A simple parsimony-based approach to assess ancestor-descendant relationships
One of the main goals of systematics is to reconstruct the tree of life. Half a century ago, the breakthrough of cladistics was a major step towards this objective because it allowed us to assess relatedness patterns among species, an abstract kind of relationship. Unfortunately, the philosophy of...
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Інститут ботаніки ім. М.Г. Холодного НАН України
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irk-123456789-1784942021-02-20T01:25:59Z A simple parsimony-based approach to assess ancestor-descendant relationships Aubert, D. Загальні проблеми, огляди, дискусії One of the main goals of systematics is to reconstruct the tree of life. Half a century ago, the breakthrough of cladistics was a major step towards this objective because it allowed us to assess relatedness patterns among species, an abstract kind of relationship. Unfortunately, the philosophy of cladism forbade to go further and to seek more realistic relationships, like the ancestor-descendant relationship, which is the expected fundamental kind of relationship of the tree of life according to Darwinian evolution. Here, I describe a simple parsimony-based procedure which can be used to transform a classical cladogram into a genuine phylogenetic tree, i.e. a caulogram. It consists in deleting as many unobserved and unnamed nodes as possible and replacing them with observed and named species. A new Bayesian non-stochastic weighting scheme is used to assess character reliability for both this procedure and classical cladogram construction. I illustrate the whole process by assessing the relationships between the species of the moss genus Didymodon sensu lato (Pottiaceae) and discuss the resulting caulogram by confronting it with the previous methodology from the evolutionary literature. I finally argue that strictly adhering to cladist epistemology is untenable and that we must seek new formal methods to find ancestral species as well as ancestral higher taxa. Однією з головних цілей систематики є реконструкція Дерева життя. Півстоліття тому проривом стала кладистика, яка виявилась важливим кроком на шляху до цієї мети, що дозволив нам визначити зв'язки спорідненості між видами, абстрактний вид спорідненості. На жаль, філософія кладизму не дозволила просунутися далі в пошуку більш реальних взаємозв'язків, таких як зв'язок предок-нащадок, який, відповідно до дарвінівської еволюційної концепції, ймовірно, є основним типом зв'язків на Дереві життя. У статті описана проста методика на основі парсимоніі, яка може бути використана для перетворення класичної кладограми у справжнє філогенетичне дерево, тобто в каулограму. Ця методика полягає у видаленні якомога більшого числа неспостережених і неіменованих вузлів та в їх заміні реально визначеними та іменованими видами. Як в цій методиці, так і при побудові класичної кладограми, для оцінки надійності ознаки використовується нова байєсівська нестохастична схема зважування. Для ілюстрації проводиться оцінка взаємозв'язків між видами мохів роду Didymodon sensu lato (Pottiaceae) з обговоренням отриманої каулограми шляхом її співставлення з попередньою методологією відповідно до еволюційних публікацій. На закінчення робиться висновок про недоцільність суворого додержання кладистичної епістемології та необхідність пошуку нових формальних методів для встановлення предкових видів, а також і предкових таксонів вищих рангів. Одной из главных целей систематики является реконструкция Древа жизни. Полвека тому назад прорывом стала кладистика, которая оказалась важным шагом на пути к этой цели, позволившим нам оценить относительные родственные связи между видами, абстрактный тип родства. К сожалению, философия кладизма не позволила продвинуться дальше в поиске более реальных родственных взаимосвязей, таких как связь предок-потомок, которая, согласно дарвинистской эволюционной концепции, является, очевидно, основополагающим типом связей на Древе жизни. В статье описана простая методика на основе парсимонии, которая может быть использована для преобразования классической кладограммы в настоящее филогенетическое дерево, то есть в каулограмму. Эта методика состоит в удалении как можно большего числа ненаблюдаемых и неименованных узлов и в замене их наблюдаемыми и именованными видами. Как в этой методике, так и при построении классической кладограммы, для оценки надежности признака используется новая байесовская нестохастическая схема взвешивания. В качестве иллюстрации проводится оценка взаимосвязей между видами мхов рода Didymodon sensu lato (Pottiaceae) с обсуждением итоговой каулограммы путем сопоставления ее с ранее применявшейся методологией по материалам эволюционных публикаций. В заключение делается вывод о несостоятельности строгого следования кладистической эпистемологии и необходимости поиска новых формальных методов для установления предковых видов, а также предковых таксонов более высоких рангов. 2017 Article A simple parsimony-based approach to assess ancestor-descendant relationships / D. Aubert // Український ботанічний журнал. — 2017. — Т. 74, № 2. — С. 103-121. — Бібліогр.: 52 назв. — англ. 0372-4123 DOI: https://doi.org/10.15407/ukrbotj74.02.103 http://dspace.nbuv.gov.ua/handle/123456789/178494 en Український ботанічний журнал Інститут ботаніки ім. М.Г. Холодного НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| topic |
Загальні проблеми, огляди, дискусії Загальні проблеми, огляди, дискусії |
| spellingShingle |
Загальні проблеми, огляди, дискусії Загальні проблеми, огляди, дискусії Aubert, D. A simple parsimony-based approach to assess ancestor-descendant relationships Український ботанічний журнал |
| description |
One of the main goals of systematics is to reconstruct the tree of life. Half a century ago, the breakthrough of cladistics
was a major step towards this objective because it allowed us to assess relatedness patterns among species, an abstract kind
of relationship. Unfortunately, the philosophy of cladism forbade to go further and to seek more realistic relationships, like
the ancestor-descendant relationship, which is the expected fundamental kind of relationship of the tree of life according
to Darwinian evolution. Here, I describe a simple parsimony-based procedure which can be used to transform a classical
cladogram into a genuine phylogenetic tree, i.e. a caulogram. It consists in deleting as many unobserved and unnamed nodes as
possible and replacing them with observed and named species. A new Bayesian non-stochastic weighting scheme is used to assess
character reliability for both this procedure and classical cladogram construction. I illustrate the whole process by assessing the
relationships between the species of the moss genus Didymodon sensu lato (Pottiaceae) and discuss the resulting caulogram by
confronting it with the previous methodology from the evolutionary literature. I finally argue that strictly adhering to cladist
epistemology is untenable and that we must seek new formal methods to find ancestral species as well as ancestral higher taxa. |
| format |
Article |
| author |
Aubert, D. |
| author_facet |
Aubert, D. |
| author_sort |
Aubert, D. |
| title |
A simple parsimony-based approach to assess ancestor-descendant relationships |
| title_short |
A simple parsimony-based approach to assess ancestor-descendant relationships |
| title_full |
A simple parsimony-based approach to assess ancestor-descendant relationships |
| title_fullStr |
A simple parsimony-based approach to assess ancestor-descendant relationships |
| title_full_unstemmed |
A simple parsimony-based approach to assess ancestor-descendant relationships |
| title_sort |
simple parsimony-based approach to assess ancestor-descendant relationships |
| publisher |
Інститут ботаніки ім. М.Г. Холодного НАН України |
| publishDate |
2017 |
| topic_facet |
Загальні проблеми, огляди, дискусії |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/178494 |
| citation_txt |
A simple parsimony-based approach to assess ancestor-descendant relationships / D. Aubert // Український ботанічний журнал. — 2017. — Т. 74, № 2. — С. 103-121. — Бібліогр.: 52 назв. — англ. |
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Український ботанічний журнал |
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2025-07-15T17:01:26Z |
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2025-07-15T17:01:26Z |
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| fulltext |
103Укр. бот. журн., 2017, 74(2)
Загальні проблеми, огляди та дискусії
General Issues, Reviews and Discussions
© D. AUBERT, 2017
Introduction
Background and Motivation
Since the sixties, cladistics has aimed to resolve the
relationships between species (Hennig, 1950, 1966).
These relationships are depicted by cladograms, i.e.
hierarchical treelike diagrams where clusters show which
two of any three species are more closely related to each
other than either is to the third one (Hennig, 1966;
Hull, 1979). This type of relationship is characterized as
“relatedness” and is supposed to represent the relative
recency of the “hypothetical last common ancestors” (or
more rigorously the order of emergence of evolutionary
novelties). It is, however, dubious that such a relationship
corresponds to a true natural process. Unless one
believes that a mother species always disappears when
it speciates (Lee, 1995), relatedness may ambiguously
refer either to a true sister-group relationship (SGR) or
to an ancestor-descendant relationship (ADR) (Aubert
2015). In the first case, the two species are descendants
of another unobserved third species (so, a true SGR is in
fact two hidden ADRs), while in the second case one of
them is a descendant of the other one. This second type
of relationship is nonetheless misleadingly represented
as a false SGR through the artificial introduction
of unobserved species on internal nodes (see Fig. 1)
if a cladogram is interpreted as a true phylogenetic
tree (here “true” means sensu Hennig, see below) or
caulogram (the word “caulogram” designates a tree that
emphasizes serial macroevolutionary transformations,
i.e. ADRs, see Zander, 2013). The internal nodes may
be avoided by representing a cladogram as a set of nested
parentheses, but the introduction of unobserved species
is still logically implied by the assumption that none of
the known species is actually an ancestor (Podani, 2013).
