Population Genetics: Migration and Selection

Population Genetics

Migration

Migration in genetics refers to the movement of alleles from one population to another, which can alter allele frequencies and genetic diversity within populations. This process is distinct from the physical movement of organisms and focuses on gene flow.

• Definition: Migration is the transfer of alleles between populations due to the movement of individuals or gametes.

• Key Factors Affecting Migration:

  • Immigration rate (m): The proportion of new individuals entering a population.

  • Difference in allele frequencies: The genetic contrast between source and recipient populations.

• Effect on Allele Frequencies: Migration can increase genetic variation and reduce differences between populations.

Migration Equation

The change in allele frequency in a population after migration can be calculated as:

$p_1' = p_1 + m(p_2 - p_1)$

• $p_1$: Initial allele frequency in population 1

• $p_2$: Allele frequency in population 2

• $m$: Migration rate (proportion of migrants)

• $p_1'$: Allele frequency in population 1 after migration

Example: Squirrel Population

A wild population of squirrels is all black ($f(b) = 1$, $f(b') = 0$). A researcher releases gray squirrels ($f(b) = 0$, $f(b') = 1$) making up 5% of the final population. The frequency of the gray allele after migration is:

$p_1' = m(p_2 - p_1) + p_1$ $m = 0.05$, $p_2 = 1$, $p_1 = 0$ $p_1' = 0.05(1 - 0) + 0 = 0.05$

Thus, the frequency of the gray allele ($b'$) is 0.05.

Solving for Migration Rate

If three of the four variables ($p_1$, $p_2$, $p_1'$, $m$) are known, the fourth can be calculated:

$m = \frac{p_1' - p_1}{p_2 - p_1}$

Example: Given $p_1 = 0.62$, $p_2 = 0.03$, $p_1' = 0.45$: $m = \frac{0.45 - 0.62}{0.03 - 0.62} = 0.288$ So, 28.8% of the population was due to migration.

Selection

Selection is the process that determines which individuals become the parents of the next generation, thereby influencing allele frequencies and evolutionary outcomes.

Natural Selection

• The environment "decides": Individuals better adapted to their environment are more likely to survive and reproduce.

• Adaptation: Populations evolve to fit their environment or perish.

• Evolution: Subtle selective pressures drive gradual change.

• Bottlenecks: Moderate pressure reduces population size and genetic diversity.

• Extinction: Massive pressure can eliminate populations.

Artificial Selection

• Humans decide: Selection is directed by human preferences.

• Goal oriented: Traits selected for appearance, use, productivity, satisfaction, or whimsy.

Fitness and Phenotype

• Fitness: The reproductive success of a genotype, often measured by the number of offspring produced.

• Mutation and Selection: Most mutant alleles are recessive to wild type, but if heterozygotes have equal or greater fitness, the mutation can persist in the population.

Fitness and Allele Frequency

Selection acts on genotypes, altering their frequencies in the next generation based on relative fitness.

Genotype	AA	Aa	aa
Genotypic frequency in parents	$p^2$	$2pq$	$q^2$
Fitness of genotypes	1	$(1-s_1)$	$(1-s_2)$
Genotypic frequency after selection	$p^2$	$2(1-s_1)pq$	$(1-s_2)q^2$

Selection Example

Given starting frequencies $p = f(A) = 0.9$, $q = f(a) = 0.1$:

Genotype	AA	Aa	aa
Frequency	$p^2$	$2pq$	$q^2$
Number	810	180	10
Fitness	1	1	0.1
After selection	810	180	1

Calculate new allele frequency: $p = \frac{810}{991} + \frac{1}{2} \frac{180}{991} = 0.908$ Change in $p$, $\Delta p = 0.908 - 0.9 = 0.008$

Selection: One Preferred Genotype (AA)

When one genotype (e.g., AA) is preferred, the change in allele frequency can be calculated using:

$p_1 = \frac{p_0(1 - s_1q_0)}{1 - 2s_1p_0q_0 - s_2q_0^2}$

• $p_0$: Initial frequency of allele A

• $q_0$: Initial frequency of allele a

• $s_1$: Selection coefficient against Aa

• $s_2$: Selection coefficient against aa

Derivation and Application

The formula is derived by calculating the total number of survivors for each genotype and normalizing the frequency of the preferred genotype.

Example: If $p_0 = 0.6$, $q_0 = 0.4$, $s_1 = 0.25$, $s_2 = 0.50$:

$p_1 = \frac{0.6(1 - 0.25 \times 0.4)}{1 - 2 \times 0.25 \times 0.6 \times 0.4 - 0.5 \times 0.16}$ $p_1 = \frac{0.6(1 - 0.1)}{1 - 0.12 - 0.08}$ $p_1 = \frac{0.54}{0.8} = 0.675$

This shows how selection can increase the frequency of the preferred genotype in the population.

Additional info: These notes cover key concepts in population genetics, specifically migration and selection, which are central to understanding evolutionary genetics and population genetics chapters in a college genetics course.