Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5

Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5 3. Well, what fraction of alleles will change? 'a' will decline by: qm = .4 x 0.00001 = 0.000004 'A' will increase by the same amount.

Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5 3. Well, what fraction of alleles will change? 'a' will decline by: qm = .4 x 0.00001 = 0.000004 'A' will increase by the same amount. 4. So, the new gene frequencies will be: p1 = p + μq = .600004 q1 = q - μq = q(1-μ) = .399996

Deviations from HWE I. Mutation A. Basics: 4. So, the new gene frequencies will be: p1 = p + μq = 1 - q + μq = 1- q(1-μ) = .600004 q1 = q - μq = q(1-μ) = .399996 5. How about with both FORWARD and backward mutation? Δq = νp - μq - so, if A -> a =v = 0.00008 and a->A = μ = 0.00001, and p = 0.6 and q = 0.4, then:

Deviations from HWE I. Mutation A. Basics: 4. So, the new gene frequencies will be: p1 = p + μq = 1 - q + μq = 1- q(1-μ) = .600004 q1 = q - μq = q(1-μ) = .399996 5. How about with both FORWARD and backward mutation? Δq = νp - μq - so, if A -> a =v = 0.00008 and a->A = μ = 0.00001, and p = 0.6 and q = 0.4, then: Δq = νp - μq = 0.000048 - 0.000004 = 0.000044 q1 = .4 + 0.000044 = 0.400044

Deviations from HWE I. Mutation A. Basics: 5. How about with both FORWARD and backward mutation? - Δq = νp - μq - and qeq = v/ v + μ

Deviations from HWE I. Mutation A. Basics: 5. How about with both FORWARD and backward mutation? - Δq = νp - μq - and qeq = v/ v + μ - and qeq = v/ v + μ = 0.00008/0.00009 = 0.89

Deviations from HWE I. Mutation A. Basics: 5. How about with both FORWARD and backward mutation? - Δq = νp - μq - and qeq = v/ v + μ - and qeq = v/ v + μ = 0.00008/0.00009 = 0.89 - so, if Δq = νp – μq, then: Δq = (.11)(0.00008) - (.89)(0.00001) = 0.0..... check.

Deviations from HWE I. Mutation A. Basics: B. Other Considerations:

B. Other Considerations: Deviations from HWE I. Mutation A. Basics: B. Other Considerations: - Selection: Selection can BALANCE mutation... so a deleterious allele might not accumulate as rapidly as mutation would predict, because it it eliminated from the population by selection each generation. (We'll model these effects later).

B. Other Considerations: Deviations from HWE I. Mutation A. Basics: B. Other Considerations: - Selection: - Drift: The probability that a new allele (produced by mutation) becomes fixed (q = 1.0) in a population = 1/2N (basically, it's frequency in that population of diploids). In a small population, this chance becomes measureable and likely. So, NEUTRAL mutations have a reasonable change of becoming fixed in small populations... and then replaced by new mutation

- Consider two populations: Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8

- Consider two populations: Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population

- Consider two populations: Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population

- Consider two populations: Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population p(new) = p1(1-m) + p2(m)

- Consider two populations: Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population p(new) = p1(1-m) + p2(m) p(new) = 0.2(0.9) + 0.7(0.1) = 0.25

Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: - How different are they, genetically? (this can give us a handle on how much migration there may be between them...) p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: - How different are they, genetically? (this can give us a handle on how much migration there may be between them...) - Compute Nei's Genetic Distance: D = -ln [ ∑pi1pi2/ √ ∑pi12 ∑ pi22] p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: - How different are they, genetically? (this can give us a handle on how much migration there may be between them...) - Compute Nei's Genetic Distance: D = -ln [ ∑pi1pi2/ √ ∑pi12 ∑ pi22] - So, for Population 1 and 2: - ∑pi1pi2 = (0.7*0.2) + (0.3*0.8) = 0.38 - denominator = √ (.49+.09) * (.04+.64) = 0.628 D12 = -ln (0.38/0.62) = 0.50 p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