Cladograms are thus ambiguous, not faithful pictures of
evolutionary history.
doi: 10.15407/ukrbotj74.02.103
A simple parsimony-based approach to assess ancestor-descendant
relationships
Damien AUBERT
Académie de Clermont-Ferrand, Ministère de l’Éducation Nationale
3, avenue Vercingétorix 63033
Clermont-Ferrand Cedex 1, France
damien.aubert@ac-clermont.fr
Aubert D. A simple parsimony-based approach to assess ancestor-descendant relationships. Ukr. Bot. J., 2017, 74(2): 103–121.
Abstract. One of the main goals of systematics is to reconstruct the tree of life. Half a century ago, the breakthrough of cladistics
was a major step towards this objective because it allowed us to assess relatedness patterns among species, an abstract kind
of relationship. Unfortunately, the philosophy of cladism forbade to go further and to seek more realistic relationships, like
the ancestor-descendant relationship, which is the expected fundamental kind of relationship of the tree of life according
to Darwinian evolution. Here, I describe a simple parsimony-based procedure which can be used to transform a classical
cladogram into a genuine phylogenetic tree, i.e. a caulogram. It consists in deleting as many unobserved and unnamed nodes as
possible and replacing them with observed and named species. A new Bayesian non-stochastic weighting scheme is used to assess
character reliability for both this procedure and classical cladogram construction. I illustrate the whole process by assessing the
relationships between the species of the moss genus Didymodon sensu lato (Pottiaceae) and discuss the resulting caulogram by
confronting it with the previous methodology from the evolutionary literature. I finally argue that strictly adhering to cladist
epistemology is untenable and that we must seek new formal methods to find ancestral species as well as ancestral higher taxa.
Keywords: ancestor, Bayesian analysis, Bremer support, evolutionary systematics, parsimony, weighting
https://doi.org/10.15407/ukrbotj74.02.103
mailto:damien.aubert%40ac-clermont.fr?subject=
104 Ukr. Bot. J., 2017, 74(2)
process from a parental population of continental
Leptoscyphus porphyrius (Vanderpoorten and Long,
2006). Moreover, we must point out that this mode
of speciation is not restricted to plants. For instance,
a recent palaeontological study of the pterocephaliid
trilobites have shown through the implementation of a
probabilistic model that the main mode of speciation (if
not the sole one) is indeed budding cladogenesis, neither
bifurcating cladogenesis nor pure anagenesis (Bapst and
Hopkins, 2017). This result is largely consistent with
the literature in other fields like the foraminifera (Aze
et al., 2011). Last but not least, the cladistic axiom that
two of any three species must be closer is false since a
single mother species may give birth to more than two
daughters. Unfortunately, cladistic algorithms force the
data to fit a dichotomous tree, which is like trying to
hammer a square peg into the round hole of an ideal
(Zander, 2013). Such a propensity to use axiomatized
synchronous (ahistorical) structures as a fundamental
framework is referred to as structuralism (Zander, 2011;
Aubert, 2015).
All of the above reasons motivate the research for new
methods able to transform cladograms, i.e. Hennig's
“phylogenetic diagrams”, into true phylogenetic trees (or
caulograms) reflecting ADRs, i.e. the real genealogical
relationships between species (Prothero and Lazarus,
1980; Paul, 1992; Alroy, 1995; Crawford, 2010; Aze
et al., 2011; Tsai and Fordyce, 2015). Contrary to what
is sometimes assumed (Gee, 2000), the probability of
encountering an ancestral species in the fossil record
or among extant species is far from being negligible
(Rieseberg and Brouillet, 1994; Crisp and Chandler,
1996; Foote, 1996; Funk and Omland, 2003; Aldous
Furthermore, even in the case of a true SGR,
unnamed nodes would imply that relatedness is a
fundamental phylogenetic relationship. This poses
epistemological problems because sisters have always
been independent entities; they may for example be
born or speciated at very different times. The fact that
one sister would have never existed does not necessarily
imply the non-existence of the other one, while the
non-existence of a mother species necessarily implies
the non-existence of all its daughter species. In fact, a
true SGR (contrary to a false SGR) only means that
both species share a ADR with the same third species.
ADRs are thus far more fundamental evolutionary
(i.e. truly “phylogenetic”) relationships than SGRs.
From a more biologically grounded perspective,
ADRs generally represent peripatric (or “budding”)
speciations. This means that a mother species tends to
disperse and invade geographically isolated locations.
From there, local populations evolve new traits through
genetic bottlenecks and directional selection. Thus,
they transform into daughter species while the principal
population remains morphologically unchanged.
This is because the latter benefits from the stabilizing
effects of a larger genetic pool and purifying selection.
One may call this phenomenon “phylogenetic niche
conservatism” (Pyron et al., 2015). It is very unlikely
that the mother species transforms entirely into two
daughter species through the gradual divergence of two
subspecies at the same time (Levin, 1993). Of course,
budding speciation is especially widespread in islands,
but is not limited to such. As an example, the endemic
liverwort Leptoscyphus azoricus of Macaronesia
has been shown to have originated through this
Fig. 1. The artefactual entities introduced by
cladistic analysis. The evolutionary model
(dichotomous splitting) used by cladistic
analysis forces us to hypothesize many
unobserved entities in order to optimize the
number of transformation events.
105Укр. бот. журн., 2017, 74(2)
disprove that the putative common ancestor and the
terminal species are distinct entities, then they are
(or at least one cannot decide). Here, the burden of
proof has just been unjustifiably reversed. Indeed, the
burden of proof lies upon a person making scientifically
unfalsifiable claims. The very existence of an unobserved
common ancestor is an unfalsifiable claim because
even if we would have sampled a species matching its
reconstructed phenotype, one could argue that since
the species has been observed then it is not the common
ancestor we were looking at. In this framework,
common ancestors are not only unobserved, but also
unobservable entities. Yet, the principle of Occam's
razor tells us that we should minimize the number of
such ad hoc entities. On the contrary, the claim that
an observed species is the same entity as the predicted
common ancestor is a falsifiable claim. It would be
theoretically sufficient to find a single autapomorphy in
order to disprove it. The existence and the observation
of common ancestors are both expected and likely from
the theory of evolution. Science must therefore always
favour the simplest explanation: if an observed species
matches the phenotype of a predicted species, then both
species are the same entity. In other words, this is the
null hypothesis we must test against alternatives. The
very concept of “metaspecies” is therefore unneeded;
all so-called unresolved species must be considered
paraspecies.
Now, not all morphological characters are equally
reliable. Characters in a phylogenetic data set that
transform as shared traits (synapomorphies) only once
in a cladogram are reputed quite stable, and so are
reliable indicators of relationships. But characters that
transform many times are rather labile and create many
homoplastic misleading relationships. What if then,
an observed species nearly matches the phenotype of
a predicted species? Are they the same? Here we must
leave naïve Popperian hypothetico-deductivism, i.e.
unweighted parsimony optimization. It is rather obvious
that if the observed autapomorphies are several stable
characters, then the null hypothesis must be rejected
in favour of the alternative one. But if the observed
autapomorphy is only a single very labile character, then
the null hypothesis cannot be convincingly rejected.
The objective evaluation of the null hypothesis therefore
demands a probabilistic quantification of characters’
reliability. As we will see, weighted parsimony can
be interpreted as a form of non-parametric (i.e. not
“model-based”) Bayesian approach.
and Popovic, 2005; Aldous et al., 2011; Ross, 2014). A
phylogenetic analysis that only results in the publication
of a new cladogram is therefore merely a preliminary
work, which demands a post-cladistic treatment in
order to eliminate the ad hoc virtual ancestors and to
clarify the nature of the relationships. The feasibility of
this objective will be demonstrated by the study of the
North American species of the moss genus Didymodon
sensu lato (Pottiaceae), which has been recently divided
into six segregate genera: Vinealobryum, Didymodon
sensu stricto, Trichostomopsis, Geheebia, Exobryum and
Fuscobryum (Zander, 2016).
This work builds on the studies of Zander (2013, 2014a,
b, c, 2016) which introduce means of diagramming
serial evolution of taxa as caulograms, and suggest
support values in terms of decibans. Although Zander
mentioned that variation in occurrence of shared traits
affects credibility, he did not detaile xplicit means of
formally measuring and incorporating variation. This
paper introduces the consistency index and successive
weighting in cladistic analysis as a means of evaluating
variability of traits, with those less variable being more
important. This study is restricted to morphological
traits.
