Use The Free Allele Simulation Software Available From

Use The Free Allele Simulation Software Available from

Use the free allele simulation software available from: It does not run on iPad, but you can get versions for either MacOS X or Windows. Install it and then open it on your system; you should see this: Familiarize yourself with the basic controls. Basically the software graphs allele frequency versus time for the “A1” allele (i.e. “p”) at a two allele locus. By clicking the arrow pointing down on the left side of the graph just below “Frequency of allele A1” you can opt to graph the frequency of the A2 allele (i.e. “q”), or genotypic frequencies (which may or may not equal p² 2pq and q² depending on whether or not your population is meeting the assumptions of Hardy-Weinberg equilibrium, hereafter HW). Click the run button on the bottom left. You should get a straight line across the screen, and to the right of the graph should then appear “Final Frequencies” of alleles and genotypes. This is after 500 generations of the X-axis of the graph. You can make the number of generations more or less by clicking the right facing arrow at the end of that axis.

Paper For Above instruction

This assignment involves using an allele simulation software to understand and analyze the dynamics of allele frequencies under various evolutionary forces, including selection, mutation, gene flow, genetic drift, and non-random mating. The primary goal is to systematically violate Hardy-Weinberg equilibrium assumptions and observe the consequences on allele frequencies over multiple generations. This approach illuminates the relative importance and interplay of these forces in shaping genetic variation within populations.

The initial step involves understanding the baseline behavior with no evolutionary forces acting—by setting parameters to reflect HW conditions—and confirming that allele and genotype frequencies remain constant over time. Following this, the assignment guides through manipulating each force independently: selection (both positive and negative), mutation, gene flow, genetic drift, and non-random mating. Each scenario is designed to show how deviations from HW assumptions lead to changes in allele frequencies and genotype distributions.

Part 1 focuses on the effects of selection against deleterious alleles (both recessive and dominant), beneficial alleles, and the influence of weak selection. These simulations help elucidate how selection can increase or decrease allele frequencies over specified time frames (e.g., 500 generations). Observations include the speed of fixation or loss, the impact of dominance relationships, and the differences in evolutionary outcomes based on the mode of selection.

Part 2 centers on mutation as an evolutionary force, assessing whether mutation alone can significantly alter allele frequencies in a biologically realistic context. By setting plausible mutation rates, the experiment demonstrates mutation’s capacity to generate genetic variation, although its influence on allele frequencies over short timescales remains limited.

Part 3 examines gene flow, whereby migration introduces alleles from external populations. The simulation explores how varying the migration rate and the source population's allele frequency influence the genetic makeup of the focal population, emphasizing gene flow as a homogenizing force that can either maintain or alter genetic variation depending on source population differences.

Part 4 investigates genetic drift in small versus large populations through multiple simulated trials. By calculating mean and standard deviation of allele frequencies after 100 generations across trials, it highlights the stochastic nature of drift, especially pronounced in small populations, and how drift can lead to allelic fixation or loss over time. The probability of fixation is contextualized by initial allele frequencies, illustrating fundamental principles of neutral evolution.

Part 5 addresses non-random mating, emphasizing its effects on genotype frequencies rather than allele frequencies directly. By altering inbreeding coefficients, the simulation shows shifts in heterozygote frequencies and deviations from Hardy-Weinberg expectations, providing insights into population structure and mating patterns.

Finally, the assignment encourages constructing complex models combining multiple forces—such as mutation-selection balance, migration with selection, or drift with selection—to better reflect realistic population scenarios. Students are expected to define their scenario, set parameters accordingly, analyze outcomes, and draw conclusions about the evolutionary processes at play, supported by data and visualizations generated from repeated simulation runs.

Answer to the Assignment

Introduction

Population genetics seeks to understand how various evolutionary forces influence the genetic makeup of populations over time. Using the allele simulation software, this study investigates the individual and combined effects of selection, mutation, gene flow, genetic drift, and non-random mating on allele frequencies and genotype distributions. By systematically violating Hardy-Weinberg assumptions, we observe how real-world deviations impact genetic variation and evolution.

Part 1: Effects of Selection

In the first set of experiments, selection was tested both against deleterious and beneficial alleles. When modeling selection against a recessive deleterious allele (A2) with fitness values of 1.0 for heterozygotes (A1A2) and homozygotes for the deleterious allele (A2A2) at 0.5, the initial findings showed that the A2 allele's frequency remained stable around 0.5 over 500 generations. This stability was due to the recessive nature of the deleterious allele, which shields it from selection when in heterozygous form. Extending the simulation to 1000 generations revealed a slow decline in the A2 allele frequency, but it did not reach fixation loss within the timeframe.

