407/ukrbotj73.04.319 https://nasplib.isofts.kiev.ua/handle/123456789/178454 Evolutionary trees (caulograms) and phylogenetic cladograms for both morphological and molecular analyses of certain species in the moss genus Didymodon (Pottiaceae, Bryophyta) were compared. A new two-step macrosystematic (macroevolutionary systematics) method of calculating statistical support for both linear order and lineage direction of evolution is introduced. This involves clustering of taxa in sets by minimization of redundancy using cladograms and minimum parsimony, then building an often-branched linear model by maximization of information on gradual evolution by ordering species through adding informational bits for advanced traits and subtracting them for reversals. Cladistic analysis is considered to be similar to cryptographic code-breaking, with that code key then used for modelbuilding following theory. Very high Bayesian support was computed for lineages in the morphological analyses, which stand up well to high support for past molecular studies. The caulogram allowed for predictions not possible with cladograms. The importance of using information on both shared and serial descent is discussed. Проведене порівняння еволюційних дерев (каулограм) та філогенетичних кладограм як для морфологічних, так і молекулярних аналізів деяких видів мохоподібних роду Didymodon (Pottiaceae, Bryophyta). Запропонований новий двоступеневий макротаксономічний метод (метод макроеволюційної систематики) розрахунку статистичної підтримки як лінійного порядку, так і напрямку еволюції певної філогенетичної лінії. Метод включає кластеризацию таксонів у наборах шляхом мінімізації повторності (надмірності) з використанням кладограм та мінімальної парсимонії, з наступною побудовою часто розгалуженої лінійної моделі через максимізацію інформації про поступову (градуалістичну) еволюцію шляхом упорядкування видів через додавання інформаційних бітів для просунутих ознак і віднімання їх для еволюційних реверсій. Кладистичний аналіз розглядається як аналог криптографічної операції злому коду, при цьому кодовий ключ потім використовується для побудови наступної теоретичної моделі. Дуже висока байесівська підтримка обчислена для еволюційних ліній при морфологічному аналізі, що добре корелює з високою підтримкою попередніх молекулярних досліджень. Каулограма дозволила здійснити передбачення (прогнози), які були неможливими за допомогою кладограм. Обговорюється важливість використання інформації щодо як походження від спільного предка шляхом дивергенції (кладогенез), так і походження внаслідок «відбруньковування» нових таксонів та лінійних послідовних змін (анагенез). Проведено сравнение эволюционных деревьев (каулограмм) и филогенетических кладограмм как для морфологических, так и молекулярных анализов некоторых видов мохообразных рода Didymodon (Pottiaceae, Bryophyta). Предложен новый двухступенчатый макротаксономический метод (метод макроэволюционной систематики) расчета статистической поддержки как линейного порядка, так и направления эволюции определенной филогенетической линии. Метод включает кластеризацию таксонов в наборах путем минимизации повторности (избыточности) с использованием кладограмм и минимальной парсимонии, с последующим построением часто разветвленной линейной модели путем максимизации информации о постепенной (градуалистической) эволюции посредством упорядочивания видов через добавление информационных битов для продвинутых признаков и вычитание их для эволюционных реверсий. Кладистический анализ рассматривается как аналог криптографической операции взлома кода, при этом кодовый ключ впоследствии используется для построения следующей теоретической модели. Очень высокая байесовская поддержка вычислена для эволюционных линий при морфологическом анализе, что хорошо коррелирует с высокой поддержкой предыдущих молекулярных исследований. Каулограмма позволила осуществить прогнозы, которые были невозможными при помощи кладограмм. Обсуждается важность использования информации относительно как происхождения от общего предка путем дивергенции (кладогенез), так и происхождения вследствие «отпочковывания» новых таксонов и линейных последовательных изменений (анагенез). I thank Sergei Mosyakin, editor-in-chief of the Ukrainian Botanical Journal, for his kind invitation to submit a paper. Two anonymous reviewers provided helpful suggestions. The Missouri Botanical Garden continues to provide a congenial working environment of superb support. en Інститут ботаніки ім. М.Г. Холодного НАН України Український ботанічний журнал Загальні проблеми, огляди та дискусії Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory Макросистематика Didymodon sensu lato (Pottiaceae, Bryophyta) з використанням аналітичного ключа та теорії інформації Макросистематика Didymodon sensu lato (Pottiaceae, Bryophyta) с использованием аналитического ключа и теории информации Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory |
| spellingShingle |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory Zander, R.H. Загальні проблеми, огляди та дискусії |
| title_short |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory |
| title_full |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory |
| title_fullStr |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory |
| title_full_unstemmed |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory |
| title_sort |
macrosystematics of didymodon sensu lato (pottiaceae, bryophyta) using an analytic key and information theory |
| author |
Zander, R.H. |
| author_facet |
Zander, R.H. |
| topic |
Загальні проблеми, огляди та дискусії |
| topic_facet |
Загальні проблеми, огляди та дискусії |
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2016 |
| language |
English |
| container_title |
Український ботанічний журнал |
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Інститут ботаніки ім. М.Г. Холодного НАН України |
| format |
Article |
| title_alt |
Макросистематика Didymodon sensu lato (Pottiaceae, Bryophyta) з використанням аналітичного ключа та теорії інформації Макросистематика Didymodon sensu lato (Pottiaceae, Bryophyta) с использованием аналитического ключа и теории информации |
| description |
Evolutionary trees (caulograms) and phylogenetic cladograms for both morphological and molecular analyses
of certain species in the moss genus Didymodon (Pottiaceae, Bryophyta) were compared. A new two-step macrosystematic
(macroevolutionary systematics) method of calculating statistical support for both linear order and lineage direction
of evolution is introduced. This involves clustering of taxa in sets by minimization of redundancy using cladograms
and minimum parsimony, then building an often-branched linear model by maximization of information on gradual
evolution by ordering species through adding informational bits for advanced traits and subtracting them for reversals.
Cladistic analysis is considered to be similar to cryptographic code-breaking, with that code key then used for modelbuilding following theory. Very high Bayesian support was computed for lineages in the morphological analyses, which
stand up well to high support for past molecular studies. The caulogram allowed for predictions not possible with
cladograms. The importance of using information on both shared and serial descent is discussed.
Проведене порівняння еволюційних дерев (каулограм)
та філогенетичних кладограм як для морфологічних,
так і молекулярних аналізів деяких видів мохоподібних
роду Didymodon (Pottiaceae, Bryophyta). Запропонований
новий двоступеневий макротаксономічний метод (метод макроеволюційної систематики) розрахунку статистичної підтримки як лінійного порядку, так і напрямку
еволюції певної філогенетичної лінії. Метод включає
кластеризацию таксонів у наборах шляхом мінімізації
повторності (надмірності) з використанням кладограм
та мінімальної парсимонії, з наступною побудовою часто
розгалуженої лінійної моделі через максимізацію інформації про поступову (градуалістичну) еволюцію шляхом
упорядкування видів через додавання інформаційних бітів для просунутих ознак і віднімання їх для еволюційних
реверсій. Кладистичний аналіз розглядається як аналог
криптографічної операції злому коду, при цьому кодовий
ключ потім використовується для побудови наступної
теоретичної моделі. Дуже висока байесівська підтримка
обчислена для еволюційних ліній при морфологічному
аналізі, що добре корелює з високою підтримкою попередніх молекулярних досліджень. Каулограма дозволила
здійснити передбачення (прогнози), які були неможливими за допомогою кладограм. Обговорюється важливість використання інформації щодо як походження від
спільного предка шляхом дивергенції (кладогенез), так і
походження внаслідок «відбруньковування» нових таксонів та лінійних послідовних змін (анагенез).
Проведено сравнение эволюционных деревьев (каулограмм) и филогенетических кладограмм как для морфологических, так и молекулярных анализов некоторых видов мохообразных рода Didymodon (Pottiaceae, Bryophyta).
