An Abundance of Forams and a Few Thoughts on D'Arcy Thompson

The sand my wife brought back from St Andrews, Scotland, in a small vial was filled to abundance with foraminifera (those tiny, single-celled protists, many of which secrete graceful calcium carbonate shells).  The hook for me was the nexus of forams and St Andrews because it was at the University of St Andrews that the biologist and classical scholar D’Arcy Wentworth Thompson (1860 – 1948) taught for over 30 years, and where he wrote the second edition of his magnum opus, On Growth and Form (the first edition was published in 1917).

In this hefty tome, Thompson espoused the singular importance of physical laws (those of engineering and physics) and mathematical principles in the shaping of organic morphology, laws and principles which in his view largely trumped evolution through natural selection.  A centerpiece for his argument was the minute foraminifera, and it’s not hard to see why.  The shapes of many foraminifera shells shout quite loudly “mathematics” and these shells have been used by Thompson and others to illustrate how mathematical spirals are found in nature, evidence, he would argue, of the preeminence of those governing forces.  Thompson wrote:

It is obvious enough that the spiral shells of the Foraminifera closely resemble true logarithmic spirals.  Indeed so precisely do the minute shells of many Foraminifera repeat or simulate the spiral shells of Nautilus [the quintessential exemplar of a logarithmic spiral in nature] and its allies that to the naturalists of the early nineteenth century they were known as Céphalopodes microscopiques [microscopic cephalopods], . . . .  (On Growth and Form, 1917 edition, p. 591)

To get some flavor of how Thompson shaped his argument with these microscopic shells, here is part of the opening paragraph of Chapter XII:  The Spiral Shells of the Foraminifera:

We have already dealt in a few simple cases with the shells of the Foraminifera; and we have seen that wherever the shell is but a single unit or single chamber, its form may be explained in general by the laws of surface tension: the assumption being that the little mass of protoplasm which makes the simple shell behaves as a fluid drop, the form of which is perpetuated when the protoplasm acquires its solid covering. . . .  When the foraminiferal shell becomes multilocular [having more than one chamber], the same general principles continue to hold; the growing protoplasm increases drop by drop, and each successive drop has its particular phenomena of surface energy, manifested at its fluid surface, and tending to confer upon it a certain place in the system and a certain shape of its own. (p. 587)

Indeed, as evolutionary biologist Stephen Jay Gould observed in a lengthy and devastatingly critical dissection of On Growth and Form, it’s at this microscopic level, the level of the foraminifera, that Thompson’s contention that physical laws are paramount in creating the shapes of living creatures may have its greatest (though certainly not complete) validity.

D’Arcy Thompson continued to maintain – and he may well have been right in some cases – that good matches between simple organic conformations (primarily the outward forms of unicellular creatures) and geometric shapes of well know mathematical definition and easily accomplished mechanical construction probably illustrate his favored principle of direct imposition by physical forces.  But he had to admit that he could not apply this line of reasoning to the basic form of a horse or a tuna.  (The Structure of Evolutionary Theory, 2002, p. 1197)

Frankly, I come away from On Growth and Form wondering whether its message for me is a truism:  evolution through natural selection cannot fashion a living shape that defies the basic laws of physics and certain mathematical principles.  In other words, there are some givens that have to be accounted for.  Science writer Philip Ball puts a positive spin on this, noting that Thompson was arguing against the propensity at the time for Darwinians to posit that every feature of an organism was an example of adaptation.  “Thompson’s insistence that biological form had to make sense in engineering terms was a necessary reminder.”  (In Retrospect:  On Growth and Form, Nature, February 2013.)

I would acknowledge that Ball seems to call me out in his article when he notes that “On Growth and Form is a book more often name-checked than read.”  Yes, I admit I’ve only dipped into it, enjoying some of its literary flourishes (which admittedly can go over the top) and appreciating some aspects of his argument, but never aspiring to read it cover to cover (the 1942 edition is over 1,000 pages long).

Ball rightly identifies the logarithmic spiral as the “central motif” of the book (which he notes “appears on the plaque commemorating Thompson’s former residence in St Andrews”).  Here is a representation of the logarithmic spiral.

(This image is in the public domain and was downloaded from Wikimedia Commons [].)

Earlier this year, my wife during her stay in Thompson’s city climbed down some steps to the shoreline of St Andrews Bay at low tide and scraped some sand into a vial.  She came away with a rich mixture of quartz, mica, bits of mollusc shell, fragments of ostracode tests, broken sponge spicules, and a wealth of foraminifera shells.  [Later edit:  I should note that I assume all of the foram shells in my sample of St Andrews sand are from organisms that recently died (hopefully not in the vial of sand as it was transported back to the States).  So, if I'm correct, they are not fossils.]

 Here’s the same image of this smidgeon of St Andrews sand with some of the prominent forams marked.

The most abundant species in this sand are from at least two genera:  Elphidium and Ammonia, shown below in that order.

For these identifications I have relied on the very nice taxonomic appendix in Quantifying Holocene Sea Level Change Using Intertidal Foraminifera:  Lessons from the British Isles by Benjamin P. Horton and Robin J. Edwards (University of Pennsylvania Scholarly Commons, 5-1-2006; originally published as Cushman Foundation for Foraminiferal Research, Special Publication, Volume 40, 2006).

I’ll close by suggesting that in the following passage from On Growth and Form is a hint that foraminifera held some intimate, personal significance for Thompson (or perhaps he was simply waxing eloquent as was his want):

But in days gone by I used to see the beach of a little Connemara bay bestrewn with millions upon millions of foraminiferal shells, simple Lagenae, less simple Nodosariae, more complex Rotaliae: all drifted by wave and gentle current from their sea-cradle to their sandy grave: all lying bleached and dead: one more delicate than another, but all (or vast multitudes of them) perfect and unbroken.  (p. 609)