Dedicated to all Zoologists

2. HIGHER TAXAAND HIGHER CATEGORY
BY
SHAHID NAWAZ
SUBMITTED TO : DR. RAFIQ HUSSAIN
DEPARTMENT OF ZOOLOGY
KOHAT UNIVERSITY OF SCIENCE AND TECHNOLOGY, KOHAT-26000 KHYBER PAKHTUNKHWA,
PAKISTAN

3. Higher taxa
A higher taxon can be defined as a set of species forming a cluster in multidimensional
morphospace separated from other such clusters by relatively large distances. Alternatively,
an ecological concept of a higher taxon is that it consists of a set of species occupying the
same upland region in an adaptive landscape. Higher taxa tend to appear earlier and lower
taxa later; the rate of morphological evolution of a lineage tends to decline with time;
marine higher taxa tend to originate in an onshore setting, lower taxa in an offshore setting.
Several different explanations are offered for these rules, none completely convincing. The
conclusion is that higher taxa are natural entities in the sense that they are discontinuous
with one another due to morphological divergence plus the extinction of ancestral stages. It
follows that the causes of their origin are a valid matter for scientific enquiry.

4. The origins of higher taxa have been an important focus of paleontologists
and others concerned with macroevolutionary patterns since the work of
George Gaylord Simpson, although interest in the topic can be traced to
Darwin. Many evolutionary biologists, including Darwin, have argued that
large morphological gaps between groups of organisms simply reflect the
extinction of intermediates—with a more adequate record than fossils usually
provide, we could trace the progression from one major group to the next.
Others have disputed this view, arguing that the morphological gaps
recognized as higher taxa by Linnean systematists are a primary evolutionary
pattern.

5. Two distinct challenges to the research program on the origin of
higher taxa have been raised over the past few decades. First, the
spread of phylogenetic systematics has placed greater emphasis on
the identification of monophyletic groups, and downplayed the
importance of morphological disparity as a criterion for Linnean
ranks. Indeed, the utility of higher taxa has been called into
question except as a convenient shorthand for denoting various
clades of organisms. Quantitative approaches to disparity ( Erwin
2007 ) have obviated the need to conflate evolutionary topology
and morphological evolution.

6. The second challenge arises from comparative evolutionary
developmental biology, or “evo-devo” ( Carroll 2008 ). This
increasingly provides a mechanistic developmental basis for
understanding the sources of morphological novelty, and has led to
increased emphasis on novelty, rather than higher taxa, as an
important research problem ( Wagner 2014 ).

7. In his new book The Origin of Higher Taxa , Tom Kemp, emeritus university lecturer in
palaeontology at the University of Oxford and a noted authority on therapsids (sometimes
known as mammal-like reptiles), provides an insightful and articulate defense of the
importance of higher taxa as an evolutionary problem, and expands upon his theory of
correlated progression ( Kemp 2007 ) as the responsible mechanism. In the sciences, a
phenomenon must be real to be studied (well, it helps anyway, except perhaps in physics),
and Kemp's defense of higher taxa as real ontological entities is based on the idea that
extinction separates evolutionary lineages into discrete morphological groups. The clumpy
nature of morphologies is indeed one of the major challenges for evolutionary biology (
Lewontin 2003 ), but extinction of putative intermediates is not the only explanation for
such a pattern, nor does it necessarily establish higher taxa as an appropriate research topic.

8. The critical issue for Kemp's model is the extent of structural, functional, and
developmental linkages within organisms. The correlated progression model relies
upon linkages across an organism being sufficient to require that morphologic
evolution via small changes in single characters will generate a stately march through
morphospace to a form that will eventually (following extinction of intermediates) be
recognized as a new higher taxon. Kemp rejects arguments for modular integration as a
means of allowing different components of an organism to evolve semi-independently.
Thus, to Kemp the primary challenge for understanding morphological novelty is
extablishing how functional integration among these different components is
maintained during the pervasive changes in development and morphology. Discussion
of the correlated progression model and how it differs from atomistic and modular
analyses of characters comprises Chapter 3 of the book.

9. Higher category
In mathematics, higher category theory is the part of category
theory at a higher order, which means that some equalities are
replaced by explicit arrows in order to be able to explicitly study
the structure behind those equalities. Higher category theory is
often applied in algebraic topology (especially in homotopy
theory), where one studies algebraic invariants of spaces, such as
their fundamental weak ∞-groupoid .

10. Strict higher categories
An ordinary category has objects and morphisms. A
2-category generalizes this by also including 2-
morphisms between the 1morphisms. Continuing
this up to n-morphisms between (n-1)morphisms
gives an n-category .

11. Just as the category known as Cat, which is the category of small
categories and functors is actually a 2-category with natural
transformations as its 2-morphisms, the category n-Cat of (small)
n-categories is actually an ( n+1)-category .
An n-category is defined by induction on n by:
A 0-category is a set, An (n+1)-category is a category enriched
over the category n-Cat. So a 1-category is just a (locally small)
category .

12. The monoidal structure of Set is the one given by the cartesian product as
tensor and a singleton as unit. In fact any category with finite products can be
given a monoidal structure. The recursive construction of n-Cat works fine
because if a category C has finite products, the category of C-enriched
categories has finite products too.
While this concept is too strict for some purposes in for example, homotopy
theory, where "weak" structures arise in the form of higher categories, strict
cubical higher homotopy groupoids have also arisen as giving a new
foundation for algebraic topology on the border between homology and
homotopy theory; see the book "Nonabelian algebraic topology" referenced
below.

13. Weak higher categories
In weak n-categories, the associativity and identity conditions are no longer strict (that is,
they are not given by equalities), but rather are satisfied up to an isomorphism of the next
level. An example in topology is the composition of paths, where the identity and ssociation
conditions hold only up to reparameterization, and hence up to homotopy, which is the 2-
isomorphism for this 2-category . These n-isomorphisms must well behave between hom-
sets and expressing this is the difficulty in the definition of weak n-categories. Weak 2-
categories, also called bicategories, were the first to be defined explicitly. A particularity of
these is that a bicategory with one object is exactly a monoidal category, so that bicategories
can be said to be "monoidal categories with many objects." Weak 3categories, also called
tricategories, and higher-level generalizations are increasingly harder to define explicitly.
Several definitions have been given, and telling when they are equivalent, and in what sense,
has become a new object of study in category theory.

14. Quasi-categories
Weak Kan complexes, or quasi-categories, are simplicial sets satisfying a
weak version of the Kan condition. André Joyal showed that they are a good
foundation for higher category theory. Recently, in 2009, the theory has been
systematized further by Jacob Lurie who simply calls them infinity
categories, though the latter term is also a generic term for all models of
(infinity ,k) categories for any k.