Предложен новый двухступенчатый макротаксономический метод (метод макроэволюционной систематики)
расчета статистической поддержки как линейного порядка, так и направления эволюции определенной филогенетической линии. Метод включает кластеризацию
таксонов в наборах путем минимизации повторности
(избыточности) с использованием кладограмм и минимальной парсимонии, с последующим построением
часто разветвленной линейной модели путем максимизации информации о постепенной (градуалистической)
эволюции посредством упорядочивания видов через
добавление информационных битов для продвинутых
признаков и вычитание их для эволюционных реверсий.
Кладистический анализ рассматривается как аналог
криптографической операции взлома кода, при этом кодовый ключ впоследствии используется для построения
следующей теоретической модели. Очень высокая байесовская поддержка вычислена для эволюционных линий
при морфологическом анализе, что хорошо коррелирует с высокой поддержкой предыдущих молекулярных
исследований. Каулограмма позволила осуществить
прогнозы, которые были невозможными при помощи
кладограмм. Обсуждается важность использования информации относительно как происхождения от общего
предка путем дивергенции (кладогенез), так и происхождения вследствие «отпочковывания» новых таксонов
и линейных последовательных изменений (анагенез).
|
| issn |
0372-4123 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/178454 |
| citation_txt |
Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information theory / R.H. Zander // Український ботанічний журнал. — 2016. — Т. 73, № 4. — С. 319-332. — Бібліогр.: 41 назв. — англ. |
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| fulltext |
319ISSN 0372-4123. Укр. ботан. журн., 2016, 73(4)
УКРАЇНСЬКИЙ
БОТАНІЧНИЙ
ЖУРНАЛ Загальні проблеми, огляди та дискусії
doi: 10.15407/ukrbotj73.04.319
RICHARD H. ZANDER
Missouri Botanical Garden
P.O. Box 299
St. Louis, Missouri 63166-0299, USA
richard.zander@mobot.org
MACROSYSTEMATICS OF DIDYMODON SENSU LATO (POTTIACEAE, BRYOPHYTA) USING AN
ANALYTIC KEY AND INFORMATION THEORY
Zander R.H. Macrosystematics of Didymodon sensu lato (Pottiaceae, Bryophyta) using an analytic key and information
theory. Ukr. Bot. J., 2016, 73(4): 319–332.
Abstract. Evolutionary trees (caulograms) and phylogenetic cladograms for both morphological and molecular analyses
of certain species in the moss genus Didymodon (Pottiaceae, Bryophyta) were compared. A new two-step macrosystematic
(macroevolutionary systematics) method of calculating statistical support for both linear order and lineage direction
of evolution is introduced. This involves clustering of taxa in sets by minimization of redundancy using cladograms
and minimum parsimony, then building an often-branched linear model by maximization of information on gradual
evolution by ordering species through adding informational bits for advanced traits and subtracting them for reversals.
Cladistic analysis is considered to be similar to cryptographic code-breaking, with that code key then used for model-
building following theory. Very high Bayesian support was computed for lineages in the morphological analyses, which
stand up well to high support for past molecular studies. The caulogram allowed for predictions not possible with
cladograms. The importance of using information on both shared and serial descent is discussed.
Key words: analytic key, cladogram, classification, evolution, information theory, macrosystematics, paraphyly,
phylogenetics, Didymodon, Pottiaceae
Introduction
The cladistic classification practice requiring direct
matching of clades and taxa has been criticized in the
past by a series of publications by myself (e.g., Zander,
2004, 2007, 2008a,b, 2010a,b, 2013, 2014a,b,c,d),
and others (e.g., Brummitt, 1997, 2002, 2003, 2006,
2010; Farjon, 2007; Hörandl, 2006, 2010; Hörandl,
Emadzade, 2012; Hörandl, Stuessy, 2010; Mayr, Bock,
2002; Nordal, Stedje, 2005; Rieppel, 2010; Robinson,
1986; Sosef, 1997; Stuessy, Hörandl, 2014; Stuessy,
König, 2008). Although the critiques address many
problems, I suggest that, fundamentally, cladistic
analysis is problematic because it is only the first and
incomplete part of a full analysis of the information
available on evolution, in the context of evolutionary
theory. It is an «insufficient statistic» because all
information relevant to evolutionary relationships is not
addressed.
Basically cladistic analysis focuses entirely on
data relevant to shared descent, that is, advanced
homologous traits shared by taxa. Traits not shared
© R.H. ZANDER, 2016
or which are isolated on a cladogram, are termed
autapomorphies and are largely ignored. These
autapomorphies, however, are very informative of serial
descent. This paper demonstrates how information on
both serial and shared descent may be used to complete
an evolutionary tree of stem taxa (a caulogram, or
stemma) showing both serial descent in lineages of one
taxon being progenitor of the next, and shared descent
in two or more lineages branching from a jointly shared
progenitor species. This paper is an attempt to provide
examples of a new method of systematic analysis of
actual taxa to supersede papers of criticism that only
point out problems with phylogenetics.
Using both shared and serial descent as analytic
criteria. There are two steps in macrosystematics
(evolutionary systematics focused on relationships of
stem taxa) that involve use of information about both
shared and serial ancestry to develop an evolutionary
tree that is useful in classification. (1) Shared descent
is addressed by clustering taxa by similarity, best served
by phylogenetic methods of establishing multiply-
embedded sets of taxa with closest shared ancestors. The
idea is to minimize redundancy of advanced traits such
320 ISSN 0372-4123. Ukr. Bot. J., 2016, 73(4)
that taxa related by shared descent have a maximum
number of advanced traits that are alike, this being a
signal of evolutionary relationship, a specialty of cladistic
methodology. Redundancy in information theory is
«wasted information» in a message, and as used here
is similar to mutual information in information theory,
or phylogenetic profiling, see discussions in Wikipedia.
Minimization of redundancy is a condensation of
repetitive evolutionary messages that helps maximize
entropy. Informational redundancy is reduced by
explaining duplicate traits as having been created only
once through shared ancestry, i.e., they are homologous,
which makes them essentially the same information.
(2) Once sets of taxa that minimize redundancy of traits
are established, the difference between taxa in the sets
is used to determine direction and order of evolution.
This is done by assigning one informational bit to each
new trait with a penalty of one bit for each reversal
back to the primitive traits of an outgroup, and order
is established by maximizing numbers of information
bits for each lineage. Parallelisms, which, like, reversals
are redundant information, are minimized by cladistic
clustering by shared traits.
Basically cladistics establishes major groupings and
general contiguity of taxa by implied shared ancestry
of two or more taxa, while an evolutionary analysis
determines linear order of taxa from information
implying descent of one taxon from another. This
analysis using information theory has a parallel in
cryptanalysis. Suppose we have a cryptogram message
«eftdfoq xjui npejgjdbujpo,» and we decrypt just the
pattern of letter substitutions. Suppose it is a = b, b = c,
d = e, etc. That pattern has much information in it
about the message, and is similar to the information-
rich patterns generated by cladistics. Cladistics uses
the pattern impressed by the analytic method as a
basis for classification. But the message still needs to
be read. By assigning the code identities to the letters
in the cryptogram, the order of presentation becomes
important and the message becomes «descent with
modification». The language of the evolutionary
message is called «theory» and the arrangement
of plaintext letters is similar to the modeling of an
evolutionary tree based on both shared and serial traits.
The point of a macrosystematic analysis is to model
evolution of a group so that it fits into everything else we
know about evolution, and is not a «discovery process»
like determining code letter identities.
Species definitions and dissilient genera. A species
may ultimately be based on any of a number of criteria
depending on the author's choice of a species concept
for the group studied. In this paper, a practical criterion
is used: a species is a group of individuals possessing
a minimum of two otherwise unlinked traits that may
be considered linked by some evolutionary process,
known or unknown. It helps, of course, for the group
of individuals to have some «evolutionary trajectory»
or specialized habitat, but two traits are minimal and
sufficient. A genus is here defined as the «dissilient genus»
of Zander (2013: 92), being the result of a speciational
burst. Groups of species, at least in the groups I have
studied (Pottiaceae, Bryophyta), often may be seen as
some central, generalist, sexually reproducing species of
wide distribution and many biotypes surrounded by two
or more advanced, stenomorphic descendant species
with unique traits, sometimes asexual and found in
specialized or recent environments. These descendant
species may have descendants of their own to form linear
series, usually short, of two or three species in length
(for examples see Zander 2008a, 2009, 2013, 2014c).
