Theoretical biology

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Phase space trajectories of a predator-prey system. One of the first mathematical subjects in theoretical biology.

The Theoretical Biology developed formal models to describe biological phenomena . To do this, she uses methods from mathematics in particular . Models and theories are developed to describe the structure and dynamics of living systems. Many fundamental findings in biology , such as the description of evolutionarily stable strategies or the replicator equations , come from theoretical biology. In its purely mathematical orientation, theoretical biology is also called biomathematics and is a sub-area of applied mathematics .

history

1920 Early standard work on pre-mathematical theoretical biology

The idea of ​​a theoretical biology developed around 1900. The term theoretical biology first appeared at a central point in 1901 in the title of the book Introduction to Theoretical Biology by Johannes Reinke . In the tradition that developed from this, the task of theoretical biology was seen less in the mathematization of biological theories than as a conceptual foundation for biology. At this point in time, biology as a discipline was only just beginning to form and the theory of the many different individual disciplines was confusing and largely contradictory. In the 19th century it was still hoped that Darwin's theory of evolution could take on the task of laying the foundation for biology. But Darwinism went through a deep crisis around 1900.

Following Reinke, numerous publications were published by authors who deal with theoretical and philosophical problems in biology. Jakob Johann von Uexküll and Julius Schaxel should be mentioned as central to this early phase of theoretical biology . Both worked with the term theoretical biology. While Uexküll wanted to develop his own new conception for biology, Schaxel tried to draw attention to the theoretical problems of biology with his book Basics of Theory Formation in Biology from 1919 and the series of papers on theoretical biology founded in the same year and to provide a forum for processing to establish these problems. Other important representatives of theoretical biology were Max Hartmann and Ludwig von Bertalanffy .

The current meaning of the term Theoretical Biology as a biology with mathematical means developed relatively late: Early protagonists of the mathematically understood Theoretical Biology were the mathematician Alfred J. Lotka and the physicist Vito Volterra , who at that time were independent systems of ordinary differential equations describing the dynamics of populations. But it was only during and after the Second World War that a broad mathematics-oriented tradition developed in theoretical biology. The influence of biologists from Russia, where the connection between mathematics and biology had a longer tradition and was more widespread, also played a major role here. Population genetics in particular was an important area here. Biologists such as Theodosius Dobzhansky , Ronald Fisher , Sewall Wright and John Burdon Sanderson Haldane , who were also among the central figures of the synthetic theory of evolution , did important pioneering work here. In 1948 Nicolas Rashevsky established the world's first graduate course in mathematical biology . From 1952 to 1954 Alan Turing laid the foundation for the mathematization of developmental biology with epoch-making results on pattern formation in biological systems, in particular the Turing mechanism named after him .

Today, however, the original program of theoretical biology as the philosophy of biology is also experiencing a new upswing.

Areas

Large areas of theoretical biology make use of mathematical methods from the field of dynamic systems to model biological relationships. There is a certain relationship in parts of theoretical biology with subject areas of theoretical computer science and bioinformatics . In these latter areas, tools from discrete mathematics are mainly used.

The areas of theoretical biology include:

Theoretical ecology

Among other things, it tries to make statements about the dynamics of populations and biocenoses . The predator-prey relationships present in almost every ecological structure of interaction prove to be fundamental . In the mathematical formulation of predator-prey models , which was first undertaken by Lotka and Volterra in the 1920s, conventional differential equations (e.g. the Lotka-Volterra equations ) and difference equations are traditionally used . One difficulty lies in the fact that many biological relationships naturally lead to non-linear equations that can only be investigated using numerical, indirect or qualitative methods.

A more application- related sub-area of theoretical ecology makes use of the possibilities of explicit computer simulation and ranges from simple multi-agent-based simulations to the computer-aided representation of entire ecosystems . Here there is a smooth transition between theoretical ecology and practical ecosystem management .

Mathematical epidemiology

Mathematical epidemiology tries to grasp questions about the form and speed of the spread of infectious diseases, as well as the effectiveness of protective measures, exactly and answer them on the basis of the theory of dynamic systems. For example, the so-called SIR model can be used to describe the epidemiology of influenza . The equations used are often closely related to the equations of theoretical ecology.

Theoretical neurobiology

As in experimental neurobiology , work is carried out on different levels of integration. The tasks of theoretical neurobiology, also known as computational neuroscience , thus extend, for example, from the modeling of one or a few ion channels to the analysis and simulation of large neuronal associations. One example is the modeling of certain brain functions, for example the generation of the day-night cycle ( circadian rhythm ). There are some close connections to neuroinformatics .

