a) from generation to generation. The model is iterated for
several generations, until genetic equilibrium is reached.
The resulting changes in gene correlations can be used to
estimate F-statistics and effective population size (see the
following).
Effective population sizes can also be estimated in three
different ways: from pedigrees, from demographic models
(sensuNunney and Campbell 1993), and from biochemical
data that reflect variable genetic loci. If pedigrees are avail-
able, effective sizes can be estimated from any of the differ-
ent gene correlations (viz., F,u, a,and d). Just as inbreed-
ing accumulates over time in a finite-sized population, the
other gene correlations also increase over time. If a popula-
tion is in equilibrium and is ideal (viz., one with no selec-
tion, no mutation, no dispersal, equal numbers of males
and females), then all of the gene correlations increase at
the same rate (Chesser et al. 1993; Sugg and Chesser 1994).
Thus, the relative change from generation to generation in
any of the gene correlations provides an estimate of effective
population size:
(5)Relative changes in gene correlations (e.g., F) are changes
in average genetic correlations from the parental genera-
tion (e.g., F) to the offspring generation (F), relative to re-
sidual genetic variation (e.g., 1 F). Since these estimates
assume genetic equilibrium, which may not typically be met
in nature (Dobson et al. 2004), it may be necessary to es-
timate average changes in gene correlations over several
generations.
Another way to estimate effective population size is to
estimate changes in genetic correlations from Chesser’s
breeding-group model (Chesser et al. 1993; Sugg and Ches-
ser 1994). The model estimates F-statistics from patterns of
matings, demography of the local population, and dispersal
patterns. In turn, F-statistics can be used to estimate effec-
tive population size. Nunney and Campbell (1993) have
termed such models “demographic methods,” because they
predict genetic patterns that should occur given the be-
havior patterns and demography exhibited by local popu-
lations. F-statistics may fluctuate less over time than gene
correlations, and thus may produce more robust estimates
of effective population size (e.g., Dobson et al. 1998; Dob-
son et al. 2004). An equation for estimating effective popu-
lation size using F-statistics from the breeding group model
(Chesser et al. 1993; Sugg and Chesser 1994) is:
Nˆe (6)4 s 3 FˆIS 1
61 FˆLSFˆIS 2Ne^1
2 ¢dNe^1
2 ¢aNe^1
2 ¢uNe^1
2 ¢F
In this equation, sis the number of social breeding groups,
and the “hats” emphasize that the effective size and F-
statistics are estimated values. Basset et al. (2001) indi-
cate that this equation should be applied to estimates of
F-statistics based on offspring, before their dispersal from
the natal area (see the following). It is important to note
that equation (6) is an estimate of effective size that is made
under simplifying assumptions, and more accurate and di-
rect measures are available (Chesser et al. 1993; Sugg and
Chesser 1994).
An alternative demographic model for estimating effec-
tive size of local populations that exhibit group structure
was developed by Nunney (1999). This model has arbi-
trary groups, and does not incorporate information about
genetic correlations (viz., influences of kinship and inbreed-
ing). Moreover, the model requires additional information
on mating patterns that may be difficult to gather, such as
the variance in male reproductive success. Nunney’s (1999)
model is more appropriate for some species than the
breeding-group model. Basset et al. (2001) used computer
simulations to show that for monogamous species and in
cases with equal dispersal of males and females, Nunney’s
(1999) model performed much better than the breeding-
group model, which greatly overestimated effective popu-
lation size. For polygynous species with sex-biased disper-
sal, however, both models were appropriate. Thus, studies
of monogamous species should use the arbitrary-group
model, even though some of the parameters will be hard to
measure.
A final way to estimate effective population size is from
biochemical estimates of F-statistics. Nunney and Campbell
(1993) termed methods for estimating effective population
size from various molecular markers (e.g., allozyme alleles,
microsatellite DNA alleles) “genetic methods,” to differen-
tiate them from demographic methods. Alleles at neutral
loci can be used to estimate gene dynamics, including effec-
tive population sizes, under the assumption of genetic equi-
librium (reviewed by Slatkin 1987). For socially structured
subpopulations, estimates of F-statistics can be made from
equations (3) and substituted into equation (6) or another
suitable equation, such as:(7)where mis the mutation rate (Hartl and Clark 1997). In a
local population that is structured into groups, but is oth-
erwise ideal, Nunney (1999) points out that effective size
can be estimated as:Ne (8)NT
11 FIL 211 FLS 2NeHT
4 m 11 HT 2Gene Dynamics and Social Behavior 167