Towards Accurate Assessments of Biological Diversity
"Discussions of taxonomic theory often refer to philosophical ideas, but such reference is often quite oblique, without a real analysis of the underlying concepts or a clear-cut demonstration that the philosophical arguments really apply. Philosophy is often a difficult subject, one which the practicing systematist may prefer to leave to the specialist. As science inevitably involves logic, and as metaphysical ideas somehow tend to creep into discussions of methodology, the systematist can scarcely help but contact an occasional philosophical notion." (Ghiselin, 1966:207).
"we often fail to solve our problems because we cannot even identify them. Under such circumstances, conceptual investigations do more than just help. They are the only way out." (Ghiselin, 1975:543)
Philosophy and Systematics
Science, inclusive of the areas of systematics, taxonomy, evolution, conservation biology, etc., involves the pursuit of knowledge regarding our natural world. However, our general methods of science do not directly concern assessing how we judge the truthfulness of the knowledge we acquire, what ideas represent mere conjecture and which represent knowledge, and whether or not we can trust our observations of the real world. Philosophy assists us in understanding these issues. Some argue that within philosophy epistemology, study of the origin, nature, and limits of knowledge, defines science.
As stated by Schuh (2000) some have argued that "systematics is something you do, not something you think about." This is an anti-intellectual view of the world and in no way justifies ignoring the inquiry into the scientific thought process itself. However, some have always involved philosophy of science in their systematic works and these are scientists that have made the most significant advances in the field. The importance of the philosophy of science to systematic biology, however, did not really become apparent to the field of systematics until about the 1960s when a new practice of systematics emerged (Hennig's Phylogenetic Systematics/Cladistics). This will be discussed in more detail, along with the scientific method in a later lecture. In some ways, however, the philosophy of science still lags behind in the general fields of evolution and conservation of our biological diversity.
There are four general areas of philosophy as it relates to systematic biology, biodiversity, and conservation science. All of these areas are part of the realm of science and affect scientists at one level or another (sensu Wiley, 1981)
Logic. Logic is the general study of the basic principles of reasoning. This area separates valid from invalid reasoning, the latter resulting in faulty conclusions. Thus, logic is an integral part of science.
Epistemology. Epistemology is the study (origin, nature, limits) of knowledge and knowledge acquisition. This is a very critical area of science. "Genuine or valid knowledge must meet certain standards. Particular scientific methods may be applied to gather such knowledge. But all scientific methods have their limits beyond which their knowledge claims are not valid. In addition, what appeared to be genuine knowledge may be replaced by new knowledge, if that new knowledge is genuine and validly gained. There are several approaches to epistemology" (Wiley, 1981:16).
Phenomenalism Suggests that only observed
phenomena can be considered genuine knowledge. - Thus, we could reduce
science to the identification and classification of
phenomena. - Represents Bridgman's
concept of operationalism practiced by some pheneticists
and, in general, by some taxonomists and
systematists. Fictionism Scientific hypotheses should
be looked upon as fictions that give order and coherence to
observations. - Theoretical statements do
not really refer to or describe real things or processes but
serve only to order observations - Nominalists that view
species as only convenient groupings serving for
communication = fictionists Realism Certain theories, concepts,
and hypotheses actually exist in the real world. - 3
tenets: 1) some theoretical
terms apply to hypothetical entities, 2) some hypothesized
entities are candidates for existence, and 3) some candidates
exist - Systematists and
taxonomists that view species as "real" are
Suggests that only observed phenomena can be considered genuine knowledge.
- Thus, we could reduce science to the identification and classification of phenomena.
- Represents Bridgman's concept of operationalism practiced by some pheneticists and, in general, by some taxonomists and systematists.
Scientific hypotheses should be looked upon as fictions that give order and coherence to observations.
- Theoretical statements do not really refer to or describe real things or processes but serve only to order observations
- Nominalists that view species as only convenient groupings serving for communication = fictionists
Certain theories, concepts, and hypotheses actually exist in the real world.
- 3 tenets:
1) some theoretical terms apply to hypothetical entities,
2) some hypothesized entities are candidates for existence, and
3) some candidates exist
- Systematists and taxonomists that view species as "real" are realists.
