Alexandria Science
Published in

Alexandria Science

New and Improved Autosomal Genetic Model

A comparison of three models, including updated amount of shared DNA between various relatives and ancestors

Figure 1. Graph of number of available segments versus the paternal lambda Poisson input, to which 22 must be added to find the average number of paternal recombinations. The colorbar refers to the difference in simulation output from the target standard deviations (3.6% for siblings and 4% for paternal grandparents). Ten times more weight was given to the difference in standard deviation for siblings since that statistic is known to one more decimal point: Diff. from Target = 10*abs(0.036 — std_dev_sib_model) + abs(0.04 — std_dev_pat_gp_model). The curved line is the predicted result from a multivariate polynomial regression of order three.
Figure 2. All of the parameters are the same as for Figure 1. The x-axis is extended farther and a few additional points are generated and plotted to show the asymptotic nature of the graph. Unfortunately, the third degree polynomial begins to miss the mark at this point (after about 3,000 segments). An exponential curve would probably fit the data better.
Figure 3. Comparison of results for three autosomal models. Each row corresponds to a simulation of 500 trials of comparison between two siblings. The first row contains results from the original model in which gene segments don’t remain in place, the second row is from the two homologue model in which gene segments have a fixed position, and the third row is from the new model with two homologues but differing recombination rates for mothers and fathers. The lower and upper limits of the 95% confidence interval (CI) are shown on either side of the average. Within the constraints and assumptions of the particular model, there is 95% confidence that shared DNA between the two relatives would fall within that range. The column ‘0% Shared’ refers to the percentage of trial runs that result in relatives not sharing any DNA. This doesn’t occur for very close relations.
Figure 4. Comparison of three autosomal models as in Figure 3. For the new model, two different pairs of grandparents must be compared: paternal grandparents (P GP) and maternal grandparents (M GP). The new and improved model results in more deviation by every measure for grandparents. Even the maternal grandparent standard deviation is higher than that of the previous models.
Figure 5. Comparisons of three autosomal models as in the figures above. Statistics are for shared percentage of DNA between oneself and an aunt or an uncle. The third row is for paternal relatives and the fourth row is for maternal relatives. Contrasting with the results for grandparents, every measure in the new model for aunts or uncles has less deviation than the previous models. Also, the deviation for aunts and uncles is lower than for grandparents by every measure. The lesson must be that, the more times recombination occurs, the closer the results will be to the average.
Figure 6. Comparisons of autosomal models as in the figures above. Statistics are for shared percentages of DNA between oneself and a full 1st cousin. The third row is for 1st cousins who are children of one’s paternal uncle. The fourth row is for children of one’s paternal aunt, the fifth for children of one’s maternal uncle, and the sixth for children of one’s maternal aunt. A child of your paternal aunt should have the same results as a child of your maternal uncle, since from the perspective of the latter, you are the former.
Figure 7. Results for an aunt or an uncle. Comparison of three autosomal genetic models, as in figures above. The third row is for a child of one’s paternal grandpa, but not paternal grandma. The fourth row is for a child of one’s paternal grandma, the fifth for a child of one’s maternal grandpa, and the sixth for children of one’s maternal aunt.
Figure 8. Results for half 1st cousins. Half 1st cousins can result from eight different ancestor/relative combinations. However, some of these are equivalent to each other. For example, the child of your father’s half-sister (by paternal grandfather) should have the same simulation results as the child of your mother’s half-brother (by maternal grandfather), since from the perspective of the latter, you are the former. Those relatives correspond to rows four and seven in the chart, which is why the 95% confidence intervals are identical for those two rows. Similarly, the confidence intervals are the same for rows six and nine.
Figure 9. Results for great-grandparents. Comparisons of three autosomal genetic models. Ancestors compared are paternal paternal great-grandpas (PP G-GP), paternal paternal great-grandmas (PP G-GM), paternal maternal great-grandpas (PM G-GP, or father’s mother’s father), paternal maternal great-grandmas (PM G-GM), maternal paternal great-grandpas (MP G-GP), maternal paternal great-grandmas (MP G-GM), maternal maternal great-grandpas (MM G-GP), and maternal maternal great-grandmas (MM G-GM).
Figure 10. Results for great-aunts/great-uncles. PP great-aunt is your paternal grandfather’s sister, PM great-aunt is your paternal grandmother’s sister, MP great-aunt is your maternal grandfather’s sister, and MM great-aunt is your maternal grandmother’s sister.
Figure 11. Results for 1st cousins, once removed. The third row shows results for a child of a son of your paternal paternal great-grandparents. The fourth row is for the child of a daughter of your same ancestors. It continues like that, with a son and then a daughter of paternal maternal great-grandparents (your paternal grandmother’s parents), maternal paternal great-grandparents, and then maternal maternal great grandparents. In model programming, I usually call these relatives ‘parents of 2nd cousins.’ That’s because the input number of generations needs to be 3 back from you in order to generate great-grandparents. From the perspective of a 1st cousin once removed, you are a descendent of their grandparents. From your perspective, they share one of your great-grandparent pairs.
Figure 12. Results for 2nd cousins. There are 16 different ways in which you could have a 2nd cousin in terms of the genders of yours and their ancestors. The third row shows results for a 2nd cousin whose paternal paternal great-grandparents are your paternal paternal great-grandparents (you are both children of sons of sons of the same great-grandparents). As in Figure 6, some of these relationships are equivalent to each other. A good way to identify those rows is by looking for ones in which the 95% confidence intervals are equal.
Figure 13. Results for 3rd great-grandparents. As in Figures 6 and 12, some of these relative relationships are equivalent.



The e-magazine of science, from astronomy to zoology

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store