Table 1.

Glossary of symbols. For both the Roman and Greek alphabets, uppercase letters precede lowercase ones. For each uppercase or lowercase letter, listing is in order of appearance of the definition in the text. The references are to the equation closest to the definition of each symbol. Thus, (2.1), (2.1)+, (2.1)− refers to (2.1), the text below (2.1), the text above (2.1), respectively. Symbols that occur only in the Appendix are not listed.

Symbol	Reference	Definition
$A_{i_n}^{\left(n\right)}$	(2.1)-	Allele at locus $n$
$\hat{A}$	(3.4)+	Region of attraction of $\hat{\rho }$
$b$	(5.17)	${(b_1,\dots ,b_{\Gamma })}^T$
$b_{\alpha }$	(5.17)+	${\hat{\overline{w}}}_{\alpha }-{\sum }_n{u}_{22,\alpha }^{\left(n\right)}$
$c_{\alpha }$	(2.1)-	Proportion of zygotes in deme $\alpha$
$D$	(3.4)-	Vector of all linkage disequilibria in an $L$-locus system
$D_{i,\alpha }$	(3.4)-	Linkage disequilibrium in gamete $i$ in deme $\alpha$
$\hat{D}$	(3.4)+	$D$ evaluated at gene-frequency equilibrium
$F$	(2.14)	$ln\tilde{w}$
$f$	(5.14)-	${(f^{\left(1\right)},\dots ,f^{\left(L\right)})}^T$
$f^{\left(n\right)}$	(5.14)	$2{\vartheta }^{\left(n\right)}{p}^{\left(n\right)}+(1-2{\vartheta }^{\left(n\right)}){\left(p^{\left(n\right)}\right)}^2$
$G$	(2.1)-	Set of all demes
$G^{\left(n\right)}$	(2.17)-	Covariance matrix for locus $n$
$h$	(2.1)-	Locus index
$I_n$	(2.1)-	Number of alleles at locus $n$
$I$	(6.8)-	Number of alleles at locus $n$ if independent of $n$
$i_n$	(2.1)-	Allelic index at locus $n$
$i$	(2.1)-	Gamete $(i_1,\dots ,i_L)$
$J$	(2.3)-	Number of gametes
$J_n$	(7.3)-	Set of alleles present at equilibrium at locus $n$
$j$	(2.1)-	Index for gamete
$j_n$	(2.4)-	Allelic index at locus $n$
$k$	(2.1)-	Index for gamete
$L$	(2.1)-	Number of loci
$L$	(2.1)-	Set of all loci
$l$	(2.1)-	Locus index
$m_{\alpha }$	(6.7)+	Backward migration rate
$n$	(2.1)-	Locus index
$O$	(7.3)+	Order symbol
$p_i$	(2.1)-	Frequency of gamete $i$
$p_{i_n}^{\left(n\right)}$	(2.1)-	Frequency of allele $A_{i_n}^{\left(n\right)}$
$p$	(2.3)-	Vector of gamete frequencies
$p_{j_h{i}_n}^{\left(hn\right)}$	(2.10)	Frequency of gamete $A_{j_h}^{\left(h\right)}{A}_{i_n}^{\left(n\right)}$
$p^{\left(n\right)}$	(2.17)-	${(p_1^{\left(n\right)},\dots ,p_{I_n}^{\left(n\right)})}^T$ (only Section 2)
$p^{\left(n\right)}$	(5.1)-	Frequency of allele $A_1^{\left(n\right)}$ in the diallelic case
$\hat{p}$	(3.4)+	$p$ at gamete-frequency equilibrium
$R_{i,jk}$	(2.1)+	Probability that gamete $i$ is produced by haplotypes $j$, $k$
${\mathbb{R}}^J$	(2.3)-	$J$-dimensional Euclidean space
$r_{min}$	(3.8)+	Smallest two-locus recombination frequency
$s_{\alpha }$	(6.2)	Directional selection coefficient in deme $\alpha$
$s_{ij,\alpha }$	(7.1)	Epistasis coefficients
$t$	(2.10)+	Time in generations
$U$	(5.9)+	Open set of parameters
$u_{i_n{j}_n,\alpha }^{\left(n\right)}$	(2.3)+	Fitness contribution of $A_{i_n}^{\left(n\right)}{A}_{j_n}^{\left(n\right)}$ in deme $\alpha$
${\overline{u}}_{\alpha }^{\left(n\right)}$	(2.6)	Mean fitness contribution of locus $n$ in deme $\alpha$
$u_{i_n,\alpha }^{\left(n\right)}$	(2.7)	Marginal fitness contribution of $A_{i_n}^{\left(n\right)}$ in deme $\alpha$
$u_{i_n,\alpha }^{\left(n\right)}$	(4.2a)	Fitness contribution of $A_{i_n}^{\left(n\right)}$ in deme $\alpha$ (only Section 4)
$V$	(5.10)-	$L\times \Gamma$ matrix with entries $V_{n\alpha }$
$V_{n\alpha }$	(5.10)-	Entry of matrix $V$
$W_{jk}$	(3.1)	Averaged fitness of $jk$ at gene-frequency equilibrium
$\overline{W}{}_{\alpha }\left(z\right)$	(5.15)	Mean fitness in deme $\alpha$ as a function of $z$
$W_{\alpha }\left(X\right)$	(6.2)	Fitness of individuals with trait value $X$ in deme $\alpha$
