Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift

Deviations from HWE

I. MutationII. MigrationIII. Non-Random MatingIV. Genetic DriftV. The Neutral Theory

Deviations from HWE

I. MutationII. MigrationIII. Non-Random MatingIV. Genetic DriftV. The Neutral Theory A. Variation 1. Phenotypic variation was often interpreted as having selective value; in fact, most studies confirmed that under one environmental condition or another, there was a difference in fitness among variations. Mayr (1963) "it is altogether unlikely that two genes would have identical selective value under all conditions under which they may coexist in a population. Cases of neutral polymorphism do not exist."

Deviations from HWE

I. MutationII. MigrationIII. Non-Random MatingIV. Genetic DriftV. The Neutral Theory A. Variation 1. Phenotypic variation was often interpreted as having selective value; in fact, most studies confirmed that under one environmental condition or another, there was a difference in fitness among variations. Mayr (1963) "it is altogether unlikely that two genes would have identical selective value under all conditions under which they may coexist in a population. Cases of neutral polymorphism do not exist."

2. In the 1960's - lots of electrophoretic work revealed a vast amount of variability - variability at the gene or protein level that did not necessarily correlate with morphological variation. Some are silent mutations in DNA, or even neutral substitution mutations. This variation results in heterozygosity.

CCC = ProlineCCU = ProlineCCA = ProlineCCG = Proline

Deviations from HWE

I. MutationII. MigrationIII. Non-Random MatingIV. Genetic DriftV. The Neutral Theory A. Variation 3. Most populations showed mean heterozygosities across ALL loci of about 10%.

- And, about 20-30% of all loci are polymorphic (have at least 2 alleles with frequencies over 1%).

Drosophila has 10,000 loci, so 3000 are polymorphic. At these polymorphic loci, H = .33

Conclusion - lots of variation at a genetic level... is this also solely maintained by selection?

Deviations from HWE

I. MutationII. MigrationIII. Non-Random MatingIV. Genetic DriftV. The Neutral Theory A. Variation B. Genetic Load

Deviations from HWE


1. "HARD" Selection can 'cost' a population individuals:

Deviations from HWE


1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of differential fitness values.

Deviations from HWE


1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of differential fitness values. - the "breeding population" is smaller than the initial population.

Deviations from HWE


1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of differential fitness values. - the "breeding population" is smaller than the initial population.

- Reproductive output must compensate for this loss of individuals

Deviations from HWE


1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of differential fitness values. - the "breeding population" is smaller than the initial population. - Reproductive output must compensate for this loss of individuals - The stronger the "hard" selection, the more individuals are lost and

the higher the compensatory reproductive effort must be.

Deviations from HWE


1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of differential fitness values. - the "breeding population" is smaller than the initial population. - - Reproductive output must compensate for this loss of individuals - The stronger the "hard" selection, the more individuals are lost and

the higher the compensatory reproductive effort must be. - The 'cost' of replacing an allele with a new, adaptive allele =

"Genetic Load" (L) L = (optimal fitness - mean fitness)/optimal fitness. Essentially, this is a measure of the proportion of individuals that will die as a consequence of this "hard" selection. The lower the mean fitness, the further the population is from the optimum, and the more deaths there will be.

B. Genetic Load1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem?

B. Genetic Load1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? - If variation is maintained by selection, we are probably talking

about "heterosis" - selection for the heterozygote where the heterozygote has the highest fitness (and both alleles are maintained). (Selection against the heterozygote can only maintain variation at equilibrium, and this is unstable).


about "heterosis" - selection for the heterozygote where the heterozygote has the highest fitness (and both alleles are maintained).

- The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection.




- Let's consider even a "best case" scenario:




- Let's consider even a "best case" scenario: - mean fitness = 1 - H((s+t)/2)




- Let's consider even a "best case" scenario: - mean fitness = 1 - H((s+t)/2) - If s and t = .1 (very weak), and H = .33 (average for Drosophila, above), then the mean fitness = 0.967.




- Let's consider even a "best case" scenario: - mean fitness = 1 - H((s+t)/2) - If s and t = .1 (very weak), and H = .33 (average for Drosophila, above), then the mean fitness = 0.967. - Not bad; not much death due to selection in this situation...





- HOWEVER, there are 3000 polymorphic loci across the genome. So, mean fitness across the genome = (0.967)^3000!





