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Just a note

The third plot shown here - the sigmoid curve - is quite common in biology, for example when one plots the percentage cumulative mortality of an organism against the dose of some compound.

Whilst ∪-shaped relationships are shown by age-mortality (bathtub) curves, ∩-shaped relationships are perhaps more common. For example, the catch of several Glossina species has been found to be increased by 'baiting' traps with 1-octen-3-ol vapour. However, above a certain threshold concentration, this kairomone becomes repellent and increasing its concentration above this threshold reduces catches. A similar relationship may occur between population density & fecundity.