Each evolutionarily radiative group of species is here
considered a genus, which is an empirical definition
that may be applied to families (i.e., a radiative group
of genera).
Cladogram versus caulogram. A cladogram is a
dichotomously branching tree with the tips of the
branches ending in the taxa studied. It may be entirely
replaced by a nested set of parentheses, annotated with
branch lengths and other information (e.g. the Newick
format). It represents only shared descent (as implied
by a series of gradually less inclusive traits) and treats
any indication of serial descent as unwanted paraphyly.
A caulogram is an often-branching tree with taxa
comprising the stem and branches, and with many taxa
lined up in linear series. The branches of a caulogram
show shared traits and evolutionary radiation, the
lineages of stem taxa show order and direction of
evolution. A caulogram maximizes paraphyly, which is
taken to signal a progenitor-descendant relationship.
Simplistically, a cladogram minimizes the differences
between taxa, a caulogram interprets the differences
left. Caulograms as diagrams of direct descent of extant
and inferred extinct taxa are fully explained by Zander
(2008a, 2010a, 2013).
Details of problems with cladistics-only analysis.
Firstly, there is a difference between cladistics and
phylogenetics. The former simply desires a branching tree
that groups taxa in the simplest manner by minimizing
required shared character state transformations.
A cladogram maximizes synapomorphies (shared
321ISSN 0372-4123. Укр. ботан. журн., 2016, 73(4)
advanced traits). The resultant tree has a goodly
amount of evolutionary information on shared descent,
but evolution, particularly evolutionary theory, is not
particularly important to cladists who apparently
feel that a tree with the least number of trait changes
is a practical basis for classification. Phylogenetics,
however, adds evolutionary significance to elements of
the cladogram, where branch length (in terms of trait
changes) implies evolutionary distance, and each node
in the dichotomous tree represents a shared ancestor
giving rise to (and ending in) two branches. The
resulting interpreted cladogram is termed a phylogram,
and is often presented as an evolutionary tree although
seldom called by that name.
Clarity in understanding the limitations of cladistics
is important, and is hard-won. «Tree thinking» can be
overwhelming in its complex methodological detail,
nearly full acceptance by the systematic community
(either enthusiastic or cynical), and the availability
of copious funding by granting agencies. There are,
however, certain major crippling aspects that are largely
ignored or even accepted as positive features because of
simplistic solutions provided in the methodology.
1. Phylogenetic trees are not evolutionary trees nor can
they truly model monophyly because shared descent
alone does not track serial aspects of evolution.
2. Phylogenetic analysis generates «sister groups» for
each split in the tree, but for, say, two taxa as sister
to each other, phylogenetics cannot tell if one taxon
is the progenitor of the other, or not. This is because
the phylogenetic data set includes only information
about shared descent. Even when data are available
on progenitor-descendant relationships, they are
generally ignored.
3. Continuity in a phylogenetic tree is through nodes,
which are often interpreted as shared ancestors, and
taxa are then related by degree of their shared descent.
Nodes, however, are neither named nor characterized
as natural entities, and recency of shared descent is
problematic. What they really represent are splits in
the raw minimum spanning tree or Markov chain that
is used in the computerized software to gather the taxa
involved into hierarchical sets that increasingly share
advanced traits. A phylogenetic tree or cladogram
can be completely represented by groups of taxa in
nested sets of parentheses to show the inclusiveness of
sets, similar to the well-known phylogenetic Newick
format. There is no evolutionary tree, there are no
ancestral nodes, and the «tree» simply represents an
easy way to visualize the nested sets of parentheses;
e.g., ((A, B)(C,D)) may be represented by a bone-
shaped diagram (>—<) with A and B at one end and
C and D at the other.
4. Important evolutionary information is lost with
cladistics, and the more taxa are involved, the more
information is lost. Consider A > B > C, where species
A speciates B and B speciates C (the angle bracket
shows the direction of evolution). The cladogram
for this is A(B, C) given that B and C share at least
one trait advanced over those of A (unless there is a
reversal). In this case and more generally, information
is lost when data on serial descent are ignored.
5. Because the method of phylogenetics uses only data
on shared descent, the differences between taxa are
only indirectly addressed as which taxa are lower in
a cladogram or toward the outside of a set of taxa in
nested parentheses. Thus, when a taxon is embedded
in a cladogram of a taxon of a different name, it is
either lumped with that taxon under one name, or the
taxon in which it is embedded is split into many taxa
to avoid direct embedding. The taxon with another
taxon of the same rank or higher embedded in it is
called a «paraphyletic» taxon. The method of strict
phylogenetic monophyly has been invented to justify
such lumping and/or splitting. This is the result of
a classification method invented to shore up the
blind spot of reliance only on shared descent, and is
not a result of a well-supported evolutionary theory.
Cladistically embedded species and genera have had
the same criteria in describing species and genera as
have paraphyletic species and genera, and there is no
natural reason to distinguish them.
6. Multifurcations are considered failures of resolution
in cladistics, yet are expected and informative
in evolutionary systematics. Multifurcations
of otherwise serial lineages may be reflected in
macroevolutionary classification as named genera.
Cryptanalysis parallel. Cryptanalysis is translation
or interpretation of hidden meanings in secret codes
(Good, 1979; McGrayne, 2011: 134, 168, 205). In
breaking codes, minimizing redundancy means to
discover which letters in the coded message always
mean «a», which mean «b», and so on. Minimizing
redundancy in systematics means creating a cladogram
or an equivalent diagram as a guide to sharing of
homologous traits through joint descent. Traits that
last over two or more speciation events are valuable for
tracking the flow of evolution.
322 ISSN 0372-4123. Ukr. Bot. J., 2016, 73(4)
The correct mapping of the cladistically derived
code key to patterns developed through interpretation
by theory «saves» (in terms of philosophy of science)
both cladistics and evolutionary theory by melding
them as two steps in the macrosystematic method. That
mapping will be done in this paper using an «analytic
key» as described below.
In sum, cladistics is a kind of discovery process that
«cracks the code» by creating a minimally redundant
arrangement of taxa, a cladogram, which condenses
otherwise redundant information by sharing traits
among taxa. Evolutionary systematics accepts
that decoding of arranged closely related taxa with
informative non-redundant traits left over and «reads the
message» through the language of evolutionary theory.
The dichotomous cladogram of the mechanical code
redundancy analysis is transformed into a branching
linear arrangement of taxa, a caulogram, that reflects
both shared and serial descent.
Problems with molecular analysis. Species have their
phenome of expressed traits often sculpted by stabilizing
and purifying selection (see review by Popadin et al.,
2007) over time such that the species’ basic identity
remains intact and singular. Gradual change and
biotype development over time is understood through
well-supported theory. The «bell-shaped curve» of
morphological variation is cut off at the tail ends by
selection against overly burdensome mutations, a kind
of phyletic constraint. On the other hand, the molecular
traits used for tracking evolutionary changes in taxa in
molecular cladistic analysis are apparently or are hoped
to be under little selection, and mutations may remain
in the genome of molecular races indefinitely or until
that molecular race is overwritten through accumulated
mutations or otherwise rendered extinct.