- HOWEVER, there are 3000 polymorphic loci across the genome. So, mean fitness across the genome = (0.967)^3000! This becomes ridiculously LOW (0.19 x 10-44) relative to the best case genome that is heterozygous at every one of the 3000 loci. - So, some individuals die because they are homozygous (and less fit) at A, others die because they are homozygous (and less fit) at B, other die because they are homozygous (and less fit) at C, and so forth...





In this case, the load is SO GREAT across the genome that almost NOBODY lives to reproduce. And those that do can not possibly produce enough offspring to compensate for this amount of death.

B. Genetic Load1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem?

So, hard selection can not be SOLELY responsible for the variation we observe... a population could not sustain itself under this amount of genetic load...

B. Genetic Load1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Solutions a. Selectionists - Not all selection is "hard", imposing additional deaths above

background mortality.


background mortality. - There is also "soft" selection, in which the death due to selection

occurs as a component of background mortality, not in addition to it.


background mortality. - There is also "soft" selection, in which the death due to selection

occurs as a component of background mortality, not in addition to it. - For instance, consider territoriality or competition for a resource.

Suppose there is only enough food or space to support 50 individuals, but 60 offspring are produced each generation. Well, each generation there are 10 deaths and there are 50 “survivors".

B. Genetic Load1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Solutions a. Selectionists

- Suppose we have a population of aa homozygotes initially. All the territories are occupied by aa individuals and 10 individuals die.



- Well, If an 'A' allele is produce by mutation and heterozygotes have the highest relative fitness (probability of acquiring a territory), then the allele "A" increase in frequency to equilibrium....




- Selection occurs, BUT THERE ARE STILL ONLY 10 DEATHS PER GENERATION.





- In this case there is NO genetic load, as selection is NOT causing ADDITIONAL mortality. It is just changing the probability of who dies.





- In this case there is NO genetic load, as selection is NOT causing ADDITIONAL mortality. It is just changing the probability of who dies.

- So, selection across lots of loci does not NECCESSARILY lead to impossible loads.... as long as it is SOFT SELECTION

B. Genetic Load1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Solutions a. Selectionists b. Neutralists


- Maybe MOST of this variation is NEUTRAL, and is simply maintained by drift as new mutant alleles sequentially replace one another.


- Maybe MOST of this variation is NEUTRAL, and is simply maintained by drift as new mutant alleles sequentially replace one another.

c. In a sense, the argument is really about selection.


- Maybe MOST of this variation is NEUTRAL, as is simply maintained by drift as new mutant alleles sequentially replace one another.


Selectionists state that selection is important for 2 reasons - it eliminates bad alleles and FAVORS advantageous alleles.


- Maybe MOST of this variation is NEUTRAL, as is simply maintained by drift as new mutant alleles sequentially replace one another.


Selectionists state that selection is important for 2 reasons - it eliminates bad alleles and FAVORS advantageous alleles.

Neutralists agree that selection weeds out deleterious alleles, but they claim that this leaves a set of alleles that are functionally equivalent - neutral - in relative value.

And changes in these equivalent alleles occur as a consequence of drift.

Deviations from HWE

I. MutationII. MigrationIII. Non-Random MatingIV. Genetic DriftV. The Neutral Theory C. Neutral Variation

Motoo Kimura1924-1994

V. The Neutral Theory C. Neutral Variation

- Variation occurs at many levels, from genes to proteins to physical and behavioral characteristics of organisms.



- adaptive phenotypic variation is due to selection.



- adaptive phenotypic variation is due to selection. - But is ALL genetic variation of selective value?



- adaptive phenotypic variation is due to selection. - But is ALL genetic variation of selective value? - "no"; obviously, silent mutations are not maintained by selection



- adaptive phenotypic variation is due to selection. - But is ALL genetic variation of selective value? - "no"; obviously, silent mutations are not maintained by selection - So, Kimura suggested that there is too much variation at the DNA

level to be explained by selection... he suggested that MOST of the variation in DNA is of NO selective value - it is NEUTRAL VARIATION.





- Curiously, the rate of replacement by drift, alone = the rate of mutation:






1) The number of new alleles produced at a locus = 2N(m), where m is the mutation rate.