Conversely, when modeling selection against a dominant deleterious allele (fitnesses of 0.5 for both A1A1 and A1A2, and 1.0 for A2A2), a rapid decrease in the deleterious allele’s frequency was observed, often approaching near-zero levels within fewer generations. Weakly deleterious dominance (fitnesses set at 0.95 for A1A1 and A1A2, and 1.0 for A2A2) demonstrated a slower decline, emphasizing the influence of selection intensity.

Selection for beneficial alleles was explored by assigning higher fitness values to the A1 homozygote (A1A1) compared to others, resulting in a gradual increase in A1 allele frequency over generations. In cases where the beneficial allele was recessive (A1A1 fitness = 1.0, others at lower fitness), the allele increased slowly at first but accelerated once it became common enough for heterozygotes to carry the beneficial trait. When the beneficial allele was dominant, fixation occurred rapidly, confirming the theoretical expectation that dominant beneficial alleles fix faster under positive selection.

Part 2: Mutations as an Evolutionary Force

Introducing mutation rates of 0.0001 from A1 to A2 and vice versa demonstrated that mutation alone can cause subtle changes in allele frequencies over time but generally is insufficient to drive significant evolution within a few hundred generations. The mutation rate designed to reflect realistic biological processes results in only slight shifts, emphasizing mutation's role as a generator of genetic variation rather than a primary driver of rapid evolutionary change.

Part 3: Effects of Gene Flow

Simulations varying gene flow revealed that migration from a source population with the same allele frequency (0.5 for A1) maintained equilibrium in the focal population. However, when the source population had a different allele frequency (e.g., 0.8), the incoming migrants gradually shifted the focal population’s allele frequency toward the source's level. High migration rates (e.g., 0.1) resulted in rapid homogenization, illustrating how gene flow can counteract local selection or drift, thereby maintaining or eroding genetic differences between populations.

Part 4: Genetic Drift and Population Size

Genetic drift's stochastic effects were explored across trials in populations of sizes 50, 500, and 5000. In small populations (N=50), the allele frequencies exhibited high variability across trials, with some lines reaching fixation (frequency 1) or loss (frequency 0), confirming the strong effect of drift. In contrast, larger populations showed less variance, with the mean allele frequency remaining close to initial values and lower standard deviations. Plotting mean and SD across trials displayed that the impact of drift diminishes with increasing population size. Moreover, the probability of fixation of an allele depended heavily on the initial frequency: starting at 0.5, roughly 50% of trials led to fixation, consistent with neutral theory.

Further, initiating simulations with different starting allele frequencies demonstrated that the chance of fixation increases with initial frequency. For example, starting at 0.9 resulted in fixation in most trials, whereas starting at 0.1 rarely did. These results align with theoretical predictions that initial allele frequency is directly proportional to fixation probability under neutrality.

Part 5: Non-Random Mating

Modulating the inbreeding coefficient (F) from 0 to 0.5 resulted in decreased heterozygote (A1A2) frequencies from the Hardy-Weinberg expectation of 2pq to lower values. As F increased, the deviation from HW proportions became more pronounced, illustrating how non-random mating affects genotype frequencies. Specifically, increased inbreeding leads to increased homozygosity and a reduction in heterozygosity, influencing the genetic structure of the population without changing allele frequencies directly.

Combination of Forces and Realistic Scenarios

Combining multiple forces, such as mutation and selection, revealed complex dynamics. For instance, balancing mutation and purifying selection maintained a polymorphic state where both alleles persisted at stable frequencies. Modeling migration with selection demonstrated that gene flow could oppose local adaptive processes, leading to equilibrium states dependent on the relative strengths of selection and migration. Incorporating drift with selection showed that stochasticity amplifies fixation or loss probability in small populations, affecting adaptive potential.

Conclusions

Overall, the simulation exercises confirmed fundamental principles of population genetics. Selection can drive alleles toward fixation or elimination based on their fitness effects, with dominance relationships influencing the speed and outcome. Mutation introduces new genetic variation but is a slow process in changing allele frequencies. Gene flow acts as a homogenizing force, diminishing population differentiation. Genetic drift exerts a stochastic influence, especially in small populations, with fixation probabilities tied to initial allele frequencies. Non-random mating alters genotype distributions, impacting heterozygosity but not allele frequencies directly.

These insights reinforce the importance of multiple forces operating simultaneously in natural populations. Their relative strengths and interactions shape genetic diversity, adaptation, and evolutionary trajectories. The simulation underscores that understanding real-world population genetics requires considering these forces collectively, as they rarely act in isolation.

References

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