The Hardy Weinberg Theorem In Genetics Biology Essay

The Hardy Weinberg Theorem In ancestrals Biology Essay launchingThe Hardy Weinberg Theorem is a mathematical formula that exclusively in wholly in bothows allelo change and ge nonype frequencies in a community of diploid or polypoid any(prenominal) unrivalleds to be interrelated, where the absolute oftness of unmatch open allelomorph is represented as p, and the relative absolute absolute oftenness of the new(prenominal) is represented as q (the sum of which = 1.0). The sum of the antithetic genotype frequencies (homozygotes and heterozygotes) similarly equates to 1.0. Where p and q be the frequencies of the alleles for a particular gene in a community, the genotype frequence can be expressed asp + 2pq + q = 1Where p = frequency of organisms that argon homozygous for the starting-class honours degree alleleq = frequency of organisms that atomic number 18 homozygous for the second allele2pq = frequency of heterozygous organismsThe Hardy Weinberg compete ntiser waistband eonian as long as thither is stochastic wedlock, no migration, no pictorial survival, no sportsman and no hereditary move (N=infinite), (Fig. 1).N = infinite foreshadow 1. A graph to come issue the Hardy Weinberg Equilibrium.Put together apply data from Lori Lawsons lecture 15, deaf(p) Evolution and Genetic Drift, 2010Therefore the universe does not evolve. If an allele or genotype frequency is seen to channel from one genesis to the next in that locationfore it is clear that one or more of the micro- growingary forces (mutation, migration etc) argon acting on those traits in the state. With tabu mutation thither argon no new alleles or genes and so no evolution. chromosomal mutation must occur in the root line to be significant in evolutionary name. J. B. S. Haldane (1892-1964) stated that the f be of germ cell di hallucinations per genesis is higher in males therefore the mutation rate depart be higher in males. Gene proceed (also called mi gration) brings new genotypes into populations and is critical for the long term survival of a population, specially if it is a chthonicsized population. For migration to beCatherine Carrick 200884273 marrowive in respect to evolution there must be successful reproduction among migrating populations. It is the movement of alleles in the midst of populations, not individuals.Wrights Island model of migration (Fig. 2) certifys that migration homogenizes populations (where they consist of similar elements uniform through forth).Genetic drift is an otherwise form of micro-evolution and leads to stochastic trades in allele frequencies. It is fundamentally a result of finite population surface and has the most rapid and out posting effect on small populations who show reduce unevenness. Drift emergences dispute mingled with populations so genetical revolution must be replenished. Mutation replenishes variation and at counterbalance there is a balance among the rate of mutation and the rate of drift. sort 2.Wrights island model. Put togetherusing data from Lori Lawsons lecture 15,Neutral Evolution and Genetic Drift, 2010Charles Darwin (1859) defined natural alternative (another micro-evolutionary force) with his four postulates 1) individuals indoors populations argon variant, 2) there is heritability (variation among individuals partly passed on from parents), 3) that in every generation there are more or less(prenominal) individuals that are fitter (survival/reproductive success) than others and 4) fitness is not random. Natural selection is the combining weight of several(predicate)ial reproduction as a result of an organisms interaction with the surroundings and the populations inherent variation. It acts on heritable (not acquired) characteristics at an individual level and not for the good of the species. However, the consequences occur in populations. This is demonstrated by melanism in the peppered moth (Biston betularia). The cau ses of melanism in the peppered moth have been well studied since the 1950s and show natural selection at work. Camouflage is key to predator turning away in the peppered moth and there are two distinct morphs. One macrocosm lily-white with ominous or cook specks (typica) and the other pre controllingly downcast (carbonaria). The former is well camouflaged on channelizes with lichen on their bark and the subsequently better suited to dark or blueened bark. During the industrial revolution in the 19th century, an increase of soot and industrial pollution coincided with the appearing of the carbonaria form. Original studies on the relation among B. betularias crypsis and lichens failed to consider two of import details firstly, that the natural resting place of the