Algorithmic and Topological Body Plans

"Of all the perennial miracles [Nature] offers, ... perhaps the most worthy of admiration is the development of a plant or of an animal from its embryo."
Thomas H. Huxley, Aphorisms and Reflections (1907)

Plant and animal body plans follow different construction rules. Plants grow and mature (primarily) using algorithmic rules; animals grow and mature (primarily) using topological rules. Of course this is not an absolute rule: plants do some things in a roughly topological way, and animals have some algorithmic aspects to their growth (the placement of hair follicles to pick just one example).

Algorithmic Plant Growth An algorithmic body plan is rule-based with random variations superimposed. The prototype for an algorithmic plan is the "knit one, perl two" rule for knitting. The body plans for plants are typically algorithmic and result in the somewhat random appearance  (and yet with order) of tree branches, and leaf veins. It is not that they have no systematic plan, it is that the plan is algorithmic: put out a new branch in a random direction according to an established rule for that species. The result is roughly symmetric in the large but apparently haphazard in the small. Tree shapes and leaf shapes follow a general pattern that is species-dependent.

A typical plant body has roots, stems, branches, leaves and flowers, but growth of these structures tends to follow rules that appear to the eye to have a certain random appearance (see Figure 1). Different species use different rules to fill out the plants, but for a given species the growth follows certain rules with some random variation superimposed. The fine growth of leaf venation in Figure 1a, for example, is driven by the need to provide adequate "plumbing" to all productive parts of the leaf. The rules vary with the species, and mathematical algorithms can capture their essence -- see Figure 2.

Examples of Algorithmic Growth in Plants
Leaf Venation Tree Branching
Figure 1a
Leaf Venation
Figure 1b
Tree Branching
Note on 1b: The placement and orientation of tree branches is probably driven by a random algorithm that dictates average separation, access to light, gravitational balance, and general shape. A similar algorithm probably also controls the placement of major veins in Figure 1a.

Algorithms that emulate Leaf Growth and Tree Branching
Fractal leaf Fractal Tree
Figure 2a
Algorithmic Leaves  
Figure 2b
Algorithmic Tree and Root Branching

Topological Animal Growth. Topological body plans take account of cell location within the body. In effect, the body parts grow according to a 3-dimensional map, and distinguish body location: anterior/posterior (head/tail), left/right, and dorsal/ventral (front/back), Topological plans can result in left-right body symmetry or anti-symmetry,  body segmentation (head, thorax, etc.), organ placement, and other complex details that algorithmic plans cannot achieve.

Example of Topological Growth
Trilobite Anatomy
Figure 3
Trilobite Anatomy
Note: For the articulated trilobite legs see the Wiki article
on the Arthropod Leg.

Hox Genes. Perhaps the most remarkable discovery of recent years is that animal body plans are controlled by a set of genes called the homeobox (hox) genes, which are essentially the same across most animal kinds that have radial symmetry -- from insects to humans. These genes apparently were created as a prelude to all of the Bilateria -- all animals that have a head-tail, top-bottom, and left-right body plan. Almost all bilateria are triploblastic -- the bodies develop from three different tissues, called the endoderm, mesoderm, and ectoderm -- and have a through gut in which food enters a mouth and exits an anus. The rare exceptions to these characteristics are thought to be regressions (reductive changes) from the general plan rather than reflective of a different body plan0.

In recent decades, these Hox genes were independently discovered in many lines of research, and the true homology of the genes was obscured by a variety of ad-hoc names. Recently an effort has been made to use a naming convention that recognizes the unity of the underlying Hox gene organization.  The following table lists the 39 human hox genes using the new terminology, which are located in four chromosomes. Note that some hox genes are "missing" -- e.g. HOXA8 and HOXA12 -- which are present in some other (very distant!) species.

