The subject of this assignment is Simulation of the Hardy-Weinberg equilibrium and the conditions of migration, natural selection, and population size that disrupt equilibrium in a Koi fish population. I need a methodology with the following information because all the simulations are already done and below will be the results of the simulations to be able to create the methodology.

Methodology: describes how the data was collected. The methodology can include study site, data collection and data analysis. Always run the model for 300 generations The situations were evaluated with individual simulations to observe how the effect of the population in equilibrium HW would be when only one parameter changed. The first observed and simulated situation shows an experimental design of the ideal Koi fish population to analyze the Hardy-Weinberg Equilibrium Model (Figures 1-3). It was observed that the size of the population remained in the margins of the carrying capacity of 200, that is, close to the value both above or below it without causing a drastic change in the size of the population, resulting in a population 191 individuals, 10 individuals less than the initial population of 200. In addition, it was observed that the proportions of the alleles and genotypes had variations during the generations resulting in that the proportion of the R allele increased from 0.44 to 0.65 and the r allele decreased from 0.56 to 0.35 giving that the genotype ratio for the homozygous recessive rr genotype decreased from 0.27 to 0.14, the heterozygous Rr genotype decreased from 0.48 to 0.42 and the homozygous dominant RR genotype increased from 0.25 to 0.44 The second situation observed was the condition that interrupts the equilibrium by migration (Figures 4 -). The three models simulated and analyzed resulted in an R allele fixation and homozygous RR genotype. In the first model (Figures 4 - 6) the Migration Rate had a value of 0.6 less than the value of 1 of the Migratory Proportion of the R Allele and it was obtained that the size of the population remained within the margins of the carrying capacity of 200 resulting in a final of 201 individuals, 1 individual more than the initial population of 200. The ratio of the R allele increased from 0.49 to 1 and that of the r allele decreased from 0.51 to 0. This change in the allelic propositions resulted in the Genotype proportions of the heterozygous Rr and homozygous recessive rr genotypes will be eliminated from the population, 0.27 and 0.48 to 0, respectively, resulting in the fixation of the homozygous dominant RR genotype, 0.25 to 1 (Figure 6). In the second model (Figures 7 - 10) the Migration Rate had a value of 0.6 greater than the value of 0.4 of the Proportion of the Migratory Allele R. This resulted in the population size having the same behavior as in the first model, but resulting in a final population of 204 individuals, 4 individuals more than the initial population of 200. The proportions of the R and r alleles had a similar behavior to the first model where the R allele increased from 0.52 to 1 and the r allele decreased from 0.48 to 0, as well as the genotypic proportions obtaining that for the homozygous recessive genotype rr there was a decrease from 0.20 to 0, heterozygous genotype Rr decreased from 0.56 to 0 and the homozygous dominant RR genotype increased from 0.25 to 1. In generation 103 ( Figure 9), it was observed that the R allele had already been fixed. The third model (Figures 11-13) the Migration Rate and the Migratory Allele Proportion R have the same value of 1, resulting in similar behavior to models 1 and 2 in population size and allele and genotype proportions. The size of the final population resulted in 220 individuals, 20 individuals more than the initial population of 200. In the proportions of alleles and genotypes, an increase in the proportion of the R allele from 0.52 to 1 and a decrease of the r allele of 0.48 was obtained. a 0 and the genotype ratio for the homozygous recessive rr genotype decreased from 0.25 to 0, the heterozygous Rr genotype decreased from 0.52 to 0, and the homozygous dominant RR genotype increased from 0.24 to 1. Fixation of the R allele occurred more rapidly is this pattern observed in the graph for Generations versus Allele Proportion in Figure 13.

