ZOOL 304, Class Notes

Chapter 3, Jan. 27 - Feb. 10.  

Text reading:  Chapter 3.

• Assignment for written preparation.
• Discussion.
  • Introduction
  • Adaptive vs. neutral evolution
  • Randomness
  • Fitness
  • Comment on text Chapter 3.
    • Fitness defined.
    • An example to illustrate basic characteristics of neutral evolution
    • How can genetic variation be neutral?
    • What are the causes of random evolutionary change?
    • Genetic drift and molecular evolution
  • Further comments on genetic drift
  • Further comments on neutral evolution
• Study questions for text reading.

Notes for chapter 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17

Introductory comments.

In the previous chapter (Chapter 2), we examined adaptive evolution.  In this chapter (Chapter 3), we consider neutral evolution.  In the next chapter (Chapter 4) we learn about genetic processes that affect genetic variation within populations.  Ultimately, all evolution must be explained in terms of these processes.  These chapters present the core concepts for understanding the mechanisms of evolution.

Adaptive evolution vs. neutral evolution

By definition, neutral evolution modifies traits in ways that do not affect fitness. In the context of evolution, "neutral" means "NOT adaptive".

Evolution of some form is inevitable whenever there is variation both in reproductive success and in heritable traits.  

• If variation in reproductive success is caused by variation in a heritable trait, then evolution of that trait is adaptive.
• If variation in reproductive success is random with respect to variation in some heritable trait, then evolutionary change in that trait is neutral (i.e., NOT adaptive).

Neutral evolution is evolutionary change which is NOT based on fitness differences.

Like fitness (below), neutrality is a relative term.  Traits are not neutral; trait variation is neutral, if the trait variants do not differ from one another in reproductive success.  Evolution is neutral if the change from one variant to another is not caused by a statistically significant difference in reproductive success.

NOTE:  The word "trait" may refer EITHER to some characteristic feature that is variable (e.g., "eye-color") OR to a particular state or condition of a feature (e.g., "blue-eyed trait" vs. "brown-eyed trait").  I usually use "trait" to refer to a feature, while I use a term like "trait variant" or "character state" to refer to a particular condition or measurement of that feature.  The term "trait" may also be used to refer either to phenotype or genotype.  In most cases, context is adequate to determine the intended usage.  

Since causation is associated with correlation (effects should be correlated with their causes), we conclude that adaptive evolution implies a correlation between some particular heritable variation and variation in reproductive success, as explained in Chapter 1 (pp. 9-10).  Absence of such correlation implies that trait variation does not affect reproductive variation, and hence that evolutionary change in the trait is neutral.  Hence our textbook defines the difference between adaptive evolution and neutral evolution on the basis of presence or absence of correlation between heritable variation and variation in reproductive success.  

It should be understood that this definition refers to a statistically significant correlation, preferably one which is predictable, at least in principle (i.e., one based on a causal relationship between the qualities of a trait and the effects of that trait on reproductive success, whether or not the actual mechanism has been demonstrated). 

This somewhat picky point is similar to the distinction made in probability, between the abstract or ideal expectation of 50 per cent heads in a series of "fair" coin flips and the realized probability in some actual series of flips, which usually differs from 50:50 by a statistically-insignificant amount.  In the process called genetic drift, the fact of drift is itself a realized correlation between some heritable variation and reproductive success.  But that correlation occurred by chance; the heritable variation did not cause the variation in reproductive success.  Although drift and other aspects of neutral may have important and biologically significant consequences, that significance should be clearly distinguished from the measure of statistical significance by which we recognize the difference between true correlation and chance correlation. 

In adaptive evolution, causation flows from heritable variation to variation in reproductive success to change in the heritable trait value.  In neutral evolution, causation flows from chance association between reproductive success and heritable variation to change in heritable trait value.  This is most easily understood in the case of genetic drift.

Randomness.

