Analytic Methods

The Hardy–Weinberg Principle measures the allele frequency of both the homozygous and heterozygous alleles in a population.3 The basic idea is that, if certain conditions existed, gene frequencies would remain constant and the distribution of genotypes could be described by the relationship

p2 + 2pq + q2 = 1

where p2 represents the frequency of the homozygous dominant genotype, 2pq represents the frequency of the heterozygous genotype, and q2 represents the frequency of the homozygous recessive genotype. The five conditions or assumptions necessary for gene frequencies to remain constant as according to Hardy-Weinberg principle are the following:

i) Infinitely large population (no genetic drift)

ii) No mutation

iii) No migration

iv) Random mating (no sexual selection)

v) No natural selection

The Hardy-Weinberg equilibrium states that gene frequencies will remain the same should these five conditions be met.3 The principle is important, because it allows a simple comparison of allele frequency to indicate if genetic changes will or is currently happening within a population. The Hardy-Weinberg conditions, however, doesn’t occur in actual situations. Random mating does not occur for a variety of reasons. Many species are divided into small local populations that are isolated from one another and mating with individuals in other local populations rarely occurs. In human populations, these isolations may be geographic, political, or social. Also, there are individuals that are chosen as mates more frequently than others because of the phenotypes they display.3 Therefore, the Hardy-Weinberg conditions are seldom met, because non-random mating is a factor that leads to changing gene frequencies. Spontaneous mutations occur and Immigration and emigration of individual organisms are common. When organisms move from one population to another, they carry their genes with them. Their genes are subtracted from the population they left and added to the population they enter, thus changing the gene pool of both populations. Also, populations are not infinitely large, as assumed by the Hardy-Weinberg concept. If numbers are small, random events to a few organisms might alter gene frequencies from what was expected.

test cross is used to determine an unknown genotype. In a test cross, the organism with an unknown genotype is crossed with an organism known to be homozygous recessive. If all of the offspring belongs to the dominant phenotype, then the unknown genotype is usually homozygous dominant. The unknown genotype tends to be heterozygous if there is a 1:1 distribution of dominant to recessive phenotypes. Test crosses is sometimes used interchangeably with the term back crosses because a test cross is used to figure out the genotype of the parent based on the phenotypes of its offspring. Parental generation represents the parents and is usually the top row on a pedigree. F1 generation or Filial 1 typically represents children. On a Punnett square, this is the row below the generation of the parents, and represents the children of the parents. F2 generation or Filial 2 typically represents the grandchildren. F2 this is the row below the F1, and represents the children of the F1 and grandchildren of the parents.3

Genes are grouped in a straight fashion on chromosomes. Alleles are swapped between homologous chromosomes during prophase I resulting in a cross over. Recombination frequency (θ), is approximately proportional to the gap between the genes on the chromosome and it represents the chance that two alleles are separated from each other during crossing over. The recombination frequency can be used to describe the strength of linkage between genes. Genes that are closely linked have recombination frequencies that are closer to 0% while genes that are more weakly linked have recombination frequencies that are near to 50%. By analyzing recombination frequencies, a genetic map that represents the relative distance between genes on a chromosome can be constructed. One map unit or centimorgan is stated to correspond to a 1% chance of recombination occurring between the two genes. If two genes are 25 map units apart, then we would be expecting 25% of the total gametes examined to show recombination somewhere between these two genes. Biometry is the use of statistical methods to understand biological data and is even able to identify genes in the population that are bad.

Natural selection is the theory that certain characteristics possessed by individuals within a species may help those individuals to have greater reproductive success, thus passing on those traits to offspring.4 The theory was built on several basic tenets including:

i) Organisms produce offspring, few of which survive to reproductive maturity.

ii) Chance variations within individuals in a population may be heritable. If these variations give an organism a slight survival advantage, the variation is termed favorable.

iii) Individuals that prevalently display these favorable variations are more likely to reach reproductive age and produce offsprings. The net result will be in an increase in these traits in future generations. Fitness is the term that denotes this level of reproductive success, and the fitness of an organism’s is directly related to the relative genetic contribution of this individual to the next generation.4

Fitness is defined as the ability to pass your genes on, or reproductive success. In most cases, no matter how good traits are, if the individual does not reproduce, then it has a fitness of zero. Individuals who reproduce more viable offspring are selected for while individuals who reproduce less viable offspring are selected against.4 Natural selection may occur as stabilizing selection, directional selection, or disruptive selection. Stabilizing selection keeps phenotypes within a particular range by operating against extremes. An example is human birth weight, which is maintained within a narrow region by the mechanism of stabilizing selection. Fetuses that weigh too little may not be healthy enough to survive, and fetuses that weigh too much can experience trauma during delivery through the relatively narrow birth canal. In addition, the larger the fetus, the more resources it requires from the mother. For all of these reasons, it is advantageous to keep birth weights within a narrow range. Stabilizing selection selects against the extreme. Directional selection selects for a trait on one extreme.4 Adaptive pressure can lead to the emergence and dominance of an initially extreme phenotype through directional selection. For example, if we have a heterogeneous plate of bacteria, very few may have resistance to antibiotics. If the plate is then treated with ampicillin (an antibiotic), only those colonies that exhibit resistance to this antibiotic will survive. A new normal phenotype emerges due to this phenomena. Natural selection is the history of differential survivorship over time. Disruptive selection selects for the extremes. For example, birds occupying a habitat with 2 distinct niches (eating berries for a living and eating seeds for a living) will develop two types of beaks: small beaks are selected for eating berries, large beaks are selected for cracking seeds and medium beak is left out.



1) Churchill, F. (1974). William Johannsen and the genotype concept. Journal of the History of Biology, 5 -30.

2) Freeman, S. (2011.). Biological Science (6th ed.). Hoboken, NY: Pearson.

3) Hartl DL, C. A. (2007). Principles of population genetics. Sunderland, MA: Sinauer.

4) Baker, J. M. (2005). Adaptive speciation: The role of natural selection in mechanisms of geographic and non-geographic speciation. Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences, 303 – 326.

5) S. Blair Hedges, S. K. (2003, April). Genomic clocks and evolutionary timescales. Retrieved from Hedges Lab:

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