moths is high in the canopy during the sidereal day and not on the trunk as previously thought, and secondly, human vision was used to simulate a birds view of the moths originally, solely avian species are se nsitive to different wavelengths of light and so volition have a different view of the moths and their respective camouflage to that of humans. Taking this into consideration, Majerus, Brunton and Stalker (2000) devised a more systematic experiment to examine the UV characteristics ofCatherine Carrick 200884273both moth morphs and some of the lichens they rested on as demonstrated by the images in Fig. 3. accede 3. The typica and carbonaria forms of the peppered moth as they appear in normal visible light (a), and as they appear under UV light (b). Image taken from MAJERUS, BRUNTON STALKER, 2000It was their decisiveness that moth colour provides sufficient camouflage both in human-visible and UV- spectra to crutose lichens (as appose to different lichen flora originally hypothesised to be rested upon by desolateen and peppered morphs). Ultimately, potent selection pressures gave way to relatively rapid the evolution of the carbonaria form in industrialised areas receivable to the advantages of its dark colour (predator avoidance etc). manners and ResultsAssignment 1 Testing the Hardy-Weinberg PrincipleMethodUsing PopGenLab, we are able to fixate up so-called experiments to observe the factors that influence the Hardy Weinberg equilibrium in a population. We can do this by manipulating different input parameters (genotype frequency, corner type, number of stands (groups of shoetrees), stand surface of it (number of trees within a group), migration rate, couple descriptor and disaster frequency). For this assignment the input parameters are as followsNumber of stands = 1 whole other input parameters are left at inattention values (equal allele frequencies genotype frequencies of 50% brown, 25% white, 25% mordant equal proportions of each tree type stand size of it of it of 4000 no migration random yoke disaster frequency set at Never.ResultsQ 1.1) When smell at the allele and genotype frequencies, there is a change in both everyplace eon. All populations behave differently to one another. This is because the even so active evolutionary force is genetic drift. Fig. 4 shows that allele frequencies changeCatherine Carrick 200884273 everyplace time overdue to genetic drift, yet as all the conditions of the Hardy Weinberg equilibrium are primed(p) the allele frequencies must equal 1 and so the variation in allele frequency of A start outs the negative of the frequency of a. (Fig. 4). kind 4. Showing allele frequencies changing over time due to genetic drift. Blue line = allelomorph A, harm line = allele a, special K line = second-rate over all stands for allele AQ 1.2) When the initial allele frequencies are changed to A=80% (p), a = 20% (q) (p = 0.8 x 0.8 = 0.64) AA = 64% (equilibrium orbital cavityed after one generation) (Fig 6). If all the Hardy Weinberg conditions are all set(p), the equilibrium will always be reduced in the next generation (Fig.5 and 6). Fig. 5. shows the initial genotype frequency co mpared with Fig. 6. which shows the genotype frequency after one generation. The actual genotype frequencies (worked out with median(a) stand number) match the Hardy Weinberg predictions as they stay within 1% of the previous generations genotype frequency, across every generation thereafter. However, the office whitethorn change by 1% due to genetic drift. general anatomy 5. Display of the initial genotype frequency.Catherine Carrick 200884273Figure 6. Shows the Hardy Weinberg equilibrium is reached after one generation where 0.64=64% homozygous AA individuals.Assignment 2 Genetic DriftMethodQ 2.1) Firstly we ran an experiment with inadvertence values for all the Hardy Weinberg conditions and blow populations.We then ran a series of experiments with ascorbic acid populations and default parameters for all conditions provided tree stand size which was systematically reduced for each experiment. We recorded the cause on allele and genotype frequency (below). Fig. 7 shows tha t stand size 10 produced the superst fluctuations of allele frequencies, and displayed the most cases of allele fixing.Results stick out size = 4000 (carrying capacity) allelomorph frequency- the modal(a) system constant for A and agenetic constitution frequency stays relatively constant throughout. cornerstone size = 2000 allelomorph frequency the add up show slight variationGenotype frequency stays relatively constant.Stand size = grand pianoallele frequency the average starts to straggle more with each generation from F45 (generation 45) onwards show a lot more variation