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Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system .
The proper way of applying the abstract mathematics of the theorem to actual biology has been a matter of some debate, however, it is a true theorem. [3] It states: "The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time." [4] Or in more modern terminology:
Logistic function for the mathematical model used in Population dynamics that adjusts growth rate based on how close it is to the maximum a system can support; Albert Allen Bartlett – a leading proponent of the Malthusian Growth Model
Log-log transformation places numbers into a geometric domain so that proportional deviations are represented consistently, independent of the scale and units of measurement. In biology, this is appropriate because many biological phenomena (e.g., growth, reproduction, metabolism, sensation) are fundamentally multiplicative. [22]
The pygmy mammoth is an example of insular dwarfism, a case of Foster's rule, its unusually small body size an adaptation to the limited resources of its island home.. A biological rule or biological law is a generalized law, principle, or rule of thumb formulated to describe patterns observed in living organisms.
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.