Humans contain 39 Hox genes in four clusters
cluster chromosome genes
HOXA chromosome 7 HOXA1, HOXA2, HOXA3, HOXA4, HOXA5, HOXA6, HOXA7, HOXA9, HOXA10, HOXA11, HOXA13
chromosome 17 HOXB1, HOXB2, HOXB3, HOXB4, HOXB5, HOXB6, HOXB7, HOXB8, HOXB9, HOXB13
HOXC chromosome 12 HOXC4, HOXC5, HOXC6, HOXC8, HOXC9, HOXC10, HOXC11, HOXC12, HOXC13
chromosome 2 HOXD1, HOXD3, HOXD4, HOXD8, HOXD9, HOXD10, HOXD11, HOXD12, HOXD13

These same genes, or close analogs to them are found in all mammals, and many are even found in insects (such as drosophilia, a genus of flies that is a favorite subject of genetic investigation) (see footnote 1).

These hox genes correlate closely with the head-tail body segmentation, and the position of the genes in the DNA reflects this anterior-posterior order (Figure 4).
The body plan first shows up in the animal blastula (a hollow sphere), which is entirely formed of undifferentiated stem cells. All animals (and only animals) pass through a blastula stage during their embryonic development [Margulis, p. 233]. From this stage on the stem cells immediately begin to differentiate based on position and orientation in the embryo, and locate the (future) head, legs, intestine, nerve system, etc1.

Hox Genes
Figure 4
Hox Gene Mapping
(Anterior to Posterior)
Favier & Dollé, Development Functions of mammalian Hox genes
Molecular Human Reproduction 3 #2 (1997)

There is extensive ongoing research into how the hox genes work in eye development, appendage development (antennae, jointed legs, etc.) and the development of color patterns. Apparently the development genes permits variation within closely defined limits. This variation is called phenotype plasticity. This variation is in addition to changes that result from radiation damage or various types of copying errors that may slip through the cell's error-checking machinery.  Apparently a mechanism exists to preserve some of these variations, so that it can (occasionally) be passed on to future generations -- perhaps within the non-coding portions of the dna.

Convergent Evolution and the Science of Evo-Devo
[Non?]Evolution in Gene Expression 1.1
"Much of what we have learned has been so stunning and unexpected that it has profoundly reshaped our picture of how evolution works. Not a single biologist ever anticipated that the same genes that control the making of an insect's body and organs also control the making of our bodies."
Sean B. Carroll (2005) [x]

"There are entire families, among the representatives of older periods, of nearly every class of animals, which, in the state of their perfect development exemplify such prophetic relations, and afford, within the limits of the animal kingdom, at least, the most unexpected evidence, that the plan of the whole creation had been maturely considered long before it was executed. Such types, I have for some time past, been in the habit of calling prophetic types. [emphasis added]."

Sharp Point          Origin of Body Plans: Hox genes

The puzzle of "Convergent Evolution" has been around since the beginnings of Evolutionary theory.  The puzzle is that  very similar features appear to have risen independently in widely diverse species. An example is the human eye (phylum Chordata) which is very similar to the octopus eye (phylum Mollusca). The answer, which is gradually emerging from the experimental science of evolutionary development, EvoDevo for short, is that the development of many if not all major organs and development structures is controlled by specifi, highly conserved gene packages that were created prior to the Cambrian explosion and which are essentially the same for huge swaths of animal types, perhaps for all of the radiata.

There is no explanation within the context of natural evolution as to how these packages arose in the first place, and why essentially the entire future development of animal life was anticipated in this early innovation.

From the viewpoint of EvoDevo, widely different morphologies occur by activating these development genes in different ways, not by creating new genes. Experiments which consist in manipulating the genetics to insert body parts in odd places has led to the identity of many of these gene packages.

Evo-Devo is the biology of evolutionary development, a branch of experimental biology that has come into being within the past few decades.

The remarkable fact that has been uncovered in evo-devo is that (virtually) the same small packages of genes, linked to specific body parts, occur across broad swaths of species. It is how these genes are expressed during regulation that determines the physical form of end product. Thus, (virtually) the same small package of "eye genes" underlies both the human's simple eye and a fly's compound eye -- the different end result comes about by how these genes are expressed.