Rationale for the Post-Cladistic Analysis
In the cladist framework synapomorphies are considered
the only evidence of common ancestry. Morphological
character mapping over the resulting cladogram allows
us to infer the phenotype of this common ancestor.
If a branch connecting such an internal node to a
terminal species bears no character transformation, and
hence has a length of zero, then the phenotype of the
common ancestor is exactly the same as the terminal
species. However, cladists generally do not regard this
as evidence that the terminal species and the common
ancestor are the same entity, and prefer to systematically
hypothesize that they are different (note that cladism is
not the same thing as cladistics; see Aubert, 2015). They
argue that only shared character transformations can
provide evidence of relationship, and that the lack of a
transformation is only a lack of evidence, not evidence
per se. At best, a species characterized by the absence of
autapomorphy is termed “metaphyletic” (Donoghue,
1985; de Queiroz and Donoghue, 1988). This means
that we do not know whether this species is holophyletic
or paraphyletic (respectively, all descendants included
or not; see Ashlock, 1971).
I would think however that this interpretation is
unscientific. It is argued that since one cannot positively
106 Ukr. Bot. J., 2017, 74(2)
Once z has been computed, we can easily
estimate q as the weighted sum of both cases, i.e.
q = z + (1 –z)/3 = 2z/3 + 1/3. Therefore the posterior
odds (ratio of probabilities), knowing F, are:
q/(1 – q) = (2z/3 + 1/3)/(2/3 – 2z/3) = (2z + 1)/(2 – 2z)
Since without knowing F, the relationship R can
only be true by chance, the prior odds were (1/3)/
(2/3) = 1/2 (i.e., 0.5:1). Hence, the evidence provided
by F can be evaluated as the ratio of odds, also known
as Bayes factor:
k = [(2z + 1)/(2 – 2z)]/(1/2) = (2z + 1)/(1 – z)
This Bayes factor is independent of the prior
probability of R, which means that q/(q – 1) = kp/
(1 – p) is always true even if p ≠ 1/3 because of some other
sources of knowledge (stratigraphy or biogeography for
example). Thus, k measures the amount of knowledge
that F adds to our previous knowledge. This evidence
provided by the consistency index is more appropriately
expressed in the logarithmic unit of bans or decibans
(dB) because this allows us to interpret evidence in an
intuitive manner and makes it possible to literally add
units of knowledge. Thus, if we get several independent
sources of evidence from different characters, we can
mentally add up units of evidence instead of doing
complicated computations. A deciban (or decihartley)
is a tenth of a ban, a unit used by Bayesian statisticians
to represent Bayes factors in hypothesis testing. The
deciban scale is here calculated with the formula:
w = 10 × log
10
k (the letter w stands for “weight of
evidence”). This scale goes from 0 to infinity, but
13 dB can be interpreted as a strong evidence (> 95%
chances to be true, see Table I). Let us mention that the
smallest intuitively detectable evidence is roughly 1 dB,
which approximately corresponds to the difference we
perceive between the odds 5:4 (around 55-56%) and the
totally equivocal 1:1 (exactly 50%) (Good, 1979, 1985).
The computation of z is a little more complicated for
multistate characters, but the problem can be reduced
to a weighted average of the reliability of each possible
pair of states. There are �
� � �
2
� such pairs. For example,
if we consider a three-state character, A and B may be
in state 0 and C and D in state 1 or 2, or A and B may
be in state 1 and C and D in state 2, or inversely. We
can therefore evaluate independently the three possible
pairs 0/1, 0/2 and 1/2. If s = 3, then one of the states
is represented by two separated monophyletic groups
instead of just one, so two of the three pairs have a z
equal to 0.5 whereas the third one have a z equal to 1,
hence a global value z = 2/3.
A Bayesian Interpretation of the Consistency Index
We consider a morphological binary character x
in a matrix of OTUs. We note s the actual number
of changes of this character occurring in the most
parsimonious dichotomous unrooted cladogram (or
at least the chosen one) and m the minimum number
of changes that it may require in any such cladogram
(i.e. one, in this case). The consistency index is thus
equal to c = m/s. Let us now consider four OTUs A,
B C, and D. We know the fact F = “A and B share the
same state of x, while C and D share another state of this
character”. The reliability of x can be regarded as the
increase in probability that the relationship R = “{A,
B} and {C, D} are two mutually exclusive monophyletic
groups” is true. We are only interested in monophyly,
not holophyly, because rooting a topology is a different
task from reconstructing it (“monophyletic” means
that the most recent common ancestor is a member
of the group, this can be tested without rooting; and
then different rootings of the tree can make this group
“holophyletic” or “paraphyletic”, i.e. containing all its
descendants or not, respectively).
The prior probability of R, i.e. not knowing F, is
theoretically p = 1/3 because there are exactly three
unrooted possible four-taxon trees and only one is
compatible with R. The posterior probability q, knowing
F, would be one if and only if both character states are
homologous for A and B, and for C and D respectively.
If either of the two states is homoplastic in these pairs
(for example it evolved independently in A and B) then
R would be true only by chance, so its probability would
be only 1/3. We must therefore evaluate the probability
z that the first case occurs.
The character x clusters the whole tree into
s + 1 monophyletic parts. There may be u monophyletic
groups with state 1 and v monophyletic groups with
state 0, so that u + v = s + 1. The probability z that A
has been randomly picked in the same monophyletic as
B and C in the same as D is therefore z = 1/(uv). Any u
and v are theoretically possible, but since convergences
and reversions are here considered equally probable,
we should generally get u ≈ v. More accurately, this is
like tossing a coin s – 1 times because of the constraint
that u ≥ 1 and v ≥ 1. Consequently, we have a simple
binomial distribution:
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� � 1
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107Укр. бот. журн., 2017, 74(2)
cannot go below m/g. This has led some systematists to
the conclusion that c must be rescaled between 0 and
1 (Farris, 1989). However, this would mean that the
amount of evolution needed for the transformation of a
cladistically uninformative character is exactly zero, i.e.
is equivalent to no transformation at all. Thus, I do not
recommend the use of the rescaled consistency index
(RCI) to calculate the evidence provided by a character
to assess the nature of a transformation of shared traits.
If s = 4, then either two states are represented by
two separated monophyletic groups, or one state is
represented by three such groups. In the first case, two
pairs have z = 0.5 and the third one z = 0.25, while in
the second case two pairs have z = 1/3 and the third one
z = 1. Provided that these supplementary monophyletic
partitions are distributed randomly among the different
states, the first case has a probability of 2/3 while
the second one has a probability of 1/3. Hence, the
global value of z = 2/3 × ( 1/2 + 1/2 + 1/4 )/3 + 1/3 ×
( 1/3 + 1/3 + 1)/3 = 25/54. Here, we observe that
(m, s) = (2, 4) implies z ≈ 0.463, which is slightly inferior
to the case (m, s) = (1, 2) where z = 0.5, although
c = 0.5 in both cases. Thus, the consistency index does
not accurately take into account the number of distinct
states. In the general case we have:
Table I. The deciban scale of the Bayesian weight of evidence.
Only the most salient values are psychologically interpreted.
Probability Odds Evidence (dB) Interpretation
1.000 + ∞ + ∞ Certain
0.990 100:1 20 Decisive (Nearly three-sigma)
0.952 20:1 13 Strong (Nearly two-sigma)
0.929 13:1 11.14
0.889 8:1 9.03
0.863 6.3:1 8 Substantial
0.800 4:1 6.02
0.760 3.2:1 5 Believable
0.750 3:1 4.77
0.666 2:1 3 Small hint
0.636 1.75:1 2.43
0.571 1.33:1 1.25
0.557 1.26:1 1 Barely worth mentioning
0.529 1.12:1 0.50
0.5 1:1 0 Totally equivocal
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If s – m = 1 then z = c = m/s, but the value of z is
generally strictly lower than that of c. The values of z are
presented in the Table II, as well as the corresponding
values of w. Note that the consistency index cannot
reach 0 even if the character is cladistically completely
uninformative. We could note g the maximum number
of transformations that the character x may undergo
among all possible cladograms in order to explain
its state distribution, i.e. the minimum between the
number of 0 and the number of 1. By definition, c
Values of z :
m
s 1 2 3 4 5
1 1
2 0.5 1
3 0.292 0.667 1
4 0.188 0.463 0.75 1
5 0.129 0.333 0.573 0.8 1
6 0.094 0.248 0.445 0.647 0.833
7 0.071 0.189 0.352 0.528 0.699
8 0.055 0.148 0.282 0.435 0.59
9 0.044 0.119 0.23 0.362 0.502
10 0.036 0.097 0.189 0.304 0.429
11 0.03 0.08 0.158 0.258 0.369
12 0.025 0.068 0.133 0.22 0.319
Table II. The consistency index understood as Bayesian evidence. The letters m and s indicate respectively the minimal and the
actual number of transformations of a character on a particular cladogram. The consistency index is defined as c = m/s. The
values of z are probabilities while the values of w are expressed in decibans (see text for formulas).