The mathematics of probability yields some strange and often counter-intuitive expectations.  The general difficulty most people have in understanding probability is powerfully demonstrated by huge profits earned by casinos and other gambling establishments.  The following are some general points with some significance for understanding stochastic processes in evolution.

• Genetic drift behaves much like a random walk.
   
• The so-called "molecular clock" is also the statistical outcome of random processes.

• Random events are unaffected by what has gone before.
  • There is never any "tendency" to restore an average.
  • There is no "balance" between alternative possibilities.
  • Events are not "directed" toward the most likely expectation (nor toward the most useful outcome).
     

• The "most likely" expectation can be extremely improbable.
  • If you flip a fair coin 100 times, the outcome of 50 heads and 50 tails is both:
    • the most likely expectation.
    • a rather improbable result.
  • Explanation.  Of all the many possible outcomes, the 50:50 ratio is the one that is most likely.  However, the probabilities for 49:51 and 51:49 are both almost as high, while 48:52 and 52:48 are also close, etc.  Thus, although 50:50 has the highest probability of any particular outcome, the absolute probability for exactly 50:50 is actually rather low (about 1 in 12).  (Results of class probability exercise.)

  • Here's an example which may be more intuitive.  If you throw darts at a target...
    • A bull's-eye is very unlikely (unless you are very skillful).
    • But the most likely expectation for each dart is a bull's eye.
    • Explanation.  A bull's-eye is more likely than a hit on any other similarly size spot located away from the point of aim.  No matter how sloppy your aim is, all the throws will be scattered around the bull's-eye (unless there is systematic bias for one side or another).  Therefore, the most likely impact site must be the center, the average of all the scattered positions.  Certainly no other particular position is more likely.  But the sum of all the other, non-bull's-eye positions is so large, that the probability of a bull's-eye remains quite low (even though it remains the "most likely" expectation).
       

• How does this apply to population genetics?
  • For finite populations, the Hardy-Weinberg model gives the most likely expectation for gene frequencies after one round of random mating.
  • However, matching that expectation exactly is extremely improbable.  Some change is almost certain.
  • These many small changes lead to "genetic drift" (more), which is often characterized as a random walk of allele frequencies.
    • At each generation, gene frequencies will almost certainly change rather than remain constant, although typically by only a small amount.
    • At each generation, the current frequencies become the source for the next generation.  There is no tendency to restore the original frequency, so sequential changes can accumulate.
    • (In the tossing of a fair coin, the current expectation is always 50:50 regardless what has gone before.  In a random walk, the current expectation of an increase or a decrease is 50:50 regardless of what past or current frequencies are.)
  • The accumulation of neutral genetic differences between related populations, due to drift, is the so-called "molecular clock".

• What is a random walk?

• The mathematical idea of a random walk is sometimes referred to as "the drunkard's walk".  In this classic, picturesque metaphor, a drunkard staggers along the sidewalk.  At each step, he may veer unpredictably either to the left or to the right.  
• In a different analogy, the result of a random walk can be compared to that of a dart game in which there is no fixed, predetermined target.  Instead, the target for each throw is a small circle drawn around the point of the previous dart, wherever that previous dart might have landed.
• In a random walk, each step takes as its starting point the position reached by the preceding step.  From that point, the direction of the next step is random.  
• In a random walk, there is no bias toward either side, nor toward the middle, nor toward the initial starting point.  
• The behavior of random walks can appear paradoxical.
  • In a random walk, at any given moment the most likely prediction for a future position is the current position.  (For population genetics, this prediction is equivalent to the Hardy-Weinberg expectation.)  Explanation:  There is no expectation for movement in one particular direction to be preferred over another.  Hence, the "most likely" position cannot be biased in any direction.  This is also the "average" position if many separate trials are averaged.
  • Nevertheless, the most-likely distance from the current position is expected to increase over time.
• The above expectations apply not only at the beginning but indefinitely, so that from any point away from the starting position, there is no preference for moving back toward the start nor further away from the start.
  