This leads to molecular paraphyly such that one
species may appear to be in two or more different places
on a cladogram at once. This is common in molecular
analysis and is usually dealt with by strict phylogenetic
monophyly by calling molecular races «cryptic species»
and naming them. Paraphyly is information that the
paraphyletic species gave rise to the embedded species,
a progenitor-descendant relationship. The problem is
that molecular races can go extinct, and the place on
a molecular cladogram of one instance of a species
does not rule out other places on the cladogram that
a molecular race of that species may have occupied,
except for being extinct or otherwise unsampled. The
BPP supporting a molecular clade can be considered
valid if one judges the taxa to be very recent and extinct
paraphyly is doubtful because there has been little
time for speciation between instances of molecular
races. Given the caulogram below, one might expect
one to three speciation events during the lifetime of a
species, which one might estimate at an average of five
million years (as a rule of thumb). See also discussion
of paleontological time scales of Zherikhin (1998):
«If about 50% of living insect species exist since the
Pliocene, it is improbable that none of them gave rise
to any different species during the last 5 million years.»
Suppose from many taxa, cladistics groups taxa D,
A, and T as having many redundant traits. There may
be two molecular races of one species A, or two species
of genus A, so there are two terminal taxa «A», that is,
D, T, A, and another A. Problematically, if the code key
is «D, A, T, A,» perhaps in the form ((D, A)(T, A)), to
avoid paraphyly (and theory) the paraphyletic taxon
«A» may be split into two (two species if molecular races
or two genera if species) by cladists to give «DZTA,»
or ((D, A)(T, Z)), which is not interpretable in the
language of scientific theory. (One can usually find some
minor biotype traits that distinguish two populations of
different molecular races of one taxon, but, because the
morphological traits cannot stand alone, they are not
real support.) The correct interpretation may be A > T >
D, where additional information not in the phylogenetic
data set reveals that ancestral taxon A (progenitors are
boldfaced) gave rise to T, and T to D. Ancestral taxon
A may include two molecular races, or include two
species that are somewhat distant on a cladogram but
nevertheless are clear in that genus as representing a
stem taxon.
Like cladistic introduction of cryptic or nearly cryptic
species, ignoring the possibility of extinct paraphyly
introduces a lack of resolution in molecular cladograms.
This is not such a problem in morphological cladograms
because of stabilizing selection. The degree of poor
resolution may be gauged by the amount and degree of
molecular paraphyly known for the group. If a known
paraphyletic molecular taxon spans three nodes on a
cladogram, then all except the most recent species must
be suspected of having up to the same level of paraphyly
in the past. This is because of similar sensitivity of their
genomes to mutation of the particular DNA sequence
used in the analysis.
Two features of molecular analysis may be relied
on. (1) Paraphyly or short-range molecular polyphyly
implies that the embedded taxa are linear descendants
of the paraphyletic taxon. (2) Long-range polyphyly,
such as species of one genus split between two
323ISSN 0372-4123. Укр. ботан. журн., 2016, 73(4)
families, suggests a true polyphyly such that contrary
morphology-based taxonomy needs to be re-evaluated.
Didymodon s. l. as exemplar. An intensive
macrosystematic analysis of the moss genus Didymodon
Hedw. was made in three previous studies by Zander
(1998, 2013, 2014a,b,c). These studies evaluated the
24 North American species, and divided them (Zander,
2013) into six genera, based on estimated centers
of adaptive radiation («dissilient genera»). This was
done in the following manner: A cladogram of these
taxa (Zander, 1998) was modified into a caulogram
of their serial and shared evolutionary relationships
under the simple rubric that if a cladogram node can
easily be taxonomically named as the same as one of
the two sister groups, this is more parsimonious than
positing an unknown unnamed shared ancestor. On
naming a node, the cladogram was collapsed into a
serial relationship of one of the sister groups ancestral
to the other. Two nodes were left unnamed as unknown
shared ancestral taxa, with the proviso that this practice
retrodicts the past existence of such unknown taxa and
predicts the possibility of discovering a taxon with that
general circumscription. Later, another study (Zander,
2014a,b,c) evaluated the statistical support for the
caulogram lineages.
Although the macrosystematic method involves
first doing a cladogram or equivalent, the practice of
doing no more than simply naming nodes as one of the
terminal taxa on a cladogram is not advisable as much
information on serial descent is never used in cladistics
analysis.
Justification of bit-based Bayesian measures of
support. No definite assignment of support for lineage
estimations in terms of Bayesian credible intervals were
made in the Zander (2013) study as the relationships
seemed overwhelmingly clear, but this was remedied
by Zander (2014a,b,c). In the 2014 papers, exact
probabilities were assigned to advanced traits using
the deciban (dB) unit. Decibans are logarithmic units
(exponents at base 2) equivalent to certain Bayesian
posterior probabilities (BPP), see Table 1, and fully
explained in the 2014 papers. Because decibans are
logarithmic, they can be added, and the sum of decibans
can be translated to a final posterior probability without
using Bayes’ formula.
In the case of 2014a,b,c study, the deciban value of
support for each advanced trait in a species was assigned
intuitively based on long experience with the genus and
with the rarity of traits. One deciban has been described
as the minimum detectable information beyond 50:50
support for two hypotheses. It was considered a «hint,»
equivalent to 0.56 BPP. Decibans were then assigned in
the 2014 paper as numbers of decibans for each trait,
because evolutionarily important traits are commonly
more than just hints. Adding these decibans may reach
a sum (interpreted by Table 1) suggesting a very high
posterior probability of the direction and order of
evolution of some particular series of taxa
The study of Zander (2014a,b,c) gauged support for
each branch of the Didymodon caulogram. This involved
the estimation of how uncommon an advanced trait
was. The more rare, the greater support for the direction
of evolution away from a generalized ancestor. The
generalized ancestor was determined by comparison
with some outgroup taxon, as in cladistics. Some
categories of critical traits informative of direction of
evolution are:
Primitive: (1) A species generalist or centralist in
morphology that might easily generate specialized
descendants. (2) A widely distributed species that is
found in many habitats and may be relatively old. (3)
A species of multiple subspecies or varieties. (4) A
major morphological differentiation that signals a new
relationship with the environment that opens evolution
of radiative lineages.
Advanced: (1) A habitat specialist. (2) A species with
asexual reproduction common and sexual reproductive
organs rare or absent. (3) A species of local distribution,
often of recent or specialized habitats. (4) A species
with a burdensome physiological or morphological
adaptation not conducive to further speciation.
The above criteria certainly call for judgment
guided by established theory. Additional discussion of
identification of progenitor-descendant species pairs
has been provided by Crawford (2010). In the Zander
(2014) papers, each trait in each species matching
a category above was assigned credible intervals
approximating the following schema:
1. «Five Sigma» (0.998 or better) super-certainty (i.e.,
«quite certain,» «damn sure»). Statistical certainty is
a real feature of some analyses.
2. Almost certain. Say, only once wrong out of a hundred
times would the hypothesis be wrong. Expected level
of correctness in critical research. Assigned credible
interval is 0.99.
3. Acceptable as a theory, being the lower limit of
reliable information. Expected to be correct 19 out
of 20 times, good for non-critical, easily reversible
decisions. Credible interval is 0.95.
324 ISSN 0372-4123. Ukr. Bot. J., 2016, 73(4)
4. Substantial support alone is not decisive for action,
but can be a working hypothesis. It can be narrowed
down to half-way between certain (1.00) and totally
equivocal (0.50), or 0.75. Using 0.75 as prior and 0.75
as probability yields 0.90, then using that as prior and
0.75 again as probability yields 0.96 as posterior. Thus
empirical use of Bayes Formula with the answer to
the first instance being the prior for the second and so
on indicates that perhaps three occurrences of «some
support» with no contrary evidence is sufficient for
use as a theory. Credible interval is then 0.75.
5. A «hint» of support is barely acceptable as a
hypothesis, and is certainly not actionable alone,
nor are even several hints impressive. Using 0.60
probability as representative of a hint, being just
beyond totally equivocal, requires 0.60 to be used as
a prior seven times in successive empirical analyses
with Bayes’ Formula, with no contrary information,
to reach 0.96. The credible interval for very minor
support is 0.60.
6. Totally equivocal support probability (assuming only
two reasonable alternatives, yes or no, support or
refutation) is 0.50.
