anisms that generate the space-time distribu- 

 tion of fish. Of particular interest is the situ- 

 ation where the spatial distribution is not fixed 

 during the fish's lifespan and the fish undergo 

 movements or migrations that are specializa- 

 tions of a more sedentary behavior. We would 

 postulate that these specializations have re- 

 sulted from a necessity for fish to ingest, on 

 the average, an amount of food that supplies to 

 the fish at least as much energy as that re- 

 quired for maintenance and growth. But the 

 food resources within the distributional ranges 

 of some fishes tended--during the course of 

 evolutionary time--to become inadequate for 

 certain life-history stages. This inadequacy 

 probably arose from either modifications in the 

 environment or from morphological or physio- 

 logical specializations. Some forms were able 

 to "escape" from the areas of inadequate 

 forage resources by evolving a migratory be- 

 havior. The purpose of this section is to dis- 

 cuss the mechanisms by which this migratory 

 behavior could have become established. 



For this discussion tne position of fisn or 

 their forage will be defined on a field of space- 

 time points. Each space-time point is indexed 

 by discrete elements of latitude, longitude, 

 depth, and time. Further, the discussion is 

 based on the axiom that a fish needs to ingest 

 a sufficient amount of food to supply it with 

 sufficient energy to survive in its ecosystem 

 (survival in the ecosystem being distinct and 

 having different requirements than survival 

 under laboratory or other artificial conditions). 

 If a fish has survived to some particular time 

 point in the ecosystem, then it obviously must 

 have survived at all time points previous to the 

 particular time point and subsequent to its 

 birth. In order for a fish to exist at a particu- 

 lar space-time point, it must be able to ingest 

 at least as much energy as is required for its 

 survival at that space-time point or be able to 

 draw on energy stores that were acquired at 

 some previous space-time point. If a fish ob- 

 tains energy by ingesting a more or less steady 

 supply of forage at a particular space point, 

 then it can remain at that space point for an 

 indefinite period of time. If however, a fish 

 cannot obtain forage at a particular space-time 

 point it must eventually find a space-time point 

 at which it can obtain forage or it will succumb 

 either from starvation, or, more likely, from 

 its inability to cope with the requirements of 

 its ecosystem. 



Whether or not a fish obtains the forage re- 



quired for its survival in the ecosystem at any 

 particular space-time point depends on the 

 quality or the structure of forage at any par- 

 ticular space-time point. The quality of the 

 forage, in terms of its ability to provide ener- 

 getic sustenance for the forager, is repre- 

 sented by the concept of a forage lattice. A 

 forage lattice is simply a three-dimensional 

 array of lattice points. Each lattice point is 

 occupied by a packet of energy in the guise of a 

 forage item or forage items which could be 

 ingested and utilized as energy by the forager. 

 The spacing between the lattice points is not 

 measured in conventional metric terms of dis- 

 tance, but rather in terms of the difference 

 between the energy available at each lattice 

 point and the energy required for the forager 

 to swim between and ingest food at the lattice 

 points. Thus, it is conceivable that lattices of 

 high forage density might be able to support, 

 energetically, less foragers than lattices of 

 lower density owing to a possible higher energy 

 content at the lattice points of the lower density 

 lattices. 



The existence of several types of forage lat- 

 tice becomes clear. First, there are suitable 

 and unsuitable lattices. The suitability of a 

 lattice at a space-time point must be expressed 

 in terms of the metabolism and behavior of the 

 species of interest considering all effects on 

 the metabolism that are specific with respect 

 to the contemporaneous, as well as to past, 

 effects of size, age, sex, etc. For example, a 

 forage lattice of diatoms might be suitable for 

 copepods, but not for tunas. Or a forage lattice 

 that has its lattice points occupied by small 

 fishes and squids might be suitable for larger 

 tunas whereas a forage lattice of copepods 

 might be necessary to support juvenile tunas. 

 Thus, a particular space-time point may con- 

 tain several lattices. Of these several lattices, 

 one may be suitable for the forager of interest. 

 The unsuitable lattices are irrelevant to our 

 problem in the sense that they have relatively 

 no greater effect on the forager. In another 

 sense the unsuitable lattices are highly relevant 

 since they define the trophic structure of the 

 community. Second, of the suitable lattices, 

 there is one that is at least optimal; the other 

 suitable lattices are suboptimal. An optimal 

 lattice is one in which the distances between 

 the lattice points is such that the energy ex- 

 pended to swim between the lattice points is 

 less than the energy which can be ingested at 

 the lattice points. By contrast, obtaining more 



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