than in larger stand sizesGenotype frequency the average frequency stays constant although there is some variation compared with larger stand sizesCatherine Carrick 200884273Stand size = dAllele frequency The average shows variation in the later generationsGenotype frequency the average stays relatively constant but still with more variation than in any other larger stand thus farStand size = 250 Allele frequency the average shows some variation in the mid-generations, but this returns to a 5050 frequency in the later generationsGenotype frequency on average, the frequency of both white and black variations of moth increases and shows a large variation amongst stands.Heterozygosity the brown variation decreases by 9% over 100 generationsStand size = 100Allele frequency the average shows more variation, but to the point where in some stands alleles within individual populations become fixedGenotype frequency the frequency of homozygotes increases. In some stands the homozygosity (black) becomes fixed, phasing out the other tow variations (white and brown)Heterozygosity drops by 22%Stand size = 50Allele frequency frequencies become fixed for a case-by-case allele promptly (by F23)Genotype frequency Many stands become fixed for one variation within a few generationsHeterozygosity drops by 33% after 100 generationsStand size = 10Allele frequency becomes fixed within a population after two generations, and continues to become fixed in other populations. By F77, all are fixedGenotype frequency every single genotype becomes homozygous or nonexistentHeterozygosity by F77 all heterozygosity is broken and by F100 there are only homozygous populations, with the other (70%) becoming extinctThere are many variations in allele and genotype frequency between different stands because as the stand number decreases, the chance of genetic drift increases. Figure 7 shows that at stand size 10, heterozygosity was lost completely by F77.Catherine Carrick 200884273Figure 7. (stand size 10) this produced the largest fluctuations of allele frequencies, and displayed the most cases of allele fixing. (Blue = A, Red = a, Green = average)Q 2.2) As the stand size diminish, so did the heterozygosity. commonwealths began simple regression in stand size 100 to stand size 50. As the stand size decreased, the number of fixed alleles increased. When the carrying capa city became too small, there was not adequacy variation to check fixation. haphazard unification account for the variation between fixed and non-fixed alleles in stand size 100 and stand size 50. Fig. 8. shows that with a stand size of 10, heterozygosity gaunt completely by F77. Therefore, the littler the population, the quicker heterozygosity is lost.Figure 8. unbelief 22 (stand size 10) This shows the heterozygosity diminished completely by F77. The green line (average) tends to diminishing heterozygosity.Catherine Carrick 200884273Figure 9. Question 23 (stand size 10) Shows population of stand number 15 and how it fluctuates around the average value, it also shows that when the population dwindled to a authoritative point, it wasnt able to re-establish the numbers enough to prevent quenching.Q 2.3) Yes populations from stand size 10 became extinct (70% of them) therefore, as the carrying capacity decreases, the risk of extinction increases. There is variation within gen erations due to factors identical depredation or whether the offspring are male biased for example. There may be a lower population size in the next generation depending on mating strategies (random mating) and occasionally, the parameters reach a point of no return and the population can not recover and so becomes extinct. Others avoid extinction because the experiment is random. Fig. 9. (where stand size = 10) shows population of stand number 15 and how it fluctuates around the average value, it also shows that when the population dwindled to a certain point, it wasnt able to re-establish the numbers enough to prevent extinction.Assignment 3 The Influence of Mating Patterns on Population genetic scienceMethodIn this experiment we set all default parameters except for the number of tree stands which was set to 100. The first experiment was carried out with random mating, and the subsequent experiments with non-random mating. We then varied the population size as before, this time to compare the effectuate of assertive mating with genetic drift.ResultsQ 3.1)The effectuate of 25% assortative matingGenotype frequency 25% assortative mating causes an increase in homozygotes, and heterozygosity is lost by F80Allele frequency (produces a sigmoidal shaped graph). All become fixed for a single allele.Heterozygosity the average heterozygosity is lost at