- Compute Nei's Genetic Distance: D = -ln [ ∑pi1pi2/ √ ∑pi12 ∑ pi22] - So, for Population 1 and 2: - ∑pi1pi2 = (0.7*0.2) + (0.3*0.8) = 0.38 - denominator = √ (.49+.09) * (.04+.64) = 0.628 D12 = -ln (0.38/0.628) = 0.50 - For Population 1 and 3: - ∑pi1pi2 = (0.7*0.6) + (0.3*0.4) = 0.54 - denominator = √ (.49+.09) * (.36+.16) = 0.55 D13 = -ln (0.54/0.55) = 0.02 (not very ‘distant’) - For Population 2 and 3: - ∑pi1pi2 = (0.2*0.6) + (0.8*0.4) = 0.44 - denominator = √ (.04+.64) * (.36+.16) = 0.61 D23 = -ln (0.44/0.61) = 0.33 p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating "like phenotype mates with like phenotype"

A. Positive Assortative Mating Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating "like phenotype mates with like phenotype" 1. Pattern: AA Aa aa .2 .6 offspring ALL AA 1/4AA:1/2Aa:1/4aa ALL aa .15 + .3 + .15 F1 .35 .3

1. Pattern: 2. Effect: AA Aa aa .2 .6 offspring ALL AA .15 + .3 + .15 F1 .35 .3 2. Effect: - reduction in heterozygosity at this locus; increase in homozygosity.

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview:

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: Inbreeding is “like mating with like”, but across the entire genome. So, heterozygosity should decline across all loci at about the same rate due to inbreeding, alone.

B. Inbreeding 1. Overview: - So, the fractional demise of heterozygosity compared to HWE expectations can be used as a direct measure of inbreeding! F = “inbreeding coefficient” F = (Hexp - Hobs)/ Hexp = (2pq - H)/2pq When this is done on multiple loci, the values should all be similar (as inbreeding affects the whole genotype).

B. Inbreeding 1. Overview: - Example: F = (2pq - H)/2pq p = .5, q = .5, expected HWE heterozygosity = 2pq = 0.5 OBSERVED in F1 = 0.3... so F = (.5 - .3)/.5 = 0.4 AA Aa aa .2 .6 offspring ALL AA 1/4AA:1/2Aa:1/4aa ALL aa .15 + .3 + .15 F1 .35 .3 As Hobs  0, F  1.0

Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects:

A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome

A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness

A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE....

A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE.... - BUT... increasing homozygosity may reveal deleterious recessives.

A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE.... - BUT... increasing homozygosity may reveal deleterious recessives. - these may be selected against (changing gene frequencies)

A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE.... - BUT... increasing homozygosity may reveal deleterious recessives. - these may be selected against (changing gene frequencies) - this reduces mean reproductive success (inbreeding depression)

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. In biological populations, this is because not all adults mate. Two Major Patterns:

1) small samples deviate more, just by chance, from the original population than large samples.

2) 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. Patterns 2. Instances where this is common: - “Bottlenecks” where population is reduced in size - “Founder Effect” where small group begins new population

- “Genetic Bottleneck” If a population crashes (perhaps as the result of a plague) there will be both selection and drift. There will be selection for those resistant to the disease (and correlated selection for genes close to the genes conferring resistance), but there will also be drift at other loci simply by reducing the size of the breeding population. Cheetah have very low genetic diversity, suggesting a severe bottleneck in the past. They can even exchange skin grafts without rejection… European Bison, hunted to 12 individuals, now number over 1000. Fell to 100’s in the 1800s, now in the 100,000’s

- “Founder Effect” and Huntington’s Chorea HC is a neurodegenerative disorder caused by an autosomal lethal dominant allele. The fishing villages around Lake Maracaibo in Venezuela have the highest incidence of Huntington’s Chorea in the world, approaching 50% in some communities. The gene was mapped to chromosome 4, and found the HC allele was caused by a repeated sequence of over 35 “CAG’s”. Dr. Nancy Wexler found homozygotes in Maracaibo and described it as the first truly dominant human disease (most are incompletely dominant and cause death in the homozygous condition).

- “Founder Effect” and Huntington’s Chorea HC is a neurodegenerative disorder caused by an autosomal lethal dominant allele. The fishing villages around Lake Maracaibo in Venezuela have the highest incidence of Huntington’s Chorea in the world, approaching 50% in some communities. By comparing pedigrees, she traced the incidence to a single woman who lived 200 years ago. When the population was small, she had 10 children who survived and reproduced. Folks with HC now trace their ancestry to this lineage. Also a nice example of “coalescence” – convergence of alleles on a common ancestral allele.

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***

Probability that OTHER allele becomes FIXED: - increases with its frequency - increase in smaller populations

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 equal frequency (if two alleles, then p = q = 0.5).

