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

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error 1. samples from a variable population may not represent the population exactly. Deviation from the populational distribution is called sampling error. This is a general statistical principle, measured by the 'variance' or 'standard deviation'. Variance among samples drawn from one population = (pq/N)

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error 1. samples from a variable population may not represent the population exactly. Deviation from the populational distribution is called sampling error. This is a general statistical principle, measured by the 'variance' or 'standard deviation'. Variance among samples drawn from one population = (pq/N) - small samples deviate more, just by chance, from the original population than large samples. - small samples differ more from one another than large samples.

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error 1. samples from a variable population may not represent the population exactly. Deviation from the populational distribution is called sampling error. This is a general statistical principle, measured by the 'variance' or 'standard deviation'. Variance among samples drawn from one population = (pq/N) - small samples deviate more, just by chance, from the original population than large samples. - small samples differ more from one another than large samples. 2. This principle relates to biological populations because the zygotes produced as an F1 generation represent a sample of the gametes produced by the parental population - not all parents mate.

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error 2. This principle relates to biological populations because the zygotes produced as an F1 generation represent a sample of the gametes produced by the parental population - not all parents mate. - causes of lower effective population size: - only a fraction of parents mate - skewed sex ratio - selection (differential reproduction) - generations overlap (increasing inbreeding/coalescence) - Fluctuation in population size (bottlenecks)

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error B. Coalescence

B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct

B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct - After an elapsed time, many of the entities will be descendants of the same successful lineage that, just by chance, has left a descendant in each generation. So, over time, average relatedness among existing entities increases.

B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct - After an elapsed time, many of the entities will be descendants of the same successful lineage that, just by chance, has left a descendant in each generation. So, over time, average relatedness among existing entities increases. - Eventually, all the entities that are present will trace their ancestry back to a single ancestor; their genealogies 'coalesce' on a single ancestor

B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct - After an elapsed time, many of the entities will be descendants of the same successful lineage that, just by chance, has left a descendant in each generation. So, over time, average relatedness among existing entities increases. - Eventually, all the entities that are present will trace their ancestry back to a single ancestor; their genealogies 'coalesce' on a single ancestor. - If the entity is a single gene or a haploid genome, this means that eventually, all the entities in the populations are the same - 'similar by descent'... If this is an allele, the allele is now FIXED f = 1.0. ***When random change occurs, it will ultimately lead to fixation and inbreeding***

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error B. Coalescence C. Evolution by Drift

C. Evolution by Drift - So, by chance, one allele in the population will become fixed. The probability = frequency in the population (p). Even one NEW allele with frequency 1/2N, has that chance of eventually becoming fixed...

C. Evolution by Drift - So, by chance, one allele in the population will become fixed. The probability = frequency in the population (p). Even one NEW allele with frequency 1/2N, has that chance of eventually becoming fixed... - How long will fixation take? It depends on the population size. Essentially, how long will it take for one gene to replace all the others, just by chance? For a single newly formed allele to take over = 4N generations

C. Evolution by Drift - So, by chance, one allele in the population will become fixed. The probability = frequency in the population (p). Even one NEW allele with frequency 1/2N, has that chance of eventually becoming fixed... - How long will fixation take? It depends on the population size. Essentially, how long will it take for one gene to replace all the others, just by chance? For a single newly formed allele to take over = 4N generations ***The time it takes for an allele to become fixed is dependent on its initial frequency and the size of the population***

IV. Genetic Drift A. Sampling Error B. Coalescence C. Evolution by Drift D. Effects on Variability

D. Effects on Variability 1. Heterozygosity is maximal when all alleles are at = frequency (if two alleles, then p = q = 0.5).

D. Effects on Variability 1. Heterozygosity is maximal when all alleles are at = frequency (if two alleles, then p = q = 0.5). 2. As genes drift from low to intermediate frequency (0.1  0.5), variation (heterozygosity) increases. But, usually, rare alleles drift to 0 and abundant alleles drift to 1, reducing heterozygosity and variation. Ht = Ho [(1 - 1/2N)^t] *** Drift, like inbreeding, leads to reduced heterozygosity over time ***

E. Subdivided Populations 1. Wahlund Effect Consider a population that is subdivided on two islands: Island 1: p=0.3, q=0.7 Island 2: p=0.7, q=0.3 Subdivided populations will have lower heterozygosity than expected by HWE when considering them as one fused population. AA Aa aa 1 0.09 0.42 0.49 2 .042 mean 0.29 whole 0.25 0.5

E. Subdivided Populations 1. Subdivided populations will have lower heterozygosity than expected by HWE when considering them as one fused population. 2. However, in a metapopulation consisting of separate populations in which drift is fixing different alleles, drift increases the variance between populations.

E. Subdivided Populations 1. Subdivided populations will have lower heterozygosity than expected by HWE when considering them as one fused population. 2. However, in a metapopulation consisting of separate populations which drift to fix different alleles, drift increases variance between populations. 3. The rate of decline in heterozygosity at the metapop level depends on the size of the demes (populations). Ht = Ho [(1 - 1/2N)^t], where: Ho = initial heterozygosity, N = mean deme size, t = number of generations, and Ht = Heterozygosity in generation t. ***Subdivision of populations will reduce heterozygosity in the population as a function of the Wahlund Effect AND increase variance due to drift. The rate depends on the mean size of the demes***

IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift****

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** 1. In small populations, offspring have a higher probability of receiving genes from a common source. For instance, if there is one gravid female that founds a population, all individuals in the next generation will be related by and average of 1/2 (full siblings).