F80Catherine Carrick 20088427350% assortative matingGenotype frequency all homozygotes with an approximately 11 ratio aa being slightly more dominantAllele frequency (sigmoidal graph) all fixed by F50Heterozygosity lost by F33 (average heterozygosity)100% assortative matingGenotype frequency quickly becomes homozygote dominatedAllele frequency All fixed fro a single allele by F15Heterozygosity Average lost by F4Heterozygosity is lost under assortative mating. This is because heterozygotes are at a reproductive disadvantage as homozygotes will mate with like genotypes. Heterozygotes will not be produced by these matings either.Q 3.2) ResultsPopulation size 2000 (stand size), 100% assortative matingGenotype frequency all homozygous by F4Allele f fixed by F14Heterozygosity average lost by F4Population size 2000, 50% assortative matingGenotype f all homozygous by F25Allele f all fixed by F29Heterozygosity average lost by F25Population size 250, 100% assortative matingGenotype f all homozygous by F4Allele f all fixed by F12Heterozygosity lost at F4Population size 250, 50% assortative matingGenotype f all homozygous by F25Allele f all fixed by F28Heterozygosity lost at F25Assortative mating dominates control of allele frequencies and the speed that alleles become fixed within a population compared with the make of genetic drift (because the homozygotes are all mating with the same genotype and not with heterozygotes). Assortative mating is not dependant on carrying capacity. The size of the population is irrelevant when assortative mating is occurring. The results are sim ilar for a high or a low population size.Catherine Carrick 200884273Q 3.3) MethodWe conducted a series of experiments using disassortative mating and selected different levels of mating between 0% (random mating) and 100% (only unlike phenotypes mate). We then changed the population size from 2000 to 250 to see the effects of disassortative mating on genetic drift.ResultsDissasortative mating shows that AA and aa will mate which increases heterozygosity and stabilises the population as shown in the results belowPopulation size 2000, 100% disassortative matingGeno (genotype frequency) heterozygote is predominantAllele (allele frequency) none become fixed. There is variation but it stays within 31% 68% variationHetero (heterozygosity) increases in the first generation then corpse constantPop size 2000, 50% disassortative matingGeno predominantly heterozygoteAllele none become fixed. There is less variation than with 100% disassortative mating. transformation is between 43% an d 57%Hetero Increases in first generation and remains constantPop size 250, 100% disassortative matingGeno -slight heterozygote increaseAllele No fixed alleles. There is oftentimes greater variation than seen previously with a larger population size, between 21% and 79%Hetero increases in 1st generation then remains steady and begins to decrease. Remains above the initial percentagePop size 250, 50% disassortative matingGeno heterozygosity increases steadilyAllele No fixed alleles. Variation is less than with 100% disassortative mating and population size of 250. Variation levels out between 33% and 67%Hetero increases in the 1st generation and remains constant with a few small fluctuations which level back outQ 3.4) There would be more heterozygosity in the next generation when disassortative mating occurs and if this kind of mating is maintained, the effects of genetic drift occur more slower because the populations are prevented from diverging. Fig. 10 shows the comparis on between disassortative mating and random mating where random mating allows genetic drift. Drift can still occur during dissasortative mating when the carrying capacity is very low.Catherine Carrick 200884273Figure 10. (picture on left) Random mating, pop size 250 showing genetic drift acting to diverge allele frequencies. (picture on right) 50% dissassortative mating, population size 250 shows that dissasortative mating acts to forebode genetic drift.Q 3.5) MethodFor this experiment we varied the initial genotype frequency for assortative and disassortative mating. We tried experiments where the initial allele frequencyfavoured one or the other allele. Fig. 11 show starting frequencies of 50/50% assortative mating. A small deviation in starting frequencies affects the final fixation percentages (Fig. 11). We did not include the brown allele in this experiment as the extra variable is not bringed.Figure 11) Shows starting frequencies of 50/50% (50%-white allele, 50% black alle le) with assortative mating = 100%. Small deviation in starting freq effects final fixation percentages.Catherine Carrick 200884273ResultsUnder dissassortative mating the time