Values of w :
m
s 1 2 3 4 5
1 13.00
2 6.02 13,00
3 3.49 8.45 13.00
4 2.28 5.55 10.00 13.00
5 1.60 3.98 7.01 11.14 13.00
6 1.17 2.98 5.33 8.12 12.04
7 0.89 2.31 4.20 6.39 9.01
8 0.70 1.82 3.38 5.20 7.26
9 0.57 1.47 2.77 4.32 6.04
10 0.47 1.21 2.31 3.64 5.12
11 0.39 1.01 1.94 3.10 4.40
12 0.33 0.86 1.65 2.66 3.81
108 Ukr. Bot. J., 2017, 74(2)
Material and Methods
Data Source
As an example to demonstrate the feasibility of the
analysis, I have used the matrix of 20 characters of 23
OTUs from Zander (1998), including 22 species from
North America of the genus Didymodon sensu lato, plus
an outgroup species Barbula unguiculata. Two additional
species and 22 supplementary characters were included
after reviewing the most recent literature (Zander, 2013,
2014a, b, c, 2016), plus the Internet website <www.
efloras.org>. The data are entirely neontological, all
species being extant (see Table III and Annex).
Weighted Parsimony Cladistic Analysis
Character transformations were generally considered as
unordered and of equal weight, except for discretized
The Bayesian pieces of evidence provided by
putative characters’ transformations can be used as
weights in a weighted parsimony cladistic analysis
and as a branch length scale in a phylogrammatic
representation of amounts of evolution separating
species. Indeed, additivity is an expected property of
distances on a phylogenetic tree, and contrary to the
raw consistency index, Bayesian evidence measured in
decibans is additive. This makes sense intuitively: if a
stable character transformation is as probable as several
more common character transformations, then they
must be represented by the same length. Therefore,
labile character transformations should be represented
by shorter branches. The (patristic) distances on such
a phylogram would represent the probability that any
character transform. It is an intuitive measure of the
“amount of evolution” between any pair of species.
Table III. The matrix of characters of Didymodon s. l. The species Barbula unguiculata is the
outgroup. The 42 characters used are presented in the annex.
1 2 3 4
B. un 01000 00000 01100 00000 00010 01000 00000 02100 20
V. vi 01011 00000 01111 01010 00110 01000 00001 01100 20
V. br 01011 10020 20211 01100 00110 01000 00001 01100 00
V. ne 01013 00020 20211 01010 11122 01000 11001 1???? ??
V. nl 01010 10010 03111 01100 00120 11000 00011 02100 20
V. mu 01010 10000 00124 01100 00010 11000 10012 ????? ??
T. au 11013 20012 01111 12020 10111 00000 00011 01100 11
T. um 21013 20002 11012 12020 10011 00101 02?11 01100 11
T. re 10012 20022 00210 12020 10120 01100 00?01 010?2 00
D. ac 01011 20001 20111 11101 00110 11100 00210 02101 10
D. ri 01011 20001 00113 11101 00110 11000 00210 02101 10
D. jo 01010 10002 00114 10101 00?00 01?10 12112 00011 02
D. ic 01011 20001 10112 11101 00110 11000 10210 02101 10
D. an 01010 10002 00114 10011 00112 01000 12010 1???? ??
E. as 32210 22010 11211 01100 00110 02110 02102 00011 01
G. fa 02010 11010 01111 10100 00000 12010 00101 01010 20
G. to 01010 11011 11110 01100 00010 120?0 02101 01012 01
G. le 02011 31000 11112 00100 00000 02100 12102 1???? ??
G. ms 21011 31020 ?0111 11100 00010 12000 00101 1???? ??
G. fe 02010 12020 01111 11100 00000 12010 12101 01010 10
G. mx 02010 12020 02111 11100 00000 03110 12302 1???? ??
G. gi 03010 11010 03111 11100 00020 03110 12302 1???? ??
F. ni 31110 10022 00101 12100 00000 02101 01002 01100 10
F. pe 30012 20022 00100 12100 00100 01000 01002 1???? ??
F. su 31110 10122 00100 12100 00100 12000 01002 1???? ??
http://www.efloras.org
http://www.efloras.org
109Укр. бот. журн., 2017, 74(2)
the trees that are less than 12.99 dB away from the most
parsimonious one were sampled and a strict consensus
tree was built. Branches whose loss is inferior to this cost
were therefore not retrieved, which means that their
Bremer support is strictly inferior to 13 dB (i.e. < 95%).
On the other hand, branches that were retrieved have a
Bremer support superior or equal to 13 dB.
Post-Cladistic Analysis
Character changes can be mapped using either
ACCTRAN or DELTRAN algorithms, so that the
mean length of every branch is estimated. Branch
length is simply the sum of weights of all character
transformations (measured in dB as assigned by the
weighted parsimony cladistic analysis, PAUP* can do
it automatically, see above) along this branch. Nodes
that are joined by very short branches correspond to
clades supported by very labile characters. Intuitively,
the support of such branches is not very strong. In fact,
if the length is inferior to 13 dB, we should generally
conclude that the branch does not exist and the two
nodes represent the same entity. Such a deletion would
have consequences on neighbouring branches (see
Fig. 3). Any procedure of elimination of unnecessary
entities may be called superoptimization (Zander, 2013).
However, we cannot proceed directly to these deletions
directly on the most parsimonious cladogram, because
we would rely on the assumption that its topology is not
strongly distorted by cladistic overfitting (it could be
possible to do so only if each and every ancestral species
gave birth to only one or two derived species, which is a
very strong assumption I do not hold).
morphometric characters and for those containing
intermediary, variable or ambiguous states. These
were considered ordered characters and were rescaled
so that their portion of the transition over their full
range represents a single transformation (see Annex).
Heuristic search of the most parsimonious cladograms
were carried on with PAUP* version 4.0a150, with 100
replicates starting with random trees, holding 10 trees
at each step, swapping on all trees with TBR algorithm,
letting reconnection limit at 8 by default and saving
multiple trees. After the initial search non-homoplastic
characters were considered equal to 13 dB while others
were reweighted according the Bayesian interpretation
of the mean consistency index (see Table II) of all
retained trees. The weights were used in the next steps
to search again the most parsimonious trees and then
compute again new weights, and so on iteratively (Farris,
1969). Computed weights were used at a precision of 2
digits after the point. The branches were systematically
collapsed (creating polytomies) when the minimum
length was zero (parameter “amb-”).
Bremer Support
The most parsimonious tree is not always the true tree.
In fact, optimization of the data over a model can
result in overfitting. This is a serious bias (see Fig. 2
for a simple illustration of this notion). In classical
cladistic analysis, Bremer support of a clade in the most
parsimonious tree is the minimum number of extra
steps required to draw a near-most-parsimonious tree
that does not contain this clade (Bremer, 1988, 1994).
In order to evaluate the support of the putative clades,
Fig. 2. The concept of overfitting. With only two parameters, a linear function can only approximate the six depicted points.
With six parameters, a polynomial function can go exactly through each of the six points. The function is thus more precise, but
obviously less accurate. In our case, each unnecessary ancestor can be regarded as a supernumerary parameter.
110 Ukr. Bot. J., 2017, 74(2)
Fig. 3. The principle of superoptimization. The goal
of superoptimization is to remove unnecessary
entities by deleting insufficiently supported
terminal or internal branches. Like in classical
character mapping, several solutions may exist
(ACCTRAN or DELTRAN). The letters “A”, “B”
and “C” indicate species, the numbers indicate
characters being transformed, and the letter “R”
indicates a reversion.
Fig. 4. How to force PAUP* to draw
a caulogram. These are parts of
phylograms drawn by PAUP*. This
software is able to map characters’
transformations according to
several optimization algorithms
(ACCTRAN, DELTRAN or MINF)
but a particular branch cannot be
directly forced to have a length of
zero. However, if we add a new OTU
identical to the putative ancestor
(here «anc1» has exactly the same
character states as G. maxima) in
an unresolved trichotomy then
PAUP* is obliged to infer that the
last common ancestor of these
three OTUs had the same character
states as the majority of them (that
is, «anc1» and G. maxima), thus
drawing two branches with a length
of zero and increasing the length of
the remaining branches. The tests
must be conducted in the context of
the tree, not in isolation. Because
the result may change according to
this very context, huge polytomies
(like the one including G. fallax,
G. ferruginea, etc.) necessitate trying
many rearrangements of outgroups
(not just pairwise tests like those
of Table V) in order to find the best
superoptimization.
