To understand the development process we’ve taken in our project we must define the terms and variables of our problem.  Following are definitions of all the terms we use in genetic science that one must understand to evaluate the project.

• Genotype- the total set of genes (DNA sequences) that control an organism’s chemistry and physiology, as distinguished from the physical appearance, of an organism or a group of organisms.
• Phenotype- the set of physical characteristics of an organism that are passed down to offspring.
• Allele- one constituent part of a pair or series of genes that occupy a specific position on a specific chromosome.
• Heterozygous- having different alleles at one or more corresponding chromosomal loci.
• Homozygous Recessive- having two recessive alleles (generally a trait is only activated with homozygous dominant and homozygous recessive generally makes the animal lose some physical feature)
• Homozygous Dominant-  having to dominant alleles (generally
• Heterozygosity- the state of an individual of being heterozygous or the relative number of heterozygous organisms in a population
• Inbreeding- mating between genetically distant populations that leads to a lesser heterozygosity and more homozygosity within and therefore, if the trait has a negative impact on a species, that population will become less and less genetically health
• Identical By Descent- two alleles are identical by descent if they are identical copies of the same allele in an earlier generation
• Inbreeding Coefficient- this is the calculable value by which scientists measure inbreeding.
• Outbreeding- mating between two individuals that are very distantly related that causes an increase in heterozygosity, generally lessening the prevalence of a negative trait within a population to make it more healthy
• Non-random Mating- mating in which individuals are selected for a certain phenotype
• Assortative Mating- positive mating between individuals of a certain phenotype (positive-same phenotype; negative- different phenotypes)
• Sexual Selection vs. Natural Selection- sexual selection- based on phenotypes ; natural selection- nature excludes weak individuals from mating either with environmental stresses or sterility

Our program is based on Mendelian genetics, which can be succinctly summarized in a Punnet Square (Fig.1), while this diagram shows both parents as heterozygotes, a parent may also be a heterozygote and the same principles would apply. In the simplest case we will focus on one gene with only two alleles, recessive and dominant. Each parent has two alleles in their genotype and can pass only one of these alleles on to their offspring and there is an equal chance that each will be passed along. Each parent contributes one allele and these two alleles make up the two allele genotype of the offspring. This process can become much more complicated if the gene has more alleles, resulting in successively larger Punnet Squares. 

While researching for this project, we came over many different case studies that showed the effects of inbreeding on a population. One, for instance, involved the New Mexico’s Rio Grande silvery minnow. Inbreeding was preventing its population from increasing because the recessive traits were coming out in the highly endangered species. This was further contributing to the demise of the species along with habitat loss. This demonstrated the problems inbreeding creates.

We are in the process of implementing equations for finding frequencies of genotypes using the frequencies of alleles and then using the genotypic frequencies obtain the inbreeding coefficient.  The following are, in order, the equations for determining the genotypic frequencies, the algebra to find the inbreeding coefficient and the already established and accepted equation to calculate the effective population size based on the traits of the organisms:

• P(Homozygous dominant set) = p2 + fpq (the first term is the allelic frequency of the dominant or capital allele; the second term is the factor by which the dominant homozygosity increases or decreases as a result of inbreeding or outbreeding)
• P(heterozygous set) = H = 2pq+ 2fpq  (the first term stands for the aA allele set and the second for the Aa allele set because either of the two can be expressed in an offspring)
• P(homozygous recessive set) = q2 + fpq (the first term represents the allelic frequency of the recessive allele; the second term is the factor by which the recessive homozygosity will increase or decrease as a result of inbreeding or outbreeding)
• H= 2pq + 2fpq can be rearranged  to form this equation:  H= 2pq(1-f)  which can be algebraically manipulated into f= 1 - (H / 2pq)  which is how in the end we solve for the inbreeding coefficient.

We have not included factors like epistasis, which is when two genes interact in such a way that the dominant of one affects the outcome trait of the other.  This is not entirely too complex but in the meantime we will perfect the process of simulating a closed mating population and then calculating the homozygosity of both the dominant, recessive, and heterozygous allele sets and from those calculating the inbreeding coefficient.  We have not found a way to calculate the lower limit of a population to prevent "dangerous" inbreeding but we will have a foundation to work from and actual data to evaluate and further research will show us what the healthy value of the inbreeding coefficient for a population would be.