Download Deleterious mutations can reduce differentiation in small, subdivided

Hereditas 130: 257-264 (1999)
Deleterious mutations can reduce differentiation in small, subdivided
populations
PEKKA PAMILO', SNAEBJORN PALSSON' and OUT1 SAVOLAINEN2
' Depurtment
of Conservation Biology and Genetics, University of Uppsulu, Sweden.
Department of Biology, University of Oulu, Finland.
Pamilo, P., Palsson, S. and Savolainen, 0. 1999. Deleterious mutations can reduce differentiation in small, subdivided
populations.-fferedituj
130: 257-264. Lund, Sweden. ISSN 0018-0661. Received February 24, 1999. Accepted April 28,
I999
We study the effects of multilocus selection on genetic differentiation at linked neutral loci by using computer simulations.
Two types of selection are examined, purifying selection against deleterious mutations and stabilizing selection at a
quantitative, polygenic trait. Deleterious recessive mutations cause background selection that is predicted to reduce the
heterozygosity at linked loci and to increase population differentiation (measured as FSTor GsT). Our simulations show
that background selection in small subdivided populations can lead to an immigrant advantage that homogenizes the
populations and reduces differentiation. Such a reduction is not observed in a case of high selfing rate (90% selfing), as
reduced variation within populations cancels out the effects on absolute differentiation caused by background selection to
give no net change in GsT. In general, inbreeding leads to increased differentiation both in a completely neutral case and
under background selection. Strong stabilizing selection at a quantitative trait with the same optimal phenotype in each
population slightly increases the level of differentiation over that observed under a neutral model.
Pekku Pamilo, Department qf Consrrvution Biology und Genetics, Uniurrsity of' Uppsulu, Box 7003, SE- 750 07 Uppsulu,
Sweden
Gene flow among closely located populations is commonly inferred from measures of genetic differentiation (SLATKINand BARTON 1989; BEAUMONTand
NICHOLS1996). WRIGHT'S(1943) island model of
migration relates, at equilibrium, the spatial distribution of allele frequencies to the number of immigrants
in each generation. At equilibrium, the level of differentiation is expected to be FST = l/(l 4N,m
4Nev), where N , is the effective population size, m is
the immigration rate and v the mutation rate. The
relationship can be easily modified for situations
where dispersal and ploidy levels are sex-dependent
(BERG et al. 1998). The application of this relationship to infer dispersal is restricted as the expected
distribution of allele frequencies requires a drift-migration equilibrium and constant population sizes,
although a similar distribution can be obtained by
sampling from an infinite source under a stochastic
demographic process (birth, death and immigration)
(RANNALA1996). Another important assumption is
the neutrality of the genetic markers used to estimate
differentiation.
The behaviour of neutral loci depends also on the
effect of selected loci elsewhere in the genome,
whether selection is directional favouring universally
(SLATKIN and
WIEHE 1998) or
locally
(CHARLESWORTH
et al. 1997) advantageous alleles,
balancing, or purifying against deleterious mutations
(CHARLESWORTH
et al. 1997). The theory of background selection focuses particularly on the effects of
+
+
recessive harmful mutations. Purifying selection
against them reduces the effective population size and
thus decreases the neutral heterozygosities at linked
loci (CHARLESWORTH
et al. 1993). The theory of
background selection further predicts that a decrease
in the heterozygosity within populations (H,) leads t o
an increase in the relative differentiation of populations measured as (HT - H,)/HT (CHARLESWORTH
et
al. 1997).
The effect of recessive harmful alleles can differ
from the above predictions when populations are
I
10" I
neutral variation
increased
variation
\
decreased
variation
1
Nhs
Fig. 1. Division of the parameter space defined by the
product Nhs and the recombination rate Y, showing the
areas where associative overdominance (increased variation) and background selection (decreased variation) affect
most the heterozygosity of linked neutral loci. The
boundaries between the three areas are not sharp. Based on
PALSSONand PAMILO
(1999)
258
P. Pnmilo et d.
small and recombination is restricted. Individuals
homozygous for many harmful alleles are likely to be
homozygous also for linked neutral markers, and
selection against such homozygotes leads to so called
associative overdominance at the neutral loci (OHTA
1971). As a result, the individual fitness is positively
associated to the number of heterozygous marker loci
in the genome (PAMILOand PALSSON1998), and the
level of population heterozygosity can exceed the
neutral expectation or at least the expectation derived
from the background selection model (Fig. 1,
PALSSONand PAMILO1999).