111Укр. бот. журн., 2017, 74(2)
parsimonious trees were searched again, and then new
weights were computed again. This second iteration
had also only one most parsimonious tree with a length
of 774.56 steps. The third iteration led to the tree and
the same weights (see Table IV).The tree is described in
Fig. 5A. I obtained 1474 trees with a score inferior to
787.55 steps. A strict consensus tree has been built from
them (see Fig. 5B). Clades that appear on the first tree
but not on the second have a Bremer support strictly
inferior to 13 dB (i.e. < 95%) and so are not retained.
If one compares the two trees obtained in Fig. 5, the
data could seem rather noisy. However, the evaluation
of 10 million random trees with PAUP* show that none
of them approaches the score of the most parsimonious
tree. The mean score was 1422.71 steps, with a
standard deviation of 46.34 steps and a skewness index
g1 = -0.5873 (or -0.4365 without weighting), which
is far more negative than the critical values needed
for such amounts of taxa and characters (Hillis and
Huelsenbeck, 1992). According to Table IV, the best
estimates of characters’ weights may be a little doubtful
for only five characters: 24, 26, 31, 32 and 36. However,
eliminating them completely does not substantially
alter the most parsimonious topology nor the consensus
tree obtained from all near-most-parsimonious trees
(data not shown).
The instability of the cladogram can thus be
attributed to the unstable phylogenetic positions of
For each putative ADR, the strict consensus
cladogram computed from all near-most-parsimonious
cladograms was modified by pruning it from the other
competing ADR hypotheses so as to compare its total
length if the two taxa retained are in a sister-group
relationship (with an unobserved common ancestor)
or in an ancestor-descendant relationship (without
any unobserved ad hoc entity). The ADR was forced in
PAUP* by copying several times the putative ancestral
species in a basal polytomy (see Fig. 4). If the total length
difference was inferior to 13 dB, then it was considered
that the null hypothesis (ADR) could not be rejected,
and so was accepted. Since there can exist only one
mother species (unless we assume that hybridization is
likely), in the case where several possible ancestors could
not be rejected, the less costly competing hypothesis
would be accepted, however only with a credibility
corresponding to the difference of the two costs (i.e.
unfortunately necessarily inferior to 13 dB).
Results
Cladistic Analysis
In the initial step of the analysis only one most
parsimonious tree was found, at a length of 155.67
steps. The consistency indices were computed for
each character and accordingly reweighted using the
Bayesian interpretation described above. The most
Table IV. The stable weights obtained after successive weighting. The best estimate of weight corresponds to the consistency index
of the only one most parsimonious tree found at the end of the iterative search. The minimum, mean and maximum weights
correspond to the minimum, mean and maximum consistency indices found among all trees that are less than 12.99 dB away
from the most parsimonious one (the mean weight is computed by rounding the mean value of s to the closest integer). Only
two iterations were necessary to obtain stable weights. The five highlighted characters are those whose best estimates differ from
their mean estimates.
Char.
Weight
Char.
Weight
Char.
Weight
best min. mean max. best min. mean max. best min. mean max.
1 7.01 7.01 7.01 7.01 15 3.64 3.10 3.64 4.32 29 3.49 2.28 3.49 6.02
2 7.01 7.01 7.01 10.00 16 1.17 0.89 1.17 2.28 30 6.02 6.02 6.02 6.02
3 8.45 8.45 8.45 8.45 17 2.98 2.31 2.98 3.98 31 1.60 0.89 1.17 2.28
4 13.00 13.00 13.00 13.00 18 3.49 2.28 3.49 3.49 32 3.98 2.31 2.98 3.98
5 4.20 3.38 4.20 5.33 19 8.45 5.55 8.45 8.45 33 10.00 10.00 10.00 10.00
6 3.38 2.77 3.38 4.20 20 13.00 6.02 13.00 13.00 34 6.02 2.28 6.02 6.02
7 5.55 5.55 5.55 8.45 21 13.00 13.00 13.00 13.00 35 2.98 1.82 2.98 5.55
8 13.00 13.00 13.00 13.00 22 13.00 13.00 13.00 13.00 36 1.17 0.89 0.89 1.17
9 0.86 0.72 0.86 1.01 23 1.17 1.17 1.17 1.60 37 3.98 3.98 3.98 5.55
10 2.31 1.82 2.31 2.31 24 1.21 1.21 1.47 1.82 38 3.49 3.49 3.49 6.02
11 2.31 1.82 2.31 2.98 25 3.98 3.98 3.98 3.98 39 6.02 6.02 6.02 13.00
12 2.77 2.31 2.77 2.77 26 2.28 0.89 1.60 2.28 40 5.55 3.98 5.55 5.55
13 3.98 3.98 3.98 5.55 27 10.00 10.00 10.00 10.00 41 1.82 1.47 1.82 1.82
14 13.00 8.45 13.00 13.00 28 1.60 0.89 1.60 1.60 42 5.55 3.98 5.55 5.55
112 Ukr. Bot. J., 2017, 74(2)
mother species relative to their daughter species which
may be wrongly grouped together because of convergent
evolution or reversions. In other words, these are hard
polytomies; they are not resolvable because of the
clear implication that a single ancestor gave birth to
several derived relatives. They are not soft polytomies
that could be solved by using more and more data. The
less resolved tree of Fig. 5B is therefore certainly more
accurate, i.e. closer to truth, than is the more precise
tree of Fig. 5A. One should not force the data into an
artificial dichotomous scheme (Hull, 1979). The data
are well structured, but not cladistically so.
Reconstruction of ADRs
As a first example, let us discuss the case of the
relationship between G. maxima and G. gigantea. The
total length of the strict consensus tree of all near-
most-parsimonious trees is 947.25 steps. If we suppose
that G. maxima is the ancestor of G. gigantea then we
get a length of 954.87 steps (see Fig. 4), whereas we
get a length of 958.24 steps if we force G. gigantea to be
the ancestor of G. maxima. In the first case, our ADR
hypothesis only costs 7.62 dB, while in the second
case it costs 10.99 dB. Neither hypothesis exceeds the
threshold, but the first one is less costly and is therefore
accepted while the second one is rejected. The fact that
the resulting phylogenetic tree seems less parsimonious
is an illusion caused by the lack of penalty accounting
for unobserved ancestors. We should actually subtract
13 dB and realize that we have just won 5.38 dB. Simple
ADRs like the above one should always be resolved first,
before tackling more complex cases.
The second example I am now going to detail is the
genus Fuscobryum, comprising three species. This case
is simple to resolve because there are no polytomies, all
dichotomies are supported at 13 dB or more. There are
therefore only three tests to conduct: is any these three
species the same as the node it is supposed to derive
from? The three trees corresponding to F. perobtusum,
F. nigrescens, and F. subandreaeoides have respectively
Fig. 5. The consensus trees. (A) Most parsimonious tree found after a heuristic search with successive weighting (stable after two
iterations). (B) Strict consensus tree built from all the 1474 trees that are less than 12.99 dB away from the most parsimonious
score.
A B
113Укр. бот. журн., 2017, 74(2)
certainly at least two independent lineages. G. fallax
may be the most primitive species in the genus Geheebia.
Indeed, if E. asperifolium is assumed to be descended
from G. ferruginea then G. fallax as potential ancestral
species is not rejected anymore, at 8.89 dB.
We need however to keep in mind that a hypothesis
that is not rejected is not necessarily the best solution.
Specifically, the pairwise tests are carried out in particular
phylogenetic contexts, so that any modification in the
neighbouring topology may change the results of the
tests. All possible rearrangements were tried to place
G. maschalogena, G. tophacea and G. leskeoides in the
right phylogenetic positions. Surprisingly, it appeared
that the best score was obtained with G. tophacea as
the sister species of G. fallax, both descended from an
unknown founding mother species of the genus. The
species G. maschalogena is finally best considered a
direct descendant of G. tophacea while G. leskeoides
is probably a direct descendant of G. fallax, just like
G. ferruginea. The genera Vinealobryum and Didymodon
sensu stricto have also been studied but the detailed
calculations are not shown here since the approach is
exactly the same as above. Many rearrangements were
tried and the best caulogram found is presented in
Fig. 6.
