Human Structural Connectomes are Heritable Jaewon Chung 1 Benjamin D. Pedigo 1 Carey E. Priebe 2 Joshua T. Vogelstein 1 1Department of Biomedical Engineering, Johns Hopkins University 2Department of Applied Mathematics and Statistics, Johns Hopkins University Summary Understanding how brain connectivity is influenced by genetics can improve our understanding of brain function and diseases. Existing methods ignore spatial arrangement of the brain or are not statistically justified. Our random graph theory and statistical approach enable formulation and testing of different models of connectome heritability. We show that brain connectivity is more similar in monozygotic twins compared to those of dizigotic twins and siblings. Other frameworks (e.g. joint graph embeddings) can be used for vertex level analysis. Data and Preprocessing Human Connectome Project Young Adult study (HCP1200) [4]. Zygosity Monozygotic Dizygotic Non-Twin siblings N 250 259 476 Sex 167 F, 83 M 140 F, 119 M 223 F, 248 M Age 29.6 (3.3) 28.9 (3.4) 28.3 (3.9) Age range 22-36 22-36 22-37 Table 1. HCP 1200 Participants and their demographics Figure 1. Outline of the ndmg (https://ndmg.neurodata.io) pipeline. Image taken from [2]. Estimating Heritability Figure 2. Outline of heritability estimation process. For semiparametric testing, we consider the three test cases: Equality up to rotation: H0 : X = WY against Ha : X ̸= WY where W ∈Rn×n and WW T = I Equality up to scaling: H0 : X = cWY for some c > 0 against Ha : X ̸= cWY for any c > 0 Equality up to diagonal transformation: H0 : X = DWY for some diagonal D against Ha : X ̸= WDY for any D Two-Sample Semiparametric Test Results Figure 3. Kernel density estimates (KDEs) of the test statistics is shown on the left column, and the empirical cumulative distribution (eCDF) of associated p-value give by null-distribution is shown on the right column. 1. Kernel density estimates (KDEs) for monozygotic twins is different from those of dizygotic twins, sibling, and unrelated. 2. Distribution of test statistics for monozygotic twins is more positively skewed compared to others. 3. Empirical cumulative distribution function (eCDF) for monozygotic twins is more concentrated near 1 compared to others. 4. This empirical finding is validated through six statistical models and tested via two sample Kolmogrov-Smirnoff test (Table 2 and 3). Two-Sample Kolmogrov-Smirnov (KS) Test Results Null hypothesis is that the two samples are drawn from the same distribution. Alternate Hypothesis Test Cases Rotation Scalar Diagonal Monozygotic < Dizygotic < .001 *** < .001 *** < .001 *** Monozygotic < Sibling < .001 *** < .001 *** < .001 *** Monozygotic < Unrelated < .001 *** < .001 *** < .001 *** Dizygotic ̸= Sibling 0.353 0.337 0.750 Dizygotic ̸= Unrelated 0.009 ** 0.009 ** 0.169 Sibling ̸= Unrelated < .001 *** < .001 *** 0.100 Table 2. P-values for KS tests on distributions of test statistics from semiparametric tests. Alternate Hypothesis Test Cases Rotation Scalar Diagonal Monozygotic > Dizygotic < .001 *** < .001 *** 0.0012 ** Monozygotic > Sibling < .001 *** < .001 *** < .001 *** Monozygotic > Unrelated < .001 *** < .001 *** < .001 *** Dizygotic ̸= Sibling 0.120 0.109 0.199 Dizygotic ̸= Unrelated < .001 *** < .001 *** 0.154 Sibling ̸=Unrelated < .001 *** < .001 *** 0.025 * Table 3. P-values for KS tests on distributions of p-values from semiparametric tests. Significance levels are marked with * (p < .05), ** (p < .01), and *** (p < .001). What's Next? 1. Vertex importance - which vertex confers the most heritability? 2. Edge importance - which edges are important? Code and Data Allanalysiswasperformedusinganopen-sourcepackageGrasPy(https://graspy.neu- rodata.io). AlldMRIimagesareopen-sourceandprovidedbytheHumanConnectome Project (https://www.humanconnectome.org/study/hcp-young-adult/overview). References [1] Avanti Athreya, Donniell E. Fishkind, Minh Tang, Carey E. Priebe, Youngser Park, Joshua T. Vogelstein, Keith Levin, Vince Lyzin