Linkage effects depend also on the mating system.
Inbreeding reduces gene flow before mating, restricts
recombination and lowers the effective population
size within populations. These features are expected
to strengthen the effects of background selection and
to reduce heterozygosity within populations and to
increase the differentiation when measured as FsT
(CHARLESWORTH
et al. 1997).
The aim of the present study is to examine the
effects of selected loci on genetic differentiation of
populations as estimated from neutral loci. We use
two different selection models, namely (i) purifying
selection against harmful recessive mutations that can
occur at many loci, and (ii) stabilizing selection with
additive allelic effects at polygenic quantitative traits
with an intermediate optimum. The underlying hypotheses are as follows.
(i) An immigrant entering a population is likely to
carry a different array of harmful mutations than the
old residents of the population do. These mutations
occur mainly as heterozygotes when rare, giving selective advantage to the descendants of the immigrant. Selection has thus a homogenizing effect and
the immigrant advantage increases the heterozygosity
within populations.
(ii) Stabilizing selection is expected to reduce the
additive genetic variance within populations as this
reduces segregational load (KIMURA1983), and partially isolated populations can become fixed at different quantitative trait loci. If the optimal phenotype is
the same in each population, an immigrant and the
gametes produced by it are expected to carry optimal
allelic arrays. However, in a later generation recombination between resident and immigrant haplotypes
leads to gametes and genotypes that depart from the
optimum and increases the phenotypic variance. Stabilizing selection can thus be predicted to reduce the
effective gene flow by selecting against the descendants of an immigrant (GOLDSTEIN
and HOLSINGER
1992).
We will here examine these models using multilocus computer simulations that also allow us to incorporate the effects of inbreeding.
Hereditas 130 (1999)
MODELS
Genomic structure. The study is based on simulating
individual multilocus genotypes. The individuals are
diploid with L selected loci and one neutral marker
located in the same chromosome. The number of
crossovers per gamete and generation follows a Poisson distribution with parameter R . The expected
number of crossovers between two adjacent loci (Y)
depends on both R and the number of loci ( L ) . The
neutral marker locus is located in the middle of the
chromosome (unless stated otherwise) and follows the
infinite allele model with a mutation rate of o = 5 x
l o p 4 per gamete per generation (v = 2 x l o p 4 when
simulating larger population sizes, see below).
Selection. We model two different types of selection. In the model of harmful alleles L = 1,000. The
harmful alleles arise at the rate U = 0.1 per haploid
gamete and each locus has the same probability of
mutating. This value corresponds roughly to the observed values of 0.5 per diploid genome in Drosophiln
(KETGHTLEY 1994) and
inbreeding
plants
(CHARLESWORTH
et al. 1990). The harmful alleles are
recessive and the mutilocus fitness of an individual is
given as
w
= (1 - s)110'11(
1 - It,y)h"t
where s is the selection coefficient against homozygotes, h is the dominance coefficient, horn is the
number of homozygous and her of heterozygous loci
within an individual. The simulations are run with
fixed values of s = 0.1 and h = 0.1.
The polygenic model has L = 100 loci affecting a
quantitative trait. Each locus can have two types of
alleles: 1 or 0. All genetic effects are additive both
within and between the loci, and the optimal phenotype is produced by an equal number of l - and
0-alleles. The individual fitnesses w, follow a normal
distribution as
w ,= exp[ - 0.5(x, - lOO)*/VI
where x, is the number of I-alleles in the genome of
an individual i, and V is the variance (parameter) of
the distribution. The shape of the fitness curve is
varied by varying the values of V.