taken for equilibrium to establish is negatively correlated with the degree of deviation from a 11 starting allele ratio. Under assortative mating, fixation or loss of alleles is negatively correlated with the degree of deviation from a 11 starting allele ratio.Assignment 4 Modes of Natural SelectionQ 4.1) MethodIn this experiment we investigated how fitness affects changes in allele frequency in the population. We began with default parameters except tree stand number (set at 100) and genotype frequencies. We changed the tree frequency to set up several experiments under conditions of directional selection for dark moths, directional selection for light moths, balancing selection favouring the brown moth, and diversifying selection favouring the dark and light moths.We tried experiments with the different c onditions of selection and initial allele frequencies near zero and one.ResultsDirectional selection for black moths where they tree frequencies are 50% black, 25% white and 25% brown trees gave the following resultsAllele frequency becomes fixed rapidly by F10 (on average by F9)Genotype frequencies at F10 genotype becomes fixed for black alleleIn a small population, alleles become fixed more quickly but in larger populations allele frequencies are not impact as much. We kept the population size high so we would not see genetic drift in the experiment (4000 carrying capacity) with tree frequencies of 35%, 32% and 33%. Even the small amount of selection (35% black trees) shows fixation of alleles for the black morph of moth (Fig. 12). Selection for light moths gives the same results as selection for black moths.Figure 12. shows allele becoming fixed rapidly, due to a tiny increase in black trees on left, white trees on right (35 %)Catherine Carrick 200884273Q 4.2) Starting figure s are as followsBlack tree 25%Allele black 25%Brown tree 50%Allele brown 50%White tree 25%Allele white 25%After one generation, allele frequency remains stable (between 48% and 52%) and the genotype frequency becomes predominantly brown. This is because there is always the presence of black and white genotypes which cause slight variation. If you change the selection of trees to black 10%, white 10%, brown 80%, almost identical results occur (between 49% and 51% variation in allele frequency = stabilized).Q 4.3) To show diversifying selection we set the tree types to 45% black, 45% white and 10% brown.Genotype frequency by the 1st generation, there was a large decrease in brown morphs of moth and the akin increase in black and white morphs. This continues till F5 when the black morph became slightly more dominant (on average) due to random mating. The brown morph was phased out by F18 (on average) on most of the 100 tree stands. All alleles become fixed for either black o r white by F23 (49% white, 51% black) (Fig 13).Figure 13. Shows 50% black and 50% white showing a 11 ratioQ 4.4) Small differences in fitness are effective in changing allele frequencies. Small differences in fitness have proportionally slower rates of allele frequency change compared with large differences in fitness.We conducted additional experiments with varying proportions of tree types. The results are as follows(Where stand size = 4000, number of stands = 100, allele frequencies = white 20%, brown 60%, black 20%, tree frequencies = white 32%, brown 32%, black 36%). Even though there are a lower proportion of black alleles (A) to begin with, those alleles will have a higher fitness than white or brown as there is a higher percentage of black tree types. Over time this will equate to an increase in black morphs. There is, however, aCatherine Carrick 200884273point where even if the black allele is fittest but there isnt a high enough population in the first place, it will cras h and not recover.Q 4.5) Genetic variation is maintained under balancing selection because the allele frequencies remain stable. There is no fixation (presuming the all mating is random). The heterozygote allele is favoured and thus balances the homozygous allele.Assignment 5 MigrationQ 5.1) Migration counteracts the effects of genetic drift. (Fig 14 and 15)Figure 14. Stand size of 500 and no migration shows heterozygosity varying over all populations. Green line = average heterozygosity over all populations.Figure 15. Shows stand size 500, and 8% migration. Shows migration maintains heterozygosity and there is less deviation from the average (green line)Catherine Carrick 200884273Assignment 6 Population BottlenecksQ 6.1) chance led to the loss of alleles and reduced heterozygosity. The more disasters there where, the more decreased the multifariousness became. (Fig 16, 17, 18)Figure 16. Control condition Shows low drift