J. evol.
Biol.
5: 25-39
1010
(1992)
061)<~92jOlO25-15
Qm 1992 Birkhiuser
Non-equilibrium
gene frequency divergence:
founder effects in natural populations
Marc G. Boileau’,
Paul D. N. Heber?
$ 1.50+020/O
Verlag, Bascl
persistent
and Steven S. Schwartz’
‘Section of Ecology und Systematics,
Cornell Unicersity,
Corson Hall, Ithaca,
New York 148X-2701,
USA;
‘Department
of Zoology, University of Guelph, Guelph, Ontario, NIG .?WI
CANADA;
‘Department
qf’ Biology, BerrJsCollege, Mount Berry Station, Rome, Georgia 3OI49,
USA.
Kels words: Gene frequency divergence; founder effects.
Abstract
The estimation of gene flow using gene frequency divergence information has
become increasingly popular becauseof the difficulty involved in the direct determination of gene flow among populations. The present study examined allozyme gene
frequencies in populations of eighteen aquatic invertebrate taxa at two sites in
northern Canada. Gene frequencies at polymorpic loci were significantly different
among 8-31 localized populations of all species at lgloolik and among IO-36
populations at Churchill confirming the generality of gene pool fragmentation in
pond-dwelling organisms. Measures of gene flow estimated from gene frequency
divergence, which assumethat gene frequency distributions are at equilibrium, were
inconsistent with the probable dispersal capacities of taxa. This provoked an
examination of historical events as alternative explanations. Both theory and
computer simulations demonstrated that when populations grow rapidly in size
after founding from few individuals, the gene frequency divergence established
during colonization is resistant to decay by gene exchange. Our work suggeststhat
gene frequency distributions are often not in equilibrium and that caution should he
employed in attempts to infer gene flow from them in natural populations.
Introduction
Theoretical studies show that gene flow among populations has an important
impact on the evolutionary potential of a species (Slatkin 1987), but the direct
25
26
Boileau.
Hebert
and Schwartz
determination
of gene exchange among natural populations is impossible for most
taxa. in principle, however, the level of gene flow can be inferred from the amount
of gene frequency divergence among populations. Wright (1943, 1951) established a
simple relationship between gene flow and the amount of gene frequency divergence
of neutral alleles among populations.
Employing an island model of population
structure. where organisms occur in discrete demes that have a uniform probability
of exchanging individuals, Wright ( 1943) demonstrated
that gene frequency differentiation (Fs7) reaches a non-zero equilibrium
whose magnitude is linked in a
simple fashion to the number of migrants.
Slatkin (1985) has more recently
developed a second indirect method of using gene frequency information
to infer
gene flow. His simulation studies established that, at equilibrium, there is an inverse
relationship between the average frequency of alleles found in only one population
(“private
alleles”; Neel, 1973) and gene flow among demes.
Indirect estimates of gene tlow require that the variance in gene frequencies
among populations
has reached equilibrium.
Yet few studies have examined the
likelihood that equilibrium has been achieved. Theoretical treatments (Latter, 1973;
Nei et nl.. 1977) have examined gene frequency divergence approaching equilibrium
when a single large population is subdivided into a number of initially identical
smaller panmictic populations. Allendorf and Phelps ( 1981) simulated such a model
and concluded that significant gene frequency divergence among fish populations
did not ncccssarily imply low levels of gene exchange. Wade and McCauley (1988)
considered theoretical situations where gent frequency divergence resulted from the
recolonization of extinct populations as well as by gene exchange. Their studies
indicated that when populations are prone to frequent extinction divergence is
anticipated.
Studies employing gene frequency divergence for the estimation of gene flow have
been rather uncritical. Numerous studies have attempted to estimate gene flow
among populations over broad geographic areas (Dobzhansky and Queal, 1938a.b;
Roberts and Hiorns, 1962; Nei and lmaizumi. 1966; Workman, 1968; Larsen et al.,
1984; Pashley and Johnson, 1986; Waples, 1987; Wehrhahn and Powell, 1987; Singh
and Rhomberg, 1987; Liebherr. 1988). The use of island models to estimate gene
flow on a macrogeographic scale is probably inappropriate becausedispersal among
demes is not likely to be either equal or symmetric. Other workers have examined
gene pool variation in more local situations (Fleischer, 1983; Caccone, 1985;
Caccone and Sbordoni 1987; Hebert and Payne, 1985; Sweeney et ul., 1986; Ward
et uf., 1987; Boileau and Hebert. 1988) but have also failed to consider the
likelihood that equilibrium has been achieved.