Inbreeding depression. The level of potential inbreeding depression is measured as Dep,,, = (CL ws,,,)/w, where w is the mean fitness within the
subpopulation and wYelfis the fitness of individuals
that would be produced by selfing. Similarly, immi- w)/
grant advantage is measured as Ado,,, = (w,,~
w,where iv is the mean fitness of offspring produced
within a subpopulation and wout is the fitness of
offspring that would be produced by selecting parents
from two different subpopulations. ivout is calculated
Effects o f multilocus selection
Hereditas 130 ( I 999)
1 x 100
4 x 25
Fig. 2. The population models examined. In most cases, the
total population size is 100, consisting of either one population with N = 100 individuals or four populations with
N = 25 individuals each and exchanging migrants according
to the island model.
by drawing 100 random pairs from two different
subpopulations and forming a putative offspring for
each such pair. Dep,,, and Adv,,, are finally calculated as means over generations.
Demoguupfry. The population follows a simple demography with fixed population sizes and discrete
generations. The population consists either of one
population with N = 100 individuals, or of four subpopulations each with N = 25 and with a migration
rate of m between all pairs of populations (Fig. 2, in
one series of simulations N gets values ranging from
100 to 500). The number of immigrants is selected
from a Poisson distribution with parameter Nm. Migration occurs before mating and the migrants are
selected randomly. In each generation, N new offspring are produced by selecting the parents on the
basis of the fitness values among the parental generation. Mating is random unless otherwise mentioned.
We also simulate a mainland-island model assuming
an infinitely large source population that contributes
immigrants to the small populations that are under
the study (see below).
Simulutions. The population is simulated first for
2,000 generations in order to stabilize the genetic
structure. Thereafter, heterozygosities and differentiation are recorded for 20,000 generations (harmful
mutation model) or 10,000 generations (quantitative
trait model). The simulations include 10 replicates for
each set of parameter values when the total population size is 100 (1 x 100 or 4 x 25) and 5 replicates
when the population is larger.
Vaviurion und difierenriution. Genetic variation at
the marker locus is measured as expected heterozygosity 1 - Zpf, where p , is the frequency of the
ith allele. Differentiation among the populations is
measured as Gsr = (HT - H,)/H,, where H, is the
expected heterozygosity in the total population and
H , the mean expected heterozygosity within the sub-
259
populations. The mean value of G,, over the generations (i) in a single simulation replicate is calculated
by weighting with the heterozygosity (HT,,), which
means that G,, = E(HT,, - Hs,,)/XHT,!,where the heterozygosities are calculated within a generation i. In
the set of simulations with large populations ( N >
IOO), Gs, is given as a mean over generations. The
expected relationship between the measures of differentiation (GsT and FST)is GsT = (n - I)F,,/n where n
is the number of subpopulations (NEI 1986).
RESULTS
Deleterious mutations
Effects of deleterious mutations are examined with
fixed values of s = h = 0.1. Background selection reduces somewhat the heterozygosity at the linked neutral locus when we assume one population of size
N = 100. The same holds for a subdivided population. The total heterozygosity in a subdivided population with N m = 1 is a little higher but very close to
the value in one large population. Restricted migration (Nm = 0.1) reduces the heterozygosity within
subpopulations but increases the total heterozygosity.
Background selection reduces the heterozygosities,
particularly the total heterozygosity HT. The changes
take place in such a way that GST decreases with
background selection (Table 1). This decrease is particularly clear when the migration rate is low and
linkage is tight.
The effect of linkage and population subdivision
on the occurrence of harmful alleles is shown by the
measures of inbreeding depression and immigrant
advantage (Table 2). Subdividing the population,
while keeping mating random within the subpopulations, increases the inbreeding depression manifold.
There are only slight differences between the two
migration rates used, and tightening linkage increases
the inbreeding depression slightly in the subdivided
populations. Reducing migration increases the immigrant advantage markedly. When the migration rate
is low ( N m = O.l), the offspring of an immigrant can
have a fitness advantage of several percent.
