Names on Nodes: Phylogenetic Query Script (Rough Draft)

T. Michael Keesey

P.O. Box 292304 Los Angeles, CA, USA 90027; keesey@gmail.com

Abstract

The MathML Definitions document shows how MathML may be used to model phylogenetic hypotheses and phylogenetic definitions. Since MathML is verbose, it may be preferable in some instance to have a more succinct scripting language with the same functionality. I have created a plain text version of the mathematical markup specified by the MathML Definitions document.

Operators and Identifiers

Category Description Formula Notes
General equality 
entity1 = entity2
 It may be desirable to use == instead (as in C and many other computer languages).
inequality 
entity1 != entity2
 Also used for exclusive disjunction ("xor"). This operator is borrowed from C.
clause 
(entity)
conditional statement 
proposition ? entity1 : entity2
 Evaluates to entity1 if proposition is true, or entity2 if proposition is false. This operator is borrowed from C.
Constants constant name 
"name"
 Internal quotes may be "escaped", e.g., "\"Iguanodon\" hoggi". Possibly single quotes (') should be allowed as well, or no quotes for names without whitespace.
declaration 
"name" := entity.
integer 
digits
 Base 10. Non-integers and negative numbers are not required, so no method is provided for denoting them.
Set Theory extensional set 
{entity1, entity2 …}
empty set 
{}
union 
set1 | set2 …
 The character ∪ would be preferable, but it is not an ASCII character.
intersection 
set1 & set2 …
 The character ∩ would be preferable, but it is not an ASCII character.
difference 
set1 - set2
 Some mathematical texts use "\", so this may be preferable.
set membership 
entity in set
 The character ∈ would be preferable, but it is not an ASCII character.
subset 
set1 <= set2
 The character ⊆ would be preferable, but it is not an ASCII character.
proper subset 
set1 < set2
 The character ⊂ (or ⊊) would be preferable, but it is not an ASCII character.
superset 
set1 >= set2
 The character ⊇ would be preferable, but it is not an ASCII character.
proper superset 
set1 > set2
 The character ⊃ (or ⊋) would be preferable, but it is not an ASCII character.
Ordered Lists extensional list 
[entity1, entity 2 …]
list element selector 
list_index
 This notation is somewhat unusual. Other languages use brackets (list[index]), but using underscores allows a clearer distinction between element selection and extensional declaration (previous item), and relate better to common mathematical notation (which uses subscripts).
Boolean Logic true 
true
false 
false
negation 
!proposition
 This operator is borrowed from C. The character ¬ would be preferable, but it is not an ASCII character. (Possibly not should be used or allowed?)
conjunction 
proposition1 && proposition2
 This operator is borrowed from C. The character ∧ would be preferable, but it is not an ASCII character. (Possibly and should be used or allowed?)
disjunction (inclusive) 
proposition1 || proposition2
 This operator is borrowed from C. The character ∨ would be preferable, but it is not an ASCII character. (Possibly and should be used or allowed?)
Functions application 
function(entity1, entity2 …)
composition 
function1 * function2
 This is an unorthodox usage of this character. The character ∘ would be preferable, but it is not an ASCII character.
Phylogeny phylogenetic graph 
P
universal taxon 
U
maximal members 
max(set)
minimal members 
min(set)
predecessor union 
prc|(set)
predecessor intersection 
prc&(set)
successor union 
suc|(set)
successor intersection 
suc&(set)
exclusive predecessors 
set1 <- set2
 set1 is the internal set; set2 is the external set.
synapomorphic predecessors 
set1 @ set2
 set1 is the apomorphic set; set2 is the representative set.
clade 
clade(set)
 If the minimal members of set1 form a cladogen (a clade ancestor), then this is equivalent to suc|(set). Otherwise, it is equivalent to (suc| * max * prc&)(set).
node-based clade 
clade(set1 | set2 …)
or 
(suc| * max * prc&)(set1 | set2 …)
branch-based clade 
clade(set1 <- set2)
or 
suc|(set1 <- set2)
 set1 is the internal set; set2 is the external set.
apomorphy-based clade 
clade(set1 @ set2)
or 
suc|(set1 @ set2)
 set1 is the apomorphic set; set2 is the representative set.
crown clade 
crown(set1, set2)
 set1 is the bounding set; set2 is the set of extant organisms.
total clade 
total(set1, set2)
 set1 is the internal set; set2 is the set of extant organisms.

