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Is the golden ratio a universal constant for self-replication?
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.ORCID iD: 0000-0003-2640-6490
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
##### Abstract [en]

The golden ratio, $\phi=1.61803...$, has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its origins in Fibonacci's sequence for rabbit reproduction''. Recently, it has been claimed that $\phi$ determines the ratio between the number of different nucleobases in human genome. These empirical examples continue to give credence to the idea that the golden ratio is a universal constant, not only in mathematics but also for biology. In this paper, we employ a general framework for chemically realistic self-replicating reaction systems and investigate whether the ratio of chemical species population follows universal constants''. We find that many self-replicating systems can be characterised by an algebraic number, which, in some cases, is the golden ratio. However, many other algebraic numbers arise from these systems, and some of them---such as $\sqrt[3]{2} = 1.25992...$ and $1.22074...$ which is also known as the \textit{3rd lower golden ratio}---arise more frequently in self-replicating systems than the golden ratio. The universal constants'' in these systems arise as roots of a limited number of distinct characteristic equations. In addition, these universal constants'' are transient behaviours of self-replicating systems, corresponding to the scenario that the resource inside the system is infinite, which is not always the case in practice. Therefore, we argue that the golden ratio should not be considered as a special universal constant in self-replicating systems, and that the ratios between different chemical species only go to certain numbers under some idealised scenarios.

##### Keyword [en]
Golden ratio, Fibonacci sequence, Self-replication, Fibonacci rabbit, Universal constant
##### National Category
Other Mathematics
##### Identifiers
OAI: oai:DiVA.org:uu-339888DiVA: diva2:1176925
Available from: 2018-01-23 Created: 2018-01-23 Last updated: 2018-01-23
##### In thesis
1. Modelling Evolution: From non-life, to life, to a variety of life
Open this publication in new window or tab >>Modelling Evolution: From non-life, to life, to a variety of life
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

Life is able to replicate itself, e.g., a microorganism is able to divide into two identical ones, and a single plant is able to forest a whole island. But life is the only example of self-replication (note that a computer virus seems able to replicate itself, but it needs the assistance of a processor such as a CPU, and thus not a truly self-replicating entity). So before the appearance of life, nothing can self-replicate. How does life, a truly self-replicating entity, evolve from substances which is not able to self-replicate? Why can it ever happen? Is there a general underlying mechanism that governs how self-replicating entities can develop de novo on Earth, or even other plants?

As long as the first life appears, it has the potential to cover the whole plant. But one single life form cannot do the job. Life has branched into a huge number of biological classes and species. Different species interact with each other, and with their environment, which, as a whole, is defined as an ecosystem. Distinct ecosystems are found at different scales and different places, e.g., microbes cross-feed and compete for resources within natural communities; and different types of cells interact by exchanging metabolite within an organism body. But, why sometimes we consider an ecosystem as an individual (such as the human body which is, in fact, an ecosystem inhabited by a huge number of microorganisms without which we cannot survive) while sometimes not? What really distinguishes an individual-level life from a system-level life? Are there general properties only a system-level life has, emerged from the interactions among its compositional individual-level life?

This thesis is to investigate these two questions by mathematical models. For the evolution from non-life to life, namely the origin of life, we build an artificial chemistry model to investigate why an independent self-replicating entity can develop spontaneously from some chemical reaction system in which no reaction is self-replicating. For the evolution from life to a variety of life, we build an artificial ecosystem model to investigate general properties of ecosystems.

##### Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2018. p. 59
##### Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 106
##### Keyword
Mathematical biology, Biocomplexity, Artificial chemistry, Ecosystem evolution, Origin of life, Self-replication, Prebiotic evolution, Collectively-catalytic, Golden ratio
##### National Category
Other Mathematics Other Biological Topics Other Chemistry Topics
##### Research subject
Applied Mathematics and Statistics
##### Identifiers
urn:nbn:se:uu:diva-339596 (URN)978-91-506-2683-4 (ISBN)
##### Public defence
2018-03-16, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15 (English)
##### Note

Fel ISBN, serie och serienummer i tryckt bok / Wrong ISBN, series and series number in the printed book.

Available from: 2018-02-20 Created: 2018-01-23 Last updated: 2018-03-19

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#### Authority records BETA

Liu, YuSumpter, David J. T.

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