Discussion
The Meaning of Parsimony
The length of the best caulogram found is 873.11 steps,
which is 98.55 more steps than the most parsimonious
cladogram at 774.56 steps. However, there are only 7
unobserved species instead of the 23 necessary internal
nodes of the cladogram. Thus, we economized by
eliminating 16 ad hoc entities. Since the procedure
we used is equivalent to the fact of considering each
additional entity as having a value of 13 dB, we can
say that we economized 208 dB, which compensate
a length of 969.46 steps, 963.66 steps and 970.15 steps.
Compared to the previous best tree of 954.87 steps,
these hypotheses have a cost of 14.59 dB, 8.79 dB
and 15.28 dB. The first and the third hypotheses
exceed the threshold and are therefore rejected, but
the second hypothesis is well below and is accepted.
This means that F. nigrescens is the extant ancestor of
F. subandreaeoides, but the last common ancestor of
the three species remains unknown. It appears that
this scenario is not exactly the one favoured by Zander
(2014c) who inferred that F. nigrescens was the last
common ancestor of the other two species.
The case of the genus Trichostomopsis is also simple
to resolve. Only four tests are needed to assess potential
ancestral species. All of them were rejected at around
25 dB except T. australasiae whose status of ancestor
of T. umbrosa costs nothing at all. Zander (2014c)
concluded that T. australasiae is the ancestor of both
T. umbrosa and T. revoluta, but my test rejected this
hypothesis at 24.34 dB. Unless the cladogram was
misleadingly distorted by an artefact of long branch
attraction we must conclude that T. australasiae and
T. revoluta are derived from a shared unknown common
ancestor. The case of D. acutus, D. rigidulus and
D. icmadophilus is more ambiguous. Any of the three
species may be the ancestor of the other two, with the
respective costs 5.51 dB, 3.64 dB and 9.15 dB. There
is however a small hint in favour of D. rigidulus, so we
accept this hypothesis. These three species may be better
considered subspecies rather than distinct species, but
more data on morphology and possible reproductive
isolation is needed to conclude definitively.
The clade Geheebia-Exobryum is a quite big polytomy
and needs many tests in order to resolve it. I estimated
the cost of ADR for each pair of species (excluding
G. gigantea which we already know is directly derived
from G. maxima). The results presented in Table V
show us that G. ferruginea is certainly the ancestor
of G. maxima (with a cost of 0 dB). In fact, both
G. ferruginea and G. Fallax could be the ancestor of all
other species. However, G. ferruginea seems to be the
direct ancestor of E. asperifolium while G. fallax would
be the one of G. leskeoides and G. maschalogena. The
species G. tophacea seems slightly closer to G. ferruginea
but has clear affinities with both G. leskeoides and
G. maschalogena, which leads to the suspicion of
convergent evolution. Both G. ferruginea and G. fallax
were tested as a potential direct ancestor of all remaining
ones, but these hypotheses were rejected at 26.41 dB
and 20.76 dB respectively. This means that there are
Table V. The evaluation of ADRs among species of the genera
Geheebia and Exobryum. Each ADR hypothesis is tested
against the corresponding SGR hypothesis. Their rejections
are expressed in decibans, the threshold of 13 dB (> 95%).
ADRs that were not rejected are highlighted.
E. as G. fa G. to G. le G. ms G. fe G. mx
>E. as - 8.78 12.96 17.94 23.48 2.46 26.4
>G. fa 61.78 - 28.19 25.23 29.89 8.01 36.53
>G. to 46.55 8.78 - 18.77 23.37 8.01 36.53
>G. le 34.61 3.98 9.32 - 21.63 6.41 29.18
>G. ms 32.22 2.98 5.95 13.66 - 7.15 29.18
>G. fe 56.23 8.78 28.19 26.61 33.01 - 28.52
>G. mx 34.75 6.96 15.27 15.86 31.84 0 -
114 Ukr. Bot. J., 2017, 74(2)
28, 31, 36, and 41. Three of them (24, 28, 31) concern
the shape of different cells. This indicates that cell
shape is generally not a good phylogenetic marker. The
general shape of the leaf (9) is also to be considered
a poorly reliable character. However, in both cases
it is hard to know if this comes from a real tendency
to evolve frequently or from the lack of a precise and
reproducible morphometric measure (in which case
the dataset should be corrected and re-analysed). The
absence of a sporophyte (36) is not a reliable character
either; therefore it seems that the loss of sexuality is very
easy to evolve in Pottiaceae.
Finally, two character transformations are unique to
one species each (autapomorphies). These are character
8 for F. subandreaeoides which uniquely have dimorphic
leaves, and character 22 for V. nevadense which uniquely
have multi-layered photosynthetic cells on the ventral
costal surface. These two unique traits strongly indicate
that these two species cannot be an ancestral to another
one, which is also the case in Zander's analysis (see below).
Comparison with Zander's Results and Methods
These results only slightly differ from those of Zander
(1998, 2013, 2014a, b, c, 2016). For example, the
phylogenetic position of E. asperifolium in these previous
studies, basal to the genus Geheebia, is arguably due a
long branch artefact. The construction of a UPGMA tree
the previous loss. Our caulogram is therefore 109.45
steps more parsimonious than the most parsimonious
cladogram.
Character reliability
In the dataset, although many characters may be
considered quite reliable at about 8 or 10 dB, very
few seem to be extremely reliable. Indeed, only three
non autapomorphic characters have a weight of 13 dB
(see Table IV). These are characters 14, 20 and 21, or
respectively margin ornamentation of the leaf, the
presence or absence of a bulge on the abaxial face, and
the presence or absence of a thin-walled pad of cells on
the adaxial face. The first one is a synapomorphy defining
the large clade made of the genera Vinealobryum,
Didymodon sensu stricto, Geheebia, Exobryum and
Trichostomopsis, but not Fuscobryum. The second one
defines the clade of the genus Didymodon sensu stricto.
And the third one defines the clade made of the genus
Trichostomopsis and the species V. nevadense. Thus, this
species may be better considered a member of this genus
(morphological convergence seems unlikely in this
context because this trait has only evolved once with a
support of at least 13 dB).
On the other hand many characters are very
labile and are accordingly weighted at less than 2 dB
(see Table IV). These are the characters 9, 16, 23, 24,
Fig. 6. The commagram depicting the
ancestor-descendant relationships
among the species of Dydimodon
sensu lato. The corresponding
caulogram has a length of 873.11
steps. The seven unknown predicted
ancestral species are represented by
question marks.
115Укр. бот. журн., 2017, 74(2)
confirmed here). In its spirit, Zander's methodology is
quite similar to continuous track analysis (Alroy, 1995),
but it is far more holistic.
We must always seek a way to formalize our
implicit (expert) reasoning into an explicit one so as
to make it reproducible by others. My methodology
necessitates no aprioristic expertise because it is more
“mechanical”, i.e. more algorithmically constrained. It
may thus be qualified as more reductionist because I do
not use some kind of informations like distribution or
environment, and also because the measures of lability
cannot be nuanced by some kind of a priori complex
knowledge. It is therefore perhaps more reproducible,
but above all completely doable by a computer. Yet,
expertise is still needed a posteriori in order to interpret
the results and evaluate their plausibility. Indeed, an
expert can suspect a bias if for example the results are
nonsensical even though they are numerically strongly
supported (Hołyński, 2010).
Perspectives on Post-Phylogenetic Systematics
(aka Modern Evolutionary Systematics)
Phylogenetic reconstruction methods are classically
classified as either model-based or not. In the first
case we have maximum likelihood (ML) and Bayesian
inference (BI), while in the second case there exist
maximum parsimony and compatibility technique,
for example (Felsenstein, 1978, 1984; Farris, 1983).
However, the term “model-based” is really ill-chosen. It
misleadingly suggests that the classical cladistic analysis
does not assume any evolutionary hypothesis and is
therefore model-free as opposed to other techniques.
This is certainly false (Friday, 1989), but we may still
distinguish between those that explicitly specify a
parametrized evolutionary dynamics and call them
stochastic models, and those that do not and therefore
call them non-parametric methods.
The main assumptions that all the above cited
techniques share are that no ancestor was sampled
and that speciation is strictly dichotomous, which are
very strong assumptions. Even if the latter is not always
lucidly claimed, it is a rather obvious consequence of the
cladistic algorithm: since one cannot (in this framework)
distinguish between a genuine polytomy and a lack of
resolution then the data are always forced into artificial
dichotomies (Hull, 1979). The method presented
in this paper, as well as Zander's, may be considered
non-parametric like the classical cladistic analysis.