Metaphysics. Metaphysics involves the study of concepts and the relationships of these concepts. To science, in particular, metaphysics is concerned with the relationships between various concepts and scientific systems of knowledge acquisition. Some logical empiricists (e.g., Karl Popper, 1968a,b) suggests that metaphysical concepts lie outside the realm of scientific inquiry. However, there exists an interaction between how we view the world (metaphysical), our collection of empirical data, and our world view based on our data (=possibly changes). Because certain metaphysical ideas do limit the kinds of hypotheses that we propose, there is at least a potential to overturn our metaphysical ideas by showing that these hypotheses are either (1) too restrictive, (2) too broad, or (3) do not fit higher theories. (modified from Wiley, 1981).
Ethics. Ethics is the study of values and moral evaluations. Ethics has a much more subtle contribution to science. However, it is a very important area for scientists in many ways.
Important in the discussion and resolution of the issue of naturalness, species, and supraspecific (higher) groups is the correct usage and understanding of ideas and terms related to these topics. Historically, discussions of species and supraspecific taxa have involved the use of four critical terms: concept, definition, group, and category. These terms have often been central to the fundamental melange that both scientists and philosophers have encountered with the issues of naturalness, species and supraspecific groups.
Communication of ideas or concepts in science is of utmost importance and hinges upon statements or definitions developed by persons formulating or discussing the concepts. Critically important to the exact communication of ideas embodied in concepts demands that we not obfuscate the terms used in definitions or statements of the concepts. Here, we confront difficulties both in the logical treatment and the evaluation of definitions.
Concepts of biological systems serve as fundamental links between pattern and process in nature, are employed in every discipline, and help guide our perception of natural systems. They are formulated by individual persons through observation, study, and synthesis (impressions and imagination) in an environment of both theory and empirical data. A concept may be relayed from one person to one or more other persons by adapting it into a statement or definition, either verbally, in writing, or graphically. Such a definition may or may not induce the same concept in the mind of the other person(s), depending upon the appropriateness, precision, and accuracy of the words used in the definition and the level of understanding of the other person. For some concepts (e.g. round vs square; chair vs table; car vs truck) one may compare statements developed by different observers with the discrete objects to see if they agree. With other, more abstract concepts (evolution, natural selection, species as taxa) it is difficult to know for sure if statements represent the same transient or hypothetical things. Here, the respective definitions can only be compared using previously agreed definitions of words used in the statement. One may also observe the effectiveness of such a concept through direct examination.
Some Terms and Definitions
In the intersection of natural sciences, taxonomy, and systematics the term taxon is often used synonymously with the term group. The term group refers to a collection of objects or things. A group can be real and have objective reality if it corresponds to qualities that are real and exclusive to it, and if it consists of things that have material existence. They may be arranged hierarchically, either as non-reticulate or reticulate groups. They may be represented at various levels of universality from groups of things to more inclusive groups of things, etc. They may be of any size and arise on the basis of intrinsic attributes and/or extrinsic factors. Organisms can be members of any number of groups so long as they possess the attributes of the said groups. Groups, however, are not like concepts. Groups develop from sense impressions of concepts and can be agreed upon and definite if the statements about them are unambiguous and decisive.
Groups and categories are distinctly different and there is no real connection between them. The tradition in codes of nomenclature artificially forces the use of taxonomic categories in a hierarchy for groups. A biological classification is a contrived system of categories used for the storage and retrieval of information about biological diversity, taxa, or groups. The concept category is a Class and has no separate existence from its use in organizing objects or thoughts; categories have no reality. Unlike groups, categories have no attributes; things or objects are not members of categories, but are parts of groups; and organisms are not members of any taxonomic category. For example, Cyprinidae is a proper name given to a group of fishes possessing certain attributes. By taxonomic convention the -idae ending denotes a traditional level of universality in the zoological hierarchy. The group Cyprinidae can be a part of many other groups (Cypriniformes, Ostariophysi, Teleostei), but is only a member of one taxonomic category, Family. Because categories have no reality the Family Cyprinidae is not a member of any other more-inclusive categories, but Cyprinidae is.
Species as a "Taxon" and "Taxonomic Category"
Before any profitable and normal discourse on species we must first distinguish between the two most common uses of the term for biological organisms in biological systems. Abundant controversy, miscommunication, and confusion on species has emerged from a traditional equivocation of this term. The term species refers to a traditional taxonomic category of the Linnaean hierarchy organizing biological diversity. This category has a higher level of universality than the category Genus and a lower level than the category Subspecies. It is strictly a placeholder in our accounting and organization of life discovered on this planet. In this usage it is traditionally cited species as category. (see also discussion above on Category).
