Fiddler crab a vital role in the preservation of wetland environments; by sifting through the sands, they aerate the substrate and prevent anaerobic conditions. Fiddler crabs live rather brief lives of no more than two years (up to three years in captivity). Male fiddler crabs use the major claw to perform a waving display as a form of female courtship. Females choose their mate based on claw size and also quality of the waving display. In many fiddler crab species, the female occupies the burrow of their mate while she lays her clutch of eggs. Research shows that the male major claw
History of manifolds and varieties spaces with a differentiable or topological structure, while "variety" refers to spaces with an algebraic structure, as in algebraic varieties. In Romance languages, manifold is translated as "variety" – such spaces with a differentiable structure are literally translated as "analytic varieties", while spaces with an algebraic structure are called "algebraic varieties". Thus for example, the french word "" means topological manifold. In the same vein, the Japanese word "" (tayōtai) also encompasses both manifold and variety. ("" (tayō) means various.) Ancestral to the modern concept of a manifold were several important results of 18th and 19th century mathematics. The oldest