Statistical Genetics 20110606 Ryo Yamada Unit of Statistical

Statistical Genetics 統計遺伝学 2011/06/06 Ryo Yamada Unit of Statistical Genetics Center for Genomic Medicine Graduate School of Medicine Kyoto University

What to study? How to study? What do you want to know? How do you want to know it?

Genetics • Genotype • Phenotype

Genetics • Genotype • Identity • Phenotype • Variation How to grab “Genotype” and “Phenotype” with their “Identity” and “Variation”. One way is to make a catalogue of facts among “them”. The other way is to give a strategy to make the catalogue.

Genotype Phenotype Intermediate phenotype Terminal phenotype

Graph (Theory) グラフ(理論)

Pedigree 家系図

Pedigree 家系図 phylogenetic tree 系統樹

Phylogety, a tree

Distance 距離

Distance: More than one definition 距離にもいろいろな定義がある

Make graph from distance info 距離情報からグラフを作る Distance is a way to quantitate relation. Three items that make a triangle can be connected as a star without changing their pathway-distance.

Difference among graphs グラフ間の違い Same or different as a tree?

Difference among graphs グラフ間の違い Topology (Shape) and length of edges 位相(形)と辺の距離 Same or different as a tree?

Items can be expressed as a tree when distance among them are given. Different “distances” give different trees.

Graphs for data-analyses グラフによるデータ解析

Heatmap Data-mining approach also uses trees.

Tree needs “distance” with its definition. Clustering methods also need definition to make tree structure. .

Data give trees and change the order in items. When the order in items are not changed and when relation among the items are displayed, it is correlation matrix.

Original data Relations among lines Relations among columns and lines

Pedigrees are NOT graphs 家系図はグラフでは　ない

Trees in classical genetics: Pedigrees

Relation between humans. Relation between chromosomes.

A human relation can be multiple chromosomal relations.

Chromosomes have two parental chromosomes. But a base has only one parental base.

Sexual and Asexual Reproduction Graph 有性生殖と無性生殖、とグラフ

Genotype Phenotype Intermediate phenotype Terminal phenotype

Types of Data データ タイプ

Categorical data and sets. カテゴリ型データと集合

Ordered and Non-ordered.

High-dimensional data and graph

Genotype Phenotype Intermediate phenotype Terminal phenotype

Components of graphs グラフの部品 Concepts of regulations/interactions 制御/相互関係の概念 Graphs are being used for biology

Networks are complex ネットワークは複雑

We can not grab the graph as a whole at once グラフ全体を一発で了解することは無理

Transition of Stata 状態推移 step-by-step 順番に Markov-chain マルコフ連鎖 Bayesian networks ベイズネットワーク

Genetic Heterogeneity and Transition of Stata 遺伝的多様性と状態推移 Three components to make genetic heterogeneity 遺伝的多様性を作る３要素 Mutations Recombinations Genetic drifts 変異 組換え 遺伝的浮動 Variants will drift out from the world.

Complementary strand, for what?

Cross-overs and recombinatios

What is the relation between crossovers and identity of origin?

What is the distribution of segment-length between crossovers? Exponential. . .

Some chromosomes leave many copies but others none.

Variants will drift out from the world.

Chromosomal relations in generations.

Population. Chronological changes. Spatial changes.

Time, Space 時間、空間 • Dimensions 次元 • Dimensions of data

Data analyses and space of data

Alleles and haplotypes and their relation.

RNA codon table

RNA codon table can be drawn as a tree.

Closed space 閉じた空間 Populations in “Space” and “Time”. Finite space vs. Infinite Space

Non-linear 非線形

Stable Equilibrium 安定 定常 Models how to handle space and time.

• ? in Statistical genetics? – Welcome • Any questions on how to handle bio-medical data ? – Also welcome Ryo Yamada, M. D. , Ph. D. Unit of Statisical Genetics 4 F Kaibou-center building phone: (+81)75 -753 -9470 fax: (+81)75 -753 -9284 ryamada@genome. med. kyoto-u. ac. jp 統計遺伝学分野 山田　亮 医学部解剖センター棟４階 http: //www. med. kyoto-u. ac. jp/E/grad_school/introduction/1525/