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A biomolecular gradient is established by a difference in the concentration of molecules in a biological system such as individual cells, groups of cells, or an entire organism. A biomolecular gradient can exist intracellularly (within a cell) or extracellularly (between groups of cells).
The gradient of a function is called a gradient field. A (continuous) gradient field is always a conservative vector field: its line integral along any path depends only on the endpoints of the path, and can be evaluated by the gradient theorem (the fundamental theorem of calculus for line integrals). Conversely, a (continuous) conservative ...
Biogeography now incorporates many different fields including but not limited to physical geography, geology, botany and plant biology, zoology, general biology, and modelling. A biogeographer's main focus is on how the environment and humans affect the distribution of species as well as other manifestations of Life such as species or genetic ...
Homogeneous regions have spatial gradient vector norm equal to zero. When evaluated over vertical position (altitude or depth), it is called vertical derivative or vertical gradient; the remainder is called horizontal gradient component, the vector projection of the full gradient onto the horizontal plane. Examples: Biology
The simplest definition for a potential gradient F in one dimension is the following: [1] = = where ϕ(x) is some type of scalar potential and x is displacement (not distance) in the x direction, the subscripts label two different positions x 1, x 2, and potentials at those points, ϕ 1 = ϕ(x 1), ϕ 2 = ϕ(x 2).
In biology, a cline is a measurable gradient in a single characteristic (or biological trait) of a species across its geographical range. [1] Clines usually have a genetic (e.g. allele frequency, blood type), or phenotypic (e.g. body size, skin pigmentation) character.
For example, species abundance usually changes along environmental gradients in a more or less predictable way. However, the species abundance along an environmental gradient is not only determined by the abiotic factor associated with the gradient but, also by the change in the biotic interactions , like competition and predation, along the ...
The gradient theorem states that if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the integral of F over some piecewise-differentiable curve is dependent only on end points). This theorem has a powerful converse: