\( % groupings of objects. \newcommand{\set}[1]{\left\{ #1 \right\}} \newcommand{\seq}[1]{\left(#1\right)} \newcommand{\ang}[1]{\langle#1\rangle} \newcommand{\tuple}[1]{\left(#1\right)} \newcommand{\size}[1]{\left| #1\right|} \newcommand{\comp}{\circ} % numerical shortcuts. \newcommand{\abs}[1]{\left| #1\right|} \newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} \newcommand{\ceil}[1]{\left\lceil #1 \right\rceil} % linear algebra shortcuts. \newcommand{\change}{\Delta} \newcommand{\norm}[1]{\left\| #1\right\|} \newcommand{\dprod}[1]{\langle#1\rangle} \newcommand{\linspan}[1]{\langle#1\rangle} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\der}[1]{\frac{d#1}{dx}} \newcommand{\lap}{\Delta} \newcommand{\kron}{\otimes} \newcommand{\nperp}{\nvdash} \newcommand{\mat}[1]{\left[ \begin{smallmatrix}#1 \end{smallmatrix} \right]} % derivatives and limits \newcommand{\partder}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\partdern}[3]{\frac{\partial^{#3 #1}}{\partial #2^{#3}}} \newcommand{\gradient}{\nabla} \newcommand{\subdifferential}{\partial} % Arrows \newcommand{\diverge}{\nearrow} \newcommand{\notto}{\nrightarrow} \newcommand{\up}{\uparrow} \newcommand{\down}{\downarrow} % gets and gives are defined! % ordering operators \newcommand{\oleq}{\preceq} \newcommand{\ogeq}{\succeq} % programming and logic operators \newcommand{\dfn}{:=} \newcommand{\assign}{:=} \newcommand{\co}{\ co\ } \newcommand{\en}{\ en\ } % logic operators \newcommand{\xor}{\oplus} \newcommand{\Land}{\bigwedge} \newcommand{\Lor}{\bigvee} \newcommand{\finish}{\Box} \newcommand{\contra}{\Rightarrow \Leftarrow} \newcommand{\iseq}{\stackrel{_?{=}}} % Set theory \newcommand{\symdiff}{\Delta} \newcommand{\setdiff}{\backslash} \newcommand{\union}{\cup} \newcommand{\inters}{\cap} \newcommand{\Union}{\bigcup} \newcommand{\Inters}{\bigcap} \newcommand{\nullSet}{\phi} % graph theory \newcommand{\nbd}{\Gamma} % Script alphabets % For reals, use \Re % greek letters \newcommand{\eps}{\epsilon} \newcommand{\del}{\delta} \newcommand{\ga}{\alpha} \newcommand{\gb}{\beta} \newcommand{\gd}{\del} \newcommand{\gp}{\pi} \newcommand{\gf}{\phi} \newcommand{\gh}{\eta} \newcommand{\gF}{\Phi} \newcommand{\gl}{\lambda} \newcommand{\gm}{\mu} \newcommand{\gn}{\nu} \newcommand{\gr}{\rho} \newcommand{\gs}{\sigma} \newcommand{\gth}{\theta} \newcommand{\gx}{\xi} \newcommand{\gw}{\omega} \newcommand{\sw}{\sigma} \newcommand{\SW}{\Sigma} \newcommand{\ew}{\lambda} \newcommand{\EW}{\Lambda} \newcommand{\Del}{\Delta} \newcommand{\gD}{\Delta} \newcommand{\gG}{\Gamma} \newcommand{\gW}{\Omega} \newcommand{\gS}{\Sigma} \newcommand{\gTh}{\Theta} % Bold english letters. \newcommand{\bA}{\mathbf{A}} \newcommand{\bB}{\mathbf{B}} \newcommand{\bC}{\mathbf{C}} \newcommand{\bD}{\mathbf{D}} \newcommand{\bE}{\mathbf{E}} \newcommand{\bF}{\mathbf{F}} \newcommand{\bG}{\mathbf{G}} \newcommand{\bH}{\mathbf{H}} \newcommand{\bI}{\mathbf{I}} \newcommand{\bJ}{\mathbf{J}} \newcommand{\bK}{\mathbf{K}} \newcommand{\bL}{\mathbf{L}} \newcommand{\bM}{\mathbf{M}} \newcommand{\bN}{\mathbf{N}} \newcommand{\bO}{\mathbf{O}} \newcommand{\bP}{\mathbf{P}} \newcommand{\bQ}{\mathbf{Q}} \newcommand{\bR}{\mathbf{R}} \newcommand{\bS}{\mathbf{S}} \newcommand{\bT}{\mathbf{T}} \newcommand{\bU}{\mathbf{U}} \newcommand{\bV}{\mathbf{V}} \newcommand{\bW}{\mathbf{W}} \newcommand{\bX}{\mathbf{X}} \newcommand{\bY}{\mathbf{Y}} \newcommand{\bZ}{\mathbf{Z}} \newcommand{\bba}{\mathbf{a}} \newcommand{\bbb}{\mathbf{b}} \newcommand{\bbc}{\mathbf{c}} \newcommand{\bbd}{\mathbf{d}} \newcommand{\bbe}{\mathbf{e}} \newcommand{\bbf}{\mathbf{f}} \newcommand{\bbg}{\mathbf{g}} \newcommand{\bbh}{\mathbf{h}} \newcommand{\bbk}{\mathbf{k}} \newcommand{\bbl}{\mathbf{l}} \newcommand{\bbm}{\mathbf{m}} \newcommand{\bbn}{\mathbf{n}} \newcommand{\bbp}{\mathbf{p}} \newcommand{\bbq}{\mathbf{q}} \newcommand{\bbr}{\mathbf{r}} \newcommand{\bbs}{\mathbf{s}} \newcommand{\bbt}{\mathbf{t}} \newcommand{\bbu}{\mathbf{u}} \newcommand{\bbv}{\mathbf{v}} \newcommand{\bbw}{\mathbf{w}} \newcommand{\bbx}{\mathbf{x}} \newcommand{\bby}{\mathbf{y}} \newcommand{\bbz}{\mathbf{z}} \newcommand{\0}{\mathbf{0}} \newcommand{\1}{\mathbf{1}} % Caligraphic english alphabet \newcommand{\cA}{\mathcal{A}} \newcommand{\cB}{\mathcal{B}} \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\cE}{\mathcal{E}} \newcommand{\cF}{\mathcal{F}} \newcommand{\cG}{\mathcal{G}} \newcommand{\cH}{\mathcal{H}} \newcommand{\cI}{\mathcal{I}} \newcommand{\cJ}{\mathcal{J}} \newcommand{\cK}{\mathcal{K}} \newcommand{\cL}{\mathcal{L}} \newcommand{\cM}{\mathcal{M}} \newcommand{\cN}{\mathcal{N}} \newcommand{\cO}{\mathcal{O}} \newcommand{\cP}{\mathcal{P}} \newcommand{\cQ}{\mathcal{Q}} \newcommand{\cR}{\mathcal{R}} \newcommand{\cS}{\mathcal{S}} \newcommand{\cT}{\mathcal{T}} \newcommand{\cU}{\mathcal{U}} \newcommand{\cV}{\mathcal{V}} \newcommand{\cW}{\mathcal{W}} \newcommand{\cX}{\mathcal{X}} \newcommand{\cY}{\mathcal{Y}} \newcommand{\cZ}{\mathcal{Z}} % Formatting shortcuts \newcommand{\red}[1]{\textcolor{red}{#1}} \newcommand{\blue}[1]{\textcolor{blue}{#1}} \newcommand{\htext}[2]{\texorpdfstring{#1}{#2}} % Statistics \newcommand{\distr}{\sim} \newcommand{\stddev}{\sigma} \newcommand{\covmatrix}{\Sigma} \newcommand{\mean}{\mu} \newcommand{\param}{\theta} \newcommand{\gthEst}{\hat{\theta}} \newcommand{\ftr}{\phi} \newcommand{\est}[1]{\hat{#1}} % General utility \newcommand{\todo}[1]{\textbf{[TODO]}] \footnote{TODO: #1}} \newcommand{\tbc}{[\textbf{Incomplete}]} \newcommand{\chk}{[\textbf{Check}]} \newcommand{\why}{[\textbf{Find proof}]} \newcommand{\opt}[1]{\textit{#1}} \newcommand{\experience}[1]{[\textbf{Personal Experience}]: #1 \blacktriangle} \newcommand{\pf}[1]{[\textbf{Proof}]: #1 \Box} \newcommand{\core}[1]{\textbf{Core Idea}: #1 \Arrowvert} \newcommand{\example}[1]{\textbf{Example}: #1 \blacktriangle} \newcommand{\error}[1]{\textbf{Error alert}: #1 \triangle} \newcommand{\oprob}{[\textbf{OP}]: } \renewcommand{\~}{\htext{$\sim$}{~}} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator*{\argmax}{arg\,max} \)

African background

The great father in Africa belonged to the the E1b-M180 clade. His descendants in thre1e great spurts from around 5300-4800 YBP expanded among the speakers of Niger-Congo languages and spread across the vast African continent. .. It is likely that the E1b-M180 lineage arose there and then penetrated deep into sub-Saharan Africa as the Niger-Congo languages diversified. Its initial expansions could have been triggered by the events of the emergence of civilization in the Egyptian cultural zone, with its bearers subsequently acquiring high status in the sub-Saharan milieu east and west. [M16]