It is important to examine to what extent the
present results are restricted by the overall small size
of the population. We remove this restriction at least
partly in a mainland-island model by allowing immigration from an infinite source. These immigrants are
assumed to carry unique neutral alleles. Using a rate
of 0.1 immigrants per generation to the total population thus doubles the number of new mutations (100
individuals with a neutral mutation rate of 5 x l o p 4
per gamete produce also 0.1 mutations per generation). The number of harmful alleles in the immi-
260
P. Pumilo et al.
Hereditas 130 (L999)
grants follows a Poisson distribution with a mean
U/2hs per gamete, and the sites of these mutations
are assumed to be randomly distributed. Immigration
from such an infinite source elevates naturally the
heterozygosities, but the values of G,, among the
subpopulations are practically unaffected (Table
I
One set of simulations have four subpopulations
with local N ranging from 100 to 500, and Nm = 0. I
(Table 3 ) . The results show that an increasing population size increases genetic differentiation with tight
linkage ( r = lop4) but not when Y =
When N
becomes larger ( > 300), the value of G,, reaches and
exceeds the level obtained for a completely neutral
model without any background selection.
Inbreeding is expected to reduce the frequencies of
harmful alleles. 20% selfing reduces the inbreeding
depression within the subpopulations (Table 2). However, the level of immigrant advantage (Table 2) and
G,, are practically unaffected by this level of selfing.
A high selfing rate (90'Yo) further increases the immigrant advantage (Table 2), but it also lowers the
heterozygosities within populations in such a way
that differentiation increases relative to the levels
under random mating or 20% selfing (Table I). It
also seems that a high selfing rate (9OYi) does not
purge harmful alleles in a single population of N =
100 as efficiently as a lower selfing rate (20%) does.
When N m = 0.1, the absolute level of differentiation
decreases as linkage gets tighter (the difference HT -
H , = 0.19, 0.12 and 0.11 with tightening linkage for
90% selfing, 0.15, 0.16 and 0.09 for 20% selfing, and
0.20, 0.16 and 0.08 for the random mating case,
values from Table 1). However, the overall effect of
reduction in both heterozygosity and absolute differentiation is that background selection does not affect
G,, when the inbreeding rate is high (90')/0).
Stabilizing selection
Stabilizing selection is simulated with three different
strengths of selection, i.e. V = 16, 100 or 500 (Table
4). When the genotype departs from the optimum by
four allelic units, the fitness is reduced to 0.61 for
V = 16, to 0.92 for V = 100 and 0.984 for V = 500. If
the departure is 10 alleles, the fitnesses are reduced to
0.04, 0.61 and 0.90, respectively. In other words, the
smaller the variance the stronger the selection.
Genetic variation at the neutral marker locus is
almost the same in the presence of stabilizing selection as for a completely neutral model in the cases
with one population of size N = 100 and with 4
subpopulations of size N = 25 each with one immigrant per generation (Table 5). The effect of stabilizing selection is more evident with restricted migration
( N m = 0.1). Tight linkage (r = l o p 3 vs. l o p 2 )reduces
the total heterozygosity a little and decreases differentiation, but the effects are small (Table 5). The
strength of selection affects the results only little, with
strong selection slightly increasing differentiation.
Strong selection ( V = 16) raises the level of differenti-
Table 1. The values of heterozygosity (HT and H,) and the amount of dijferentiution (GJ for the model of
harmjul recessive alleles (s = h = 0.1). The values are given jbr various migration rates among the subpopulations.