Examples

Formula Prose or Diagram Notes 
P :=
[
	{
		"Aves*", 
		"Palaeognathae*",
		"Struthio camelus",
		"Tetrao major",
		"Vultur gryphus"
	},
	{
		["Aves*", "Vultur gryphus"],
		["Aves*", "Palaeognathae*"],
		["Palaeognathae*", "Struthio camelus"],
		["Palaeognathae*", "Tetrao major"]
	}
].
  • Aves
    • Vultur gryphus
    • Palaeognathae
      • Struthio camelus
      • Tetrao major
 This defines a simple phylogenetic context (a directed, acyclic graph where vertices are taxonomic units and arcs represent immediate descent). 
"Tinamus major" := "Tetrao major".
 Tinamus major is Tetrao major. These are objective synonyms under the zoological code. 
"Aves" := clade("Struthio camelus" | "Tetrao major"
                | "Vultur gryphus").
 Aves is all successors of the maximal common predecessors of Struthio camelus, Tetrao major, and Vultur gryphus. 
"Saurischia" := clade("Megalosaurus bucklandii"
                <- "Iguanodon bernissartensis").
 Saurischia is all successors of the (common) predecessors of Megalosaurus bucklandii exclusive of all predecessors of Iguanodon bernissartensis. 
"Avialae" := clade("wings used for powered flight"
                   @ "Vultur gryphus").
 Avialae is all successors of the predecessors of Vultur gryphus to share wings used for powered flight synapomorphically with Vultur gryphus. 
"Aves" = crown("Avialae", "extant")
       = crown("Saurischia", "extant")
 Aves is equivalent to the avialan crown clade and the saurischian crown clade. 
"Pan-Aves" := total("Aves", "extant").
 Pan-Aves is the avian total clade. 
"Avemetatarsalia" := clade("Aves" <- 
                     "Crocodylus niloticus").
 Avemetatarsalia is all successors of the (common) predecessors of Aves exclusive of all predecessors of Crocodylus niloticus. 
"Pan-Aves" = "Avemetatarsalia"
 Pan-Aves is equivalent to Avemetatarsalia. 
"Ichthyornithes" := clade("YPM-VP 1450" 
                 <- "Struthio camelus"
                    | "Tetrao major"
                    | "Vultur gryphus").
 Ichthyornithes is all successors of the (common) predecessors of the organism represented by YPM-VP 1450 exclusive of all predecessors of Struthio camelus, Tetrao major, and/or Vultur gryphus. YPM-VP 1450 is the Ichthyornis dispar holotype specimen. 
"Ichthyornis" := clade("Ichthyornithes"
                 & ("apomorphy 2"
                    | "apomorphy 5"
                    | "apomorphy 6"
                    | "apomorphy 7" 
                    | "apomorphy 8" 
                    @ "YPM-VP 1450")).
 Ichthyornis is all successors of all ichthyornithean predecessors of the organism represented by YPM-VP 1450 to share apomorphies 2, 5, 6, 7, and 8 synapomorphically with the organism represented by YPM-VP 1450. The numbers refer to apomorphies described by Clarke (2004). 
"Pan-Biota" :=
(clade * prc&)("Homo sapiens").
 Pan-Biota is all successors of all (common) predecessors of Homo sapiens. 
"Biota" := crown("Pan-Biota", "extant").
 Biota is all successors of the maximal common predecessors of all extant members of Pan-Biota. 
"S" := "Otaria byronia" | "Odobenus rosmarus"
       | "Phoca vitulina".
"Pinnipedia" :=
             (max * prc&)("S") <= ("flippers" @ "S")
             ? clade("S") : {}.
 If the maximal common predecessors of the specifiers (Otaria byronia, Odobenus rosmarus, and Phoca vitulina) possessed flippers synapomorphic with those of the specifiers, then Pinnipedia is all successors of the maximal common predecessors of the specifiers. Otherwise, Pinnipedia is empty.