• How does the random walk apply to population genetics?
  • Genetic drift (more) is a random walk with absolute endpoints.
  • In genetic drift, as in a random walk, the random change at each generation begins with the frequencies of the previous generation.
  • There is no "force" that would restore the original frequencies.
  • For any particular allele, the process of genetic drift ends when the frequency of that allele becomes 0 or 1.  Once the random walk for that allele reaches either limit (extinction or fixation), the random walk is over.
  • Consider the drunkard's walk metaphor.  Imagine a drunkard staggering along a sidewalk.  If the drunkard staggers all the way to one side of the sidewalk, he will fall into the gutter and be carted off by the police.  He's then gone from the sidewalk.  If he staggers to the other side of the sidewalk, he runs into the wall, sits down, and stays there until morning.  At each step, there's no way to predict which way he will stagger.  But if he's closer to one side, that's the side he is most likely to reach first.  (To apply the metaphor, each locus in the genome is a different sidewalk. If the locus has some variation, then there is a drunkard staggering on that sidewalk.)
  • The most likely expectation, or the expected average over many trials, is given accurately by the Hardy-Weinberg model.
  • However, in any particular case, the more generations that pass, the farther are gene frequencies likely to be from the initial expectation.
  • In finite populations, an allele will be lost when its frequency drifts to zero.  From that point on, the alternative allele will be "fixed" in the population.
  • Drift to extinction/fixation is itself a stochastic expectation, a "most likely" result over enough generations.  But there is no "force" requiring drift to reach that result in any particular case.
     
• What is the molecular clock?

  The molecular clock is the random but statistically predictable accumulation of neutral genetic differences (particularly single-base substitutions) among related populations.

  If two or more populations (or species) originate from the splitting of a single ancestral population (or species), drift will occur independently in each population.  In each population, particular neutral alleles will drift to fixation, but these events will be different in each population.  The net result is an accumulation of genetic differences among the populations, increasing the variation among the populations.

  The molecular clock is NOT very clock-like.  It is the noisy (but somewhat statistically-predictable) outcome of random processes.

  Measuring time with the molecular clock is rather like flipping a coin every so often and then guessing how much time has elapsed by counting the total number of heads that have appeared.  

  The "clock" operates at different rates in different genes, in different lineages, and at different times.

  For more, see Stearns & Hoekstra, Chapter 12, pp. 244-245.

Comments on Chapter 3

• Fitness defined.
• An example to illustrate basic characteristics of neutral evolution
• How can genetic variation be neutral?
• What are the causes of random evolutionary change?
• Genetic drift and molecular evolution

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Fitness defined

Chapter 3 introduces the word fitness as a substitute for "reproductive success".  This makes for more concise word use, and we shall adopt this use.

However, care is in order.  Many words in evolutionary biology, such as "adaptation" and even "evolution" itself, are typically used rather casually, often with misplaced confidence that the intended meaning will be apparent from context.  However, the word fitness is often used with a very precise, mathematically-defined meaning, where it is often designated by the quantitative variable w.  (Sewall Wright, who introduced w as a designation for fitness, is said to have explained that w stands for "worth".)  

Fitness is often easier to define and apply in a mathematical model than it is to measure or demonstrate in an actual population.  And there are many distinct mathematical definitions for fitness.  

Whenever you encounter the term fitness, think "relative fitness", think differences in reproductive success.

Like reproductive success, fitness is best understood as a relative term.  That is, it only makes sense to measure the fitness of each individual or genetic variant in relation to some standard.  A standard fitness value of 1 is commonly assigned as a measure either for the average reproductive success of one prevailing variant (the "wild-type") or else for the average reproductive success of an entire population.

The standard value of 1 for average fitness is not assigned arbitrarily.  It is important to appreciate the reason:  Over the long term, the average reproductive output of each individual in a stable population must necessarily be 1.  If it were greater than one, the population would increase indefinitely (and overrun the world).  If it were less than one, the population would shrink until it eventually vanished into extinction.