'Closed system' refers to our basic model in which no immigrants arrive from any source outside the populations
studied (Fig. 2), and ,j-ee' refers to the model with one population of size N = 100
((I) Closed system
Neutral
r = lo-'
r=
0.16
0.14
0.12
0.16
0.16
0.14
0.14
0.14
0.13
0.15
0.14
0.12
0.34
0.35
0.37
0.15
0.14
0.13
0.33
0.29
0.20
0.13
0.13
0.12
0.59
0.53
0.40
0.25
0.28
0.35
0.56
0.50
0.41
( b ) Immigration from an injnite source
Neutral
r=
r=10-~
( c ) 20% selfing
Neutral
r = 10-3
r=10-~
0.15
0.14
0.15
0.15
0.16
0.12
0.13
0.14
0.10
0.16
0.16
0.14
0.25
0.27
0.19
0.10
0.11
0.10
0.59
0.57
0.46
0.14
0.13
0.10
0.12
0.08
0.10
0.09
0.06
0.06
0.25
0.24
0.24
0.27
0.18
0.16
0.08
0.05
0.05
0.72
0.71
0.70
(d) 90%~srlfing
Neutral
r=
r=
Hereditas 130 (1999)
Effects o f multilocus selection
26 1
Table 2. The observed inbreeding depression Dep,,,,, = (w- w,<,,,)/w and the immigrant advantage Adv,,,?,,7= (woufw)/w in the model ojhurmful alleles,for cmes with either random mating within the subpopulations or with selfing.
The values are given j o r various migrution rates among the subpopulations, and Yree ' refers to the model with one
population of size N = 100
Mating
Free
Nin = 1
Dep,,,
DeP,",
Adv,,,
Dep,,,,
Adv,,,,
10-4
0.026
0.02 1
0.087
0. I00
0.026
0.028
0.074
0.098
0.065
0.094
10-~
0.008
0.007
0.061
0.069
0.034
0.038
0.055
0.069
0.068
0.102
0.020
0.015
0.009
0.009
0.049
0.054
0.009
0.009
0.089
0.117
r
Random
10-3
20% selfing
90% selfing
lo-3
10-4
ation above that of a completely neutral model,
whereas weak selection ( V = 100 or 500) keeps the
differentiation at the same level as for a completely
neutral model.
Nm
= 0.1
fragmented populations pointing out that the consequences can be different from those in large
populations.
The studies by CHARLESWORTH
et al. (1997) and
us show that the amount of genetic differentiation
can be affected by background selection, and this
DISCUSSION
effect depends on the population size. The present
results apply particularly to endangered species that
Genetic differentiation depends on the population
live in small and fragmented populations. It is known
size, level of gene flow and the effects of selection. In
that the heterozygosity-reducing effects of bdckthe absence of selection, subdivision increases the
ground selection can change to heterozygosity-inoverall effective population size by a factor of l/(l creasing effects of associative overdominance when
FsT)(BARTONand WHITLOCK1996) and a subdithe product Nhs is small (PAMILO
and PALSSON1998,
vided population can maintain genetic variation more
PALSSONand PAMILO1999, Fig. 1). The present
easily than a single continuous population of the
results show that associative overdominance can fursame total size. Selfing reduces the effective populathermore reduce differentiation among populations.
tion size, and the amount of gene flow is also devalThis is opposite to the earlier conclusions of
ued by 1 F, where F is the equilibrium inbreeding
CHARLESWORTH
et al. 1997. Although they pointed
coefficient in an infinite population with the same
out the possibility of immigrant advantage, their
amount of selfing (NORDBORG
1997). Differentiation
simulations did not show it. They detected a slight
in metapopulations is further affected by the dynamics of extinction-recolonization events (INGVARSSON tendency for decreased diversity component between
populations (HT - H,) which could be caused by
1997). The present results confirm that differentiation
immigrant advantage (they used nucleotide diversities
can also be affected by selection at linked loci. Stabin instead of H but the interpretation is the same).
lizing selection can increase differentiation even when
However, reduction of the total heterozygosity was so
the optimal phenotype is the same in all subpopulalarge that the overall effect of background selection
tions, but the effects are rather weak and apparent
was an increase of differentiation (FST). The reduconly with strong selection. Local adaptation can sigtion of the between-population component of genetic
nificantly strengthen that effect (CHARLESWORTH
et
diversity is not predicted by the analytical theory,
al. 1997).
probably because the theory assumes linkage equiNeutral loci are affected by selection at linked loci
librium between loci.