Theoretical evolutionary biology

Theoretical evolutionary biology uses mathematical methods to investigate the dynamics of evolving systems. Classical Theoretical Evolutionary Biology is based in large part on the influential work of Fischer, Wright, and Haldane . A more recent branch of theoretical evolutionary biology is evolutionary game theory, for which John Maynard Smith, among others, laid important foundations. The focus of interest is on the so-called replicator dynamics and evolutionarily stable strategies as a common abstraction of self-replicating systems . The basic equations of the replicator dynamics are partly related to Lotka-Volterra systems via diffeomorphisms, as works by Hofbauer show. In recent times there has been a greater focus on finite populations. In finite populations, stochastic effects play a larger role. Martin A. Nowak extended the concept of the evolutionarily stable strategy to the case of finite populations.

Further mathematically oriented fields of theoretical biology

development

Theoretical biology, which has been expanding rapidly in the Anglo-American cultural area for a long time, is also on the rise in Germany. The establishment of several chairs for theoretical biology testifies to this; a diversification of the research topics can be observed. The Institute for Theoretical Biology at the Humboldt University in Berlin is a center of theoretical biology in Germany . Historically, some non-mathematical areas of biology have occasionally been counted as theoretical biology.

Education

Theoretical biology is not compulsory at all universities as a regular subject of basic studies or bachelor’s training.

Theoretical biology can currently be studied as a major in biology at the Humboldt University in Berlin and the University of Bonn. Although the type and scope of mathematics education for biology students has been greatly increased in some places, only a small proportion of biologists still has knowledge that enables them to research theoretical biology.

Several universities offer the opportunity to study theoretical biology as part of a mathematics degree with a focus on applied mathematics. The University of Greifswald offers, Booth 2018, the undergraduate course "biomathematics", Bachelor of Science and Master of Science ( "B.Sc." and "M.Sc") to. In addition, the universities of Vienna and Oxford, among others, offer a specialization in theoretical biology. Vienna offers a master’s degree. The department focuses on quantitative methods in developmental biology with the help of high-resolution micro-CT imaging, as well as modeling and theoretical integration of development processes.

During and after your doctorate, you can continue your studies at numerous research institutes that specialize in theoretical biology.

literature

  • Bonner, JT 1988. The Evolution of Complexity by Means of Natural Selection . Princeton: Princeton University Press.
  • Bammert, J., Jesdinsky, HJ , Walter, E. , Otto, C., Roßner, R. Biomathematik für Mediziner , Teubner. 3rd edition, 1988.
  • Nicholas F. Britton: Essential Mathematical Biology. Jumper
  • Hertel, H. 1963. Structure, Form, Movement . New York: Reinhold Publishing Corp.
  • Mangle, M. 1990. Special Issue, Classics of Theoretical Biology (part 1). Bull. Math. Biol. 52 (1/2): 1-318.
  • Murray, J. Mathematical Biology. Jumper
  • Prusinkiewicz, P. & Lindenmeyer, A. 1990. The Algorithmic Beauty of Plants . Berlin: Springer-Verlag.
  • Thompson, DW 1942. On Growth and Form . 2nd ed. Cambridge: Cambridge University Press: 2nd vols.
  • Vogel, S. 1988. Life's Devices: The Physical World of Animals and Plants . Princeton: Princeton University Press.
  • Signs of Life: How Complexity Pervades Biology , with Ricard V. Sole, Basic Books, 2001, ISBN 0465019277
  • How the Leopard Changed its Spots: The Evolution of Complexity , Scribner, 1994, ISBN 0025447106
    (German: The Leopard who loses his spots , Piper, Munich 1997, ISBN 3492038735 )
  • Form and Transformation: Generative and Relational Principles in Biology , Cambridge Univ. Press, 1996.
  • Mechanical Engineering of the Cytoskeleton in Developmental Biology (International Review of Cytology) , with Kwang W. Jeon and Richard J. Gordon, Academic Press, London 1994, ISBN 0123645530
  • Theoretical Biology: Epigenetic and Evolutionary Order for Complex Systems with Peter Saunders, Edinburgh University Press, 1989, ISBN 0852246005
  • Lotka, AJ (1925): Elements of Physical Biology . Williams and Wilkins, Baltimore. ISBN 0486603466
  • Lotka, AJ: Analytical Theory of Biological Populations (The Plenum Series on Demographic Methods and Population Analysis). New York: Springer US (Plenum Press), 1998. ISBN 0306459272

Web links

Specialist journals

Research institutions

Professional societies

Individual evidence

  1. ^ J. Maynard Smith: Evolution and the Theory of Games. Cambridge University Pressm 1982.
  2. ↑ University of Greifswald - All subjects in alphabetical order (pdf; 77.5 kB; 3 pages), as of June 15, 2018, p. 1, accessed on October 28, 2018.
  3. ^ Department for Theoretical Biology University of Vienna