Regulatory genes control the basic defining features of animal body shapes in particular (as distinguished from plants), through the homeobox (hox) genes. Such things as bilateral symmetry are controlled by these genes. It is gene regulation that results in the left side growing as the mirror-image (more or less) of the right side, even though the mirror image objects (human hands, for example) are physically separated as they grow. It is gene regulation that forms a fly's compound eye and a human's simple eye, and both grow in mirror-image pairs: the underlying genes are the same.

Is commonality "proof" of descent? Not for a creationist -- any more than the physical similarity of appendages, for example. The interesting issue is how gradual changes can be passed on to other generations? What is the mechanism? How much variability is built in, and how expressed? etc. The parameters of change are interesting1.2.

The question of where the packages came from in the first place? How are they made? They first appear in the fossil record suddenly and fully formed, in the Cambrian Explosion.

Body Plans.  Both plants and animals grow in a building-block fashion. The body plans involve algorithmic growth (typical of plants), modular construction, and the use of repeated parts with modification (typical of animals).

The remarkable insight of evo-devo is that behind the modules and repeated parts are small packages of genes that are essentially the same for all animals that have the corresponding body part. For example, virtually all animals that have eyes, whether simple or compound, have the same small package of eye genes; all animals that have jointed appendages (legs, antennae, etc.) have the same small package of appendage genes, and so on for other sensor systems: for nerves, muscles, digestive and circulatory systems, etc. The well-known homologous systems (Figure 4) have at root a shared gene package: the differences between the species are not so much the result of new genes, but of how those genes are expressed.

This observation has radically changed the former understanding of Convergent Evolution.

Gegenbaur 1870 hand_homology
Figure 4
Homologies to the Hand
Different expressions of the same gene package.

Forelimb Homology
Figure 5
Forelimb homology
Different expressions of the same gene package.
Wilhelm Leche (1850-1927)

Evo-devo concerns not the creation of new genes, but of new ways to express a highly conserved set of genes. The question of how the genes got there in the first place is thus separate from the question of how the gene expression changed over time, just as the question of how life first arose is separate from the question of how life evolved.

The essential features of evo-devo -- the "simple rules that shape animal form and evolution?" are:

(1) Each specialized animal body structure and system is developed from a small and highly conserved gene package. The differing morphologies are determined by gene expression controlled through the homeobox development genes.

(2) The gene package for a body structure
anticipates a broad range of end morphologies.

(3) The development genes include a built-in ability to vary  the gene expression within  certain limits;

(4) There is some mechanism to pass on variations in gene expression to succeeding generations -- in part this is through Mendelian genetics, but it is also through expression gene parameters that are preserved in the genetic information (DNA and the "cloud" of accompanying information).

The net effect of Evo-Devo is to replace the concept of convergent evolution (repeated appearance of the same organ in widely different species) with the concept of a common ancestral package of homeobox genes01.03. As one scientist expressed it, "Long before animals with limbs (tetrapods) came onto the scene about 365 million years ago, fish already possessed the genes associated with helping to grow hands and feet."01.04

"We must suppose that when the Author of Nature creates an animal or plant, all the possible circumstances in which its descendants are destined to live are foreseen, and that an organization is conferred upon it which will enable the species to perpetuate itself and survive under all the varying circumstances to which it must be inevitably exposed."
Lyell, Principles of Geology (1850)
Ch. 35: Transmutation of Species, p. 560

The Bottom Line

• Animal species across many phyla use the same gene packages to code for eyes, appendages, and other body parts and systems, even though the appearance of those body parts in the adult may be radically different. The different end products are determined by development rules -- how, when and where genes are turned on and off -- not by the genes themselves. Homologous body parts arise because of the use of similar genes.

• The development (homeobox or hox) genes that control gene expression, are likewise essentially the same across many animal phyla.