and the effects depend on whether selection favours
It seems evident from our results that the differenadvantageous alleles (SLATKINand WIEHE 1998),
tiation-reducing effect of associative overdominance
purges deleterious alleles (CHARLESWORTH
et al.
weakens with increasing population size in a qualita1997, this study) or is stabilizing (GOLDSTEIN
and
tive
agreement
with
the
predictions
by
HOLSINGER1992, this study). It is not straightforCHARLESWORTH
et al. (1997). One should note that
ward to say what is the overall effect, especially as
the predicted neutral GSTin our simulations (Table 3)
that effect also depends on the population structure,
decreases with increasing N , because the role of muamount of gene flow and extinction-recolonization
tations becomes more important with the increasing
dynamics. We have shown possible effects in small,
+
262
P. Pando et al.
Hereditas 130 (1999)
Table 3. The values of heterozygosity ( H , and Hs) and the umount oj' dilferentiution (GST),for the model with
aLleles. The uulws ure giwn .fix fwo r e ~ ( j n ~ ~ irutes,
n u t and
~ ~ ~the~ local pnpulution size N runging
h a r m ~ urecessive
~
from 100 to 500. The nuinher qf inimigr~uit.vin euclz subpopulation is Nnz = 0.1 per generation. Note that the
expected neutral di&entiution E,,(GhYT)
depends on the populution size as the nuniher qf mutations (2Nu) increases
with N . The mutation rute qf thcj murker is v = 2 x
N
100
200
300
400
500
y=
,.
10-3
=
MG)
10-4
HT
HS
GST
HT
HS
GST
0.287
0.447
0.525
0.726
0.587
0.087
0.146
0.206
0.314
0.291
0.526
0.556
0.563
0.580
0.490
0.166
0.223
0.541
0.648
0.400
0.058
0.055
0.174
0.234
0.148
0.360
0.467
0.616
0.627
0.6 I8
product Nu. With a large population size, the number of harmful alleles per genome decreases and the
linkage disequilibria are weaker. As a consequence,
the associative effects lose significance unless linkage
is very tight. The important population size is given
by the species population size rather than the local
size within subpopulations (CHARLESWORTH
et al.
1997). The mainland-island model with an infinite
source of immigrants did not, however, change our
results. The assumption that each immigrant carried
a new marker allele maximised the linkage disequilibria in our simulations and contributed to this
result. We have elsewhere examined the role of different parameters ( N , h, s, r, u ) as determinants of
associative overdominance in a single population
(PAMILOand PALSSON1998, PALSSONand PAMILO
1999). It seems reasonable to assume that parameter
combinations leading to associative overdominance
within populations (see Fig. 1) also affect the patterns of differentiation most.
Inbreeding is generally predicted to strengthen the
effects of background selection (CHARLESWORTH
et
al. 1993, 1997). A selfing rate of 90% increased F,,
fourfold in the simulations of CHARLESWORTH
et
al. (1997). We detected a clear, but much weaker,
effect. Differentiation in a selfing population increased even in a completely neutral model, and
background selection had no additional effect. A
low selfing rate (20%) in our study showed a very
mild (if any) effect. Selfing is expected to be negatively correlated with the migration rate ( HEDRICK
1990) but this was not assumed in our simulations,
and the inbreeding effects were caused by a reduction of the effective population size and recombination rate. The increased immigrant advantage in a
selfing population reduces differentiation, whereas
background selection promotes relative differentiation by reducing the within-population heterozygosity. The overall level of differentiation remains
0.507
0.48 1
0.458
0.436
0.417
largely unchanged. It should be emphasized that we
have not explored the effects of varying selection
(varying s and h). For values used, 20% selfing
purged harmful alleles in a single population of size
N = 100, whereas 90% selfing led to a higher inbreeding depression (Table 2). It seems likely that
high inbreeding leads to accumulation of harmful
alleles ( P A M I L O
et al. 1987), to homozygosity within
the inbred lines and to a large fitness difference
between inbred and crossbred individuals. The specific outcome of this process must depend on both h
and s (HEDRICK1994). We should note that the
level of inbreeding depression in our simulations is
smaller than that observed in many organisms
(RALLSet al. 1988; BARRETTand KOHN 1991).
