Mathematical and theoretical biology
Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter.
Because of the complexity of the living systems, theoretical biology employs several fields of mathematics,[5] and has contributed to the development of new techniques.
[citation needed] Fritz Müller described the evolutionary benefits of what is now called Müllerian mimicry in 1879, in an account notable for being the first use of a mathematical argument in evolutionary ecology to show how powerful the effect of natural selection would be, unless one includes Malthus's discussion of the effects of population growth that influenced Charles Darwin: Malthus argued that growth would be exponential (he uses the word "geometric") while resources (the environment's carrying capacity) could only grow arithmetically.
One founding text is considered to be On Growth and Form (1917) by D'Arcy Thompson,[7] and other early pioneers include Ronald Fisher, Hans Leo Przibram, Vito Volterra, Nicolas Rashevsky and Conrad Hal Waddington.
Some reasons for this include: Several areas of specialized research in mathematical and theoretical biology[10][11][12][13][14] as well as external links to related projects in various universities are concisely presented in the following subsections, including also a large number of appropriate validating references from a list of several thousands of published authors contributing to this field.
Many of the included examples are characterised by highly complex, nonlinear, and supercomplex mechanisms, as it is being increasingly recognised that the result of such interactions may only be understood through a combination of mathematical, logical, physical/chemical, molecular and computational models.
Ronald Fisher made fundamental advances in statistics, such as analysis of variance, via his work on quantitative genetics.
Work in this area dates back to the 19th century, and even as far as 1798 when Thomas Malthus formulated the first principle of population dynamics, which later became known as the Malthusian growth model.
Various models of the spread of infections have been proposed and analyzed, and provide important results that may be applied to health policy decisions.
In evolutionary game theory, developed first by John Maynard Smith and George R. Price, selection acts directly on inherited phenotypes, without genetic complications.
The solution of the equations, by either analytical or numerical means, describes how the biological system behaves either over time or at equilibrium.
They have recently produced a generic eukaryotic cell cycle model that can represent a particular eukaryote depending on the values of the parameters, demonstrating that the idiosyncrasies of the individual cell cycles are due to different protein concentrations and affinities, while the underlying mechanisms are conserved (Csikasz-Nagy et al., 2006).
The parameters are fitted and validated using observations of both wild type and mutants, such as protein half-life and cell size.
In a simulation, given a starting vector (list of the values of the variables), the progression of the system is calculated by solving the equations at each time-frame in small increments.
The presence of these special steady-state points at certain values of a parameter (e.g. mass) is represented by a point and once the parameter passes a certain value, a qualitative change occurs, called a bifurcation, in which the nature of the space changes, with profound consequences for the protein concentrations: the cell cycle has phases (partially corresponding to G1 and G2) in which mass, via a stable point, controls cyclin levels, and phases (S and M phases) in which the concentrations change independently, but once the phase has changed at a bifurcation event (Cell cycle checkpoint), the system cannot go back to the previous levels since at the current mass the vector field is profoundly different and the mass cannot be reversed back through the bifurcation event, making a checkpoint irreversible.
