Mechanisms of Evolutionary Change

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WHAT IS IT?

This is a model of the Hardy-Weinberg (HW) equilibrium. The HW principle predicts the genotypic frequencies that will be observed in a population over the course of generations given particular allele frequencies, and given that five assumptions (discussed below) hold true in the population.

Given two alleles, A and a, and the frequencies of each allele in the population, freq(A)=p and freq(a)=q, the HW principle predicts:

1) p + q = 1. That is, since A and a are the only alleles at this locus in the model population, the allelic frequencies of A and a must add up to 1.

2) The genotypic frequency of AA homozygotes in the population is p^2. The frequency of aa homozygotes is q^2. The probability that any given member of the population will inherit two A alleles is p x p. The frequency of heterozygotes is 2pq. The probability that any given member of the population will inherit one A and one a allele is p x q x 2, since a heterozygote can inherit allele A from its mother and allele a from its father, OR allele a from its mother and A from its father. p^2 + 2pq + q^2 = 1. That is, the frequencies of both types of homozygotes and the frequency of heterozygotes must add up to 1, since these are the only possible combinations.

These predictions hold true given certain assumptions about the population all hold true. Five of those assumptions can be examined through this model.

1) Large (infinite) population size. In small populations, chance differences in reproductive success and mating choices can produce deviations from the predictions of HW.

2) No selection. There is no systematic difference in the survival or reproductive success of organisms with different genotypes.

3) No mutation. The alleles are inherited from one generation to the next without being changed by mutation.

4) No migration. No organisms leave the population, and no new ones come in.

5) Random mating. Organisms choose mates at random with respect to the alleles of interest in the model.

If any of these assumptions do not hold true in a population, the observed genotypic frequencies will deviate from the predictions of HW in particular ways depending on the assumption(s) that is (are) violated.

This is a model of the Hardy-Weinberg (HW) equilibrium. The HW principle predicts the genotypic frequencies that will be observed in a population over the course of generations given particular allele frequencies, and given that five assumptions (discussed below) hold true in the population.

Given two alleles, A and a, and the frequencies of each allele in the population, freq(A)=p and freq(a)=q, the HW principle predicts:

1) p + q = 1. That is, since A and a are the only alleles at this locus in the model population, the allelic frequencies of A and a must add up to 1.

2) The genotypic frequency of AA homozygotes in the population is p^2. The frequency of aa homozygotes is q^2. The probability that any given member of the population will inherit two A alleles is p x p. The frequency of heterozygotes is 2pq. The probability that any given member of the population will inherit one A and one a allele is p x q x 2, since a heterozygote can inherit allele A from its mother and allele a from its father, OR allele a from its mother and A from its father. p^2 + 2pq + q^2 = 1. That is, the frequencies of both types of homozygotes and the frequency of heterozygotes must add up to 1, since these are the only possible combinations.

These predictions hold true given certain assumptions about the population all hold true. Five of those assumptions can be examined through this model.

1) Large (infinite) population size. In small populations, chance differences in reproductive success and mating choices can produce deviations from the predictions of HW.

2) No selection. There is no systematic difference in the survival or reproductive success of organisms with different genotypes.

3) No mutation. The alleles are inherited from one generation to the next without being changed by mutation.

4) No migration. No organisms leave the population, and no new ones come in.

5) Random mating. Organisms choose mates at random with respect to the alleles of interest in the model.

If any of these assumptions do not hold true in a population, the observed genotypic frequencies will deviate from the predictions of HW in particular ways depending on the assumption(s) that is (are) violated.

HOW TO USE IT

Population size The "initial-population-size" slider determines the carrying capacity of the system.

The "proportion-allele-A" slider bar determines the initial frequency of the allele A. The frequency of allele a is determined by calculating freq(a) = 1 - freq(A).

Gene Flow/Migration New organisms will enter the population. They genotypes can either be AA "homo-dominant-immigration", AA "hetero-immigration", or aa "homo-recessive-immigration". The sliders represent the number of individuals entering the population each turn (i.e. 30% * 100 initial population = 30 individuals/generation). If all three sliders are at the right, 90% of the initial population enters the population at each time step. If all three sliders are set to 0%, there is no gene flow during the simulation.

Natural Selection Certain phenotypes have a higher likelihood of dying after each generation. Those who die are then unable to pass their genes on to the next generation. The "selection-against-blue" slider increases the rate of mortality of blue individuals. The "selection-against-red" slider increases the rate of mortality of red individuals. If both sliders are set to 0%, there is no gene flow during the simulation.

