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In forestry, periodic annual increment (PAI) is the change in the size of a tree between the beginning and ending of a growth period, divided by the number of years that was designated as the growing period. [1] For sigmoid growth, the graph of PAI increases rapidly and then quickly declines, approaching zero. PAI may go negative if a tree ...
The mean annual increment (MAI) or mean annual growth refers to the average growth per year a tree or stand of trees has exhibited/experienced up to a specified age. For example, a 20-year-old tree that has a stem volume of 0.2 m 3 has an MAI of 0.01 m 3 /year.
Graph of mean annual increment. Biologists use the concept of maximum sustainable yield (MSY) or mean annual increment (MAI), to determine the optimal harvest age of timber. MSY can be defined as “the largest yield that can be harvested which does not deplete the resource (timber) irreparably and which leaves the resource in good shape for ...
"Due to the exponential rate of increase, at any point in the chain reaction 99% of the energy will have been released in the last 4.6 generations. It is a reasonable approximation to think of the first 53 generations as a latency period leading up to the actual explosion, which only takes 3–4 generations." [4]
The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time.
For example, we might want to calculate the relative change of −10 to −6. The above formula gives (−6) − (−10) / −10 = 4 / −10 = −0.4, indicating a decrease, yet in fact the reading increased. Measures of relative change are unitless numbers expressed as a fraction. Corresponding values of percent change would be ...
This formulation has appealing properties such as no change being equal to zero, a 100% increase is equal to 1, and a 100% decrease is equal to −1. However, verbally referring to a doubling as a one-fold change and tripling as a two-fold change is counter-intuitive, and so this formulation is rarely used. Volcano plot showing metabolomic data ...
In nonstandard analysis, a field of mathematics, the increment theorem states the following: Suppose a function y = f(x) is differentiable at x and that Δx is infinitesimal. Then Δ y = f ′ ( x ) Δ x + ε Δ x {\displaystyle \Delta y=f'(x)\,\Delta x+\varepsilon \,\Delta x} for some infinitesimal ε , where Δ y = f ( x + Δ x ) − f ( x ...