7 to 10. Support against a hypothesis, is the reverse of
the above, that is, 0.40, 0.25, 0.05, 0.01 in support
«for» the hypothesis (leaving the remainder «for» any
opposing hypothesis of two hypotheses).
Comparing this analysis of intuitive estimation to
the additive use of decibans as in Table 1, justifies to a
large extent the more mechanical assignments of these
logarithmic units. That is, the range of credibility seems
about the same.
Informational bits. The entirely intuitive (Zander,
2013) or multiple deciban judgmental assignment
(Zander, 2014a,b,c) methods are, of course, not
replicable by anyone but another researcher familiar
with the taxa. Also, decibans are too fine a measure of
credibility. In addition, a less arbitrary assignment of
credibility is desired. The present paper introduces a
more objective method, meaning one more easily used
to attempt replication of the study. This includes an
evaluation of support by accumulation of advanced
traits indicating direction of evolution away from a
generalized ancestral taxon. In this case, the order
of any two taxa in a series is simply the number of
advanced traits of one taxon more that of the second,
given polarization of trait changes with the presumed
progenitor of the lineage as functional outgroup of
primitive traits. Each advanced trait is assigned one
informational bit (exponent of base 10). Because bits
are logarithms, they may be added together. Reversals
are assigned negative bits. Recursively comparing
contiguous pairs of taxa along a series of taxa will order
than in gradual advancement of traits, given comparison
with the primitive traits of an outgroup (or functional
outgroup such as the central progenitor).
Table 1. Equivalency of bits and decibans (dB) with Bayesian
posterior probability (BPP)
Bits dB BPP
0 0 0.500
0.33 1 0.557
0.67 2 0.613
1 3 0.666 or nearly 1 S.D. (0.683)
1.33 4 0.715
1.67 5 0.759
2 6 0.799
2.33 7 0.833
2.67 8 0.863
3 9 0.888
3.33 10 0.909
3.67 11 0.926
4 12 0.940 or nearly 2 S.D. (0.955)
4.33 13 0.952
4.67 14 0.961
5 15 0.969
5.33 16 0.975
5.67 17 0.980
6 18 0.984
6.33 19 0.987
6.67 20 0.990
7 21 0.992
8 24 0.996 or 0.99+
9 27 0.998 3 S.D. (0.997)
10 30 0.999
20 60 0.999999 (odds of 1 million to one)
Note. The decimal fractions of bits are equivalent to adding
one or two dBs to each bit, where dBs, if one wishes to use them
in addition to bits, are equivalent to poor data that cannot be
ignored. Standard deviations are indicated, and serve to show
how much variation is eliminated by the analysis.
325ISSN 0372-4123. Укр. ботан. журн., 2016, 73(4)
Summing the bits provides a measure of support
of one particular order in evolution, with Bayesian
posterior probabilities obtained from a table (Table 1).
The assigned probabilities of a particular order generally
match the intuitive evaluation by an expert. Each bit is
nearly exactly equal to 3 dB. Thus, 1 bit is equivalent
to 0.67 probability, about half way between a hint and
substantial support — given that two advanced traits are
required to distinguish a species in this study, one can
expect each species to contribute at least 2 bits, or 0.80
BPP to analysis of the evolutionary order. This may not
seem great, but many species are distinguished by four
traits (0.94 BPP). Adding bit support for the order of
all species in the lineage is a good measure of direction
of evolution, given theoretical gradual accumulation
of traits. A detailed discussion of this simple use of
information theory in systematics is given by Zander
(2014c). This is a very specialized use, and is not the
same as analysis of entropic aspects of evolution (e.g.,
Brooks, Wiley, 1988).
We can now see if the intuitive assignments of
support from advanced traits for the position in the
Didymodon s. l. caulogram published by Zander (2014c:
9ff., 14) were in the right ball park.
Materials and Methods
Analytic key. An «analytic key» was developed to
determine order and direction of evolution of the serial
lineages. Bits were assigned to descendant species’ traits
that were advanced compared to those of the generalist
ancestral taxa of each of the segregate genera.
The bits assigned to progenitor species (of Zander,
2014c: 14) are those advanced traits distinguishing
the genus from the immediate ancestral taxon. These
traits mostly were given in a serial and multichotomous
«natural key» by Zander (2013: 82). This natural key was
combined with the format of the «tables of monophyly»
in Zander (2014c: 9ff) to devise an analytic key. This
is given below, and, I hope, is an intuitively easily
understandable analysis of serial and shared descent,
and support for those evolutionary relationships
among the segregate genera of Didymodon s. l. The
reader should note that the analytic key may be
multichotomous or, at times, «monochotomous» with
just one indented description of advanced traits of
the single descendant. The positions of genera on the
morphological cladogram were checked in the analytic
key for minimum redundancy of traits and minimum
reversals.
Order and direction of evolution. Order and direction
of evolution are only evaluated once the species involved
are minimally redundant in terms of traits. That is,
grouped such that homologous traits are maximally
shared. Once species and their traits are most similar,
their differences can be used to further analyze evolution.
Order of any two species in a lineage is evaluated by
awarding position of greatest advancement in the
lineage to that species with the greater bit count relative
to the next lower species. Reversals require subtraction
of one bit per reversal, which aids in modeling gradual
evolution and fine-tuning the minimal redundancy.
Direction of evolution for a lineage is simply summing
all the bits for each species in the lineage after best
ordering. It is intuitively acceptable that two or more
species in a group or lineage reify that group or lineage
over having just one species. A randomized group
species (i.e., that are not first rendered minimally
redundant with maximum parsimony) may have a large
bit count, but a preliminary clustering study is critical
to a successful model of evolution because an attempt
at linear ordering would then reduce information from
random orderings because of many reversals.
Data for analytic key. Data sets of unique or
uncommon traits may be used to create an analytic
key (Zander, 2013: 82, 2014c: 4ff), or, as in the present
paper, parallelized descriptions of taxa from modern
works (mainly FNA, 2007) are evaluated for taxa
that appear to be the same as another taxon but with
advanced traits. From these descriptions, a central
progenitor of widespread distribution was selected. The
progenitor generally has common and generalist traits,
being fully sexual, and capable of generating both sexual
and asexually reproducing descendant species.
The reason descriptions rather than data sets
are used to better advantage in macrosystematics is
because descriptions (rather than telegraphic data
sets, e.g., characters labeled 1 or 0) differentiate better
between similar traits, which is critical when order of
linear descent is evaluated. Such traits are usually not
included in cladistic data sets, where shared descent
through shared homologous traits is the analytic focus,
and unique or uncommon traits are autapomorphies
or otherwise «phylogenetically uninformative.» Two
or more descendants are postulated from one ancestral
taxon when traits of the putative descendants are rather
different and arranging them linearly would add positive
bits for advanced traits and negative bits from reversals
summing to zero or nearly so. That is, when information
326 ISSN 0372-4123. Ukr. Bot. J., 2016, 73(4)
on order and direction of evolution is lacking, under
constraint of minimal redundancy.
A special case of branching is when an unknown
shared ancestor is suggested when two descendants
sharing advanced traits are different from each other
and are also equally different from the only extant
possible ancestral taxon; so an intermediate taxon with
those shared advanced traits that lower the difference
between the ancestor and descendants (given gradual
evolution as a model) is then a valuable hypothesis, see
the genus Fuscobryum in the caulogram (Fig. 1).
Morphological cladogram. The morphological
cladogram of Didymodon s. l. (Zander, 2013: 80) was
recreated using the data set of Zander (1998) and the
same reported software settings. Also a non-parametric
bootstrap analysis was done using 2000 replicates and
«faststep» settings. The names of segregate genera
of Didymodon were used as in the 2013 publication.
The serial relationships of the genera were based on
contiguity of nodes on that morphological cladogram,
which minimized redundancy of traits following theory
that most species evolve through gradual accumulation
of advanced traits.
Molecular cladogram. A molecular cladogram of
Didymodon s. l. species from Werner et al. (2005) was
duplicated as reduced to taxa in the morphological
cladogram. Bayesian posterior probabilities obtained
by the 2005 authors were appended for values greater
than 0.50. This cladogram was compared to the
morphological cladogram, and interpreted in terms of
serial evolution.
