Logical and set theory models for gastropod larvae, North American birds and seals of the world

Abstract

Two logically valid models are used to compare the gastropod (snail) larvae of Atlantic and Pacific equatorial oceans with birds of North America. One model is this: if there is an environment that supports many species, then there are many species that are supported by one or more environments. This model says that the many species are supported by one environment in the ocean but are supported both by one environment and each species by its own environment among birds on land. A second model is this: if one environment is suited to many species then the many species are suited (adapted) to the one environment – this of course can be reversed, if species are suited to environment then environment is suited to species; so environment and species are suited to each other. This model is applicable to gastropod larvae of the ocean and the birds of North America. A set theory model is applied to the 32 species of seals (and sea lions) of the world. A set theory model is this: a bijective relation between each species and its environment or locale is such that there is a one-to-one correspondence between each species and its unique area or environment; whereas a surjective relation allows overlap of several species occupying the same area in a non one-to-one correspondence. There are 19 bijective seal species and 13 surjective seal species. Bijective cases are the North American birds interpreted as each being supported by and suited to its own area or environment. Surjective cases are many gastropod larvae supported by or suited to one ocean environment.