Fitness is also context-dependent.  Thus measurements of fitness only make sense for a particular population with a particular gene-pool, existing at a particular time within a particular set of environmental conditions.

This is the real reason why it makes little sense to speak of adaptive evolution leading to progress.  Even though selection always, inevitably, tends to preserve the more-fit among different available variants, there is no context-independent quality which "advances" or "improves".  (As noted just above, any population that survives over the long haul must have an average fitness of 1.)

An emphasis on context-dependence of fitness is important for clear thinking.  Here's another way to express the concept.  In spite of everyday usage, traits do not cause fitness.  Rather, in some specified context, differences among traits are responsible for relative differences in fitness.  

There's an analogous concept in genetics.  There is no such thing as a gene which causes a trait.  Rather, in some specified genetic and environmental context, differences between genes are responsible for trait differences.

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Characteristics of neutral variation

After defining fitness (see above), the textbook presents an example of experimental evolution in E. coli.  This example is intended to emphasize the reality of neutral genetic variation.  Such neutral genetic variation can take two forms:

• Genetic variation which does not affect phenotype and hence cannot affect fitness.
• Genetic variation which does affect phenotype but nevertheless does not affect fitness.

Two significant points should be noted:

• Neutrality is context-dependent.  (That is, variation which is neutral in one context may turn out to have important effects if conditions change.)
• Neutrality is relative; it depends on comparison among different variants.  

  As always, evolution is all about variation.  Two or more trait differences are neutral only in relation to one another (i.e., if they do not differ in fitness).  When we refer to "a neutral mutation", the mutant allele is not neutral all by itself.  There is an implied comparison with an original or "wild-type" allele, such that bearers of the mutant allele do not differ in fitness from those bearing the wild-type.

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How can genetic variation be neutral?

Molecular biology provides the basis for understanding several forms of neutral variation, which may involve any of the following.

• Synonymous codons.  Alleles which differ in DNA sequence but encode the same peptide sequence are expected to be neutral or nearly neutral.
• Functionally equivalent amino acids.  Alleles which encode peptide sequences which differ in some insignificant way (e.g., substitution of one small, neutral amino acid for another small neutral amino acid, in a non-critical site) are expected to be neutral or nearly neutral.
• Non-coding DNA.  Alleles which differ in the sequence of some non-functional DNA (e.g., a pseudogene) are expected to be neutral or nearly neutral.
• Canalized development.  Alleles whose potential functional differences are buffered (smoothed over or cancelled out) by other mechanisms are expected to be neutral or nearly neutral.

  Some caution is appropriate.  Some of what appears to neutral genetic variation may have some significance which has not yet been fully appreciated.  Nevertheless, much molecular variation is consistent with quantitative theoretical predictions regarding neutral variation (more).

Some DNA variation that is expressed as phenotypic variation may nevertheless be neutral if it is not be correlated with reproductive success.  Like molecular variation that does not affect phenotype, phenotypic variation is also neutral if it does not affect fitness.

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What are the causes of random evolutionary change?

Neutral evolution involves genetic variation that is not correlated with fitness.  With no such correlation, such evolutionary change is often described as random.  

Note that the word "random" is hard to define satisfactorily.  

Mutation introduces new alleles at random.  

When used to describe mutation, "random" means that the origin of an allele is unrelated to its particular effect on fitness.  But note that mutations are certainly NOT random in the sense of "every possible mutation is equally probable".  Some specific types of mutation are much more likely than others.  Some gene and chromosomal locations are much more prone to mutation than others.  And quite a few genetic mechanisms function in ways which influence the type and location of mutations (for example, by concentrating variation in certain regions such as the genes which create antibodies).  The "randomness" of mutation means simply that no known mechanism is capable of causing specifically advantageous mutations.

Mutations come in many varieties.  These include "point mutations" affecting individual nucleotides; insertions, deletions, inversions, translocations, and duplications of various sizes (ranging from a few nucleotides to significant pieces of chromosomes); and wholesale duplication of the entire genome (leading to polyploidy).  Evidence for gene duplication is provided by the existence of multigene families.