The term species also refers to naturally occurring biological entities or the highest level of biological organization participating in natural processes such as speciation, selection, adaptation, reproduction, competition, and many other natural processes. This usage of species refers to such things given the names Homo sapiens (human), Salmo trutta (brown trout), Mus musculus (house mouse), Tyrannosaurus rex, etc. In this usage it is traditionally cited species as taxon. Importantly, one of these terms is part of a constructed classification that humans impose on nature for communication (species as category), the other refers to the actual products of nature (species as taxon).
Species vs Supraspecific (higher) Taxa
Naturalness applies to both
(1) the single lineages of biological diversity that we identify, name, and place in the Category Species of the Linnaean hierarchy and
(2) two or more lineages grouped together, given a name, and a taxonomic rank above the level of species, termed supraspecific category.
Naturalness also applies to other possible supraspecific groupings that could also be recognized and formally named, but are not given a formal taxonomic name and rank in the Linnaean hierarchy. Actually, these would include any grouping of more than two species (Etheostoma duryi species group, the North American cyprinid Chub, Shiner, and Western clades, etc.)
Species and Naturalness
It is assumed by most realists that the binomials that exist represent naturally occurring entities of life that behave as lineages (sexual or asexual). More about this will be discussed below under the topic of Metaphysics and Species.
Supraspecific Taxa and Naturalness
Mathematically, when you examine the possible permutations of the number of possible supraspecific groupings of species it is nearly inconceivable. The number of possible arrangments of bifurcating trees (what supraspecific taxa) are based on increases exponentially.
10 2 x 106 22 3 x 1023 50 3 x 1074 100 2 x 10182 1,000 2 x
102,860 10,000 8 x
1038,658 100,000 1 x
10486,663 1,000,000 1 x
105,866,723 10,000,000 5 x
2 x 106
3 x 1023
3 x 1074
2 x 10182
2 x 102,860
8 x 1038,658
1 x 10486,663
1 x 105,866,723
5 x 1068,667,340
Because there is but a single tree of life or speciation of life we may infer from this that some supraspecific groupings are better than others in that they more accurately reflect the natural pattern of descent of life. These groupings should be natural and should have an objective basis in evolutionary history. These supraspecific taxa are the "best" of the inconceivable number of possible ones that could be recognized.
What is Natural?
As discussed by Wiley (1981) and others, the term natural is somewhat elusive when it is applied to the field of systematics. Nearly all systematists and taxonomists will argue that their system of classification is natural. However, there is a history of usage of this term that is applicable to the question and should be reviewed here.
Natural has been applied in at least three basically different systems of classification.
This is an essentialists view of the world. Herein, a group is considered natural if the entities placed in the group share or agree in the characteristics that embody the essence of the group. These characters are both necessary and sufficient for group membership (Wiley, 1981). They are also expected to resemble one another in additional characteristics (Crowson, 1970). Essential characters were often thought of as those features most important in the functioning of the organisms. For Linnaeus his classification of plants (Species Plantarum 1753) was based largely on the reproductive morphology of the plants.
This form of naturalness, as discussed in lecture 1, is based on early taxonomic studies where groups were thought to possess an essence. Furthermore, this form of classification is based on the principle of logical division of Theophrastus (c. 370-287 B. C.) that is a set-theory rule of dichotomy (one group has the character and the other does not). This is how dichotomous keys are devised and they do not necessarily reflect patterns of descent.
While Aristotelean naturalness is not supported today it is interesting to note that many of the groups identified by these essential characters are still recognized today and supported as phylogenetically natural groups. The reason for this is that early naturalists guided by this form of essentialism identified "essential" characteristics of these groups that are today identified as synapomorphic (=shared-derived characters) that are critical to identifying phylogenetically natural supraspecific groupings.
Groups exhibiting this form of naturalness are composed of members that resemble each other (in overall similarity) more than they resemble any non-member. They are all more similar to each other for the characters examined than any of the members are to a member outside of the group.
After a long period of use of Aristotelean naturalness, where only a "essential" characters were used in developing classifications of biodiversity some naturalists moved to a system that incorporated all morphological features (=total morphology). This system also became known as one of general similarity of the different life stages of organisms. These naturalists also argued for a degree of constancy in the characters used. "Essential" characters were no longer considered necessary or sufficient for group membership. Rather, inclusion in a group is based on sharing the maximum of all possible number of characters ( or overall similarity).
