#BIS101 F2013 Lecture 5: Quantitative Traits
Skip 18.1 (but read def. of haplotype)
Skip inbreeding
Skip box 18.5, 18.6
##qualitative traits
- red or green, wrinkled vs. round, etc.
- discrete states
- usually simple genetic basis -- one or two genes
##quantitative traits
- height, IQ, etc. not discrete
- usually complex genetic basis -- many genes or QTL
- each QTL is a normal Mendelian locus, but their effects combine to form phenotype
- Simple example w/ two loci. each big allele adds 1 to phenotype
A cross AABB with aabb and look at F2 (draw out A's and B's). Showing possible genos/phenos,
| A locus | B locus | Phenotype |
|---|---|---|
| 1 1 | 1 1 | 4 |
| 1 1 | 1 0 | 3 |
| 1 1 | 0 1 | 3 |
| 1 1 | 0 0 | 2 |
| 1 0 | 1 1 | 3 |
| 1 0 | 1 0 | 2 |
| 0 1 | 1 0 | 2 |
| 1 0 | 0 1 | 2 |
| 0 1 | 0 1 | 2 |
| 1 0 | 0 0 | 1 |
| 0 1 | 0 0 | 1 |
| 0 0 | 1 1 | 2 |
| 0 0 | 1 0 | 1 |
| 0 0 | 0 1 | 1 |
| 0 0 | 0 0 | 0 |
but there will be 2 of each het (1:2:1 Mendel), so distribution of phenos will be:
and it looks like (draw):
As you get more and more loci, becomes normal.
Most phenotypes of interest are quantitative.
- Even color (how much of the pigment)
- Disease: Diabetes not all the same
Statistically, you assume a quant. trait is controlled by an infinite number of genes
- obv. not infinite, but in many cases (human height) it's probably hundreds or thousands
- not all have to have same effect as above. e.g fw2.2 tomato size
- but each gene here isn't special. can have different effect size, but all follow Mendel.
####Phenotypic variation
The equation: V_P = V_G + V_E (what is variance?)
- V_P we can measure: Sum(x-xbar)^2/n
- explain genetic variance, what is environmental varianc
Redraw histogram w/ variation around values due to environment.
- e.g. take identical twin mice and I give one lots of food, and the other none. V_E will determine all of phenotypic difference!
####Heritability
H^2=V_G/V_P = broad sense heritability
heritability is the % of phenotypic variation due to variation in genes
- NOT whether or not a trait varies
- NOT whether or not it's genetic
- e.g. fitness in natural populations
- in humans reproduction: lots of choice/culture/economy going into how many kids
- doesn't mean ability to reproduce is not genetic, just that much of the variance is V_E
- keep the genes the same, but increase environmental variance, heritability goes down
- NOT explain between group differences
- because environments may differ & depends on environ
- if we take mouse weight, heritability in mouse weight will differ in an environment where mice are starved and in an environment where there is lots of food (perhaps)
- NOT % due to genes
- 80% narrow sense heritability for height NOT mean 20% of your height is environmental
- means 20% of the total variation seen among population is due to environment
- even when high, doesn't mean all change due to genes
- Dutch height has increased maybe 16cm over last 150 years
- not very long for nat. selection to work (~7 generations)
- probably mostly due to improved health care, food, etc.
- V_G may change as allele frequencies change (popgen)
| A locus | B locus | Phenotype |
|---|---|---|
| 1 1 | 1 0 | 3 (3.2) |
| 1 1 | 0 0 | 2 (2.2) |
| 1 0 | 1 1 | 3 (2.7) |
| 0 1 | 0 1 | 2 (1.5) |
| 0 0 | 1 0 | 1 (0.8) |
| 1 0 | 0 0 | 1 (1.2) |
V_P=0.6777 (or 0.8) V_G=0.677 (or 0.8) no V_E
Redo with parenethetical numbers
Now V_P = 0.71 (or 0.85) and V_G same at 0.677, remainder is V_E
We usually don't know genes, so can't directly calculate V_G.
####How to estimate
One way to estimate broad sense, in humans, is looking at twins separated.
Genes identical, environment diff. Similarity must be due to genes.
Covariance in phenotype: (Sum(X-Xbar)(Y-Ybar))/n <- first and second twin
V_E falls out if we assume no correlation, thus Covariance between twin 1 and twin 2 is all genetic -> V_G
From twin studies:
| Trait | H^2 |
|---|---|
| Height | 0.88 |
| Waist circumference | 0.25 |
| IQ | 0.69 |
| alcoholism | 0.5 |
| autism | 0.9 |
| religiosity | 0.4 |
V_G = V_A + V_D +V_I
- V_A additive -- stuff we most care about b/c responds easily to selection and easy to model and work with, dominance, interaction b/t genes)
h^2=V_A/V_P = narrow sense heritability -> can calculate from phenotypic means of progeny
narrow sense is what geneticists care about, what responds to selection, etc.
Think about selecting on a phenotype -- selection wants bigger mouse:
AA 20 cm Aa 15 cm aa 10 cm
Selection is easy.
AA 20 cm Aa 20 cm aa 10 cm
Selection doesn't work as well because brings along a little a with many of the big A.
Can estimate heritability by covariance between parents and offspring
- same environment, offspring inherit 1/2 genes from parent
- so COV(p-o)=1/2 V_A
####Breeder's equation R=h^2*S
If you know heritability (from some other estimate) you can predict response to selection on quant. trait
Different from response to selection on a single locus (what we will talk about in popgen)
But also if I select on a trait, can use response to estimate narrow sense heritability.
What does low h^2 mean ? means that won't respond to selection well b/c most of phenotype is not due to additive genetic effects
####Mapping QTL
looking for statistical association between a genetic marker and a phenotype
Draw cross between fluffy rabbit and hairless rabbit
- draw 1 pair of chromosomes w/ markers
- phenotype varying among offspring
- statistical association that everytime you see marker X, ~10% fluffier
| M1 | M2 | M3 | M4 | Phenotype |
|---|---|---|---|---|
| MM | Mm | Mm | mm | 3.89 |
| Mm | Mm | mm | Mm | 1.29 |
| MM | mm | Mm | Mm | 3.63 |
| mm | MM | MM | Mm | 5.42 |
| MM | Mm | Mm | mm | 3.37 |
| Mm | MM | mm | MM | 1.99 |
| Mm | mm | Mm | mm | 3.05 |
| MM | mm | Mm | MM | 3.91 |
| mm | Mm | MM | Mm | 5.26 |
| mm | Mm | mm | mm | 1.04 |
| -0.02 | 0.01 | 0.97 | 0.1 |
Can you cross 2 parents w/ same phenotype and get variation ?
- yes, think two people exactly 5'7"
- Example w/ our two locus system: AAbb = 2 and aaBB = 2 and AABB = 4 and aabb = 0.
Parents can harbor alleles that don't make initial sense
- AABBcc x aabbCc (4 x 1 phenotype)
- new allele in low parent that not present in high parent!
Since crosses and linkage mapping are hard in some organisms (humans), we do association mapping. Also seen as GWAS -- genome wide association study.
Genotype a large number of unrelated individuals and look for the correlation there.
Nice example in humans: cilantro taste - SNP explains whether you like the taste of cilantro
Lots of statistical issues. E.g. twitter example claiming left-handedness is not genetics. Lots of genes of small effect ≠ nongenetic.