added note reminding readers of def of F12

Chapters/Pheno_var.tex

@@ -588,7 +588,10 @@ \subsection{The covariance between relatives}
 \begin{equation}
 Cov(X_1,X_2) = r_0 \times 0 + r_1 \frac{1}{2}V_A + r_2  V_A =
 2 F_{1,2} V_A  \label{additive_covar_general_rellys}
-\end{equation}\\ 
+\end{equation}\\
+where $F_{1,2}$ is our coefficient of kinship, i.e. the probability that two alleles sampled at random
+from our pair
+individuals $1$ ans $2$ are IBD (see eqn \eqref{eqn:coeffkinship}).
 %% Need to define F 1,2 -- EBJ
 So under a simple additive model of the genetic basis of a phenotype,
 to measure the narrow sense heritability we need to measure the

Chapters/chapter-01.tex

@@ -744,7 +744,6 @@ \section{Allele sharing among related individuals and Identity by Descent}
 %JRI: text says ``Below'' but float ends up above
 
 
-
 You and your first cousin will share at least one allele of your genotype at all of the polymorphic loci in these purple regions. There's a range of methods to detect such sharing. One way is to look for unusually long stretches of the genome where two individuals are never homozygous for different alleles. By identifying pairs of individuals who share an unusually large number of such putative IBD blocks, we can hope to identify unknown relatives in genotyping datasets. In fact, companies like 23\&me and Ancestry.com use signals of IBD to help identify family ties.
 
 As another example, consider the case of third cousins. You share one of eight sets of great-great grandparents with each of your (likely many) third cousins. On average, you and each of your third cousins each inherit one-sixteenth of your genome from each of those two great-great grandparents. This turns out to imply that on average, a little less than one percent of your and your third cousin's genomes ($2 \times (1/16)^2 =0.78\%$) will be identical by virtue of descent from those shared ancestors. A simulated example where third cousins share blocks of their genome (on chromosome 16 and 2) due to their great, great grandmother is shown in Figure \ref{fig:third_cousin_IBD}.

math_background/Equation_sheet.txt

@@ -12,7 +12,7 @@ Decay of LD		;	Decay of Heterozygosity	~
  $D_t=  (1-r)^t D_0$	,~~\eqref{eqn_LD_decay}	;	  $H_t = \left(1-\frac{1}{2N_e} \right)^tH_0$	,~~\eqref{eqn:loss_het_discrete}
 		;		
 Equilibrium level of neutral heterozygosity		;	Coalescent time and time to MRCA	~
-  $H = \frac{4N_e\mu}{1+4N_e\mu} \approx 4N_e\mu  $,~~\eqref{eqn:hetero}	;	$\E[T_k] = \frac{2 N_e}{ {k \choose 2} },~~~~\E[T_{MRCA}] =4N_e(1-1/n) $	~
+  $H = \frac{4N_e\mu}{1+4N_e\mu} \approx 4N_e\mu  $,~~\eqref{eqn:hetero}	;	$\E[T_k] = \frac{2 N_e}{ {k \choose 2} },~~~~\E[T_{MRCA}] =4N_e(1-1/n) $,~\eqref{eqn:E_T_i} \eqref{TMRCA_neutral}
 		;		
 Number pairwise diffs. \& segregating sites	~	;	Expectation of $\dNdS$	
 $\E[\pi] = 4N_e\mu ,~~ \E[S] = 4N_e\mu \sum_{k=n}^2 \frac{1}{k-1} $,~~\eqref{eqn:pi_expectation},~\eqref{eqn:seg_sites};	$\dNdS = (1-C-B) +  2 N B f_B $	,~~\eqref{eqn:dNDS_C_B}