Friday, 15 August 2014

Unintelligently Designed Fractal Ediacarans

A paper published recently in PNAS, showing how the earliest forms of multicellular life probably evolved and diversified according to a few simple mathematical rules, raises an important question for creationists which we can confidently expect them to ignore completely.

This early evolution occurred at a time when there would have been little or no cell specialisation and, perhaps more importantly, when there would have been no predators and the only competition would have been for limited resources in terms of dissolved nutrients. Quite simply, the organism which absorbed more nutrients would have produced more copies of itself.


Rangeomorph fronds characterize the late Ediacaran Period (575–541 Ma), representing some of the earliest large organisms. As such, they offer key insights into the early evolution of multicellular eukaryotes. However, their extraordinary branching morphology differs from all other organisms and has proved highly enigmatic. Here we provide a unified mathematical model of rangeomorph branching, allowing us to reconstruct 3D morphologies of 11 taxa and measure their functional properties. This reveals an adaptive radiation of fractal morphologies which maximized body surface area, consistent with diffusive nutrient uptake (osmotrophy). Rangeomorphs were adaptively optimal for the low-competition, high-nutrient conditions of Ediacaran oceans. With the Cambrian explosion in animal diversity (from 541 Ma), fundamental changes in ecological and geochemical conditions led to their extinction.

During this early period in the history of life on Earth, although single-celled organisms (then only archae and bacteria) had been evolving for some 2-2.5 billion years, they had not evolved photosynthesis, so would not have been dependent on sunlight as an energy source, and nor had they evolved aerobic respiration because there was little or no free oxygen (produced later by photosynthesising algae and then green plants) so the only challenge organisms faced was to absorb enough nutrients and to excrete enough waste through their surfaces.

This requirement limits the size of a single cell because, as the cell volume increases, the ratio of its surface area to its volume diminishes. This diffusion problem sets an effective limit on cell size depending on the concentration of nutrients in its environment for the simple reason that the rate of diffusion is a function of the concentration and the surface area - the larger the area the higher the rate of diffusion but the higher the volume the more the demand for nutrients.

You can prove this for yourself by calculating the surface area and volume of a sphere for a list of radii, using the following formulae:

Volume =43 * π * Radius3
Surface Area =4 * π * Radius2

and plotting these on a graph. The clue is that the volume increases as the cube of the radius while the surface area only increases by the square of the radius. This is shown in the chart on the right where the red and green lines show how the volume and area increase relative to the radius. The blue line shows how the volume to surface area ratio falls parabolically as the radius increases. In other words, each unit of volume had to be 'serviced' by a smaller and smaller unit of surface area.

This is a basic problem for biology and probably the one reason why cells stayed small. It underpins a great deal of anatomy and physiology and explains a great deal of the complexity of multicellular organisms which have had to evolve respiratory, transport and excretory systems to cope with it, and, in the case of animal life which eats plants and maybe other animals, digestive systems.

This problem is solved in modern multicellular organisms by transport systems such as blood, or by a system of microtubules as in insects by which oxygen is supplied to the body through pores in their body. These systems all require cell differentiation and specialisation. In the earliest multicellular organisms with no cell specialisation, each organism being little more than a colony of individual cells, the only way size could be achieved was by keeping the surface area to a maximum.

It just so happens that this is achieved by a fractal body-plan in which every sub-unit is a smaller version of the larger unit. This packs the maximum body surface into the minimum space and so maximises the rate of nutrient and waste diffusion across the organism's surface. The organisms which get the most nutrients make the most copies of themselves.

All that is required is a simple mechanism controlling how the cells replicate and arrange themselves and this only needs to be repeated at a constant ratio of each unit of length and the result will be a fractal. This could be controlled by, for example, chemical gradients with cell reproduction being stimulated at a particular threshold. The paper by Jenifer F. Hoal Cuthill and Simon Conway Morris describes how a body plan based on the same general mathematical principle could diversify into a range of different forms to suit the precise "unique ecological and geochemical conditions in the late Proterozoic".

The Ediacaran biota appears to have disappeared quickly once other body plans evolved, maybe out of one or more Ediacaran or maybe by evolving independently from single cell colonies. The method they had diversified by was probably an evolutionary dead end, capable only of providing a solution to the diffusion problem. They thus became easy food for metazoans which evolved in the so-called Cambrian explosion.

So now the question for creationists to answer is why did a supposed intelligent designer design this simple method for making large organisms but which turned out to be so unsuitable later on when it apparently designed predators and much more elaborate systems for overcoming the limitations imposed by simple absorption of nutrients through the body surface, and why can these body plans be completely explained by the operation of simple mathematics in the prevailing conditions, with no need for intelligence or a designer?

Was it just not a very intelligent designer in those days, or, just like a natural process with no magic, no intelligence and no ability to plan ahead, did it need to start simply and build on this by trial and error?

This link gives more details including animations showing how these fractal organisms would have grown.

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  1. The blue line apparently falls hyperbolically (not exponentially) according to 1/R, hence should've been labeled SA/Volume.
    The inverse ratio Volume/SA is a linear function of R and as such would've looked a straight ascending line.

    1. Thanks for the correction.

      I changed the calculation in Excel but forgot to change the label. I'll redo the chart and correct the text.

  2. Rosa, this blog article should be an eye-opener for creationists, but I'm afraid they're not interested in reading this sort of articles that explain life's "march" from simplicity to complexity. And like Jehovah's witnesses they're probably more or less strictly forbidden to read articles and books not approved of by their leaders. To avoid cognitive dissonance - which can evoke doubts if there really exists a divine creator of life - and instead continue believing in imaginary friends in heaven is much more important for those people.

    Nevertheless, I intend to give some link tips in this comment. Why not start with this link: ?

    Don't forget to download this one-pager: .

    Even our brains are built by evolution using fractals. Here is a quote taken from the following article's abstract: :

    The introduction of fractal geometry for the quantitative analysis and description of the geometric complexity of natural systems has been a major paradigm shift in the last decades. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives. Fractal geometry is a mathematical model that offers a universal language for the quantitative description of neurons and glial cells as well as the brain as a whole, with its complex three-dimensional structure, in all its physiopathological spectrums.

    For fractal neurons, also take a look at .

    For those very much interested in fractals in nature I recommend these 19 pages, full of explaining pictures and easy to understand texts:

  3. Just now I read another article on the web, this time about speciation:

    A quote from that one: As niches are filled up by new species speciation slows down. Comes to a halt, even. This makes sense, as the niches are ways of life that organisms can have, if there are no other ways of life currently available, thing will stay the same. This is in line with a mode of speciation driven by niches, in accordance with the Ecological Species Concept by Van Valen (1976)*.

    I hope that creationists will read also that article, but I'm afraid they don't dare to do it, because the speciation processes described in it confirm the evolutionary mechanisms and contradict divine creation.


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