Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Foster's rule into larger versions of themselves (insular gigantism) while others became smaller versions of themselves (insular dwarfism). He proposed the simple explanation that smaller creatures get larger when predation pressure is relaxed because of the absence of some of the predators of the mainland, and larger creatures become smaller when food resources are limited because of land area constraints. The idea was expanded upon in "The Theory of Island Biogeography", by Robert MacArthur and Edward O. Wilson. In 1978, Ted J. Case published a longer paper on the topic in the journal "Ecology". Foster's rule Foster's rule, also known as the