Structural Adaptation

Abstract
An important principle of adaptation is that when two quite different entities occur under the same condition one is adapted and the other is not adapted. This is expressible in set theory in the following way. The set {(a₁R₁b₁), (a₂R₂b₂), (a₃R₃b₃), (a₄R₄b₄), (a₅R₅b₅)} says the mussel’s experimentally determined property to be open at 1ºC, a₁, has adaptedness, R₁, to an ocean temperature of 1ºC, b₁, and likewise for 5º, 10º, 15,º, and 20ºC. But the set {(a₁ not R₁b₁), (a₂ not R₂b₂), (a₃R₃b₃), (a₄R₄b₄)} says the oyster’s experimentally determined property to pump water at 13ºC, a₃, has adaptedness, R₃, to an ocean temperature of 13ºC, and likewise for 19ºC, a₄, but not for 1ºC, a₁, and 7ºC, a₂. In this detailed way the mussel’s being adapted throughout a 1º-20ºC range is compared to the oyster’s not being adapted throughout a similar range. Another example of the application of set theory to the issue of adaptation is given by the application of functions to birds. The function of adaptedness, f, of the breeding chickadee, a₁, and its area, b₁ is such that the function of adaptedness binds breeding species to area: f(a₁) = b₁. But the non-breeding chickadee species is bound by adaptation to the same area (since chickadees do not migrate); thus where a₂ is the non-breeding chickadee, f(a₂) = b₁. So f(a₁) and f(a₂) converge on b₁. This is surjective, an incomplete adaptation. Migratory sparrow species have a northern breeding area and a southern wintering non-breeding area. Thus the function of adaptedness binds the breeding sparrow to its breeding area, f(a₁) = b₁; the function of adaptedness binds the non-breeding sparrow to its non-breeding wintering area, f(a₂) = b₂. This is bijective, a complete adaptation, wherein two quite different entities, breeding species and behaviorally quite different non-breeding species, are both adapted to two quite different areas. In the first principle both adaptedness and unadaptedness occur; in the second principle only adaptedness occur.

A Brief Review of Adaptation
So often adaptation and natural selection are considered in the same breath. Natural selection produces adaptation – the selected is better adapted – according to Williams (1966, pp. 25-27), to Sober (1984, pp. 171-208), to Stern (1970), to Mayr (2001, pp. 147-157) and to so many others. Thus Stern says “whatever has been produced by selection is to be designated as better adapted”. But consider the reverse: adaptation produces natural selection – the better adapted is selected. This is what Stern seems to say when “we were able to define an adaptation as any characteristic which caused its possessors to produce …more offspring than they would in its absence”.

Is it interesting in what way such principles are presented? Let us see. Natural selection means having greater reproductive success, it should be noted. Employing the comparative idea of more, better, greater, etc., Brandon (1990, p. 11) says “If a is better adapted than b in environment E, then (probably) a will have greater reproductive success than b in E”. Putting the matter in this two-part if-then format really is a clarifying procedure. But what is most interesting is what is not said. Why is it not said that if a does not have greater reproductive success, then a is not better adapted? Perhaps this is obvious. But perhaps it would open up a vista too alien to be considered.

The slender vista presented so far is expanded appreciably when Brandon reverses and changes slightly his description of the last paragraph. Thus the part starting with if, call it p, will be “a is better able to survive and reproduce in E than b”, and the part beginning with then, call it q, will be “a is better adapted than b in E”. And the whole affair is then q if p and q only if p, which is shortened to q if and only if p¹. Brandon presents this shortened form, but he does this, as noted, in a different way: ‘a is better adapted than b in E iff [if and only if] a is better able to survive and reproduce in E than b”. Why is this different? The structural form of presentation is, yes, an important difference, as will be seen later. But the striking difference is in the word ‘able’. Able-to-survive seems so close to ability-to-survive, where ability is a property, a trait.

Munson (1971), in his discussion, introduces trait when he expands our view by going from “Trait T of organism O is adaptive in environment E” to “O has T and T is advantageous to O in E”. So one can see, in passing, that adaptive and advantageous overlap, they are true of many of the same organisms apparently. But trait, though an important ingredient, does not get attention in itself. Munson, impatiently, covers a medley of matters. There is an arresting switch in details when ‘in E’ changes to ‘to E’. Thus he says “Organism O is adapted to environment E”, “Species S is adapted to E” (better adapted can replace adapted). One little word makes all the difference. For one single entity, organism or species, is adapted to one single entity, a certain environment. One could say succinctly: x is adapted to y – a tight connection.
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¹ ‘If and only if’ means ‘q if p and q only if p’, as noted. But ‘q if p’ is the same as ‘if p then q’ and ‘if q then p’ can be expressed as ‘q only if p’ – so that ‘if p then q and if q then p’ reduces to ‘q if and only if p’.

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