$W$	(7.3)+	Open set of parameters
$w_{ij,\alpha }$	(2.1)-	Fitness of genotype $ij$ in deme $\alpha$
$w_{i,\alpha }$	(2.1)	Marginal fitness of gamete $i$ in deme $\alpha$
$w_{i,\alpha }$	(4.1)-	Fitness of gamete $i$ in deme $\alpha$ (only Section 4)
${\overline{w}}_{\alpha }$	(2.1)	Mean fitness in deme $\alpha$
$\tilde{w}$	(2.13)	Geometric-mean fitness
${\hat{\overline{w}}}_{\alpha }$	(3.1)-	${\overline{w}}_{\alpha }\left(\hat{\rho }\right)$
$X$	(6.1)	Value of quantitative trait
$X_{ij,\alpha }$	(6.1)	${\sum }_n{\gamma }_{i_n{j}_n,\alpha }^{\left(n\right)}$
$\hat{x}$	(5.11)+	${(c_1/{\hat{\overline{w}}}_1,\dots ,c_{\Gamma }/{\hat{\overline{w}}}_{\Gamma })}^T$
$z^{\left(n\right)}$	(5.14)	$f^{\left(n\right)}\left(p^{\left(n\right)}\right)$
$z$	(5.14)+	${(z^{\left(1\right)},\dots ,z^{\left(L\right)})}^T$
$\alpha$	(2.1)-	Deme index
$\beta$	(2.1)-	Deme index
$\Gamma$	(2.1)-	Number of demes
${\gamma }_{i_n{j}_n,\alpha }^{\left(n\right)}$	(6.1)+	Contribution of $A_{i_n}^{\left(n\right)}{A}_{j_n}^{\left(n\right)}$ to trait value
${\gamma }_{i_n{j}_n}^{\left(n\right)}$	(6.6)	Deme-independent contribution of $A_{i_n}^{\left(n\right)}{A}_{j_n}^{\left(n\right)}$ to trait value
${\gamma }_{\alpha }$	(6.6)	Genotype-independent contribution to trait value
${\Delta }_J$	(2.3)-	Simplex in ${\mathbb{R}}^J$
$\Delta$	(2.15)-	Difference operator
${\delta }_{ij}$	(2.17)-	Kronecker delta
${\vartheta }_{i_n{j}_n}^{\left(n\right)}$	(3.6)	Degree of intermediate dominance
${\vartheta }_{i_n{j}_n}^{\left(n\right)}$	(6.5)	Degree of intermediate dominance at trait level
${\vartheta }^{\left(n\right)}$	(5.7)	Degree of intermediate dominance in the diallelic case
$\vartheta$	(5.9)+	${({\vartheta }^{\left(1\right)},\dots ,{\vartheta }^{\left(L\right)})}^T$
$\vartheta$	(6.15)-	${\vartheta }_{12}$
${\vartheta }_{i_n}^{\left(n\right)}$	(6.8)	Degree of intermediate dominance of $A_{i_n}^{\left(n\right)}$ at the trait level
$ϵ$	(7.1a)-	Small positive parameter
$\Lambda$	(2.11)	$\{p\in {\Delta }_J:{\rho }^{\prime }=\rho \}$
$\hat{\Lambda }$	(2.18)	$\{p\in {\Delta }_J:\rho =\hat{\rho }\}$
$\Xi$	(2.12)	Linkage-equilibrium manifold
${\xi }_{i_n{j}_n}^{\left(n\right)}$	(2.8a)	Averaged relative fitness of $A_{i_n}^{\left(n\right)}{A}_{j_n}^{\left(n\right)}$
${\hat{\xi }}_{i_n{j}_n}^{\left(n\right)}$	(2.18)+	${\xi }_{i_n{j}_n}^{\left(n\right)}$ at gene-frequency equilibrium
${\xi }_{i_n}^{\left(n\right)}$	(2.8b)	Averaged relative fitness of $A_{i_n}^{\left(n\right)}$
${\hat{\xi }}_{i_n}^{\left(n\right)}$	(2.18)+	${\xi }_{i_n}^{\left(n\right)}$ at gene-frequency equilibrium
${\overline{\xi }}^{\left(n\right)}$	(2.8c)	Averaged mean fitness at locus $n$
${\hat{\overline{\xi }}}^{\left(n\right)}$	(2.18)+	${\overline{\xi }}^{\left(n\right)}$ at gene-frequency equilibrium
${\xi }_{i_n}^{\left(n\right)}$	(4.3)	Averaged relative fitness of $A_{i_n}^{\left(n\right)}$ (only Section 4)
$\rho$	(2.3)-	Vector of allele frequencies
$\rho$	(5.1)	Vector of allele frequencies (diallelic case)
$\hat{\rho }$	(2.18)-	$\rho$ at gene-frequency equilibrium
${\Sigma }_0$	(7.1b)+	Set of equilibria without epistasis
${\Sigma }_{w\left(ϵ\right)}$	(7.1b)+	Set of equilibria with epistasis
${\varphi }_{i_n}^{\left(n\right)}$	(6.11)	Allele specific factor of fitness excess
$\Omega$	(2.3)	Gene-frequency space
$\Omega$	(5.1)	Gene-frequency space (diallelic case)
′	(2.2)	Value of quantity in next generation
$\subseteq$	(2.3)-	Subset
${}^T$	(2.3)-	Transposition of a vector
$\text{int}$	(5.9)+	Topological interior of a set
$\mathrm{rank}$	(5.12)	Rank of a matrix
$dim$	(5.11)+	Dimension of a linear subspace
$ker$	(5.11)+	Kernel of a linear map or matrix
${\nabla }^{\left(n\right)}$	(2.17)+	Gradient operator