Population+Genetics,+Inbreeding,+and+Risk+Management

=Objectives=


 * 1. Be able to use addition and multiplication rules of probability theory to calculate the outcomes of simple genetic crosses/experiments.** (p.540-541)

__Addition Rule__ Add probabilities for mutually exclusive events. i.e., if you flip a coin, you will get either heads __or__ tails.

__Multiplication Rule__ Multiply probabilities to determine probabilities of independent events. i.e., if you flip a coin twice, it is the probability that you will get a heads __and__ a tails.


 * 2. Be able to define and calculate allele frequency, genotype frequency, and phenotype frequency. Students are expected to be able to correctly solve patternsthat require such calculations.** (p.543)

__Allele Frequency__ The proportion of a specific allele relative to all other alleles in a population. For two alleles //A// and //a// present in a population, the relative frequencies are //p// and //q//, respectively. The sum of their proportions is: p + q = 1

Therefore, if you know the frequency of one allele in the population, say //A//, you can determine the frequency of the other allele as: q = 1 - p

You should also know the binomial form, p^2 + 2pq + q^2 = 1, if you are given genotype or phenotype frequencies.

__Genotype Frequency__ Proportion of a specific genotype relative to all other genotypes in a population.

__Phenotype Frequency__ Porportion of a specific phenotype relative to all other phenotypes in a population.


 * 3. Be able to explain why deleterious alleles are maintained in a population and to describe the theroetical basis for the hardy-Weinburg law** (p.544, 546-548)

When alleles for a gene are in HW equilibrium, the persistecne of recessive traits and deleterious genes can be maintained with the frequencies of p^2 + 2pq + q^2 = 1, as long as the requirements of Hardy-Weinburg equilibrium are met.


 * 4. Be able to describe what factors are required for maintanence of Hardy-Weinburg equilibrium.** (p.544)

HW equilibrium requires the maintanence of five factors: (1) Random Mating (2) Infinitely large population (i.e., no genetic drift) (3) No Mutations (or more specifically, no //net// mutations, meaning the number of new alleles arising is balanced by the number of alleles lost) (4) No migration into or out of the population (5) No selection of traits (


 * 5. Be able to explain how complicating factors affect usage of the Hardy-Weinburg law.** (545-548)

__Non-random Mating__ (1) Assortive Mating: when partners select each other based on a shared trait/characteristic (like with like) based on ethnic background, religion, level of intelligence, etc.

(2) Consanguinous Mating: mating between closely related individuals that can lead to increased homozygosity.

__Small Population Size__ (1) Genetic Drift: random drift of allele frequencies can lead to fixation of genes (2) Founder Effect/Bottleneck: Skewed allele frequencies after recovery; can propogate any trait, not just bad ones

__Mutation__ Rate not usually high enough to impact equilibrium, but new mutations can alter allelic frequencies

__Migrations__ Slow diffusion of alleles across a racial/geographic boundary can cause some alleles to be gained/lost.

__Selection__ Differences in reproductive fitness allows certain individuals to propagate genes more than others by having more offspring. Heterozygote advantage may also faciliate in the propagation of alleles that may be deletarious when in homozygotes.


 * 6. Be able to apply Hardy-Weinburg law to the solving of practical genetic problems such as calculating allele and carrier frequencies.** (p.550, 551)

HW theorem: (p + q)^2 = p^2 + 2pg + q^2


 * ||p (A)||q (a)||
 * p (A)||p^2 (A,A)||pg (A,a)||
 * q (a)||pg (A,a)||q^2 (a,a)||

Frequency of phenotypically normal individuals is p^2 + 2pg Frequency of carriers is 2pg Frequency of affected individuals is q^2

In the special case of X-linked traits, remember that while heterozygous mothers can still produce gamates with both alleles, the fathers can produced not only gamates with two alleles, but can also pass on a Y chromosome instead, making a 2x3 square.


 * ||p (X^A)||q (X^a)||Y||
 * p (X^A)||p^2 (X^A,X^A)||pq (X^A,X^a)||p (X^A,Y)||
 * q (X^a)||pq (X^A,X^a)||q^2 (X^a,X^a)||q (X^a,Y)||

The frequency of expected frequency or disease frequency is actually q^2 + q. That is, they consist of individuals who are genotypically (X^a,X^a) or (X^a,Y). However, if it is assume that the disease is rare, you can basically assume that all individuals who will be affected will be males and have the (X^a,Y) genotype.