Some of the earliest naturalists employing this system included Adanson (1763), de Jussieu (1789), de Candolle (1813) and Asa Gray! This system was adopted in the 1960s and 1970s by numerical taxonomists or pheneticists and included Sokal and Sneath (1963), Sneath and Sokal (1973), and Davis and Heywood (1965). These latter authors refer to naturalness of groups in terms of Gilmour naturalness, a topic that will be discussed later in the semester under the discipline of phenetics. Many of the modern-day pheneticists claim their roots with Adanson!
Groups exhibiting this form of naturalness are composed of members that share a common ancestor not ancestral to any other group. In other words, members in this group are more closely related to each other than any of them are to members outside of the group.
With the development of evolutionary thinking and the concept of lineages participating in descent with modification naturalists began thinking of natural groupings being those descended from common ancestors. With this, the natural system became a phylogenetic system.
What is a natural taxon?
In taxonomy of the 20th Century (and probably even today) many might have said that a natural taxon is one that a competent taxonomist (or systematist) says it is!
One might also argue that a natural taxon is one that can be defined and discovered by a set of operations.
Neither of these philosophies of natural taxa is what an evolutionary biologists or phylogenetic systematists would interpret at being natural. Wiley (1981) refers to naturalness in science as carrying the connotation of "existing in nature, neither artificial nor man-made." Thus, we may define natural taxon in the following way.
an entity consisting of a single or two or more lineages existing in nature, either currently or historically, independent of the abilities of Homo sapiens to perceive it.
Connotations associated with this definition (sensu Wiley, 1981):
1. Natural taxa exist via descent with modification whether or not there are systematists, or even Homo sapiens, around to perceive or name them.
2. Because they exist in nature, natural taxa must be discovered, they cannot be invented by Homo sapiens.
3. Natural taxa originate according to natural processes (=selection, adaptation, speciation) and thus must be consistent with natural processes.
4. When proposing a natural taxon, that is, when hypothesizing that a particular group of organisms or group of species is natural, we invoke all of the connotations implied in 1-3.
Many famous systematists responsible for both theoretical and empirical advances in the field have identified the natural taxon concept with groupings that exist in nature.
Simpson (1961:55) professed the idea that "The taxa of natural classifications must have some relationship . . . with groups of whole organisms really existing in nature.
Crowson (1970:275) also argues that "a perfectly natural classification of plants and animals might even be considered as objectively existing, and thus requiring to be discovered rather than invented."
[the idea of being taxa being discovered vs invented will be discussed more fully at another time]
Hennig (1966) viewed natural taxa was those groups in the phylogenetic system characterized by individuality and reality.
What exists in nature?
One may ask what really exists in nature?
We may say that things we suspect to exist in nature as discrete entities are things we can explain or describe in reference to perceived natural processes or laws.
Wiley (1981) uses the example of physicists and the various elements. For physicists elements are natural entities because the elements and their interactions are understood by certain physical laws and the processes these laws describe.
In biological systems there are many kinds of natural entities not dealt with by taxonomists and systematists (or believed to be so) because we can explain their characters and their interactions in terms of scientific theories.
cells and subcellular parts (cell theory)
atoms (atomic theory)
planets (planetary theory)
individual organisms (reproductive theory, ontogeny for multicellular organisms)
populations (population biology/genetics theory)
communities (community theory)
ecosystems (various ecological theories at the system level)
Below, we shall see that species as taxa and supraspecific taxa are also natural entities. We shall also see that species as taxa are different kinds of natural entities than supraspecific taxa and are believed to be more similar to the above listed natural entities (in some ways) in biological systems.
To fully understand natural groups referable to species or supraspecific taxa we must understand and consider the differences between what philosophers and systematists refer to as Classes, Individuals, and Historical Groups. Important references and discussions of these terms can be found in Ghiselin (1966, 1969, 1974, 1980), Hull (1976), and Wiley (1981).
Unfortunately, the term class has two distinct meanings that can be easily confused if not used concisely. There is the taxonomic category Class used in the Linnaean hierarchy. The term class is also used as a metaphysical term by philosophers and logicians Classes, in the metaphysical sense, have very distinct qualities and are employed constantly by everyone and probably by many species other than Homo sapiens.
A class is a construct with members. Membership is determined by a class definition or class concept. A class is spatiotemporally unrestricted or unbounded with no unique beginning or ending, it does not participate in natural processes and does not change through time and space, it lacks cohesion and may lack continuity, it possess a general rather than a proper name, there are instances of them, and their constituents are members not parts. Finally, and very importantly, classes have definitions that specify the necessary and sufficient qualities that something must have to be a member.