The second situation observes the conditions that interrupt the equilibrium by natural selection through the simulations of the parameters of the mating strength (Figure 4-) and the relative genotypic efficiency (genotypic relative fitness) (Figures -29). In both parameters, it could be observed that one of the alleles and / or genotypes was preferred to the others. The first simulation evaluates the evolutionary parameter of the pairing strength by observing two models. In the first model (Model 1) (Figures 14-17) where the strength of the pairing is positive with a value of 0.4, it was obtained that the size of the population decreased significantly, moving away from the margins of the carrying capacity of 200 until reaching a final population of 0 individuals (Figure 17). This change was observed for generation 121 (Figure 16). Despite the population having been eliminated, the allelic and genotypic proportions had the following changes: the proportion of the R allele of 0.49 increased to 1.08 and for the r allele of 0.51 it decreased to 0 and the genotypic proportion for the homozygous recessive genotype rr had a decreased from 0.22 to 0.02, heterozygous Rr genotype decreased from 0.50 to 0.17 and the homozygous dominant RR genotype increased from 0.29 to 1. The population of this model prefers the homozygous dominant RR genotype, thus representing a directional selection. The second model (Model 2) (Figures 18-20) where the pairing is negative with a strength value of -0.4 observed a behavior in the size of the population different from model 1. The size of the population showed increases and behaviors. decreases moving away and closer to the margins of the carrying capacity of 200, without increasing from this value, resulting in a final population of 189 individuals, 11 individuals less than the initial population observed in the graph of "Generations versus Population Size" ( "Generations versus Population Size") in Figure 20. In the case of allelic proportions, the same behavior of model 1 was observed where the R allele increased from 0.02 to 0.57 and the r allele decreased from 0.98 to 43. However, the Genotype proportions did not behave in the same way, resulting in a decrease in the homozygous recessive genotype rr from 0.23 to 0.11, an increase in the heterozygous genotype Rr 0.47 to 0.63 and a decrease in the genotype. homozygous dominant type RR from 0.30 to 0.26. The population of this model prefers the Rr genotype, which represents a stabilizing selection. The second simulation evaluates the Relative Genotypic Fitness evolutionary parameter using three models where the effect of the variation of one of the three genotypes is analyzed. Model 1 where the Relative genotypic Fitness is rr = 0.6, Rr = 1 and RR = 1. The population size was kept in the margins of the carrying capacity of 200 resulting in a final population of 178 individuals. The proportion of the R allele of 0.49 increased to 0.75 and for the r allele of 0.51 it decreased to 25, the genotype proportion for the homozygous recessive rr genotype decreased from 0.27 to 0.04, the heterozygous Rr genotype decreased from 0.43 to 0.42 and the homozygous genotype dominant RR increased from 0.30 to 0.54. During the generations an increase and decrease in the behavior of the proportion of allele R could be observed

Model 2 where the Relative genotypic Fitness is rr = 1, Rr = 0.6 and RR = 1. The size of the population had a decrease at the beginning of the generations, but then it remained in the margins of the carrying capacity of 200 resulting in a final population of 182 individuals, 18 individuals less than the initial population. The proportion of the R allele from 0.53 decreased to 0 and for the r allele of 0.47 increased to 1, the genotype proportion for the homozygous recessive genotype rr had an increase from 0.23 to 1, the heterozygous genotype Rr decreased from 0.49 to 0 and the homozygous genotype The dominant RR decreased from 0.28 to 0. During the generations, a decrease in the behavior of the proportion of R allele was observed, leaving only the proportion of the r allele in the population.

Model 3 where the Relative Genotypic Fitness is rr = 1, Rr = 1 and RR = 0.6. The size of the population had a brief decrease at the beginning of the generations, but the rapid increase remained in the margins of the carrying capacity of 200 resulting in a final population of 190 individuals. The proportion of the R allele from 0.53 decreased to 0.11 and for the r allele of 0.47 increased to 89, the genotype proportion for the homozygous recessive rr genotype had an increase from 0.28 to 0.80, the heterozygous Rr genotype decreased from 0.48 to 0.19 and the homozygous genotype Dominant RR decreased from 0.24 to 0.01. During the generations it was possible to observe an increase in the behavior of the proportion of the R allele and a rapid decrease that remained in a slight fluctuation until the generation ... decreasing drastically, being almost eradicated until the generation.

Then there was a drastic increase in the proportion of the R allele to decrease and stay at 0.01. The fourth and final situation assesses the violation of the population size assumption for the HW equilibrium. The simulation for the population demographic parameter Initial size of the population evaluated two models. Model 1 where the initial population size is 350 much larger than a carrying capacity of 200. The population size decreased from 350 to the margins of the carrying capacity of 200 resulting in a final population of 189 individuals. The change occurred in the first generations and the population decline was drastic. The proportion of the R allele of 0.48 increased to 0.77 and for the r allele of 0.52 it decreased to 0.23, the genotype proportion for the homozygous recessive genotype rr had a decrease from 0.24 to 0.05, heterozygous genotype Rr decreased from 0.45 to 0.35 and the homozygous genotype Dominant RR increased from 0.31 to 0.60. The behavior of the proportion of the R allele was a continuous increase, having only a few generations where there was a decrease, however, this rapid decrease increased.