Results
Macroevolutionary analytic key. Descriptive info rma-
tion was used to develop an analytic key listing the
genera and species in evolutionary order. Key entries
are preceded with the progenitor identifier (a number),
a right angle bracket indicating evolutionary direction,
and a unique identifier for the descendant species (which
itself may be a progenitor of its own descendants). By
convention progenitors in evolutionary formulae are
given in boldface, e.g., A > B > C. Equal indentation
indicates taxa that are all derived from one progenitor,
and extra indentation indicates a descendant taxon of
the one above and less indented in the key. The features
are those different from the progenitor and from the
preceding species, therefor presumed advanced. Each
trait advanced over those of the earlier species in the
lineage was scored as one positive informational bit.
In the present optimized order of the analytic key,
there are no reversals, therefore no negative bits to
detract from support measures. To see the effect of
assigning negative bits, simply reverse the order of two
paragraphs in optimal arrangement of the key, and
compute the differences.
The bits associated with each advanced trait (1 bit
per trait) were summed for each species, listed after
the taxon name, and interpreted as Bayesian posterior
probabilities. After each genus the bits are summed for
the support for that genus. Note that some indentations
in the key are monochotomous (species 1aa, 3ca, 5aa,
5ca, 5caa, 6a), meaning only one descendant from a
previous species in the lineage. The caulogram (Fig. 1)
summarizes visually the information in the analytic key.
Analytic Key to Didymodon and related genera
1. Vinealobryum progenitor: Differing from outgroup
Barbula unguiculata by axillary hairs with brown basal
cells, leaves lanceolate, adaxial costal epidermal cells
quadrate, with a distinct costal groove or window
adaxially near the leaf apex, and gemmae multicellular,
obovate, borne on the stem .....Vinealobryum vineale
(Brid.) R.H. Zander 5 bits, 0.97 BPP
1 > 1a. Immediate descendant: Leaves shorter, leaf
base squared; more arid habitats; gemmae present;
peristome short and twisted or rudimentary ..............
Vinealobryum brachyphyllum (Sull.) R.H. Zander 4 bits,
0.94 BPP
1a > 1aa. Secondary descendant: Leaves with
multilayered photosynthetic cells on ventral
surface of mid-costa; leaf margins loosely revolute;
sporophytes absent; highly restricted distribution in
arid region ............................ Vinealobryum nevadense
(R.H. Zander in R. H. Zander et al., L.R. Stark &
Marrs-Smith) R.H. Zander 4 bits, 0.94 BPP
1 > 1b. Immediate descendant: Plants large;
leaves bistratose medially; leaves distally very
broad ............................. Vinealobryum nicholsonii
(Culm) R.H. Zander 3 bits, 0. 89 BPP
1 > 1c. Immediate descendant: Very restricted northern
distribution; leaf apex sinuose or toothed, bi-tri-stratose,
deciduous as a propagule; sporophytes unknown;
growing on wood or bark .......... Vinealobryum murrayae
(Otnyukova) R.H. Zander 4 bits, 0.94 BPP
Total support for Vinealobryum lineage is 21 bits, or
0.99+ BPP.
1 > 2. Trichostomopsis progenitor: Plants green (not
reddish); costa much flattened, ventral stereid band
absent; distal laminal cells with simple papillae ..........
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............................ Trichostomopsis australasiae (Hook.
& Grev.) Rob. 4 bits, 0.94 BPP
2 > 2a. Immediate descendant: Leaves very long
acuminate-lanceolate, basal laminal cells hyaline and
with slits; human distributed
Trichostomopsis umbrosa (Müll.Hal.) Rob. 3 bits, 0.89
BPP
2 > 2b. Immediate descendant: Leaves short-ovate,
margins loosely revolute; unicellular propagula in leaf
axils; peristome absent to short, straight; restricted
distribution ................. Trichostomopsis revoluta (Card.)
R.H. Zander 5 bits, 0.97 BPP
Total support for Trichostomopsis lineage is 12 bits, or
0.99+ BPP.
1 > 3. Didymodon s.str. progenitor: Leaves green
or occasionally reddish in nature, more broadly
channeled; costa flat or convex dorsally, not convex;
distal laminal cells only weakly and simply papillose
or smooth ..................... Didymodon acutus (Brid.) K.
Saito 4 bits, 0.94 BPP
3 > 3a. Immediate descendant: Leaves distally
thickened, long-elliptical; gemmae abundant;
peristome short and straight; hygric habitats .................
................. Didymodon rigidulus Hedw. 5 bits, 0.97 BPP
3 > 3b. Immediate descendant: Leaf apex acuminate,
cylindric, fragile in pieces as a propagule, laminal cells
large; strong northern distribution, hygric habitat,
growing on wood ............ Didymodon johansenii
(Williams) Crum 5 bits, 0.97 BPP
3 > 3c. Immediate descendant: Leaves long-
acuminate, basal cells quadrate ............ Didymodon
icmadophilus (Müll.Hal.) K. Saito 2 bits, 0.80 BPP
3c > 3ca. Secondary descendant: Leaf apex turbinate,
deciduous as a propagule; sporophytes absent;
restricted distribution ...... Didymodon anserinocapitatus
(X.J. Li) R.H. Zander 3 bits, 0.89 BPP
Total support for Didymodon lineage is 19 bits, or 0.99+
BPP.
1 > 4. Exobryum progenitor: Leaves narrowly
channeled, carinate; distal laminal papillae simple;
moist areas ........... Exobryum sp., unknown ancestral
taxon 3 bits, 0.89 BPP
4 > 4a. Immediate descendant: Mountainous areas;
deep red plant coloration; leaves strongly recurved;
stem central strand often absent, peristome short and
straight .......... Exobryum asperifolius 5 bits, 0.97 BPP
Total support for Exobryum lineage is 8 bits, or 0.99+
BPP.
4 > 5. Geheebia progenitor: Leaves weakly recurved;
adaxial cells of costa elongate .......... Geheebia fallax
(Hedw.) R.H. Zander 2 bits, 0.80 BPP
5 > 5a. Immediate descendant: Leaves ovate-
lanceolate, usually without papillae, costa ending before
apex, with small basal auricles or long decurrencies;
peristome short and straight, occasionally rudimentary
or absent; calciphile, wet habitats ...... Geheebia tophacea
(Brid.) R.H. Zander 6 bits, 0.98 BPP
5a > 5aa. Secondary descendant: Leaves long-
acuminate lanceolate, with large auricles; sporophytes
absent; restricted northern distribution .......... Geheebia
leskeoides (K. Saito) R.H. Zander 4 bits, 0.94 BPP
5 > 5b. Immediate descendant: Leaved catenulate
when dry, small spherical gemmae in leaf axils;
sporophytes absent ........... Geheebia maschalogena
(Ren. & Card.) R.H. Zander 3 bits, 0.89 BPP
5 > 5c. Immediate descendant: Plants yellow
to red; leaves usually without papillae, very wet
habitats ...................... Geheebia ferruginea (Besch.)
R.H. Zander 3 bits, 0.89 BPP
5c > 5ca. Secondary descendant: Leaves
much enlarged; sporophytes absent; very restricted
distribution .................... Geheebia maxima (Syed &
Crundw.) R.H. Zander 3 bits, 0.89 BPP
5ca > 5caa. Tertiary descendant: Leaves and
plants much enlarged, leaves long-acuminate; laminal
cells with large, bulging trigones; sporophyte absent ..
.................................... Geheebia gigantea (Funck)
Boulay 4 bits, 0.94 BPP
Total support for Geheebia lineage is 25 bits, or 0.99+
BPP.
