# Is scalable growth the main reason why Darwinian systems select Fibonacci sequences?

The other day I was thinking about evolution of multi-cellular organisms, and why from the earliest onset of the development of communal cellular structure building, life may have selected a simplest possible strategy for building scale-able structures.

We humans employ relatively complex mathematics and measuring tapes to engineer structures, and we build them to full size, or modular so they assemble. We like proportionality, and there are strength and weight considerations associated with it, but we are not entirely ruled by these considerations. But it maybe that life is far more dependent on proportionality considerations. Life grows sequentially from a single cell, and each cell possesses both the building machinery, and what must be a relatively simple genetic program to govern growth. Because the generic programming operates on the basis of individual cells, there is conceivably a limit to the complexity of program you can expect life to be employing. And even if genetic coding is capable of tremendous complexity, life’s still going to select the simplest most effective approach. So how does lifes growth system achieve such consistently proportional results?

The answer may reveal itself, when you try to conceive of a building method that achieves the same outcome life does. That is to say, building a small scale structure, that will later scale up to full size through a growth cycle, and maintain a proportionality. If for example you build a small scale brick building, whereby the bricks can replicate and divide like living cells. Then so long as each brick does so at an overall synchronous rate, starts with select proportions and follows a very simple program governing growth that abides a proportionality which stays constant at all scales. Like the Fibonacci series rectangle does. Then the building can be scaled up through a smooth growth cycle while remaining structurally proportional. What you start with will determine your end result. And most importantly, having used a minimalistic coding system.

So what’s interesting, is that this is potentially a sound reasoning for why Fibonacci series emerges from such a fundamental level within Darwinian life. Life in the oceans subsisted as single celled organisms, but as soon as it started experimenting with multi-cellular structures, it needed to solve these issues of scale-able growth.

If this is correct, then it opens a fascinating window on a process of early life. Who knows what types of biological evolutionary insights might be derived from it.

Does this scenario sound plausible to more people than just me?

• I didn't know there was something called theoretical biology! highly thought inducing!...I need to find some references for the answer in my head. Commented Aug 10, 2016 at 9:14
• @KoustavPal I didnt know there was either. Here's a documentary which played a part in my realizing youtube.com/watch?v=h1qVloZKmdM Commented Aug 10, 2016 at 10:18
• In any science there is theoretical side of this science. Theoreticians build hypotheses that can be tested. Theoretician also often build the necessary statistical tools. Btw, I am a theoretician Commented Aug 10, 2016 at 18:23
• The question is very long and lack any kind of formatting. I am too lazy to read it. If you want people to make effort to read your questions, try to make them as appealing as possible. Also, by experience, long wordy question are often bad questions (but I can't tell for yours as I haven't read it but seeing expression like "Darwinian life" is not encouraging :)). Commented Aug 10, 2016 at 18:24
• Okay. This is the book and it is not that obscure. I read an old edition which was in my university library. Commented Aug 11, 2016 at 10:46

I really wanted to put my thoughts into words as to why biological systems conform to Fibonacci's series.

What you say is entirely plausible and it does make sense. But what I wanted to address was why do these systems conform to it.

It is because of the interactions with the environment

Explaining this concept on multicellular organism first requires answering the same question in bacteria. Towards this end, I would like to point you towards this wiki page

It comes down to parameters such as medium concentration and hardness, parameters which we can influence. If we can extrapolate from this that cells, any cells will always follow a chemokine/nutrition gradient then we can start to understand why the system conforms to a fibonacci sequence.

Next, check out this video on a wound healing assay, what i would like to bring to your notice is that you'll find the cells replicate and move at the same rate.

If you follow a chemokine gradient, and move at approximately the same rate as your 2 billionth cousin, wouldn't you end up inevitably creating a symmetric structure?

Finally, I would, point you towards this article, where they explain a phenomenon called cell migration. This is particularly responsible for creating the symmetry which you see. And this is a similar article as the top one but it should be open access. Both support an idea which has been observed, I tried searching for the video but couldn't find it. The idea being that cells migrate collective, but there are some cells which are leaders and some followers. The leaders lead the collective migration (creating some sort of chemokine gradient) while the followers follow this gradient.

I attended a seminar last year by D Gilmour from EMBL. He showed us this particular video on collective cell migration and deposition of small clusters of cells which go on to establish the lateral line in zebrafish. You will find that a periodicity exists in this migration pattern. He relates it to a ligand activation. The related article to the video should be this one (I thought so after reading the abstract)

• Thank you Koustav for your detailed answer. There's quite a bit here to think about, and follow up on. I'll go through everything you presented Commented Aug 16, 2016 at 5:02