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** 1. In small populations, offspring have a higher probability of receiving genes from a common source. For instance, if there is one gravid female that founds a population, all individuals in the next generation will be related by and average of 1/2 (full siblings). 2. Also, over time, coalescence is more rapid in a small population than in a large population; so the population will sooner reach a point where autozygosity is likely. after t generations: Ft = 1 - (1- (1/2N)^t) Ht = (1- (1/2N)^t)Ho)

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** 3. As we saw from the Wahlund Effect, a subdivided population will decline in mean heterozygosity. And we can measure this divergence as a proportional loss of heterozygosity: (2pq - H)/2pq

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** 3. As we saw from the Wahlund Effect, a subdivided population will decline in mean heterozygosity. And we can measure this divergence as a proportional loss of heterozygosity: (2pq - H)/2pq HEY!!! BUT THIS WAS THE FORMULA FOR INBREEDING, TOO! F = (2pq - H)/2pq This also equals = 1 - (1 - (1/2N)^t) with N = effective size of each deme.

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** 1. In small populations, offspring have a higher probability of receiving genes from a common source. For instance, if there is one gravid female that founds a population, all individuals in the next generation will be related by and average of 1/2 (full siblings). 2. Also, over time, coalescence is more rapid in a small population than in a large population; so the population will sooner reach a point where autozygosity is likely. 3. As we saw from the Wahlund Effect, a subdivided population will decline in mean heterozygosity, and increase inbreeding. *** SO! Drift causes a reduction in variability, an increase in inbreeding, and a decrease in heterozygosity. However, it INCREASES the variance BETWEEN populations, reflected in increased divergence and a decline in mean heterozygosity ***

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** SO SO SO!!! DRIFT CAUSES: inbreeding loss of heterozygosity in metapopulation divergence

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

1. Historically, all phenotypic variation was interpreted as adaptive. V. The Neutral Theory A. Variation 1. Historically, all phenotypic variation was interpreted as adaptive. - many 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."

1. Historically, all phenotypic variation was interpreted as adaptive. V. The Neutral Theory A. Variation 1. Historically, all phenotypic variation was interpreted as adaptive. - many 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 – electrophoresis revealed LOTS of variability. - variability at the gene or protein level that did not necessarily correlate with morphological variation. - These are silent mutations in DNA, or even neutral substitution mutations. This variation results in heterozygosity.

1. Historically, all phenotypic variation was interpreted as adaptive. V. The Neutral Theory A. Variation 1. Historically, all phenotypic variation was interpreted as adaptive. 2. In the 1960's – electrophoresis revealed LOTS of variability. - variability at the gene or protein level that did not necessarily correlate with morphological variation. - These are silent mutations in DNA, or even neutral substitution mutations. This variation results in heterozygosity. 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?

V. The Neutral Theory A. Variation B. Genetic Load

V. The Neutral Theory A. Variation B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals:

1. "HARD" Selection can 'cost' a population individuals: V. The Neutral Theory A. Variation B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of lower fitness

1. "HARD" Selection can 'cost' a population individuals: V. The Neutral Theory A. Variation B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of lower fitness. - the "breeding population" is smaller than the initial population.

1. "HARD" Selection can 'cost' a population individuals: V. The Neutral Theory A. Variation B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: - those that die as a consequence of lower fitness. - the "breeding population" is smaller than the initial population. - Reproductive output must compensate for this loss of individuals if the population is to persist in the face of this selective pressure.

1. "HARD" Selection can 'cost' a population individuals: V. The Neutral Theory A. Variation B. Genetic Load 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.

1. "HARD" Selection can 'cost' a population individuals: V. The Neutral Theory A. Variation B. Genetic Load 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.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem?

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "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).

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. Let's consider even a "best case" scenario:

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. Let's consider even a "best case" scenario: - mean fitness = 1 - H((s+t)/2)

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. 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), then the mean fitness = 0.967.

B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. 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), then the mean fitness = 0.967. - Not bad; not much death due to selection at this one locus...

B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. 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), then the mean fitness = 0.967. - Not bad; not much death due to selection at this one locus... - HOWEVER, there are 3000 polymorphic loci across the genome!!! So, if selection is maintaining this variation, then mean fitness across the genome = (0.967)^3000!

B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. 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), then the mean fitness = 0.967. - Not bad; not much death due to selection at this one locus... HOWEVER, there are 3000 polymorphic loci across the genome!!! So, if selection is maintaining this variation, then mean fitness across the genome = (0.967)^3000! - This is ridiculously LOW (.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... ALMOST EVERYBODY DIES!!!!

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "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). - The problem is that load can be high in this situation, because lots of homozygotes are produced each generation, just to die by selection. 3. 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. - across the genome, there is a huge genetic load 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. 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...

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. Solutions a. Selectionists - Not all selection is "hard", imposing additional deaths above background mortality.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. Solutions a. Selectionists - Not all selection is "hard", imposing additional deaths above 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.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. Solutions a. Selectionists - Not all selection is "hard", imposing additional deaths above 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 "winners".

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. Solutions a. Selectionists - Suppose we have a population of aa homozygotes initially. All the territories are occupied by aa individuals and 10 individuals die.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. 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....

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. 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.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. 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.

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. 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. - So, selection across lots of loci does not NECCESSARILY lead to impossible loads.... as long as it is SOFT SELECTION

1. "HARD" Selection can 'cost' a population individuals: B. Genetic Load 1. "HARD" Selection can 'cost' a population individuals: 2. Why is this a problem? 3. Scenario 4. Solutions a. Selectionists b. Neutralists