- So, if the average mutation rate is 1 in 10,000, but there are 20,000 individuals (2N = 40,000 alleles), then on average 4 new alleles will be produced by mutation every generation.








2) Each allele has a probability of fixation = 1/2N.








2) Each allele has a probability of fixation = 1/2N. 3) So, the rate of replacement = (number of new alleles formed) x

(probability one become fixed) = 2N(m) x 1/2N = m per generation.

V. The Neutral Theory C. Neutral Variation D. Predictions and Results


1. Rates of molecular evolution should vary in functional and non-functional regions



- Rates should vary in different codon positions. Variation at the third position should be higher, because these are usually silent mutations. Mutations at the first two position change amino acids, and these changes are deleterious.



- Rates should vary in different codon positions. Variation at the third position should be higher, because these are usually silent mutations. Mutations at the second position change amino acids, and these changes are deleterious. PATTERN CONFIRMED.




- Rates should vary in coding and non-coding regions. Variation in Introns should occur more rapidly than variation in exons, since introns are not transcribed and are also invisible to selection.




- Rates should vary in coding and non-coding regions. Variation in Introns should occur more rapidly than variation in exons, since introns are not transcribed and are also invisible to selection. PATTERN CONFIRMED





- Rates should vary in functional and non-functional regions of proteins.





- Rates should vary in functional and non-functional regions of proteins. PATTERN CONFIRMED






- Rates should vary between vital proteins and less vital proteins.






- Rates should vary between vital proteins and less vital proteins. PATTERN CONFIRMED



2. Rates of replacement (substitution of one fixed allele by another that reaches fixation) should be constant over geologic time.




- If changes are random and occur at a given rate, then they should "tick" along like a clock.





- Selection should slow change when an adapted complex occurs, and speed rates when a new adaptive combination occurs, like in obviously adaptive morphological traits. - PATTERNS CONFIRMED (usually).





- Selection should slow change when an adapted complex occurs, and speed rates when a new adaptive combination occurs, like in obviously adaptive morphological traits. - PATTERNS CONFIRMED (usually).




3. Rates of morphological change should be independent of the rate of molecular change.





- "Living Fossils" show extreme genetic change and variation, yet have remained morphologically unchanged for millenia. And, the rate of genetic change in this morphologically constant species is the same as in hominids, which have changed dramatically in morphology over a short period.





- "Living Fossils" show extreme genetic change and variation, yet have remained morphologically unchanged for millenia. And, the rate of genetic change in this morphologically constant species is the same as in hominids, which have changed dramatically in morphology over a short period. PATTERN CONFIRMED

V. The Neutral Theory C. Neutral Variation D. Predictions and Results E. Problems and Resolutions


1. Selection also explains different mutation rates in functional and non-functional regions


1. Selection also explains different mutation rates in functional and non-functional regions Essentially, since most adaptive changes should be slight, fewer mutations in functional regions are likely to improve function. So, the rate of change is "constrained" to only those changes that are neutral or ADAPTIVE. Also, a change of one AA is likely to cause a smaller change if it is in a less functional region. "Tweeking" less functional regions might be adaptive, whereas "tweeking" functional regions are more likely to be deleterious.



2. A truly neutral clock should tick off mutations at a constant rate. But should this ticking occur per unit time, or per generation?




- Since mutations produce new alleles (a new "tick"), and mutations only occur during replication of the DNA, it would seem that a truly neutral clock should tick at a rate dependent on the generation time of the organism.





- Species with rapid generation times should accumulate mutations at a faster rate than long-lived species with slower generation times.






- This is true of non-coding DNA... but not true for proteins, as we have seen. Proteins accumulate mutations in absolute time, not generational time.






- This is true of non-coding DNA... but not true for proteins, as we have seen. Proteins accumulate mutations in absolute time, not generational time. THIS IS INCONSISTENT WITH THE NEUTRAL MODEL

V. The Neutral Theory C. Neutral Variation D. Predictions and Results E. Problems and Resolutions F. The Nearly Neutral Model (Ohta)


- Ohta included the very weak effect against slightly deleterious mutations. He found that, if s < 1/2Ne, then alleles are essentially neutral and become fixed as drift would predict.



- In other words, in small populations, drift predominates unless selection is fairly strong (in a population of Ne = 5, drift will predominante unless s > 0.1).



