SUMMARYThis paper shows that a number of models of the maintenance of polymorphism in a heterogeneous environment, including those of Levene and Dempster, can be derived from a simple assumption about the way in which the numbers and kinds of individuals emerging from a niche depend on the number of eggs laid in it. It is shown that for such models, unless selective advantages per locus are large, protected polymorphism requires that the relative niche sizes lie in a narrow range. This lack of robustness applies also to models of stable polymorphism proposed by Clarke and by Stewart & Levin. Excluding models relaying on habitat selection or restricted migration, the only models which may escape this criticism are diploid models with partial dominance with respect to fitness, such as one proposed by Gillespie, in which in all niches the fitness of heterozygotes is higher than the arithmetic mean of the homozygotes.

A polytypic value is one that is defined by induction on the structure of types. In Haskell types are assigned so-called kinds that distinguish between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to polytypic programming were restricted in that they only allowed to parameterize values by types of one fixed kind. In this paper we show how to define values that are indexed by types of arbitrary kinds.

Our objective is to provide a model in type theory, using identity types, for parametric polymorphism, subtypes and inheritance. The resulting programming language is a monomor-phic language that has the advantages of polymorphic languages. Since the implementation is using only identity types and since identity types are primitive components of type theory, desirables like type safety, uniqueness of types and the soundness of the system are given at no cost. That is, unlike competing approaches, this way of modeling poly-morphism is not through an extension of the type theory; rather we are using a primitive component of the theory hence no extra work is needed to check whether this new functionality of the system has any side effects on its type safety, uniqueness of types and soundness.

Polygenic inheritance first discover by Herman Nilsson-Elhe and East in kernel color in wheat. Charles Davenport and Gertrude C Devenport was discovered the inheritance of skin color in human. Character or trait refers to any property of an individual showing heritable variation. It includes morphological, physiological, biochemical and behavioural properties. Some characters are governed by one or few genes. Such traits are referred to as qualitative characters or oligogenic characters.

It is quite common for the same material to crystallize in different arrangements of the molecules in the crystal. This phenomenon is referred to as polymorphism and it happens for elements, pharmaceuticals, biological compounds and proteins. In this article we present a brief review of polymorphism, stressing its physical aspects, types and applications. We discuss why it is important to understand the phenomenon, and the need to develop ways of controlling it. We also outline some legal issues related to it.