Model-based studies, such as ours, predict the pattern of differentiation from the defined evolutionary
process, whereas the empirical studies generally aim
Table 4. Fitness of individuals under stabilizing selection depending on how muny ullelic units the genotype departs ,from the optimum. The calues are ,for
three d@wiit strengths qf selection us indicated by
the uuriunce ( V ) of the ,fitness distribution
Departure from the
optimum
0
I
2
4
6
8
10
15
20
Fitness for different strengths
of selection
V=16
V = 100
V=500
1
0.969
0.883
0.606
0.325
0.135
0.044
0.001
0.000
I
0.995
0.980
0.923
0.835
0.726
0.606
0.325
0.135
1
0.999
0.996
0.984
0.965
0.938
0.905
0.799
0.670
263
Effects of multilocus selection
Hereditas 130 (1999)
Table 5. Distribution of genetic variation among populations when there is stabilizing selection. H , and G,,
measure the genetic variation and &?eventiation at the linked marker, nb and n , are the numbers o j heterozygous
polygenic loci when the gametes are taken randomly from two dijfferent subpopulations or from the same
population, respectively
10-2
16
100
500
0.16
0.16
0.16
9.6
12.5
14.0
0.166
0.153
0.203
0.156
0.145
0.144
11.6
14.4
15.5
9.5
12.0
12.8
0.377
0.317
0.366
0.672
0.598
0.596
27.7
27.6
27.3
7.8
9.7
10.0
10-3
16
100
500
0.15
0.14
0.20
10.1
12.7
13.8
0.157
0.154
0.190
0.151
0.145
0.147
11.7
14.3
15.4
9.7
11.9
12.7
0.286
0.294
0.300
0.633
0.579
0.573
24.8
26.7
27.5
8.0
9.8
10.5
n
n
0.33
‘3.59
NPiitral mnrlpl
16
I <
to infer the process from the observed pattern. A s
pointed o u t by FELSENSTEIN
(1 982) such an inference
is problematic as different processes can lead to a
similar pattern. Additional difficulties are caused by
the artificiality of the island model and by the large
stochastic variation of the single-locus estimates of
FST (or GST). It is also important to note that the
estimates are diversity-dependent in the sense that the
homozygosity within populations sets the upper limit
t o FST, this can become restrictive with highly variable markers. Multilocus data narrow down the
confidence limits of the estimates and they also
provide information for more detailed analyses. It is
possible to compare the patterns of differentiation in
different parts of the genome and relate them to the
recombination rates in order t o infer possible effects
of linked selected loci (CHARLESWORTHet al. 1997).
Multilocus estimates allow also assignment of single
individuals t o the populations of origin, which can
reveal individuals who (or whose parents) have been
immigrants (DAVIES et a]. 1999). Even though it is
true that it is difficult t o infer dispersal and demography ( e g for conservation purposes) from the genetic
studies alone (STEINBERGand JORDAN1997), they
have many advantages over demographic studies
when one wants t o estimate gene flow and genetic
consequences of dispersal.
ACKNOWLEDGEMENTS
We thank Kent Holsinger and Martin Lascoux for valuable
suggestions during an early phase of the work and the
reviewers for constructive comments. The work of PP and
SP has been financially supported by the Environmental
Protection Agency of Sweden and by the Carl Trygger’s
Foundation, and that of 0s by the Environment and
Natural Resources Research Council of Finland and by the
Natural Sciences Research Council of Sweden.
REFERENCES
Barrett SCH and Kohn JR, (1991). Genetic and evolutionary consequences of small population size in plants:
implications for conservation. In: Genetics and conservation of rare plants (eds. DA Falk and KE Holsinger),
Oxford University Press, Oxford, p. 3-30.
Barton N H and Whitlock MC, (1996). The evolution of
metapopulations. In: Metapopulation biology (eds. I
Hanski and ME Gilpin), Academic Press, New York, p.
