# Population Genetics

The modern definition of evolution is specific: evolution is defined as the change in allelic frequencies in a population with time. A change in the allelic frequency for one gene does not necessarily result in what we think of evolution, but rather, if changes occur in many genes, the result may be evolution. We usually refer to all of the genes, and all of the alleles, in a population as the*gene pool*. Thus, the diversity and variation of every population can be ascertained by examining the gene pool.

Recall from Chapter 19 that alleles are different varieties of genes caused by mutations in the DNA. To understand evolution, we must understand the genetics of a population, not just of an individual. In 1908, two researchers, G. H. Hardy and G. Weinberg, set out to understand this via the use of mathematics. They reasoned that, if no genetic changes were taking place over time, then a population would be in equilibrium and would not change. If this were true, the frequency of each allele in a population could be calculated rather easily. Knowing the frequency of each allele would allow for the description of the genotypic frequencies within the population as well.

**For example,**consider a genetic trait with two alleles, the dominant allele

*A*and the recessive allele,

*a*. Since there are only two alleles of this gene in the population, the sum of the frequency of the two alleles must be one. If we assign symbols to these frequencies (i.e. the frequency of

*Î‘*can be represented by

*p*, and the frequency of

*a*can be represented by

*q*), then we can express this idea as:

*p* + *q* = 1

Furthermore, if we know

*p*and*q*, we can calculate the frequencies of the various genotypes. If mating is random in a population, then this mating can be expressed as the probability of alleles coming together in any combination. Mathematically we can express this as (p + q) X (p + q). Since p + q = 1, the product of this equation also equals 1. With some algebraic manipulation, this equation becomes*p*^{2} + 2*pq* + *q*^{2 }= 1

Each term represents one genotype; specifically, the frequency of the homozygous dominant (

*AA*) in the population is expressed by the term*p*, the homozygous recessive (^{2}*aa*),*q*, and the heterozygote (^{2}*Aa*)*2pq*.

**Example :**If

*p*= 0.85, then we could calculate

*q*(1 - 0.85 = 0.15). In addition, we could calculate the frequency in the population of

*AA*(0.085 X 0.85 = 0.72),

*Aa*(2 X 0.85 X 0.15 = 0.26) and

*aa*(0.15 X 0.15 = 0.02). If we consider a population of 1000 individuals, we would predict that 0.72 X 1000, or 720, would be of the genotype

*AA*, 0.26 X 1000, or 260, would be

*Aa*, and 0.02 X 1000, or 20, would be

*aa*.

We can also determine the frequency of the alleles given raw numbers in the population. For example, if, in a population, 800 individuals were found to be of the genotype

*AA*, 160 were*Aa*, and 40 were*aa*, then we can calculate allelic frequencies given the formulae:

The total number of

*A*alleles in a population is expressed as

**( 2 X # of AA ) + (# of Aa )**

as homozygous dominant individuals have 2

*A*alleles, and heterozygotes have only 1*A*allele. Similarly, total number of*a*alleles in a population is expressed as

**(2 X # of aa ) + (# of Aa)**

as homozygous recessive individuals have 2

*a*alleles, and heterozygotes have only 1*a*allele. The total number of alleles in the population is equal to

**2 X # of individuals**

as each individual in the population has two alleles for every gene, including the gene of interest. Thus, our equation to find p becomes:

We can similarly determine

*q*, or we can remember that*p + q = 1*. Therefore*q*= 0.12.Also remember that genes can have more than two alleles. Similar equations can be used to describe the frequencies in this case. If all the alleles of a gene occur in the same proportions for many generations, these alleles are called

*balanced polymorphisms*. However, if the allelic frequencies are seen to change from one generation to the next, the population is not in equilibrium.