The term "individual" has also been used and confused as a synonym for two very different meanings, one in common lay dialogue and the other in metaphysical dialogue. Most scientists and laypersons use individual to refer to a specific organism. In this usage I will refer to individual. Philosophers and logicians use the term individual in a very different way, in a metaphysical sense, referring to a particular thing, a particular, an entity, a system. In this usage I will refer to individual.
Individuals have very distinct qualities. Individuals are spatiotemporally restricted with unique beginnings and endings, they participate in natural processes and can change through time and space, they possess cohesion and continuity, they possess proper rather than general names, there are no instances of them, and their constituents are parts not members. Finally, individuals do not have definitions, they cannot be defined. Rather, they only have descriptions or diagnoses.
What is meant by instances and
By instances, we mean that a single, among many, particulars of the same individual cannot be taken as the individual. For example, if species as taxa are considered individuals then Charles Darwin is a part or an instance of Homo sapiens. We would not say that Charles Darwin is a Homo sapiens or a member of Homo sapiens. If species as taxa are considered classes then Charles Darwin would be considered a member of the species. Ghiselin (1975) also uses the example of the individual states of the United States of America and notes that California is a part of the USA but is not a USA.
Individuals can refer to a variety of particulars or systems having different levels of integration and an individual is not required to be physically contiguous. A person is an individual and an individual, composed of other integrated organizational levels of individuals commonly referred to as particular electrons, atoms, molecules, cells, tissues, organs, etc. The United States of America is an individual with a proper name (in class called Nations) despite the known fact that two of the states are separated from the "lower" 48 states by Canadian territories and international waters.
Distinguishing Classes and Individuals
The distinction between classes and individuals is absolute. However, interestingly enough, there can be interaction or reticulation between these metaphysical categories in terms of their members and parts, respectively. Members of classes can be other classes or individuals and the parts of individuals can be both other parts or classes.
This term was coined by Wiley (1980, 1981) to refer to natural, supraspecific taxa that are derived from individuals. These taxa have qualities of both individuals and classes and thus do not really fit into either of these metaphysical categories. Natural taxa are spatiotemporally bounded entities like individuals. However, these taxa are distinct from individuals in several ways. Thus, natural supraspecific taxa are referred to as either "a special type of individual," "historical entity," or "historical group."
Species have cohesion via sexual reproduction (sexual species), evolutionary stasis (asexual and sexual species), and similar responses of the particular organisms of a species to extrinsic factors of evolution.
No active cohesion because it is composed of individual evolutionary units that have the potential to evolve independently of each other.
Sexually reproducing species have historical (from ancestral lineage) and ongoing (reproductive ties, etc.) continuity.
Have only historical continuity as all parts have descended from a common ancestral species.
Units of evolution.
Those containing more than one species are units of history, not evolution. No evolutionary process is known to operate on supraspecific groups together as a unit.
Important implications of Historical Groups (modified from Wiley, 1981).
1. No ongoing processes gives an historical group cohesion; continuity is only historical.
2. There is no known process, other than speciation, by which supraspecific taxa can arise.
3. Thus, supraspecific taxa must be historical units that result from speciation. There is no origin of supraspecific taxa except through the origin of species because species are the largest units of evolution.
4. Genealogical lineage splitting and other speciation processes are both necessary and sufficient conditions for the origin of natural supraspecific taxa. Those supraspecific taxa that do not accurately document these necessary and sufficient conditions cannot be natural taxa. (e.g., paraphyletic and polyphyletic groups).
5. A natural supraspecific taxon cannot overlap another at the same level of universality. Given two natural supraspecific taxa one cannot contain taxa more closely related to taxa in another group . (e.g., paraphyletic and polyphyletic groups). (see Wiley, 1981:76 for further discussion).
6. Historical groups must be justified by an investigator in terms of evidence for common ancestry. Species (as individuals) have no adequate definition other than their insertion into history. Thus, species are "christened" into existence (Ghiselin, 1974), but historical groups must be justified by characters that demonstrate their status as natural groups. Later, we will find that the evidence needed involves evidence to defend monophyly, synapomorphic characters or shared-derived characters.
