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A significant example of directional selection in populations is the fluctuations of light and dark phenotypes in peppered moths in the 1800s. [16] During the industrial revolution, environmental conditions were rapidly changing with the newfound emission of dark, black smoke from factories that would change the color of trees, rocks, and other ...
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, [1] introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of ...
As a consequence of this type of selective pressure, our hypothetical rabbit population would be disruptively selected for extreme values of the fur colour trait: white or black, but not grey. This is an example of underdominance (heterozygote disadvantage) leading to disruptive selection.
Examples of human phenotypic variability: people with different levels of skin colors, a normal distribution of IQ scores, the tallest recorded man in history - Robert Wadlow - with his father. Human variability, or human variation, is the range of possible values for any characteristic, physical or mental, of human beings.
As particular examples of Banach spaces, Dunford & Schwartz (1958, Chapter IV) consider spaces of sequences of bounded variation, in addition to the spaces of functions of bounded variation. The total variation of a sequence x = ( x i ) of real or complex numbers is defined by
There are few examples of genes with direct evidence of stabilizing selection in humans. However, most quantitative traits (height, birthweight, schizophrenia) are thought to be under stabilizing selection, due to their polygenicity and the distribution of the phenotypes throughout human populations.
The size of a tomato is one example of a complex trait. Complex traits are phenotypes that are controlled by two or more genes and do not follow Mendel's Law of Dominance. They may have a range of expression which is typically continuous. Both environmental and genetic factors often impact the variation in expression.