Mathematical and theoretical biology

The Theoretical Biology developed formal models to describe biological phenomena. For this purpose, it uses particular methods from mathematics. There are models and theories developed to describe the structure and dynamics of living systems. Many fundamental insights of biology, such as the description of evolutionarily stable strategies or even the Replikatorgleichungen come from theoretical biology. In its purely mathematical orientation Theoretical Biology is also called biomathematics and is a branch of applied mathematics.

• 7.1 journals
• 7.2 Research Facilities
• 7.3 Societies

History

The idea of ​​a theoretical biology developed around 1900. Central spot, the term theoretical biology 1901 Introduction first appears in the title of the book in the theoretical biology of Johannes Reinke on. In the developing itself from this tradition, the task of theoretical biology, however, was seen even less in the mathematization of biological theories, but rather as a conceptual foundation for biology. The biology was just beginning to take shape at this time as a discipline and the theory of existence of many individual disciplines was confusing and contradictory in many parts. In the 19th century, people had hoped that the theory of evolution could take over the task of a foundation for biology. But Darwinism went through a deep crisis in 1900.

Following Reinke numerous publications by authors who deal with the theoretical and philosophical problems of biology published. As central to this early phase of theoretical biology are especially Jakob Johann von Uexküll and Julius Schaxel mentioned. Both worked with the concept of theoretical biology. While Uexküll wanted to develop its own new concept for biology, Schaxel tried to make on the theoretical problems of biology attentively and with his book Fundamentals of theory formation in biology in 1919 and founded the same year Series treatises on theoretical biology a forum for processing these problems to establish. Other important representatives of theoretical biology were Max Hartmann and Ludwig von Bertalanffy.

Today's meaning of the term as a Theoretical Biology Biology mathematically developed relatively late: Early protagonists of mathematically understood theoretical biology were around 1925/26, the mathematician Alfred J. Lotka and Vito Volterra, the physicist who at that time independently Systems of ordinary differential equations describing the dynamics of populations disclosures. But it was only during and after the Second World War, a wide math-oriented tradition developed in theoretical biology. Here, the influence of biologists from Russia played a major role, where the combination of mathematics and biology had a longer history and a wider distribution. In particular, the population genetics was an important area here. Theodosius Dobzhansky biologists such as Ronald Fisher, Sewall Wright and John Burdon Sanderson Haldane, who were also the central figures of the synthetic theory of evolution, have made important pioneering work here. 1948 followed by the establishment of the world's first graduate degree program in Mathematical Biology by Nicolas Rashevsky. Between 1954 - 1956 Alan Turing laid with epoch-making results of pattern formation in biological systems, the basis for the mathematization of developmental biology.

These days, however also experienced the original program of theoretical biology as a new philosophy of biology upswing.

Areas

Length branches of theoretical biology make use of mathematical methods from the field of dynamical systems for modeling biological contexts. A certain relationship exists in parts of the theoretical biology with topics of theoretical computer science and bioinformatics. In these latter areas, especially tools from discrete mathematics are used.

Among the areas of theoretical biology are among others:

Theoretical Ecology

Here, an attempt, among other things, to make statements about the dynamics of populations and biological communities. As fundamentally prove to the present in nearly every ecological interaction structure predator-prey relationships. In the mathematical formulation of predator-prey models, which was first made ​​in the 20s of the last century by Lotka and Volterra, classic way come mainly ordinary differential equations (such as the Lotka -Volterra equations) and difference equations for use. A difficulty lies in the fact that many biological contexts lead naturally to non-linear equations which can only be studied through numerical, indirect or qualitative methods.

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

Mathematical Epidemiology

Questions on the form and speed of the spread of contagious diseases and the effectiveness of protective measures, the mathematical epidemiology attempts to accurately summarize and answer based on the theory of dynamical systems. For example, the so-called SIR ​​model can be used to describe the epidemiology of influenza. The equations used are often related to the equations of theoretical ecology close.

Theoretical Neurobiology

Work is carried out, as well as in experimental neurobiology at different levels of integration. The tasks of the theoretical neurobiology, also called computational neuroscience, thus for example, extend from modeling one or a few ion channels to the analysis and simulation of large neuronal associations. An example is the modeling of certain brain functions, such as the generation of the day - night cycle ( circadian rhythm ). There are some close ties to the neuro computer science.

Theoretical Evolutionary Biology

The theoretical evolutionary biology studied by mathematical methods, the dynamics of evolving systems. The classical theoretical evolutionary biology is mainly based on the influential work of Fischer, Wright, and Haldane. A younger branch of theoretical evolutionary biology is the evolutionary game theory to the other under John Maynard -Smith created an important basis. In the center of interest there as a common abstraction of self-replicating systems, the so-called evolutionarily stable strategies and Replikatordynamiken. The basic equations of the replicator dynamics are partially related through diffeomorphisms with Lotka -Volterra systems, such as work by Hofbauer show. More recently, a stronger involvement with finite populations takes place. In finite populations, stochastic effects play a larger role. The concept of evolutionarily stable strategy has been extended by Martin Nowak to the case of finite populations.

More mathematically oriented fields of Theoretical Biology

• Artificial life
• Theoretical Developmental Biology
• Theoretical Immunology

Development

More recently, in the Anglo - American region has long been rapidly expanding Theoretical biology is understood in Germany on the rise. Evidence of the establishment of several chairs of Theoretical Biology; it can be a diversification of research topics to be observed. A Centre of Theoretical Biology in Germany, the Institute for Theoretical Biology at Humboldt University in Berlin dar. Historically, occasionally counted some non mathematical areas of biology to theoretical biology.

Study

As a regular subject of undergraduate or Bachelor of Theoretical Biology Education is not compulsory at all universities.

As a major in the study of biology can be studied, among other things at the Humboldt University in Berlin and Bonn University Theoretical Biology at present. Although the nature and extent of the mathematics education of biology students were greatly increased in some places, continues to have the capability to participate in research in theoretical biology, only a small part of the biologists have knowledge.

At several universities, it is possible to study Theoretical biology in the context of a mathematics degree with a focus in applied mathematics. As the only university in Germany, Ernst -Moritz- Arndt- University Greifswald offers the undergraduate course " Biomathematics diploma " (since the winter semester 2008 "Bachelor of Science "). Besides this, among others, the Universities of Vienna and Oxford to a specialization in the field of theoretical biology. Vienna offers a master's program. Focus of the department are quantitative methods in developmental biology using high-resolution micro - CT imaging, as well as modeling and theoretical integration of development processes.

During and after the PhD studies can be continued at now numerous specialized in Theoretical Biology research institutes.