Even if weights are used here, they do not quantify a
part of the evolutionary process but our confidence in
our inferences. However, the two assumptions that no
indeed revealed that this species does not cluster within
the genus Geheebia (data not shown), which is probably
due to an accelerated evolution. The species V. vineale
is here revealed as being derived, not ancestral to all the
other species, but its rather conservative morphology
explains the previous conclusion. The prime ancestor
of this complex seems extinct or pseudoextinct, i.e.
anagenetically transformed into another species. It is
really not surprising given that this species is supposed
to be quite old: the more time passes, the less likely a
species remains unchanged. On the contrary, the more
recent ancestors of this complex of species are still alive.
In fact, exactly half of them (12) have unobserved direct
ancestor.
The other differences with Zander's results are minor
and are certainly due to the different set of data I used.
They may merit a careful re-examination but I shall
not comment them any further since the purpose of
this study is primarily methodological. I will therefore
not make any formal taxonomic decision. However,
it seems now unclear that E. asperifolium deserves its
own genus. The results also suggest that V. nevadense
may be better treated as belonging to Trichostomopsis.
A patrocladistic analysis may be conducted in order to
test the consistency of the remaining genera (Stuessy
and König, 2008). It seems that they fit more or less the
definition of dissilience (Zander, 2013), that is a core
species with several radiative species bursting from this
core. The scheme seems however more complex than
previously thought, including not only distinct lineages
or stirps radiating from the same core, but also stirps
arising from otherstirps.
The main difference between Zander's methodology
(Zander, 2014a, b, c) and mine is that he attempts
to assess ADRs by seeking among available species
which one is the more likely candidate to the status
of ancestral species. The contrast between SGR and
ADR hypotheses is not done explicitly. However, the
ancestral species are not found directly, but through
the successive elimination of the less probable
candidates, that is those with obvious derived traits.
The weighting of the different traits is also done in a
Bayesian framework; however, he follows an intuitive
scheme which ultimately relies on expertise, i.e. a
long-standing experience with regard to trait stability.
Moreover, he does not use only morphological data,
but also other kinds of information like distribution
or environment. For example T. umbrosa occurs in
human environments contrary to the case with the
other Trichostomopsis species, which indicates that it is
probably not the ancestral species we are seeking (as it is
116 Ukr. Bot. J., 2017, 74(2)
evolutionary dynamics of a genus or a family (Sepkoski,
1996).
Conclusion
The results of this study support the following major
conclusions:
• Ancestor-descendant relationships (ADRs) are
knowable;
• Didymodon, Geheebia, Fuscobryum, Vinealobryum
and Trichostomopsis are dissilient genera (from Latin
dissiliens, which means “bursting apart”, see Zander,
2013);
• Consistency index can be interpreted in a Bayesian
framework, measured in decibans and used as a
weighting scheme for cladistic parsimony analysis;
• Bremer support can also be interpreted in a Bayesian
manner and measured in decibans;
• There exist simple and objective ways to transform
a cladogram depicting only putative SGRs into a
caulogram depicting real ADRs (and real SGRs).
Another obvious consequence of this study is
that autapomorphies or “uninformative” cladistic
characters and character states should never be pruned
from matrices. This would strongly bias the data for any
post-cladistic analysis. In the same manner, labile and
even very labile characters should be studied and added
to matrices so that the data are as complete as possible.
These requirements are also needed in order to not bias
stochastic cladogram reconstructions such as likelihood
methods or Bayesian inference.
My procedure, as well as Zander's, are limited
heuristics and are not guaranteed to find optimal
solutions. They are rather constraining guides that
help organize the data, so that the systematists can
reconstruct an evolutionary scenario and make
taxonomic decisions accordingly. My study clearly
revealed that the length of a cladogram is not the
sole parameter we need to minimize, but that the
minimization of unobserved entities is also an important
parameter to take into account. This naturally led to an
equivalence relationship between these two parameters,
which can be translated into a new objective function
that a specialized algorithm could minimize by trying
many rearrangements of the possible topologies. This
function is simply as it follows:
S = L + 13n
S is the score we want to minimize, L is the total length
of the tree (on the deciban scale) and n is the number
of unobserved ancestral species required by the tree
topology. The minimization of this function is not
ancestor was sampled and that speciation is strictly
dichotomous are explicitly rejected because they are not
realistic. Our post-phylogenetic analyses are therefore
based on a distinct evolutionary model which is more
empirically grounded (Zander, 2013). A stochastic
approach that would also reject these two assumptions
is conceivable and should actively be sought.
Some cladists have insisted that ancestral species
cannot be recognized as such, and that ADRs are
therefore unknowable (Nelson, 1973; Farris, 1976).
These claims seem to be fundamentally based on a
particular version of nominalist epistemology (Aubert,
2015). As a consequence, anybody that does not
endorse this very philosophy could simply refuse these
assertions without further justification, scientific realists
for example (Sankey, 2001). Hull (1979) warned: “In
general, I think it is very bad strategy for proponents of
a particular scientific research program to stake their
future on epistemological considerations, especially on
our inability to know something.” Indeed, epistemology
should not be seen as an a priori set of constraints that
dictate what science can do or cannot do. Epistemology
should be handled in a more empirical manner,
mainly in order to take a global view a posteriori on
the achievements of science. A one-way relationship
between epistemology and science is really a kind of
sterilizing metaphysics which has its modern origins
in German Idealism (especially Kant's Critique of Pure
Reason). Only a genuine dialogue between both can be
fruitful: this is dialectics, not metaphysics.
As a consequence of their hypothetico-deductivist
framework, cladists seem afraid of type I errors, i.e. not
being able to reject the null hypothesis (the relationship
is an ADR) when it is wrong, so they always reject it
by default (all relationships are SGRs), which logically
leads to many type II errors (many of the supposed SGRs
are in fact ADRs). It is necessary to overcome this by
proposing new methods of caulogram reconstruction,
and also new methods in taxonomy. Indeed, as opposed
to cladograms it is widely recognized that caulograms
cannot be directly translated into ahierarchical
classification because of the named ancestors it
includes. Contrary to SGRs, ADRs highlight that
“Evolution is paraphyly all the way” (Brummitt, 2002).
This is obviously true for species: paraphyletic species
(like G. fallax) are not less real than holophyletic ones,
paraphyly does not preclude them from being “natural
entities” (i.e. biological species). This is also true for
higher taxa which cannot all be made holophyletic
(Brummitt, 2002; Aubert, 2015). More importantly,
paraphyly or holophyly have really no influence on the
117Укр. бот. журн., 2017, 74(2)
Annex
Gametophyte Characters:
1. Colour of plants:
0. green to red-brown
1. green, often blackish (never reddish)
2. glossy green or very bright green
3. yellow- or orange-brown to red- or black-brown.
2. Stem height (Ordered):
0. less than 1 cm.
1. 1–2 cm.
2. 2.5–3.5 cm.
3. more than 4 cm.
3. Stem central strand (Ordered):
0. always present, strong.
1. variable, present or absent.
2. weak or absent.
4. Axillary hairs:
0. with all cells hyaline.
1. with brown basal cells.
5. Specialized asexual reproduction:
0. absent, or deciduous leaf apex.
1. present, axillary, multicellular.
2. present, axillary, unicellular.
3. tubers present on rhizoids.
Leaf Characters:
6. Leaf stance when dry:
0. spirally twisted, weakly spreading.
1. erect-appressed, not twisted.
2. appressed-incurved.
3. catenulate.
7. Leaf stance when moist and removed (Ordered):
0. spreading to weakly recurved, commonly lying flat.
1. spreading to spreading-recurved and weakly keeled.
2. strongly recurved and keeled.
8. Leaf polymorphism:
0. monomorphic.
1. dimorphic, the smaller leaves strongly concave in
series in some parts of the plant.
9. Leaf shape (Ordered):
0. short- to long-lanceolate.
1. variable or intermediate.
2. deltoid to ovate-lanceolate.
10. Leaf channelling above mid-leaf (Ordered):
0. with a narrow groove along ventral surface of costa.
1. variable or intermediate.
2. broadly concave to nearly plane.
11. Leaf base:
feasible manually by a human being because of the huge
number of possible topologies. The best way to proceed
for now is to reduce the problem by selecting small areas
in a cladogram and resolve them individually as it was
done in this study:
1. Collect a morphological data set as complete as
possible, including autapomorphies and other
“cladistically uninformative” characters;
2. Find the most parsimonious cladogram through
an iterative procedure which uses Bayesian weights
measured in decibans (dB);
3. Collapse all the branches whose Bremer support is
not at least 13 dB (> 95%);
4. In the distinct parts of this strict consensus cladogram,
try all possible pairwise arrangements by contrasting
the shorter SGR trees with the corresponding longer
ADR trees;
5. ADR hypotheses should be rejected only if the trees
of corresponding SGR hypotheses are at least 13 dB
shorter;
6. In order to address huge polytomies, all possible
arrangements (or at least all likely ones) should be
tried to find the shortest configuration, but taking
into account the number of unnamed ancestors
eliminated (see above formula).