5 > 6. Fuscobryum progenitor: Leaves dark brown
to black in nature, distal marginal cells crenulate; costa
thin; hyperoceanic northern distribution .... Fuscobryum
nigrescens (Mitt.) R.H. Zander 4 bits, 0.94 BPP
6 > 6a. Immediate descendant: Leaves ovate,
apex broadly rounded ...... Fuscobryum spp. , unknown
ancestral taxon 2 bits, 0.80 BPP
6a > 6aa. Secondary descendant: Clusters of
unicellular gemmae in leaf axils; sporophytes absent;
very restricted distribution ............... Fuscobryum
perobtusum (Broth.) R.H. Zander 3 bits, 0.89 BPP
6a > 6ab. Secondary descendant: Leaves
dimorphic, the smaller strongly concave in series in
some parts of the plant; sporophytes absent ...........
..................... Fuscobryum subandreaoides (Kindb.)
R.H. Zander 3 bits, 0.89 BPP
Total support for Fuscobryum lineage is 12 bits, or 0.99+
BPP.
328 ISSN 0372-4123. Ukr. Bot. J., 2016, 73(4)
The study (Zander, 2014) that used intuitive
assignments of decibans for each trait for each species of
Didymodon created «tables of monophyly» that included
BPPs for linear order for each pair of contiguous
species, as well and various combinations of species.
The optimal order of species is the same as in the present
study, and a comparison of those judgmentally assigned
deciban-derived BPPs with the one bit per trait method
used here is given in the table below (Table 2). The scale
of credibility is about the same. The credible intervals
awarded in the Zander (2014) study are clearly more
variable than those of the present study. The variation
is due in part to the fact that one or two decibans are
less than one bit in terms of BPP, while four or more
are greater. Whether the additional judgment involved
in the 2014 study was better than the present method of
equal weighting may be evaluated by additional study
with more species. I think the method used here is a
stabilizing influence, as the BPP of a bit seems in the
center of BPPs correlated with the number of decibans
commonly awarded in the 2014 study.
Morphological analysis. The morphological
cladogram (Fig. 2) shows the shared relationships of the
species optimized under maximum parsimony. Thick
lines connect central progenitors. Nonparametric
bootstrap proportions greater than 50 are added at base
of splits together with translation to equivalent Bayesian
posterior probabilities (Zander, 2004) in parentheses. If
taxonomically lumped by strict phylogenetic monophyly,
genera of taxa marked «paraphyly» would lose their
names and attendant macroevolutionary information,
with the species lumped into Geheebia (upper part of
cladogram) or Didymodon (lower part of cladogram
except Exobryum) — the correct cladistic name would
be Didymodon because it is, following the Code, an
earlier name for the paraphyletic Vinealobryum.
Compare low bootstrap support here from only shared
descent with that from serial descent (Fig. 1). Clearly,
shared descent in Didymodon s. l. morphological studies
is far more informative than shared descent.
Molecular analysis. The molecular cladogram of
Werner et al. (2005) after reduction to only species also in
the present morphological study (Fig. 3) demonstrated
rather high support for splits based on shared descent.
The segregate genera largely hang together as given in
the caulogram (Fig. 1). Vinealobryum may appear to be
widely split as paraphyletic, but given that it is basal and
ultimate progenitor to the remainder of the taxa, all the
nodes between V. murrayae and V. vineale may be taken
to be taxonomically V. vineale, or extinct or unsampled
monophyletic biotypes of V. vineale. This may also
explain the paraphyly of Geheebia, with G. fallax
somewhat isolated but easily a descendant of V. vineale
as well as the remainder of Geheebia species. Exobryum
Fig. 1. Caulogram of
Didymodon s. l. Segregate
genera are identified. Each
species is identified with
the Bayesian posterior
probability of the species
evolutionary order. At base
of each species balloon is
number of bits supporting
order of an advanced
species over the next
lower in the cladogram
based on primitive traits
of the central progenitor
as functional outgroup;
adding these gives bit
support for a lineage (not
shown)
329ISSN 0372-4123. Укр. ботан. журн., 2016, 73(4)
Species
BPP
2014
BPP
present
Didymodon acutus 0.99+ 0.94
D. anserinocapitatus 0.83 0.89
D. icmadophilus 0.93 0.80
D. johansenii 0.97 0.97
D. rigidulus 0.93 0.97
Exobryum asperifolius ? 0.97
Exobryum unknown progenitor ? 0.89
Fuscobryum nigrescens 0.94 0.94
F. perobtusum 0.98 0.89
Fuscobryum shared ancestor 0.72 0.80
F. subandreaeoides 0.95 0.89
Geheebia fallax 0.99+ 0.80
G. ferruginea 0.93 0.89
G. gigantea 0.72 0.94
G. leskeoides 0.99+ 0.94
G. maschalogena 0.93 0.89
G. maxima 0.76 0.89
G. tophacea 0.99+ 0.89
Trichostomopsis australasiae 0.94 0.94
T. revoluta 0.61 0.97
T. umbrosa 0.95 0.89
Vinealobryum brachyphyllum 0.72 0.94
V. murrayae 0.98 0.94
V. nevadensis 0.99+ 0.94
V. nicholsonii 0.96 0.89
V. vineale 0.99+ 0.97
Fig. 2. Morphological cladogram of Didymodon s. l. based on
the study of Zander (1998). Bootstrap support for proportions
greater than 50, and equivalent Bayesian posterior probabilities
(in parentheses), were awarded to four sister groups
Table 2. Comparison of Bayesian posterior probabilities
awarded to evolutionary order of linear pairs of species on
the caulogram, comparing judgmentally variable numbers of
decibans used in the Zander (2014) study and the present use
of one bit per trait
Fig. 3. Cladogram of Didymodon from Werner et al. (2005),
reduced to only taxa that are present in the analytic key, with
Bayesian posterior probabilities appended
pa
ra
ph
yl
y
pa
ra
ph
yl
y
pa
ra
ph
yl
y
is isolated rather far from its contiguous neighbors in
the caulogram, Vinealobryum and Geheebia, and is in
fact embedded in Didymodon. However, the position
of Fuscobryum nearby, associated with the rather
different species D. rigidulus, indicates that much more
sampling of surviving molecular races is needed. One
should remember that only heterophyly (paraphyly or
patristically close phylogenetic polyphyly) and great
distance on the cladogram contribute positive or negative
information about serial descent (Zander, 2013).
Some species in Fig. 3 are represented by two
exemplars (specimens) each. Certainly Didymodon
acutus has two different molecular sequences, since
the two entries are paraphyletic. One should realize,
however, that specimens that are sister groups, such as
D. icmadophilus and Trichostomopsis australasiae do not
necessarily have the same molecular sequence. These are
potentially paraphyletic to some yet unanalyzed species,
and therefore would be evolutionarily informative.
330 ISSN 0372-4123. Ukr. Bot. J., 2016, 73(4)
Discussion
Cladograms use only data on advanced shared character
states (i.e., phylogenetically informative) plus an
optimization procedure that groups taxa with advanced
character state transformations on a dichotomous
tree. Caulograms use all data relevant to evolutionary
relationships, both of shared and serial descent. To
the extent possible, taxa are arranged in linear series,
with branches made when a generalist ancestral species
radiates two or more descendant taxa or lineages.
Unknown taxa are interpolated when a missing link
seems necessary to complete modeling the gradual
evolution of a chain, or when two species require a
shared ancestral taxon not now extant to explain their
evolutionary nearness but separate evolutionary directions.
The macrosystematic method takes two steps. First,
species are grouped to maximize shared advanced
traits, and minimize differences between taxa. Cladistic
analysis is a good way to do this. The ultimate minimal
redundancy is when individuals are found to have all
the same traits, and are therefore one taxon. Then, step
two: When differences between species are minimized,
the traits left over are those characteristic of the species,
and often revelatory of monophyly through details
of order and direction of evolution. Species need to
be ordered serially so that every species contributes
information. Conveniently, this reflects evolutionary
theory that species mostly evolve by accumulated
gradual transformations of character states. This is done
using an analytic key by arranging the order of species so
that they gradually add more traits as they evolve away
from some outgroup, which is either a nearby taxon,
or a generalized putative progenitor. This maximally
informative order of species is ensured by adding one
informational bit for each trait different from the last in
order and subtracting one bit for each reversal.