• The identification of the gene packages and hox genes is unequivocal, and has been determined by extensive laboratory experimentation and DNA sequencing.
- To a natural evolutionist, these common gene packages prove descent from a common ancestor.
- To a creationist, they are the expected result of a common creator who re-uses the genetic material.

The origin of the hox genes and the gene packages is unknown to science, although the first sudden appearance of the body parts in the Cambrian era (about 540 Ma) is well attested -- trilobites, for example, had all of them -- and so the existence of the gene packages and the hox genes at that time can be inferred by analogy to modern species. Information that determines exactly how a given species expresses the gene packages is located in portions of the DNA that do not code for genes. Additional information may reside with the accompanying molecules that are present in the fertilized egg when development begins.

Sir Charles Lyell (1797–1875) on Evo-Devo

... Of course the science was unknown in his day, but the following observation fits right into the theory (and capsulizes my principle objection to evolution as it is usually presented.

"Lamarck enters upon the following line of argument: The more we advance in the knowledge of the different organized bodies which cover the surface of the globe, the more our embarrassment increases, to determine what ought to be regarded as a species, and still more how to limit and distinguish genera. ... The greater the abundance of natural objects assembled together, the more do we discover proofs that every thing passes by insensible shades into something else.I must here interrupt the author's argument, by observing, that no positive fact is cited to exemplify the substitution of some entirely new sense, faculty, or organ, in the room of some other suppressed as useless. All the instances adduced go only to prove that the dimensions and strength of members and the perfection of certain attributes may, in a long succession of generations, be lessened and enfeebled by disuse; or, on the contrary, be matured and augmented by active exertion. It was necessary to point out to the reader this important chasm in the chain of evidence, because he might otherwise imagine that I had merely omitted the illustrations for the sake of brevity; but the plain truth is, that there were no examples to be found; and when Lamarck talks "of the efforts of internal sentiment," "the influence of subtle fluids," and "acts of organization," as causes whereby animals and plants may acquire new organs, he substitutes names for things; and, with a disregard to the strict rules of induction, resorts to fictions, as ideal as the "plastic virtue," and other phantoms of the geologists of the middle ages. It is evident that, if some well-authenticated facts could have been adduced to establish one complete step in the process of transformation, such as the appearance, in individuals descending from a common stock, of a sense or organ entirely new, and a complete disappearance of some other enjoyed by their progenitors, time alone might then be supposed sufficient to bring about any amount of metamorphosis. The gratuitous assumption, therefore, of a point so vital to the theory of transmutation, was unpardonable on the part of its advocate."
Lyell, Principles of Geology (1850)
Ch. 35: Transmutation of Species, p. 546

"No facts of transmutation authenticated" -- ibid., p. 556.

Lyell's point, translated into modern terms, is even more powerful: that the only evolution that is observed in the fossil record can be expressed in terms of evolutionary development.  "Substitutions of a new sense, faculty or organ" simply does not occur. Evo-devo may produce remarkable divergences, but they develop from a common, conserved package of genes. Totally new gene packages represent a quite different and higher level of achievement, and (arguably) simply do not arise.


^n0 See

1 Wikipedia:  "a prototypic Hox gene cluster containing at least seven different Hox genes was present in the common ancestor of all bilaterian animals." The names used for the hox genes has been changing in recent years, as the closeness of the genes across the animal phyla are recognized. For example the Eyeless gene is now called Pax6.


The hox genes attach to the DNA and control gene expression by turning on and off the expression of specific genes. It seems likely that the parameters for this gene expression are stored in non-coding portions of the dna. All hox genes are headed by a dna marker of 183 base pairs called the homeobox and the corresponding 61 amino acid section of the hox proteins (which forms two spirals that attach to the dna) is called the homeodomain. This uniquely identifies all hox genes, and is essentially the same over a large swath of animal phyla "from fruitflies to man." Hox genes across the animal species forms the subject matter of evolutionary developmental biology (evo-devo).