Note that an automatized program could test many
more topologies than a human being and do so very
quickly. Since several decades, whatever the analyses
conducted, the amount of data has become huge
and phylogenetic studies therefore rely heavily on
computers. As a consequence, phylogeneticists tend
to do only what available software allows them to do.
That is why the methods for assessing ADRs needed
to be first formalized – as it was done in this study, or
by Zander (2013, 2014a, b, c, 2016) – and then must
be implemented in new software or in new packages
for already existing software. I cannot stress enough
the importance for evolutionary systematics to head
towards informatics.
Acknowledgements
I would like to sincerely thank Richard Zander who
provided me the initial files and also some insightful
comments on an early draft of this paper. I would also
like to thank the two reviewers who brought many useful
suggestions.
Compliance with Ethical Standards
The author Damien Aubert declares that he has no
conflict of interest.
118 Ukr. Bot. J., 2017, 74(2)
22. Multi-layered photosynthetic cells on ventral
surface of mid-costa:
0. absent.
1. present.
23. Costa superficial ventral cells:
0. elongate, more than 2:1.
1. quadrate or very short-rectangular (at least near
apex).
24. Costa width at midleaf (Ordered):
0. 2–3(–4) cells.
1. 4–5(–6) cells.
2. (5–)6–9 cells.
25.Guide cells (Ordered):
0. nearly always one layer.
1. variable (one or two layers).
2. two (or three) layers.
Basal Characters:
26. Basal laminal cells:
0. differentiated medially or across the leaf.
1. weakly differentiated.
27. Basal laminal cell walls (Ordered):
0. very thin, hyaline, possibly perforated by transverse
slits.
1. thin to weakly thickened, not perforated.
2. usually thick, not perforated.
3. always thick and porose.
28. Basal laminal cell shape:
0. quadrate or very short-rectangular.
1. rectangular.
Upper Laminal Characters:
29. Upper laminal cell width:
0. (7–)8–10(–12) µm.
1. (11–)13–15 µm.
30. Upper laminal cell shape:
0. quadrate or very short-rectangular, rarely
transversely elongate.
1. in rather distinct rows, often longitudinally
elongate.
31. Upper laminal cell lumens:
0. mostly rounded.
1. mostly angular.
32. Papillae:
0. usually present, simple, possibly bifid or multifid,
(1–)2–3 per lumen.
1. low, massive and lens-shaped or scablike.
2. essentially absent, rarely simple, weak and
domelike, one per lumen
0. scarcely differentiated to oblong, gradually or
quickly narrowed to the insertion.
1. well-differentiated ovate, possibly winged or
auriculate.
2. well-differentiated rectangular, squared.
12. Leaf length (Ordered):
0. 0.9–1.5 mm.
1. 1.2–2.5 mm.
2. 2.0–3.5 mm.
3. 3.5–5.0 mm.
Margin and Apex Characters:
13. Margin flexion:
0. plane or nearly so.
1. recurved in lower 1/2 or 3/4.
2. recurved or revolute to apex.
14. Margin ornamentation:
0. minutely crenulate.
1. entire (smooth or papillose).
2. often notched laterally.
15. Apex shape:
0. rounded or obtuse (only occasionally broadly
acute).
1. broadly to narrowly acute, variable.
2. very long acuminate, whiplike.
3. narrowly acute, thickened, but not deciduous.
4. swollen as a propagulum, deciduous.
16. Apex ending:
0. of a clear conical cell or mucro.
1. rounded and obscure.
Costa Characters:
17. Costa ending:
0. clearly тexcurrent, usually as a short mucro.
1. percurrent or ending to 2 cells before the apex.
2. ending more than 2 cells before the apex.
18. Costa hydroids:
0. present.
1. absent.
19. Well-developed specimens with ventral (adaxial)
costal stereid band (Ordered):
0. present.
1. weak, variable.
2. absent.
20. Costa abaxial shape:
0. clear dorsal bulge present.
1. dorsally flattened.
21. Adaxial thin-walled pad of cells:
0. absent.
1. present.
119Укр. бот. журн., 2017, 74(2)
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0. thin to evenly thickened, convex on both sides of
lamina.
1. irregularly thickened, convex on both sides of
lamina.
2. evenly thickened, moderately bulging on both
sides or only abaxially.
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1. absent.
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0. 0.3–0.6 cm.
1. 0.6–1(–1.2) cm.
2. (0.8–)1–1.7(–2.5) cm.
38. Capsule size:
0. 0.5–1.5 mm.
1. 1.25–2.5 mm.
39. Number of peristome teeth, when present:
0. 32 teeth, or possibly 16 cleft to base.
1. 16 teeth.
40. Tooth shape:
0. usually twisted
1. usually straight.
2. essentially absent.
41. Tooth length, when present (Ordered):
0. 50–300 µm.
1. 300–800 µm.
2. 800–1500 µm.
42. Spore size (Ordered):
0. 8–12 µm.
1. 13–15 µm.
2. 16–20 µm.
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121Укр. бот. журн., 2017, 74(2)
Обер Д. Простий підхід до оцінки зв'язків предок-нащадок
на основі парсимонії. Укр. бот. журн., 2017, 74(2): 103–121.
Академія Клермон-Феран,
Міністерство національної освіти Франції
Однією з головних цілей систематики є реконструкція
Дерева життя. Півстоліття тому проривом стала кладис-
тика, яка виявилась важливим кроком на шляху до цієї
мети, що дозволив нам визначити зв'язки спорідненості
між видами, абстрактний вид спорідненості. На жаль,
філософія кладизму не дозволила просунутися далі в
пошуку більш реальних взаємозв'язків, таких як зв'язок
предок-нащадок, який, відповідно до дарвінівської
еволюційної концепції, ймовірно, є основним типом
зв'язків на Дереві життя. У статті описана проста методи-
ка на основі парсимоніі, яка може бути використана для
перетворення класичної кладограми у справжнє філоге-
нетичне дерево, тобто в каулограму. Ця методика полягає
у видаленні якомога більшого числа неспостережених
і неіменованих вузлів та в їх заміні реально визначени-
ми та іменованими видами. Як в цій методиці, так і при
побудові класичної кладограми, для оцінки надійності
ознаки використовується нова байєсівська нестохастич-
на схема зважування. Для ілюстрації проводиться оцінка
взаємозв'язків між видами мохів роду Didymodon sensu
lato (Pottiaceae) з обговоренням отриманої каулограми
шляхом її співставлення з попередньою методологією
відповідно до еволюційних публікацій. На закінчення
робиться висновок про недоцільність суворого додер-
жання кладистичної епістемології та необхідність по-
шуку нових формальних методів для встановлення пред-
кових видів, а також і предкових таксонів вищих рангів.
Ключові слова: предок, байєсівський аналіз, індекс
Бремера, еволюційна систематика, парсимонія,
зважування
Обер Д. Простой подход к оценке связей предок-потомок
на основании парсимонии. Укр. бот. журн., 2017, 74(2):
103–121.
Академия Клермон-Ферран,
Министерство национального образования Франции
Одной из главных целей систематики является рекон-
струкция Древа жизни. Полвека тому назад прорывом
стала кладистика, которая оказалась важным шагом на
пути к этой цели, позволившим нам оценить относи-
тельные родственные связи между видами, абстрактный
тип родства. К сожалению, философия кладизма не по-
зволила продвинуться дальше в поиске более реальных
родственных взаимосвязей, таких как связь предок-по-
томок, которая, согласно дарвинистской эволюционной
концепции, является, очевидно, основополагающим
типом связей на Древе жизни. В статье описана простая
методика на основе парсимонии, которая может быть
использована для преобразования классической кладо-
граммы в настоящее филогенетическое дерево, то есть в
каулограмму. Эта методика состоит в удалении как мож-
но большего числа ненаблюдаемых и неименованных
узлов и в замене их наблюдаемыми и именованными ви-
дами. Как в этой методике, так и при построении клас-
сической кладограммы, для оценки надежности при-
знака используется новая байесовская нестохастическая
схема взвешивания. В качестве иллюстрации проводится
оценка взаимосвязей между видами мхов рода Didymodon
sensu lato (Pottiaceae) с обсуждением итоговой кауло-
граммы путем сопоставления ее с ранее применявшейся
методологией по материалам эволюционных публика-
ций. В заключение делается вывод о несостоятельности
строгого следования кладистической эпистемологии и
необходимости поиска новых формальных методов для
установления предковых видов, а также предковых так-
сонов более высоких рангов.
Ключевые слова: предок, байесовский анализ, индекс
Бремера, эволюционная систематика, парсимония,
взвешивание
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