D. Effects on Variability 1. Heterozygosity is maximal when all alleles are at equal 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 (same size): 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. Island 1: p=0.3, q=0.7 Island 2: p=0.7, q=0.3 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 which drift to fix different alleles, drift increases variance between populations. 3. We measure this as the fractional loss of ‘mean heterozygosity’ compared to the total HWE heterozygosity: (2pq - H)/2pq = (0.5 - 0.42)/ 0.5 = 0.08/0.5 = 0.16 AA Aa aa 1 0.09 0.42 0.49 2 .042 mean 0.29 whole 0.25 0.5

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** 1. 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**** 1. 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 2. HEY!!! BUT THIS WAS THE FORMULA FOR INBREEDING, TOO! F = (2pq - H)/2pq

IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** SO! Drift causes: - a reduction in variability - an increase in inbreeding - a decrease in heterozygosity - an increase in the variance between subpopulations - a decline in mean heterozygosity

****F. Relationships Between Inbreeding and Drift**** IV. Genetic Drift ****F. Relationships Between Inbreeding and Drift**** SO! Drift causes: - a reduction in variability - an increase in inbreeding - a decrease in heterozygosity - an increase in the variance between subpopulations - a decline in mean heterozygosity Inbreeding AND the degree of divergence in subpopulations are measured the same way

Small subpopulations will diverge more rapidly than large subpopulations

Diverge can occur due to selection, too. But if we use non-coding ‘markers’ that are selectively neutral, divergence must be due to drift (and genetic isolation). Can find genes under effect of selection because they change more rapidly than the mean rate of 1000’s of marker genes (Higher Fst than mean).

Loci on chromosome #7 in humans – and genes that have changed more rapidly than drift would suggest.

****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

Even in the same landscape, the degree of population subdivision will vary among organisms that use the environment in different ways.

Even in the same landscape, the degree of population subdivision will vary among organisms that use the environment in different ways. Solitary predators have large home ranges and interbreed freely

Even in the same landscape, the degree of population subdivision will vary among organisms that use the environment in different ways. Sheep, limited range and,with harem-forming social groups, have smaller effective population sizes because few males mate. Solitary predators have large home ranges and interbreed freely

CFP = “Canonical Florida Panthers” EVG = “Everglade Florida Panthers” Fig. 1 (A and B) Southern Florida (1995, left; 2007, right) with locations of breeding-age Florida panthers (>1.5 years old), geographic features, number (N) alive, and effective population size (Ne). CFP = “Canonical Florida Panthers” EVG = “Everglade Florida Panthers” TX = Texas Panther AdmFP = Admixed Florida Panther (hybrid w TX) AdmFP+SEM = hybrid with escaped panther from Seminole Reservation (A and B) Southern Florida (1995, left; 2007, right) with locations of breeding-age Florida panthers (>1.5 years old), geographic features, number (N) alive, and effective population size (Ne). Labeled colored areas in (A) demarcate public land (23): Fakahatchee Strand Preserve State Park (FSPSP), Picayune Strand State Forest (PSSF), Florida Panther National Wildlife Refuge (FPNWR), BCNP, Big Cypress Seminole Indian Reservation (SEM), Okaloacoochee Slough State Forest (OSSF), and Everglades National Park (EVER) and in (B) show panther habitat. Circles are coded by ancestry: CFP, TX females (with a B if a successful breeder), EVG, AdmFP, and SEM. Pie charts illustrate the genetic heritage of the population (fig. S1 and table S2) (13). Warren E. Johnson et al. Science 2010;329:1641-1645 Published by AAAS

Fig. 3 (A) Minimum annual subadult and adult panther population size and inferred genetic heritage from 1986 to 2007. (A) Minimum annual subadult and adult panther population size and inferred genetic heritage from 1986 to 2007. CFPs are yellow, EVGs pink, TXs red, CFPxTX-F1s and EVGxTX-F1s orange, TX-BCs and other AdmFPs shades of orange, and genetically uncharacterized individuals (Unk) gray (13). The black line is an independent minimum-count estimate from surveys of tracks, spoor, and other field evidence (2). (B) Mean yearly adult multilocus heterozygosity. (C) Yearly mean age of adults. (D) Projected survivorship (probability of surviving to an age) curves for female Florida panthers of different genetic heritages with standard error bars (13). Male trends are similar (table S4). Warren E. Johnson et al. Science 2010;329:1641-1645 Published by AAAS