The four principles of adaptation and their set theory foundation

There are four principles of adaptation enunciated in [Ecol. Model. 156 (2002) 61]. The first is that if two quite different entities occur under the same condition, then one is adapted and the other is not adapted to this condition. An example is a set of five experimentally determined algae division rates at five temperatures from 1 °C to 20 °C; these are paired with five ocean temperatures from 3 °C to 20 °C. The set of five pairs shows a relation of being adapted in the case of several species but in the case of another species a relation of being adapted at higher temperatures but a relation of not being adapted at lower temperatures. cond principle is that if one entity occurs under two quite different conditions, then it is adapted to one condition but is not adapted to the other condition. An example is 17 sets, or associations, of species of the North American forest related by being adapted to moist conditions; and five sets, or associations, of the North American forest related by being not adapted to non-moist conditions. ird principle is that if one entity is adapted to a second, then the second entity is adapted to the first. An example is a set of three coastally restricted species (the western red cedar and redwood and the eastern white cedar) and the set of their locales. There is a functional relation between these sets: the function of adaptation binds each species to its locale—this is invertible; the function of adaptation binds each locale to its species. For certainly the species would not be where it is if its locale were not adapted to it. urth principle is that if two or more quite different entities occur under two or more quite different conditions, then each entity is adapted to its condition. Examples are the migration of three North American sparrow species. Each species can be divided into breeding species and non-breeding species. Then the third and fourth principle can be combined: the function of adaptation assigns to each breeding species its northern breeding area which is adapted to it and the function of adaptation assigns to each non-breeding species its winter, non-breeding area, which is adapted to it.