Genetic Drift

Lecture 03

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Genetic Drift is a consequence of chance events

• random in direction, perhaps better called "genetic chance"
• Represents a departure from Hardy-Weinberg assumptions
  • We will begin the examination of the consequences of drift by discussing it in isolation from other H-W departures but it happens no matter which other departures are occurring
    • i. e., selection and drift, mutation and drift, migration and drift, etc. all occur
• the rate of change due to random chance is dependent on population size (inversely dependent)

Fixation - fixation is the loss of all alleles for a locus save one (this allele said to be fixed)

• drift will produce fixation given enough time
• which allele will be fixed?
  • without selection favoring a single allele, all alleles have the same probability of being fixed
  • in a population there are 2N alleles (N = population size), so any allele present in the population today has a probability of being fixed some time in the future equal to 1/2N
• under what circumstance are small populations most likely?
  • rare species are, by definition, found only in small population sizes (threatened or endangered species belong in this category also)
  • even species characterized by large population sizes may be subjected to small population size dynamics when:
    • a new population is founded (called a Founder Event)
      • the founders may lack all of the alleles of the source population or may have a gene frequency that differs from the source population
      • what is the chance that a founding population will be homozygous at a given locus?
      • assume only two alleles in the source population, n = number of founders, and the chance of drawing an individual with allele A is p (a is q) then

Pr(homozygosity) = p²ⁿ + q²ⁿ

• the probability falls quickly as n, the number of founders, increases but this may still be an important source of variation between populations if the number of founders does tend to be small
• environmental extremes cause populations to crash, even if they subsequently regrow to their previous size
• a crash followed by an increase in population size is called a Bottleneck
• the amount of time it takes to fix an allele is also dependent on population size, directly dependent this time

Coalescence

• looking back, instead of ahead, is follows that all alleles in the population today are the descendents of a single allele that existed some time in the past
• the alleles in today's population are said to coalesce to this single ancestor
• ancestral allele is called the coalescent
• how long ago the coalescent existed depends, assuming that it did exist, on the population size (now and in the past), selection strength, mating system, and other aspects of the life history of the organism being studied
  • currently this approach is being used to estimate the history of one or more populations, something once impossible to do without explicit historical records (almost never available)
  • This link will take you to the Lamarc site, the website for one team of researchers who make available software to estimate population parameters based on the coalescent
  • (LAMARC stands for Likelihood Analysis with Metropolis Algorithm using Random Coalescence - how's that for creative acronyming, if not totally accurate spelling)

Heterozygosity and Drift

• We have seen that drift can cause fixation, but what is its effect in larger populations?
• to get the idea of what drift will do to a population over time, consider what will happen in one generation to the frequency of homozygotes in the population (compared to the same frequency in the previous population) in the case of two alleles
  • f is the proportion of homozygotes in the current generation (which is at H-W equilibrium as selection, etc. are not occurring), so

f = p² + q²

• you can generalize this for more than two alleles by using p as the probability of homozygosity at each of i alleles so that:

• there are two ways to become a homozygote in the next generation, if we consider the possibility of self-fertilization:
  • two gametes from the same individual combine, which has a probability of 1/2N (N = population size)
  • two gametes  with the same gene but from different individuals combine.  The probability of this is the probability of picking a second gamete that is not from the same individual, which is = 1 - (1/2N) [notice that the two probabilities so far add to one].  If we are producing homozygotes, we have to multiply this probability times the probability that the individual is a homozygote, f
• the probability of being a homozygote in the next generation, f' is then the sum of these two independent probabilities of producing a homozygote

• if you begin with p = .6 and N = 100, homozygosity will drift upward, reaching near fixation in hundreds of generations:

Heterozygosity

• measure of genetic variation
  • on a per locus basis
• for any locus, it is the chance that two alleles, drawn at random, are different
  • logically, there is a complementary relationship between H and f, such that H = 1 - f and (substituting in the equation above)
  • in the case of more than two alleles (modified from general case for f above):

• the change in heterozygosity due to drift decreases over time and is predicted by:

• really confusing terminology due to meaning of heterozygous individuals (populations can be heterozygous even if all the individual within are homozygous), better term is gene diversity
  • sequence data has meant that we can look at genetic variation by site and this variation is usually measured as pi, the total number of nucleotide differences between  two sequences divided by the length of the sequence (to facilitate comparisons among sequences of different sizes

Mutation and Drift

Some aspects of point mutations (also called substitutions)

Relative Frequency (estimated from changes in pseudogenes)

As you can see, transitions are more common than transversions (and not symmetric!)

redundancy in the genetic code means that many third position substitutions are selectively neutral as they cannot affect the primary sequence of the encoded protein

Insertions and Deletions (Indels)

• Analysis of these are often problematic and the most common response is to ignore them when comparing sequences (is this acceptable beyond its practicality?)
  • can't tell if an indel of more than one bp is a single evolutionary event or multiple events
  • if the location of indels is not random, they will tend to overlap and make sorting the events that produce the observed pattern difficult or impossbile
• when doing alignments of two or more sequences, it is usually to create multiple indels so that the base pairs aligned are homologous base pairs
• however, if you insert enough indels, you can match most sequences without any substitutions
• so when to insert an indel and when to accept that a substitution has occurred is often determined by penalizing an indel more (in terms of evolutionary distance) than a substitution (which is usually a distance of 1 or close to it)
• when an indel lowers the overall score for the entire sequence comparison, it is accepted, when it does not it is rejected

Mutations at the gene level (and at the position level in a sequence) are often subject to reversion