- In other words, in small populations, drift predominates unless selection is fairly strong (in a population of Ne = 5, drift will predominante unless s > 0.1).

- In large populations, selection predominates, even if it is fairly weak (if Ne = 10,000, then selection will predominate if s > 0.00005).


SO..... (GET READY FOR THIS!!!!)

F. The Nearly Neutral Model (Ohta)SO. - We observe a constant AA substitution rate across species, even

though we would expect that species with shorter generation times should have FASTER rates of substitution.

Sub

. R

ate

Short GEN TIME Long

EXP.

OBS.



- So, something must be 'slowing down' this rate of substitution in species with short gen. times. What's slowing it down is their large populations size, such that the effects of drift, alone, are reduced.

Sub

. R

ate

Short GEN TIME Long

EXP.

OBS.

LARGE POP. SIZE




- Likewise, species with long generation times have small populations, and substitution by drift and fixation is more rapid than expected based on generation time, alone.

Sub

. R

ate

Short GEN TIME Long

EXP.

OBS.

SMALL POP. SIZE




- Likewise, species with long generation times have small populations, and substitution by drift and fixation is more rapid than expected based on generation time, alone.

Sub

. R

ate

Short GEN TIME Long

EXP.

OBS.

SMALL POP. SIZE

SO. - The constant rate of AA substitution across species is due to the balance between generation time and population size.


SO. - The constant rate of AA substitution across species with different

generation times is due to the counter-balancing effect of population size, which is inversely correlated with generation time.

V. The Neutral Theory C. Neutral Variation D. Predictions and Results E. Problems and Resolutions F. The Nearly Neutral Model (Ohta) G. Conclusions


- Neutral variability certainly exists; in non-coding DNA, especially.



- However, it is possible that selection maintains molecular variation as well, particularly in coding regions.



- However, it is possible that selection maintains molecular variation as well, particularly in coding regions.

It is also possible that selection maintains variability in non-coding

regions, as well, if these are "functional" in a structural or regulatory manner.

IV. Selection and Other Factors

A. Mutation


A. Mutation

- Mutation can maintain a deleterious allele in the population against the effects of selection, such that:


A. Mutation


q(eq) = √(m/s)


A. Mutation


q(eq) = √(m/s)

- more deleterious alleles are maintained if m increases, or if selection differential declines... (if it is not that bad to have it)…


A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Locus

- consider a locus with selection against the heterozygote

p = 0.4, q = 0.6 AA Aa aa

Parental "zygotes" 0.16 0.48 0.36 = 1.00

prob. of survival (fitness) 0.8 0.4 0.6

Relative Fitness 1 0.5 0.75

Corrected Fitness 1 + 0.5 1.0 1 + 0.25

formulae 1 + s 1 + t

peq = t/(s + t) = .25/.75 = 0.33


A. Mutation


1. Single Locus

- consider a locus with selection against the heterozygote

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75


A. Mutation


1. Single Locus

- suppose there is random movement up the 'wrong' slope?

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75


A. Mutation


1. Single Locus

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

- if this is a large pop with no drift, the population will become fixed on the 'suboptimal' peak, (p = 0, q = 1.0, w = 0.75).


A. Mutation


1. Single Locus

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

- BUT if it is small, then drift may be important... because only DRIFT can randomly BOUNCE the gene freq's to the other slope!


A. Mutation


1. Single Locus

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

- And then selection can push the pop up the most adaptive slope!


A. Mutation


1. Single Locus

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

- The more shallow the 'maladaptive valley', (representing weaker selection differentials) the easier it is for drift to cross it...


A. Mutation


2. Two Loci - create a 3-D landscape, with "mean fitness" as the 'topographic relief"

Suppose AAbb and aaBB work well, but combinations of the two do not (epistatic, like butterfly mimicry).

f(A)

1.0

1.0f(B)


A. Mutation



Again, strong selection or weak drift will cause mean fitness to move up nearest slopes.

f(A)

1.0

1.0f(B)


A. Mutation



Only strong drift or weak selection and some drift (shallow valley) can cause the population to cross the maladaptive valley.

f(A)

1.0

1.0f(B)


A. Mutation


- so, the interactions between drift and selection are necessary for a population to find the optimal adaptive peak... think about this in the context of peripatric speciation.... THINK HARD about this...

Documents

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift