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Rocky Shore Snails and The Second Principle of Adaptation
Whereas in the first principle of adaptation two quite different entities under one condition have all adaptednesses in one case and not all adaptednesses in the second case; in the second principle next one entity occurs under two conditions, having adaptedness to one but not having adaptedness to the other.

Rocky shore snails are shown in Table 2, from Vermeij (1978, p. 60). There are two groups of species, one from temperate locations and a second from tropical locations. Each group is an element in a set, set A of rocky shore snails. Each element belongs to A, aA, a2A. The problem is to distinguish the two elements in terms of adaptation.

There are two more sets. What the numbers in the table show is that lesser or no toothed apertures are present in temperate locations, b1, and greater toothed apertures are present in tropical locations, c1, that less or no elongate apertures are present in temperate locations, b2, and greater elongate apertures are present in tropical locations, c2, that lesser or no inflexible operculums are present in the temperate locations, b3, and greater inflexible operculums are present in the tropical locations, c3, that less or no strong external sculpture is present in the temperate locations, b4, and greater strong external sculpture is present in the tropical locations, d4. Thus, a set of four properties, where each biB, and another set of four properties, where each ci C, portray an increase in defense properties from the temperate average, 3.58%, to the tropical average, 18.9%. These properties are inferred to be defense properties against predation, a predation indicated by shell injuries, shown very well by a number of pictures in Vermeij (1978, pp. 57-60). But a striking feature is that the frequency of repaired shells, repaired from injuries in living snails, is much less in temperate locations than in tropical locations, having a frequency of 0.07 for three snail species of the temperate British Columbia coast and 0.30 for three species of the tropical Costa Rican coast. Thus, the conclusion would seem to be that the set of lesser defense properties is related to an element d1 of better adapted species (in temperate locations) and the set of better defense properties is related to an element d2 of worse adapted species with respect predation (in the tropics). In the tropics, in spite of better defenses, snails suffer more from predation and so are worse adapted.

A diagram of the relations of the sets A, B, C, and a final set D is this:

A   B   D
         
a1
b1
b2
b3
b4

d1
  R1   R3  
    C    
         
a2
c1
c2
c3
c4

d2
  R2   R4  

One element of A is related, R1, to the slight amount of its four defense properties of B. Another element of A is related, R2, to the ample amount of its four defense properties of C. Elements of B are related, R3, to the adaptedness to slight predation, d1. Elements of C are related, R4, to the unadaptedness to marked predation, d2.

Thus the defense properties connect the two elements of A to better and worse adaptednesses, the two elements of D.

Thus the single set A of rocky shore snails emerges as having better adaptedness, d1B, and as having worse adaptedness, d2D.

Thus the second principle of adaptation is portrayed : the set, the rocky shore snail, has adaptedness only to slight predation if and only if it has unadaptedness to marked predation (one entity under two conditions is adapted to one and not adapted to the other). The basic structure requirement of separation of entity from its essential properties and from an environmental property (predation) has been incorporated.

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