Patterns

A couple of weeks ago, I offhandedly added a small brachiopod specimen to my fossil collection, picking it up as a raffle prize at a fossil club meeting.  The tag associated with it gave its scientific name as well as the location where it was found – Eichwaldia reticulata; Silurian brachiopod; Waldron Formation; Flat Rock, Indiana.  (The Silurian Period was from 444 to 416 million years ago.)  Frankly, I often don’t accept at face value the labels that other collectors apply to such fossils and so I typically end up doing some research on them.  In this instance, as is frequently the case, the impulse was the right one; the tag was wrong as to genus name.  Since 1994, it’s been Eodictyonella, and wasn’t Eichwaldia after the late 1890s when Dictyonella was generally accepted.  (Anthony D. Wright, Eodictyonella, a New Name for Dictyonella Hall, 1868, Not Dictyonella Schmidt, 1868, Journal of Paleontology, July 1994)

Brachiopods in general have seen much better days.  The few extant species of these marine organisms are the remnants of a vast array of species that widely populated the oceans until the mass extinction at the end of the Permian (251 million years ago).  Though they look like mollusks with two valves, they are not, constituting their own phylum.  Brachiopods were once so abundant that it’s common to find slabs of shale imprinted with shells in such huge numbers that the distinctive symmetrical patterns of individual shells are superimposed one upon another in a riotous array.  The picture below shows such a spread of fossils from the Devonian (416 to 359 million years ago) in a chunk of shale found on a mountain roadcut in West Virginia.

After unpacking the mystery of the name of this little Silurian fossil (a cast, I believe, of the exterior of both valves), the next step was to put it into a drawer with a label and be done with it.  The picture below shows the fossil along side a penny for scale; the brachiopod is ½ inch in length.  Not much to look at.

But fossils almost invariably reward a closer look.  Prompted by descriptions in the literature on Eodictyonella, I took a jeweler’s loupe to the fossil and discovered the marvelous exterior ornamentation that species in this genus exhibit.  Macro photographs of both sides of the fossil show these patterns.

I found the fossil’s geometric array of intersecting arcs, clearly evident despite the wear and tear of over 400 million years, spellbinding.  The arcs appear to originate on either side of where the two valves come together in a point, the brachiopod’s beak or umbo.  The cells in the grid pattern appear to expand and contract depending upon the contour of the surface of the brachiopod, particularly as edges are reached.

The grid cells or pits in the network pattern on the Eodictyonella brachiopod contain one or more small openings or puncta which, according to Anthony Wright, connect to pores that open on the inner shell surface.  Wright cites research suggesting that the pits in the shells may have been part of a defensive network against predators seeking to drill through the shells.  Each of the openings in the shell may have contained organic caeca or sacks which held some form of organic material which, based on evidence from extant brachiopods, may “be beneficial in that punctate shells are less bored by predators, suggesting that caecal secretion inhibited penetration . . . .”  (Anthony D. Wright, The External Surface of Dictyonella and of Other Pitted Brachiopods, Paleontology, Volume 24, Part 3, 1981, p. 475)

The network pattern on the Eodictyonella is startlingly familiar, reminiscent of what one sees in the double spiral patterns of plant leaf or floret arrangements (phyllotaxis) such as in the picture below of the head of a sunflower (Helianthus).  The two systems of spiral arcs flow in opposite directions.

I’ve always felt that these double spiral patterns in plants offer a glimpse into a profound, underlying natural order.  When the leaves or florets in phyllotaxis patterns are numbered from youngest to oldest and displayed on a two-dimensional surface, adjacent leaves or florets along each of the systems of arcs have the same numerical relationship to one another (e.g., along one arc, leaf or floret numbers may differ by five, and by eight along an arc flowing in the opposite direction).  For each plant species, its pair of phyllotaxis numbers (for the two systems of swirls) has been found to be adjacent pairs in the Fibonacci sequence, that sequence of numbers in which the last entry is the sum of the two previous entries (0, 1, 1, 2, 3, 5, 8, 13, 21, . . . .).  The sequence was first laid out in the 13th century by Italian mathematician Leonardo of Pisa.  The connection to the Fibonacci sequence isn’t some mathematical magic, some mystery.  Rather, as science writer Philip Ball explains, the connection flows naturally because this arrangement provides for the most efficient packing together of leaves or florets.  (Ball, The Self-Made Tapestry:  Pattern Formation in Nature, 1999, p. 106 – 107)  Do I understand why this is so?  To be honest, not yet.  So, maybe it does remain a bit mysterious to me.

Although something similar may not be playing out in all of the external ornamentation of Eodictyonella, partly because the surface over which the pattern appears differs markedly from those involving plant leaves or florets, in certain areas the impulse may be the same.  Wright describes the pattern as an “apparently complex network of variably rhombohedral to hexagonal pits” arising from “simple radial growth modified by the inevitable geometrical results of closer packing of the pits,” as well as changes in the pace at which shell material is deposited along the growing edge of the shell and waves in the growing edge.  (p. 475, emphasis added)

In The Self-Made Tapestry, Ball argues that evolution cannot contravene certain fundamental forces, physical or chemical, as it shapes life.  As a consequence, he posits, similar forms and patterns may repeatedly appear in living organisms, as well as elsewhere in nature.  I wonder if the similarity between the phyllotaxis patterns and those appearing on the Eodictyonella may reflect such a constraint.  Ball writes,

 There are . . . forces guiding appearances that run deeper than those that govern life.  (p. 4)

Source of Photographs

All of these photographs are mine except for the one of the sunflower.  That photograph is by L. Shyamal and is reproduced here under the Creative Commons Attribution-Share Alike 2.5 Generic License.  It is found at Wikimedia Commons.