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

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

The diversity of phytoplanktonic populations in oceanic, coastal, and estuarine regions

In the deep ocean north of Bermuda, during spring and summer, conditions for growth are poor, but physical conditions, such as high salinity and great depth, are favorable to the marine phytoplankton. The dominant species in a sample constitute a modest proportion of the cells counted, and a considerable diversity of species is observed...

Modelling ecology from logic

Submitted to Ecological ModellingThe thesis of this essay is that logically valid formulations guarantee correct and coherent summaries of scientific data. Several studies are presented that can be shown to be inadequate or simply wrong by logical procedures. But large and small aspects of nature are described and then summarized correctly by logically valid formulations

The application of set theory to ecology

Sets and membership are part of the structure of the world. Sets and membership hold nature together

The deduction theorem and ecology

Submitted to Ecological ModellingThe deduction theorem is based primarily on the formula [A superset of (B superset of C)] superset of [(A superset of B) superset of (A superset of C)]. The fisheries of Newfoundland, Iceland, and west Greenland have three aspects, a first aspect of abundance of cod or herring, aspect A, a second aspect of overfishing or overfishing plus hydrographic change, aspect B, and a third aspect of collapse of the cod-herring fishery or shift to shrimp, aspect C. Each aspect implies, connects to the next either in [A superset of (B superset of C)] sequence or in the [(A superset of B) superset of (A superset of C)] double sequence. The Mississippi River system has three parts, the drainage area of the inner U.S.A., part A, the plankton-rich, low salinity plume to the west of the Mississippi delta, part B, and the oxygen-depleted near-bottom layer of the plume, part C. These parts are connected, as shown by the implication connective, superset of . There are two indirect applications of the deduction theorem. The first is three aspects of hotspots, each hotspot being a region having a set of many indigenous species and having set of endangered species, the two sets being identical by having all the same species (the principle of extensionality). The second indirect application is three logically valid formulas that describe most of the natural world. A is contraposition, an example of which is: a vertebrate is adapted to year-round temperate temperature if it is functional (active) year-round; if and only if a vertebrate is not adapted to year-round temperate temperature only if it is not functional (not active) year-round. B is equivalence, an example of which is: if a North American bird species is adapted to its area, then its area is adapted to it, and if its area is adapted to the species, then the species is adapted to its area – equivalent to: species is adapted to area if and only if area is adapted to species. C is constructive dilemma, an example of which is: all insects are in diapause or non-diapause condition; all insects, if in diapause condition, are winter adapted; and all insects, if in non-diapause (winged) condition, are summer adapted: therefore, all insects are winter adapted or summer adapted. The three logically valid formulas, contraposition, equivalence, and constructive dilemma are thus parts of the larger logically valid formula of the deduction theorem. The empirical data, of considerable value in themselves, become of very great value when inserted into the validity formulas, which seem of limited value without the empirical input. Thus the intent of this several-layered study is just to probe into the underpinnings of nature and to attempt to create some order in our perception of these underpinnings

Essays in philosophical biology

Philosophical biology, one might venture to assert, is an effort to delve as deeply as possible into the underpinnings of biological structure. Consequently the effort will be, first, to understand how continuity can be maintained in the drastic change from cold-blooded to warm-blooded vertebrates, from the property of cold-bloodedness to the property of warm-bloodedness. The effort will be extended, second, to consider how properties, in the fully explained sense provided by philosophers, can be used to explain winter and summer adaptedness, and to explain adaptedness and non-adaptedness. Finally, the effort will take up, third, what is deeply germane in a distinction between two environments, the ocean and land environment – for the relational supporting and the attributional suited to dictate very different accounts of environment and species in the Pacific Ocean and on the North American continent. The three efforts just mentioned will be presented as: I. Can evolution be philosophically integrated?; II. Properties and adaptation; III. A view of two worlds

The biology and philosophy of adaptation

A logico-linguistic analysis is presented first, in which the symbolization of being adapted, having an adaptation, and having adaptedness is explained. Next the linguistic-realistic divide is portrayed. This is explained as ‘adapted’ the word being true of some ‘x’ and ‘adapted’ the word referring to an external entity adapted. The external entity adapted is true of some real organism x, and this organism exemplifies the property of being adapted. Finally, the external world of properties is portrayed. Thus the property of overwintering in angiosperms by bare limbs, seeds, and underground parts dictates winter adaptedness; the property of spring-summer growth of leaves, of annual plants and of above-ground parts dictates summer adaptedness. Also the property of overwintering in diapause insects and in hibernating mammals and southern flying birds dictates winter adaptedness, while the property of spring-summer growth and activity of non-diapause insects, of non-hibernating mammals, and northern mating birds dictate summer adaptedness. And year-round functionality dictates year-round adaptedness and year-round non-functionality dictates year-round non-adaptedness, exemplifications of the first pair being in non-hibernating mammals and of the second pair being in cold-blooded vertebrates and gymnosperms

The distribution of phytoplankton, and its relationship to hydrography, between southern New England and Venezuela

Data obtained on numerous cruises, from southern New England to the Caribbean Sea, between September 1956 and August 1963 form the basis for this study on the relationship of flora to hydrography. Seaward from the southern New England coast, with salinity increasing, the quantity of phytoplankton in near-surface water (0-25 m) decreases while the proportion of oceanic species increases. In the Sargasso Sea, in summer, the stratification and flora are similar from north to south, but in winter, when there is a difference in stratifi cation of the upper 200 m in the northern and southern portions, there is a parallel difference in the abundance of many species...

Natural selection, microevolution and macroevolution

The use of logical validity and empirical data will show that natural selection occurs at the micro-evolutionary level but does not occur at the macro-evolutionary level

Distribution of phosphorus in Great Pond, Massachusetts

Inorganic phosphate and total phosphorus were determined during 1950 in Great Pond, Massachusetts. Except in deeper water during summer, the concentration of inorganic phosphate was less in Great Pond than in its sources of fresh and salt waters. In summer the total phosphorus concentration was greater in the Pond than in the Sound or River, this being particularly so in deep water of the Pond...