> For example, if the frequency of q is 1/10,000 or 0.0001, then q^2 would be 1/100,000,000 or 0.00000001; this means that q^2 + q is 0.00010001. Because the q is so small, q^2 is practically negligable compared to q and can be ignored, so the disease frequecy is basically just q or 0.0001.

The frequency of unaffected individuals would be p^2 + 2pq+ p with genotypes of (X^A,X^A), (X^A,X^a), and (X^A,Y), respectively. The frequency of carriers would be 2pq with the genotype of (X^A,X^a).


 * 7. Be able to describe the relationship between mutation and selection in maintaining mutant alleles in populations that are in Hardy-Weinberg equilibirum and the differences observed for alleles causing Autosomal Dominant, Autosomal Recessive, and X-linked Recessive traits.** (p.556)

In populations, new alleles that arise by mutation are maintained or removed by selection.

Selection arises from differences in reproductive fitness, a measure of the number of offspring of an individual that survives to reproduce, compared to an appropriate control group.

Fitness (f) can equal between 0-1 Coefficient of selection equals 1-f or, s

Patients with f = 0 have disorders that never reproduce or produce children that cannot reproduce. All observed cases arise from new mutations only.

Patients with f =1 have essentailly normal reproductive fitness and observed cases are likely due to inheritance and rarely do to newly arising mutations.

In order for a mutant allele to remain in HW equilibrium, the mutation rate per generation (mu) must be sufficient to balance the proportion of mutant alleles (q) lost in each generation from selection (s).

__Autosomal Dominant__ mu = sq mu =(1-f)q

__Autosomal Recessive__ Selectionagainst deleterious recessive mutation is much less influential on allel frequencies because the frequency of affected individuals (aa) upon which selection acts represents a much smaller fraction of the total population.

__X-linked Recessive__ If phenotype is benign and males survive to reproduce, 1/3 of mutant alleles are males and 2/3 are females. Because selection only acts on hemizygous males, mu must equal selection coefficient times q/3.

mu = sq / 3 mu = (1-f)q / 3

If phenotype is lethal, 1/3 of all copies of mutant allele from males will be lost every generation. For the observed disease incidnece to be mantained, mutant alleles lost must be replaced by recurrent production of newly-arising mutations.


 * 8. Be able to define coefficient of relationshp and coefficient of inbreeding. Students will be expected to calculate (a) the proportion of alleles shared between close relatives and the (b) proportion of homozygous loci expectedin the children born to closely-related couples.**

__Coefficient of Relationship__ Measure of proportion of genes shared by two individuals. Proportion of genes shared is the probability athat a particular allele is shared. Coefficient of relationship is 1/2 for first degree relationships, 1/4 for second degree relationships, and 1/8 for third degree relationships.

__Coefficient of Inbreeding (F)__ Measure of the probability that a homozygote has recieved both alleles from the same ancestral source. Also the proportion of loci for which a person is homozygous. F is always 1/2 the coefficient of relationship


 * Genetic Relationship**||**Co. Relationshop**||**Co. Inbreeding**||
 * First Degree||1/2||1/4||
 * Second Degree||1/4||1/8||
 * Third Degree||1/8||1/16||

__First Degree Relationships__ Parent-Child Brother-Sister

__Second Degree Relationships__ Uncle-Niece Aunt-Nephew Double-first Cousins Brother-Half Sister

__Third Degree Relationships__ First Cousins

If two first cousins marry and produce a child, each parent shares common grandparents. As a thrid degree relation, the father and mother will both be 1/8 related to the grandfather and share a (1/8)x(1/8) or 1/64 risk of sharing a deletarious allele from the common grandfather. There is a similar risk that they will share a deletarious allele from a common grandmother, so the total risk is (1/64)+(1/64) or 1/32 risk that the child will be homozygous for a deleterious allele carried by the grandparents.


 * 9. Be able to apply Bayesian probability calculations to the solving of pedigree analysis problems, specifically, to Autosomal Dominant and Autosomal Recessive forms of inheritance.**

Prior probability - initial probability of an event Conditional probabilities - probabilities determined by observations or posterior information, usually in the from of results/numbers of previous births or information from biochemical tests Joint Probability - Probability resulting in the multipliction of the prior probability with each appropriate conditional probability Posterior/Relative Probability - Probability resulting from dividing the joint probability for each event by the sum of the joint probabilities.

Relative Probability = (Prior Probability)x(Conditional Probabilities) / (Sum of Joint Probabilities)