183-21 0.
Beaumont MA and Nichols RA, ( I 996). Evaluating loci for
use in the genetic analysis of population structure. Proc.
R. Soc. Lond. B 263: 1619-1626.
Berg L, Lascoux M and Pamilo P, (1998). The infinite
island model with sex-differentiated gene flow. Heredity
81: 63-68.
Charlesworth B, Charlesworth D and Morgan MT, (1990).
Genetic loads and estimates of mutation rates in highly
inbred plant populations. Nature 347: 380-382.
Charlesworth B, Morgan MT and Charlesworth D, (1993).
The effect of deleterious mutations on neutral molecular
variation. Genetics 134: 1289-1303.
Charlesworth B, Nordborg M and Charlesworth D, (1997).
The effects of local selection, balanced polymorphism
and background selection on equilibrium patterns of
genetic diversity in subdivided populations. Genet. Res.
70: 155-174.
Davies N, Villablanca FX and Roderick GK, (1999). Determining the source of individuals: multilocus genotyping in nonequilibrium population genetics. Trends Ecol.
Evol. 14: 17-21.
Felsenstein J, (1982). How can we infer geography and
history from gene frequencies? J . Theor. Biol. 96: 9-20.
Goldstein DB and Holsinger KE, (1992). Maintenance of
polygenic variation in spatially structured populations:
rules for local mating and genetic redundancy. Evolution 46: 412-429.
Hedrick PW, (1990). Mating systems and evolutionary
genetics. In: Population biology: ecological and evolutionary viewpoints (eds. K Wohrmann and S Jain),
Springer-Verlag, Berlin, p. 83-1 18.
Hedrick PW, (1994). Purging inbreeding depression and the
probability of extinction: full-sib mating. Heredity 73:
363-372.
264
P. Pamilo et al.
Hereditas 130 (1999)
Ingvarsson PK, (1997). The effect of delayed population
growth on the genetic differentiation of local populations subject to frequent extinctions and recolonizations. Evolution 51: 29-35.
Keightley PD, (1994). The distribution of mutation effects
in Drosophila rnelanoguster. Genetics 138: 1315- 1322.
Kimura M, (1983). The neutral theory of molecular evolution. Cambridge University Press, Cambridge.
Nei M, (1986). Definition and estimation of fixation indices. Evolution 40: 643-645.
Nordborg M, ( 1 997). Structured coalescent processes on
different time scales. Genetics 146: 1501 15 14.
Ohta T, (1971). Associative overdominance caused by
linked detrimental mutations. Genet. Res. 18: 277286.
Palsson S and Pamilo P, (1999). The effects of deleterious
mutations on linked, neutral variation in small populations. Genetics (in press).
Pamilo P and Palsson S, (1998). Associative overdominance, heterozygosity and fitness. Heredity 80: 38 1 389.
Pamilo P, Nei M and Li W-H, (1987). Accumulation of
-
mutations in sexual and asexual populations. Genet.
Res. 49: 135-146.
Ralls K, Ballou J and Templeton A, (1988). Estimates of
lethal equivalents and the cost of inbreeding in mammals. Cons. Biol. 2: 185-193.
Rannala B, (1996). The sampling theory of neutral alleles
in an island population of fluctuating size. Theor. Pop.
Biol. 50: 91-104.
Slatkin M and Barton NH, (1989). A comparison of
three indirect methods for estimating average levels of
gene flow. Evolution 43: 1349-1368.
Slatkin M and Wiehe T, (1998). Genetic hitch-hiking in a
subdivided population. Genet. Res. 71: 155- 160.
Steinberg EK and Jordan CE, (1997). Using molecular
genetics to learn about the ecology of threatened species: the allure and the illusion of measuring genetic
structure in natural populations. In: Conservation biology for the coming decade, 2nd ed. (eds. PL Fiedler
and PM Kareiva), Chapman and Hall, London, p.
440-460.
Wright S, (1943). Isolation by distance. Genetics 28: 114138.