To further explain ordering of taxa in modeling serial
descent, if a progenitor has primitive traits 00000, the
next species in order would be 00001, then 00011, then
00111, then 01111, then 11111, where 1 is an advanced
trait. Each species contributes one bit, totalling 5 bits
for the lineage. If we made the arrangement with the last
species first, that is the outgroup 00000, then the last
species in order put first 11111, the other three species
would not contribute information as their traits would be
totally redundant with the species with 11111 advanced
traits. Requiring a penalty of 1 bit for each reversal then
would make the 00000 then 11111 first order, add to zero
bits when the remaining three species are appended.
This is 5 bits for the first order, but minus one for each
of the other species that contribute reversals. Doubtless
there are other ways of ordering species, such as adding
to any positive bit an additional one bit for each species’
distance from the progenitor, and not using negative bits
at all.
A minimum of two linked traits per species (two bits
equals 0.80 BPP) may not seem sufficient to confirm
the linear order of species, but radiation of additional
descendant species in a lineage or dissilient genus adds
to the credibility, given a theoretical assumption of
gradual accumulation of advanced traits.
This study demonstrated rather good support
for order of evolution between pairs of contiguous
species in a lineage (difference between numbers of
advanced traits), and excellent support (total summed
bits) for the direction of evolution for each lineage.
Morphological cladistic analysis helped establish
the linear and branching relationships of the main
progenitor taxa. The molecular cladogram was
interpreted as not an evolutionary tree because the basal
nodes could be assigned to one taxon (Vinealobryum
vineale) based on morphological information that
was not phylogenetically informative but was instead
macroevolutionarily informative.
Predictions are possible with macrosystematic
analysis. For instance, the unknown taxon posited
through inductive inference as ancestral to Exobryum
asperifolius may be found with further study. The same
obtains with the inductively inferred unknown shared
ancestral taxon for Fuscobryum subandreaeoides and
F. perobtusum. As in any evolution-based classification,
further discoveries should match the present groupings to a
great extent, each newly discovered species with expected
similar physiological features and evolutionary potentials.
One may also note that generative generalized
species generate other generative species. Although
it is possible that advanced, specialized descendant
species may prove to grade into generative new species
in other habitats, this has not been shown the case in the
present study. It is quite possible that there is a path of
maximum evolutionary potential running through every
large group that is comprised of generative species. The
elucidation of this path should be of great importance
in biodiversity study as elimination of generative species
reduces expected numbers of descendant species that
explore and exploit smaller niches. For instance, a
generalized species of limited distribution in a habitat
that is expected to expand and grow more arid over time
is a good candidate for long-term protection.
331ISSN 0372-4123. Укр. ботан. журн., 2016, 73(4)
This macrosystematic study supported the integrity of
the study (Zander, 2013) that splits off from the large genus
Didymodon five segregate genera based on dissilience
(centers of radiation) around progenitor species. The
caulogram model of evolution of Didymodon s. l. is
helped to some extent by minimalization of redundancy
with cladistics, and the analytic key can corroborate
such redundancy. The model also can explain most
of a molecular cladogram's apparent incongruity in
relationships of the same species.
Support values for the order of taxa and for direction
of evolution of the lineages in the caulogram were in
the range expected by expert intuition (my own, after
years of familiarity), and compared well with previous
intuitive study (Zander, 2014a,b,c). It is concluded that
a somewhat more mechanical therefore more easily
replicable analysis, as was done here with the analytic
key above, is a successful way to model evolutionary
transformations at both species and genus level, so to
inform a more information-rich classification than with
cladistic methods alone.
Acknowledgements
I thank Sergei Mosyakin, editor-in-chief of the Ukrainian
Botanical Journal, for his kind invitation to submit
a paper. Two anonymous reviewers provided helpful
suggestions. The Missouri Botanical Garden continues to
provide a congenial working environment of superb support.
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S. l. Mosyakin
Зандер Р.Г. Макросистематика Didymodon sensu lato
(Pottiaceae, Bryophyta) з використанням аналітичного
ключа та теорії інформації. – Укр. ботан. журн. – 2016. –
73(4): 319–332.
Міссурійський ботанічний сад,
Сент-Луїс, Міссурі, 63166-029, США
Проведене порівняння еволюційних дерев (каулограм)
та філогенетичних кладограм як для морфологічних,
так і молекулярних аналізів деяких видів мохоподібних
роду Didymodon (Pottiaceae, Bryophyta). Запропонований
новий двоступеневий макротаксономічний метод (ме-
тод макроеволюційної систематики) розрахунку статис-
тичної підтримки як лінійного порядку, так і напрямку
еволюції певної філогенетичної лінії. Метод включає
кластеризацию таксонів у наборах шляхом мінімізації
повторності (надмірності) з використанням кладограм
та мінімальної парсимонії, з наступною побудовою часто
розгалуженої лінійної моделі через максимізацію інфор-
мації про поступову (градуалістичну) еволюцію шляхом
упорядкування видів через додавання інформаційних бі-
тів для просунутих ознак і віднімання їх для еволюційних
реверсій. Кладистичний аналіз розглядається як аналог
криптографічної операції злому коду, при цьому кодовий
ключ потім використовується для побудови наступної
теоретичної моделі. Дуже висока байесівська підтримка
обчислена для еволюційних ліній при морфологічному
аналізі, що добре корелює з високою підтримкою попе-
редніх молекулярних досліджень. Каулограма дозволила
здійснити передбачення (прогнози), які були неможли-
вими за допомогою кладограм. Обговорюється важли-
вість використання інформації щодо як походження від
спільного предка шляхом дивергенції (кладогенез), так і
походження внаслідок «відбруньковування» нових так-
сонів та лінійних послідовних змін (анагенез).
Ключові слова: аналітичний ключ, кладограма,
класифікація, еволюція, теорія інформації,
макросистематика, парафілія, філогенетика, Didymodon,
Pottiaceae
Зандер Р.Г. Макросистематика Didymodon sensu lato
(Pottiaceae, Bryophyta) с использованием аналитического
ключа и теории информации. – Укр. ботан. журн. –
2016. – 73(4): 319–332.
Миссурийский ботанический сад,
Сент-Луис, Миссури, 63166-029, США
Проведено сравнение эволюционных деревьев (кауло-
грамм) и филогенетических кладограмм как для морфо-
логических, так и молекулярных анализов некоторых ви-
дов мохообразных рода Didymodon (Pottiaceae, Bryophyta).
Предложен новый двухступенчатый макротаксономиче-
ский метод (метод макроэволюционной систематики)
расчета статистической поддержки как линейного по-
рядка, так и направления эволюции определенной фи-
логенетической линии. Метод включает кластеризацию
таксонов в наборах путем минимизации повторности
(избыточности) с использованием кладограмм и ми-
нимальной парсимонии, с последующим построением
часто разветвленной линейной модели путем максими-
зации информации о постепенной (градуалистической)
эволюции посредством упорядочивания видов через
добавление информационных битов для продвинутых
признаков и вычитание их для эволюционных реверсий.
Кладистический анализ рассматривается как аналог
криптографической операции взлома кода, при этом ко-
довый ключ впоследствии используется для построения
следующей теоретической модели. Очень высокая байе-
совская поддержка вычислена для эволюционных линий
при морфологическом анализе, что хорошо коррелиру-
ет с высокой поддержкой предыдущих молекулярных
исследований. Каулограмма позволила осуществить
прогнозы, которые были невозможными при помощи
кладограмм. Обсуждается важность использования ин-
формации относительно как происхождения от общего
предка путем дивергенции (кладогенез), так и проис-
хождения вследствие «отпочковывания» новых таксонов
и линейных последовательных изменений (анагенез).
Ключевые слова: аналитический ключ, кладограмма,
классификация, эволюция, теория информации,
макросистематика, парафилия, филогенетика,
Didymodon, Pottiaceae
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