Space-Time Participate in Natural
Process Change through
time Constituents Instances Names Definitions Descriptions Diagnoses Organization
Participate in Natural Process
Change through time
As discussed earlier, there are a multitude of ways to group two or more taxa that exist on this planet. Of these, only some of them can be referred to as natural groupings. In systematics there are specific terms developed to differentiate between natural and non-natural groupings. One may also refer to this dichotomy of groupings as natural and artificial groups, where artificial refers to human constructs imposed on a natural order (genealogical relationships) that do not reflect the natural order. Technically, these terms do not relate to natural entities known as species (as taxa) because they are not biologically relevant; they are not appropriately used at this level of universality. Species are natural by virtue of their insertion into history.
Unfortunately, some researchers have used these different group-related terms differently and their definitions do differ (see Wiley, 1981:84)
Monophyletic group: A group that includes an immediate common ancestral species (known or hypothesized) and all of its descendants (ca. Farris, 1974).
[Note: Also referred to as Holophyletic group by Evolutionary Systematists].
Hennig (1966) (1) A group of species
descended from a singe ("stem") species and which includes
all species descended from this stem species. (2) A group of species in
which every species is more closely related to every other
species than to any species that is classified outside of
the group. (3) (Characterization) A
group based on synapomorphous similarities. Ashlock (1971) A group whose most recent
common ancestor is cladistically a member of the
group. Nelson (1971) A group into which have been
placed species that are assumed to be descendants of a
single hypothetical ancestral species, that is, a complete
sister-group system. Farris (1974) (1) A group that includes a
common ancestor and all of its descendants. (2) (Algorithm dfn.) - A
group with unique and unreversed group membership
(1) A group of species descended from a singe ("stem") species and which includes all species descended from this stem species.
(2) A group of species in which every species is more closely related to every other species than to any species that is classified outside of the group.
(3) (Characterization) A group based on synapomorphous similarities.
A group whose most recent common ancestor is cladistically a member of the group.
A group into which have been placed species that are assumed to be descendants of a single hypothetical ancestral species, that is, a complete sister-group system.
(1) A group that includes a common ancestor and all of its descendants.
(2) (Algorithm dfn.) - A group with unique and unreversed group membership characters.
Paraphyletic group: A grouping that includes the immediate common ancestor and some, but not all, of the descendant taxa. [Note: Evolutionary Systematists also recognize these types of groups as Monophyletic groups.]
Hennig (1966) (1) A group of species that
has no ancestor in common only with them and thus no point
of origin in time only to them in the true course of
phylogeny. (2) (Characterization)- A
group based on symplesiomorphous similarities. Ashlock (1971) A group that does not
contain all of the descendants of the most recent common
ancestor. Nelson (1971) An incomplete sister-group
system lacking one species or one monophyletic species
group. Farris (1974) (1) A group that includes a
common ancestor and some but not all of its
descendants. (2) (Algorithm dfn.) - A
group with unique but reversed group membership
(1) A group of species that has no ancestor in common only with them and thus no point of origin in time only to them in the true course of phylogeny.
(2) (Characterization)- A group based on symplesiomorphous similarities.
A group that does not contain all of the descendants of the most recent common ancestor.
An incomplete sister-group system lacking one species or one monophyletic species group.
(1) A group that includes a common ancestor and some but not all of its descendants.
(2) (Algorithm dfn.) - A group with unique but reversed group membership characters.
Polyphyletic group: A grouping that does not include a most recent common ancestor; the most recent common ancestor is assigned to some other group and not to the group itself.
Hennig (1966) (1) (Inference) - A group in
which the ancestor is not included in the group. (2) (Characterization)- A
group based on convergent similarities (homoplasious
characters; non-homologous characters) Ashlock (1971) A group whose most recent
common ancestor is not a member of the group. Nelson (1971) An incomplete sister-group
system lacking two species or monophyletic species groups
that together do not form a single monophyletic
group. Farris (1974) (1) A group in which the
most recent common ancestor is assigned to some other group
and not to the group itself. (2) (Algorithm dfn.) - A
group whose membership characters are not uniquely
(1) (Inference) - A group in which the ancestor is not included in the group.
(2) (Characterization)- A group based on convergent similarities (homoplasious characters; non-homologous characters)
A group whose most recent common ancestor is not a member of the group.
An incomplete sister-group system lacking two species or monophyletic species groups that together do not form a single monophyletic group.
(1) A group in which the most recent common ancestor is assigned to some other group and not to the group itself.
(2) (Algorithm dfn.) - A group whose membership characters are not uniquely derived.
Farris' definitions - Paraphyly of Reptilia
Farris' definitions - Paraphyly of Reptilia