1.1 The material in this box is inspired by the book by Sean B. Carroll, Endless Forms Most Beautiful: The New Science of Evo Devo, W.W. Norton (2005). Citations in brackets are to pages in this book. See also the box and note on Reductive Evolution.

1.2 At one time, the offical Soviet dogma included "Lysenkoism" -- the inheritance of acquired characteristics (such as lopped-off tails?). "A school of pseudoscience that flourished in the Soviet Union from the early 1930s to the mid-1960s, in violent opposition to traditional biology." (

^n01.03  Pax Genes  -- evolutionary conservation of Pax gene family. Pax genes are developmental control genes that encode transcription factors.  --  "Anatomically widely different designs of animal eyes have long been thought to arise independently multiple times during evolution. This view has been challenged about a decade ago by the landmark discoveries that a highly conserved transcription factor Pax6 plays a key role in eye morphogenesis both in flies and mammals. Since then, more evidence has emerged for redeployment of Pax6 and some other developmental control genes in the genetic programme underlying eye formation throughout the animal kingdom. ...The origin of Pax genes predates the origin of eyes or even nervous system. The ancestral Pax gene (PaxB) related to Pax2/5/8 was identified in the sponge that has neither eyes nor the nervous system. Cnidaria are the most basal animals that posses either simple or complex (lens containing) eyes as well as Pax genes. PaxB gene in a cnidarian Tripedalia is expressed in lens and retina and is able to activate both lens crystallin as well as opsin reporter genes (Kozmik, 2003). The data indicate that modern Pax2 and Pax6 genes evolved from a cnidarian PaxB ancestor by duplication and diversification in Bilateria."

Pichaud and Desplan, Pax Genes and Eye Organogenesis (2002): "Until the realization that Pax6 was involved in the development of very divergent types of eyes, it was widely accepted that various eyes represented examples of convergent evolution. Such convergence reflects the critical advantage of being able to perceive the environment as soon as the sophistication of the nervous system allowed the interpretation of images (i.e. after the split between major branches). Therefore, eyes are thought to have arisen independently ~40–60 times through evolution"

Pax genes and eye organogenesis "Pax6 is a highly conserved gene that controls eye development in all species where it has been tested. ...Until the realization that Pax6 was involved in the development of very divergent types of eyes, it was widely accepted that various eyes represented examples of convergent evolution.  Was Pax6 already present very early on in a primitive species where it was involved in the development of a photosensitive organ (‘proto-eye’), before functional image-forming eyes first appeared (a form of pre-adaptation)? Or instead, are we missing a critical early link when Pax6 first appeared, a real ancestor ‘eye’ from which all eyes evolved—that is, an organ with photoreceptors, pigment cells and the ability to focus light to form images or to detect motion?"

"Pax-6 is so important that it’s largely the same in very distantly related animals (the technical term is ‘conserved’). You can take the version of Pax-6 from a mouse and shove it into a fly, and it will still be able to trigger the development of an eye. Even though these misplaced eyes have been activated by a mouse gene, they have the compound structure of typical fly eyes. This underlies the role of Pax-6 as a conductor – its job is to coordinate an orchestra of other eye-producing genes." --  Discover Magazine (July 27, 2010), Jellyfish eye genes suggest a common origin for animal eyes. Note: The Pax6 gene in humans has 422 amino acids and resides on Chromosome 11.

Kimball Biology Pages:
  "Despite their structural differences, both insect and vertebrate eyes depend on related genes for their development."

^n01.04  New Genetic Data Overturn Long-Held Theory Of Limb Development., (5/27/2007). A similar statement is made by Grenier et al, Evolution of arthropod Hox genes Current Biology (1997)  "Conclusions: A complete arthropod Hox gene family existed in the ancestor of the onychophoran/arthropod clade. No new Hox genes were therefore required to catalyze the arthropod radiation; instead, arthropod body-plan diversity arose through changes in the regulation of Hox genes and their downstream targets."

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