Mutations Mutations, with respect to these two color alleles, occur at low frequencies in these populations. For simplicity, this model does not simulate the introduction of new alleles. It only changes current alleles. The "mutation-dominant-to-recessive" slider changes the probability that an "A" allele will mutate into a "a" allele. The "mutation-recessive-to-dominant" slider changes the probability that an "a" allele will mutate into a "A" allele. If both sliders, are set to 0%, there are no mutations occurring during the population.

Random Mating During reproduction, one allele from each parent is paired with that from another parent. Using the "mate-with" drop-down, individuals can "mate" with any random individual ("random") or one of their neighbors ("neighbor").

Run The "species" chooser allows the user to select from a list of possible icons to represent the organism as they move around the world.

Clicking the "Run simulation" button initializes the world with a population of organisms of the selected species, with the specified allele frequencies. It will then start the population in motion and will run for 99 generations.

Graphs Graphs track the genotypic frequencies, phenotypic frequencies, and allele frequencies over time as the model runs. Monitors display the current values for each of these.

THINGS TO NOTICE

Note that the genotypic and phenotypic frequencies approximate the values predicted by the HW formulas. Try calculating the predicted values based on the allele frequencies you have specified (or the current allele frequencies obtained by the current A and a alleles present in the population) and compare these to the actual values produced by the model as it runs. The model itself does not make use of the HW formulas, but produces values similar to those predicted by HW by the interactions of the model organisms.

Note the random changes in the genotypic, phenotypic, and allelic frequencies over time. These changes are more apparent with smaller population sizes, but can still be observed even with populations in the thousands. These random changes result from random differences in the survival and reproductive success of individuals each generation, and are called genetic drift. Genetic drift has a bigger effect on the makeup of small populations than larger ones. Theoretically, the HW assumption of "large population" requires an infinitely large population in order to completely eliminate the effect of drift.

Note that the population size will not always match exactly the value selected by the "population-size" slider. In fact, during each reproduction cycle, the population size will rise well above this value, and then fall back roughly to the specified population size at the end of the culling cycle. However, because mortality for each organism is determined by a certain probability, the final population size will not be exactly the specified value, although it will be close.

THINGS TO TRY

Experiment with the settings of the model to create violations of the five assumptions described above. The Hardy-Weinberg equilibrium describes a theoretical population that cannot exist in the real world; perhaps its greatest value is in describing a population where no evolution is occurring, in order to better understand real populations where one or more of the five assumptions are violated, and evolution is occurring.

1) Large (infinite) population size. Try running the model with populations of different sizes in order to observe differences in the strength of genetic drift. 2) No selection. Try experimenting with different degrees of selection against (increased mortality of) the blue and yellow phenotypes. You will observe that selection against the recessive phenotype (yellow color) takes much longer to completely remove the a allele from the population, even with heavy selection against the yellow phenotype. Why is this? What does this tell us about the persistence of recessive genetic disorders in the population? 3) No mutation. Experiment with different mutation rates from dominant to recessive, or recessive to dominant. What happens if there is a large rate of mutation in both directions? 4) No migration. Experiment with different rates of immigration of blue and yellow individuals. How does immigration of individuals of a particular color effect the overall genetic makeup of the population? 5) Random mating. The "mate-with" chooser can cause the organisms in the model to choose mates completely at random, selecting any other organism in the world as a mate. You can also cause organisms to mate with a neighbor, so that organisms must be adjacent in order to mate with each other. Note what happens to the frequency of heterozygotes when organisms are mating with their neighbors. Also note that increasing the dispersal rate (the distance the organisms move each time step) decreases the effect of mating with neighbors on the phenotypic makeup of the population. Why does this happen?

CREDITS AND REFERENCES

Current NetLogo simulation addapted for BIOL 3445 - Introduction to Evolution

Origional NetLogo simulation:

Hardy-Weinberg Classroom Model (2009) Kenneth Letendre Departments of Biology and Computer Science University of New Mexico kletendr@unm.edu

Council-Garcia, C.L., S. Ligon, B. Milne, R. Thornhill and D. Swenton. 2004. Biology 203L: Evolution and Ecology Lab Manual. Hardy, G. H. (1908). "Mendelian proportions in a mixed population". Science 28: 49 � 50. Stern, C. (1943). "The Hardy�Weinberg law". Science 97: 137�138. Weinberg, W. (1908). "�ber den Nachweis der Vererbung beim Menschen". Jahreshefte des Vereins f�r vaterl�ndische Naturkunde in W�rttemberg 64: 368�382.

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