This is not the place to discuss the evolutionary significance of various types of mutation.  But it should be noted that certain mutational variants may be neutral at the time of their origin and yet nevertheless become profoundly significant for subsequent adaptive evolution.  This is especially evident in the case of gene duplications.

Once mutations are introduced into a population, various mechanisms determine whether or not the new alleles will increase in frequency.  

• Alleles which confer greater fitness will be favored by selection.
• Alleles which confer reduced fitness will be eliminated by selection. 
• All alleles will also be affected by random processes.

Random processes in population genetics are all of those processes by which alleles vary in reproductive success in ways uncorrelated with fitness.  

• The "Mendelian lottery" operates through the basic mechanism of sexual reproduction, wherein gametes are created in a way that appears in most cases to be mathematically random.  For any heterozygous locus, the process of meiosis assures a probability of 0.5 that a given allele will appear in some particular individual gamete (and hence participate in the formation of a specific individual zygote).  Basically, gamete production and subsequent fertilization are largely independent of gamete genotype.  [There are some interesting exceptions, wherein some alleles of certain genes seem to increase the likelihood that gametes containing these alleles will be produced and/or participate in fertilization.]
• Genetic bottlenecks are substantial but non-selective reductions in population size (e.g., by some calamity unrelated to individual fitness, such as fire or hurricane) in which much of a population's prior variation is eliminated.  
• The founder effect occurs when a new population is formed by colonization from a large parent population.  This is, in effect, a genetic bottleneck at the point of origin for the new colony.
• Selective sweeps (see p. 52) have some effects similar to genetic bottlenecks.  Selective sweeps occur whenever strong selection changes the frequency of a selected allele more rapidly than genetic recombination can act to cause independent assortment of closely linked loci.  During a selective sweep, alleles that are not subject to selection on the basis of their own influence on fitness may nevertheless be favored or eliminated incidently, by "hitchhiking" with selected alleles of nearby genes.  
• Genetic drift refers to the total set of processes wherein random sampling of allelic variation (whether by the "Mendelian lottery" or by chance survival unrelated to fitness or by chance matings unrelated to fitness) leads to changes in allele frequency from generation to generation.  (The effects of selective sweeps and genetic bottlenecks are usually considered separately from genetic drift).  Genetic drift behaves like a "random walk".  
  • Also see summary of Key Points about Genetic Drift.

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Genetic drift

"Genetic drift" refers to the net accumulation of neutral genetic change due to statistical fluctuations in allele frequencies.  This change due to drift has two principal effects, reducing genetic variation within any single population and accumulating genetic variation among related populations.  

Genetic drift has some considerable significance for evolutionary biology, especially for understanding and interpreting variation which may be observed at the molecular level.  

• The frequencies of neutral alleles are expected to fluctuate at random.  This fluctuation may be modelled as a "random walk".
• Over long-enough spans of time, any given neutral allele is expected to drift unpredictably either to fixation or to elimination.
  • In effect, this means that, Genetic drift, acting alone over time, will reduce and eventually eliminate neutral genetic variation within a population.
  • This also means that, Genetic drift, acting alone over time, will increase neutral genetic variation among related populations, by accumulating random genetic differences.
• If neutral mutations are introduced into a population, their fate will be determined by drift.
  • Because the initial frequency of a new mutation is very low (1/N, one allele in the entire gene pool), most new neutral mutations will be lost to drift.
  • However, over long-enough spans of time and with lots of new neutral mutations, some new neutral mutations are expected to drift to fixation.
  • Neutral allele substitutions are expected to accumulate at a statistical-predictable rate over time.  This effect is referred to as the molecular clock.
• Because many classes of mutation appear to be effectively neutral, much molecular evolution probably results from drift.

See summary of Key Points about Genetic Drift.

For more extensive discussion, see genetic drift and neutral evolution.

Notes for chapter 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17

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