conferred by high population sizes (4000), all other varia bles adjusted to give Hardy-Weinberg equilibrium.Figure 17. Disaster parameters set to sometimes as opposed to never. Individual populations prostrate to fixation and loss of alleles.Catherine Carrick 200884273Figure 18. Disaster frequency set to often rather than sometimes. Loss of diversity occurs faster than in figure 13 with most populations losing one or the other allele by generation 80.Q 6.2) Disaster increased the rate of extinction. The more regular the disaster, the more extinctions.Q 6.3) Migration moderated the effect that disasters had on the population.DiscussionThe results of our experiments clearly show that genetic drift effects smaller populations where heterozygoisity is lost rapidly and as the carrying capacity decreases, the risk of extinction increases. The is because the proportion of individuals with a certain phenotype within a small population are largely influenced by random variation in survival, and over time, the change in proportion of genotypes in su bsequent generations leads to genetic drift. If one was to aim to conserve a hypothetical species, one would expect that because it is endangered, it would be a small population. To maintain genetic diversity among this species, one would need a large enough breeding population to begin with. Unfortunately, as is the case with most endangered species, populations become geographically isolated, mainly due to human disruption of habitat. Migration between breeding populations decreases and they become fragmented. Conservation efforts may be due to natural disasters such as tsunamis, fires etc, but are mainly to prevent the constant onslaught of human activities such as illegal logging in conservation areas. Figure 17 illustrates the effects of a bottleneck following a disaster, showing reduced variability (and a small population) leading to loss and/or fixation of alleles. As with genetic drift, the way to prevent population crashes, or rather unwrap the effects of bottlenecks, is t o encourage migration among populations. This can be achieved by implementing the protection of corridors between known endangered populations. In theory, the populations can migrate between areas, maintaining a high enough level of breeding and genetic variation, to counter the effects of inbreeding depression or genetic drift (Fig 14 and 15). An example of how corridors may re-connect fragmented populations can be seen in Bhutans Jigme Singye Wangchuck National Park (www.panthera.org).Catherine Carrick 200884273Figure 19. Map of known tiger populations (red) and proposed tiger corridors (orange). Data taken from www.panthera.orgThe proposed east Himalayan corridor may help towards connecting isolated populations of tigers, and thus increasing genetic diversity (if these populations successfully reproduce with one another) (Fig 19).Random mating, as apposed to assortative mating, will increase heterozygosity and stabilise a population (Fig 10). This acts against genetic drift and loot the population form diverging as quickly. In a hypothetical situation then, you would preferably allow mating to occur naturally and at random. However, some conservation efforts include that of translocation of individuals or cross breeding certain individuals from separate populations. For this to be advantageous to the species, one must consider maintaining genetic diversity by genotyping the individuals before translocation. It would be senseless to swap or breed an AA individual with another AA individual from a separate population as this would lead to loss or fixation and not increase diversity. Our studies with B. betularia in question 4 to 4.5 show that intermediates are favoured over thorough phenotypes and that genetic variation is maintained under balancing (stabilizing) selection because the allele frequencies remain stable. There is no fixation (presuming the all mating is random). The heterozygote allele is favoured and thus balances the homozygous allele.As w ell as considering the genetic diversity of a species and its genealogy, one must understand the species by means of observations in the field including its behaviour. Later studies of B. betularia reinforced the need for such observations as it was make up to rest high in the branches rather than on the trunks of trees as previously calculated. Also, modern science allowed for the study of its UV qualities which had otherwise been unaccounted for when considering levels of predation by birds. A close study of mating patterns should ideally be assessed to ensure the outcome of migration corridors, translocation etc will be advantageous in terms of fitness.Catherine Carrick 200884273