3 Analysis of Population Structure
59
quantify the amount of structure among groups in order to learn something about the
demographic past of the full collection of individuals. Although these populations
are ideally identified with the aid of the previously presented methods, it is not
uncommon to have assessments based on geography-only defined populations. It
may still be of value to contrast these predefined populations in order to affirm that
they do correspond to separate biological populations.
3.3.1 Genetic Differentiation at the Population Level
3.3.1.1 F ST
Introduced by Sewall Wright (Wright 1949), F ST is one of the first measures
of genetic differentiation (sometimes referred to as “genetic distance”) among or
between populations. There are many variations on the original definition, and the
usefulness of F ST and relatives is still a debated topic (e.g., Holsinger and Weir
2009; Rousset 2013; Jost 2008; Ryman and Leimar 2009). F ST was originally
defined as the correlation between gametes chosen randomly from within the same
subpopulation relative to the entire population or, equivalently, as the departure
of genotype frequencies from Hardy–Weinberg expectations relative to the entire
population (see Holsinger and Weir 2009 for a thorough review of F ST ). A common
definition for more practical purposes is
F ST =
Var (p i )
E [p i ] (1 − E [p i ])
,
(e.g., Holsinger and Weir 2009) where Var(p i ) is the variance in allele frequencies
across subpopulations and E[p i ] is the expected allele frequency. There are other
formulations, including (Nei 1973) in terms of heterozygosity,
G ST =
H T − H S
H T
,
where H T is the total (pooled) heterozygosity and H S is the mean heterozygosity
across subpopulations. Note that these definitions are all coined in terms of genetic
variation. If demography is the primary interest, these definitions may not be ideal
since the distribution of genetic variation depends on the mutational process as well
as demography—via the genealogical process. Slatkin (1995) isolated the purely
genealogical aspect of F ST by studying the limit as the mutation rate approached
zero and showed that F ST can be expressed in terms of expected coalescent times
F ST =
t s − t w
t s
,
where t s is the average time for two randomly picked genes—from the whole
population—to find a common ancestor and t w is the average time for two genes
59
quantify the amount of structure among groups in order to learn something about the
demographic past of the full collection of individuals. Although these populations
are ideally identified with the aid of the previously presented methods, it is not
uncommon to have assessments based on geography-only defined populations. It
may still be of value to contrast these predefined populations in order to affirm that
they do correspond to separate biological populations.
3.3.1 Genetic Differentiation at the Population Level
3.3.1.1 F ST
Introduced by Sewall Wright (Wright 1949), F ST is one of the first measures
of genetic differentiation (sometimes referred to as “genetic distance”) among or
between populations. There are many variations on the original definition, and the
usefulness of F ST and relatives is still a debated topic (e.g., Holsinger and Weir
2009; Rousset 2013; Jost 2008; Ryman and Leimar 2009). F ST was originally
defined as the correlation between gametes chosen randomly from within the same
subpopulation relative to the entire population or, equivalently, as the departure
of genotype frequencies from Hardy–Weinberg expectations relative to the entire
population (see Holsinger and Weir 2009 for a thorough review of F ST ). A common
definition for more practical purposes is
F ST =
Var (p i )
E [p i ] (1 − E [p i ])
,
(e.g., Holsinger and Weir 2009) where Var(p i ) is the variance in allele frequencies
across subpopulations and E[p i ] is the expected allele frequency. There are other
formulations, including (Nei 1973) in terms of heterozygosity,
G ST =
H T − H S
H T
,
where H T is the total (pooled) heterozygosity and H S is the mean heterozygosity
across subpopulations. Note that these definitions are all coined in terms of genetic
variation. If demography is the primary interest, these definitions may not be ideal
since the distribution of genetic variation depends on the mutational process as well
as demography—via the genealogical process. Slatkin (1995) isolated the purely
genealogical aspect of F ST by studying the limit as the mutation rate approached
zero and showed that F ST can be expressed in terms of expected coalescent times
F ST =
t s − t w
t s
,
where t s is the average time for two randomly picked genes—from the whole
population—to find a common ancestor and t w is the average time for two genes