Model 2 where the initial population size is 50, much less than the carrying capacity of 200. The population size increased from 50 to the margins of the carrying capacity of 200 resulting in a final population of 198 individuals. The change occurred in the first generations and the increase in population was drastic. The proportion of the R allele from 0.49 decreased to 0.15 and for the r allele from 0.51 increased to 0.85, the genotype proportion for the homozygous recessive genotype rr had an increase from 0.26 to 0.71, heterozygous genotype Rr decreased from 0.52 to 0.28 and the homozygous genotype Dominant RR decreased from 0.22 to 0.01. The behavior of the proportion of the R allele was a continuous decrease having only a few generations where there was increase. However, this rapid increase decreases. The simulation for the population demographic parameter for the female to male sex ratio evaluates two models. Model 1 where the female to male sex ratio has a value of 0.1 and less than a value of 0.5. The size of the population decreased drastically away from the margins of the carrying capacity of 200, resulting in a final population of 0 individuals. The change was continuous and in generation 88, the population was eradicated. The ratio of the R allele from 1 decreased to 0.33 and for the r allele from 0 increased to 0.67, the genotype ratio for the homozygous recessive rr genotype increased from 0.20 to 1, the heterozygous Rr genotype decreased from 0.51 to 0.33 and the homozygous genotype Dominant RR decreased from 0.30 to 0.17.

Model 2 where the female to male sex ratio has a value of 0.9 and greater than the value of 0.5. The size of the population remained in the margins of the carrying capacity of 200, resulting in a final population of 199 individuals. The proportion of the R allele from 0.50 decreased to 0.30 and for the r allele from 0.50 increased to 0.70, the genotype proportion for the homozygous recessive genotype rr had an increase from 0.22 to 0.50, heterozygous genotype Rr increased from 0.51 to 0.40 and the homozygous genotype Dominant RR decreased from 0.27 to 0.10. The simulation of the population demographic parameter compares the behavior of the Mortality Rate with the size of the offspring. Model 1 where the Mortality Rate has a value of 13 and is greater than the value of 5 for the size of the brood. The size of the population decreases away from the margins of the carrying capacity of 200 resulting in a final population of 47 individuals. The population in the generations had a fluctuation that did not increase more than 100 individuals or decrease from 30 individuals. The proportion of the R allele from 0.47 increased to 0.89 and for the r allele decreased from 0.50 to 0.11, the genotype proportion for the homozygous recessive rr genotype had a decrease from 0.25 to 0.02, the heterozygous Rr genotype decreased from 0.52 to 0.17 and the homozygous genotype Dominant RR increased from 0.27 to 0.81. The proportion of the R allele in the first generations increased, but had a gradual decrease until almost eliminated, however, it increased dramatically until the 300th generation.

Model 2 where the Mortality Rate has a value of 5 and is less than the value of 13 for the size of the brood. The size of the population remained in the margins of the carrying capacity of 200 resulting in a final population of 200 individuals. The proportion of the R allele from 0.33 decreased to 0.31 and for the r allele increased from 0.67 to 0.69, the genotype proportion for the homozygous recessive rr genotype increased from 0.25 to 0.50, the heterozygous Rr genotype decreased from 0.50 to 0.38 and the homozygous genotype Dominant RR decreased from 0.25 to 0.13. The last simulation was an observation of how the evolutionary parameter of the Mutation Rate could affect this population of Koi fish. The first model evaluated when the value of R ar is 0.009 and greater than the value of ra R of 0.001 where it was obtained that the population size remained within the margins of the carrying capacity of 200, resulting in a final population of 197 individuals. , 3 individuals less than the initial population of 200. The proportion of the R allele from 0.51 increased to 0.65 and for the r allele of 0.49 it decreased to 0.35, the genotype proportion for the homozygous recessive genotype rr had a decrease from 0.24 to 0.10, genotype heterozygous Rr decreased from 0.52 to 0.49 and homozygous dominant RR genotype increased from 0.25 to 0.41 Model 2 where the Mutation Rate for R to r is 0.001 and less than the value of 0.009 for r to R. The size of the population was kept in the margins of the carrying capacity of 200 resulting in a final population of 202 individuals. At some point in the generations there were significant decreases in population size but it recovered rapidly returning to the capacity margins of .. of 200. The proportion of the R allele of 0.55 decreased to 0.51 and for the r allele of 0.45 it increased at 0.49, the genotype ratio for the homozygous recessive rr genotype increased from 0.21 to 0.1230, the heterozygous Rr genotype decreased from 0.55 to 0.51, and the homozygous dominant RR genotype increased from 0.24 to 0.26.