• this is not expected for complex characters governed by many loci and many alleles
  • the next mutation to the entire system of genes contributing to the phenotype is unlikely to be at the same position as the initial mutation and so is not likely to cause reversion
  • as more mutation accrue to the entire system, the likelihood that a mutation that cause reversion becomes even less likely
• for characters determined by one or a few genes, reversion becomes more likely
  • ex. - ability of a microbe to utilize a particular carbon compound as a source of energy
  • often this is governed by only a few genes (a transport gene in the membrane, an enzyme to split polymers into monomers, and perhaps an enzyme to modify the monomer into a substrate found in glycolysis or the Krebs cycle)
• so given that p is frequency of A, m is the rate of change from A to a, and a is the frequency of change from a to A is n
  • m and n are usually their Greek equivalents but these are not always displayed well in all browsers, so I will use English here
  • m and n are rates but are used here as the proportion of each allele that will mutate into the other allele during a single time interval (size dependent on the situation)

p_t+1 = p_t (1 - m) + (1 - p_t)n

• as the total number of changes depends on the rate and the gene frequency, an equilibrium frequency is possible where to total of mutations is matched by the total reversions. Call this rate p*

• so, as m increases, p* decreases and as n increases, p* also increases, although not in a linear fashion
• Drift and Mutation can balance on another, such that fixation is staved off by the appearance of the allele through mutation.  The equilibruim values for homozygosity and heterozygosity, where disappearance is balanced by mutation, depends on the mutation rate and the population size:

• population size is critical when assessing the effects of drift, so it is meaningful to ask how to measure it
• Effective Population Size (N_e)
  • the true size of the population when adjusted for population parameters that make the simple head count inappropriate
  • N_e should have been used for all of the equations above!
• the estimation of the probability that two randomly chosen allels are the same is affected by:
• sex ratio - each sex contributes half of the alleles to the next generation, even when one sex is rare in the present generation.  The rare sex's genotypic ratios will then have a greater influence than the more numerous sex.
  • We can correct for this problem with Wright's famous formula: 

• population size change - when estimating over more than a single generation, you should use the harmonic mean population size, not the arithmetic mean population size
  • the harmonic mean is the inverse of the mean of the inverses of the population sizes being considered (t is the number of generations being considered):

• you can link to an old worksheet on effective population size done for the ecology class several years ago by clicking on this link (use your browser's back button to get back to here)
• population sub-division and mating groups - both of these will effectively lower the population N_e but the corrections needed are too complex to discuss here
• variation in fecundity - when some females have more offspring than others, those with high fertitility have a greater effect on the genotypic composition of the next generation than those with lower fertility
  • Wright supplied the formula, which depended on the variance in k, the fecundities of the population's females:

• Drift will dominate when there is no selective pressure on an allele (or very small selective advantage or disadvantage)
• Adaptation is produces by natural selection, but much evolution might be due to drift
  • e. g.,  change in non-coding sequences (that also have no other function) such as intergenic spacers, pseudogenes, and some third positions in codons

• argued that genetic load, if multiplicative, of even small selection coefficients, within a large gene would make one allele almost lethal in most cases
• molecular clock is dependent on neutral drift
  • rates have been shown to be constant for some genes but not the same rate for all genes evolving at a constant rate.
  • in some cases, loci have been shown not to be very "clock-like" in that they have not always evolved at a constant rate (environmental genes)
  • neutral theory and the clock
    • generation rate of change or absolute rate of change?
      • absolute rates related to change induced by environmental damage (thymine dimer formation, etc.)
      • generational rate dependent on damage caused by replication, etc. that happens during cell division
        • a locus in two organisms with different generation times (generations of cell replication in germ lines, not generations of individuals) absolute rates would be the same but differ if due to generational changes (longer generations times mean fewer chances of change and lower rates of evolution)
• Constraints
• a question under investigation now and for some time has been "what constrains evolution?"
  • functional constraints - a protein must do its job and changes that interfere with that are not likely to have high fitness.
  • developmental constraint - a change to a locus must still interact with other loci to produce a viable phenotype
    • this second constraint has been of growing interest as we begin to understand development (to some degree and only in some model organisms)
    • remains at this time an area of potential constraint more than one of demonstrated constraints.

• this is an area confined, at this point, to molecular data
  • look for patterns of change in the molecules that are characteristic of selection vs those characteristic of neutral drift
• remember, selection does not always have the same effect
  • stabilizing selection (sometimes called negative selection in that it resists change) will reduce the number of changes made over neutral drift
  • directional selection (sometimes called positive selection in that it promotes changes to the molecule) will increase number of changes over neutral drift
• dN/dS ratio (Non-synonymous / Synonymous) a measure of change within proteins potentially subject to natural selection (Non-synonymous) to Synonymous changes not subject to selection (= neutral change)
  • Comparisons have been made within and between species for specific loci
  • Three areas of interest
    1. Low Ratios (significantly below 1) - indicator of negative (stabilizing) selection
    2. Ratios near Unity - indicator of drift
    3. High Ratios (significantly above 1) - indicator of positive (directional) selection
• Convergence
• when similar adaptations arise independently in different lineages, changes that appear in all lineages are convergent evolution and can be interpreted and evidence of stabilizing selection at that site.
• Codon Bias
  • codon usage is not uniform
    • difference in mutation rates might account for it
    • selection might also explain it
      • different number of tRNA genes produce different frequencies of tRNAs for each codon
        • codons evolve to match tRNA frequencies so that translation is most efficient
      • some codon-tRNA matches may be more stable and favored for that reason

Last updated January 28, 2008