Evolution and Natural Selection

Darwin, in 1859, published the Origin of Species, arguing that organisms evolve over time by natural selection.

The process of evolution by natural selection rests upon three premises:

Parents with characteristics that improve fitness are more likely to have offspring. If heritable, these characteristics increase in frequency leading the population to change over time (=evolve).

Fitness

An understanding of the genetic basis of life has provided support for Darwin's first and third premises, explaining how new variants can be produced (mutation of the DNA) and how traits can be inherited (genetic transmission from parents to offspring).

We turn now to the second premise, that selection occurs.

Darwin (1859) in the Origin of Species argued:

"As many more individuals of each species are born than can possibly survive, and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected."

Examples of Selection

Some Definitions

  • Gene: Segment of the DNA, generally a region that codes for a single protein.
  • Locus: A site on a chromosome (usually synonymous with gene).
  • Allele: A variant of a gene (a particular sequence).
  • Genotype: The alleles carried by an individual at a gene.
  • Haploid: Individuals that carry one copy of each gene.
  • Diploid: Individuals that carry two copies of each gene.
  • Genotype: The alleles carried by an individual at a gene.
  • Homozygote: Individual that carries two identical alleles.
  • Heterozygote: Individual that carries two different alleles.
  • Fitness: The average contribution of one allele or genotype to the next generation.

What factors might contribute to fitness?

Fitness

Consider a haploid population with two alleles (A, a).
  • NA = number of A individuals
  • Na = number of a individuals
  • N = total number of individuals (NA+Na)
  • RA = average number of surviving offspring per A individual
  • Ra = average number of surviving offspring per a individual
In this population, the frequency of A individuals is:

The frequency of a individuals is:

A individuals will have on average NA RA offspring, while a individuals will have Na Ra offspring on average.

The frequency of A individuals among the offspring is therefore:

More Definitions

  • Absolute Fitness (R): Average number of surviving offspring (eg RA).
  • Relative Fitness (W): Fitness of one genotype divided by the fitness of a reference genotype (say Wa=1 and WA=RA/Ra)
  • Selection coefficient (s): The amount by which relative fitnesses differ from 1 (eg s = WA-1)

Point 1: It is often easier to measure relative fitness rather than absolute fitness.

Point 2: Population genetics models generally require only relative fitnesses, eg

Fitness

Now consider a diploid population with two alleles and three genotypes (AA, Aa, aa).

  • WAA = relative fitness of AA individuals
  • WAa = relative fitness of Aa individuals
  • Waa = relative fitness of aa individuals

These may be ordered in a number of ways:

  • WAA > WAa > Waa Directional selection (favoring A)
  • WAA < WAa < Waa Directional selection (favoring a)
  • WAA < WAa > Waa Overdominant selection (heterozygote advantage)
  • WAA > WAa < Waa Underdominant selection (heterozygote disadvantage)

More terms to remember:

If WAA=WAa, allele A is said to be "dominant" and allele a is said to be "recessive".

[Note: geneticists usually name alleles that are recessive with lower case letters (eg ubx) and those that are dominant with upper case letters (eg Ubx).]

If WAa=Waa, allele a is said to be "dominant" and allele A is said to be "recessive".

Even more terms to remember:

"Additive" "Partially dominant" "Partially recessive"

Dynamics without selection

Consider a diploid population with two alleles (A and a).

Relative fitnesses of AA, Aa, and aa all equal one. Let

  • x = frequency of AA individuals
  • y = frequency of Aa individuals
  • z = frequency of aa individuals

x+y+z=1. Why?

Case 1: Individuals produce haploid gametes that form a gamete pool.

The frequency of allele A in the gamete pool will be? p =

The frequency of allele a in the gamete pool will be? q =

Gametes unite at random in the gamete pool to produce diploid offspring. To calculate offspring frequencies we use mating tables.

Gamete Mating Table

These are known as the Hardy-Weinberg frequencies.

Point 1: Populations not at Hardy-Weinberg reach Hardy-Weinberg equilibrium after only one generation of random mating (as in the above example). Caveat: Generations must be discrete.

The frequency of allele A in the next gamete pool will be? p' =

The frequency of allele a in the next gamete pool will be? q' =

Point 2: In the absence of selection and mutation, allele frequencies stay constant. Segregation does not change allele frequencies.

Zoology 500 D

Dynamics without selection

Case 2: Individuals mate and these mating pairs produce offspring.

Will Hardy-Weinberg frequencies still obtain?

Again, to calculate offspring frequencies we use mating tables.

Individual Mating Table

This shows that x'=p2: Hardy-Weinberg equilibrium is reached after only one generation of random mating.

Since the allele frequency of A in the parents is x+y/2=p (by definition), and since the allele frequency of A in the offspring equals x'+y'/2 = p2 + 2 p q/2 = p (p+q) = p , the allele frequencies again remain constant.

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