The present study has two goals: to compare the extent of gene frequency
divergence in a group of speciesco-occupying a habitat and to ascertain whether
the observed divergence represented an equilibrium condition. Pond organisms were
chosen for study because their demes are discrete and dispersal among them may
well be equally probable at least in physically compact regions (Talling. 1951;
Jeffries, 1989). Prior studies on the genetics of the invertebrate fauna of ponds have
concentrated on cladoceran crustaceans. which typically reproduce by cyclic
parthenogenesis. These studies have shown large gene frequency differences among
Non-equilibrium
divergence
27
local populations of these taxa (Hebert, 1974; Hebert and Moran, 1980; Schwartz
and Hebert, 1987). The fragmented gene pools of cladocerans are thought to arise
as a consequence of founder effects associated with a reliance on passive dispersal
and the ability of single parthenogenetic individuals to found populations. There
remains a need to establish the generality of such gene pool fragmentation in
bisexual pond-dwelling organisms. The current investigation involved the analysis
of genetic differentiation among populations of 18 invertebrate taxa at two sites in
arctic Canada. Both sites had a high density of ponds and were located in areas of
active isostatic rebound so that the pond habitats were less than 3000 years old
(Andrews, 1970; Klassen, 1983). Becausegene frequency divergence was noted in all
taxa and there was no association between the extent of differentiation and our
qualitative estimates of vagility we considered the possibility that gene frequencies
were not in equilibrium.
Material and methods
Gene frequencies in populations of pond invertebrates were studied at two sites
in the Canadian Arctic: 11 taxa at Igloolik, N.W.T. (69 N; arctic) and 10 taxa at
Churchill. Manitoba (59. N; subarctic). Both sites have abundant pond habitats
( > 5 km-‘). Ponds chosen for study were ordinarily separated by at least 10 meters
from their nearest neighbour. Analysis was restricted to species which reproduce
sexually or by cyclic parthenogenesis.
Collections at lgloolik were made between July 30 and August 15 of 1986 and
1987 from ponds broadly distributed over the western half of the island. Eight
crustacean taxa were included in the survey including: two anostracans ~
Branchinectu pcrlucfo.vu and Artemiopsis stefun,s.wni; three copepods He.Fpcrocfiuptonzltseiseni, Eurytemoru compositu and Cyclops canadensis; two cladocerans - ChJdorus sphnericus and Eurycercus gfaciafis; and one notostracan ~
Lepidurus arcticus. In addition Mesostoma arctica, a rhabdocoel turbellarian, and
two collembolans (Isotomurus ciliatus and Podura aquuticrr) were analyzed.
Collections at Churchill were made between June 15 and August 31, 1984- 1988.
Nine crustacean species were analyzed including: one anostracan ~ Branchinectu
pmludosa; one ostracode - CJprinotus glurrcus; three cladocerans - Ceriodaphnia
reticuiatu, Eurj,cercus g1rrcicrfi.sand Simocephalus l’etulus; and four copcpods ~
HesperoLfiuptomusarcticus, Hesperodiaptomus rictoriuensis, Heterocope septentrionalis and Leptodiuptomus t)*rrefli. The turbellarian, Mesostoma arctica, was also
analyzed.
Freshwater ponds at Churchill occur in two distinct habitats; quartzite rock
bluffs adjacent to Hudson Bay and low-lying tundra (Weider and Hebert, 1987).
Sampling of the former habitats concentrated on two rock bluffs (A and C), which
lie approximately 1500 m apart, and which have been the subject of several earlier
studies (Hcbert and Payne, 1985; Weider and Hebert, 1987; Boileau and Hebert,
1988). Rock bluffs are compact and ponds on a single bluff may be less than 10 m
apart, whereas tundra ponds are typically separated by hundreds of meters or more.
28
Boileau.
Hebcrt
and Schwart?
In the present study an effort was made to include populations from both habitat
types, although some species (e.g., H. se~tenfrionalir)
occur in only a single habitat
type.
Twenty-four
individuals from each of 2 3 populations per taxon at both sites
were examined for allozyme variation in 2 ~20 enzyme systems. Variation
was
classified as a genetic polymorphism
only when the phenotypes of putative heterozygotes were congruent with those expected on the basis of the usual quaternary
structure of the enzyme in question (Harris and Hopkinson
1977; Richardson et al.
1986). If this preliminary survey identified polymorphism
at one or more loci, gene
frequencies at these loci were determined by analyzing 24 -48 individuals
from
additional populations.
Loci that were polymorphic
in one or more taxa included:
amylase (AMY),
aldehyde oxidase (AO), glutamate oxaloacetate
transaminase
(GOT), mannose-6-phosphate
isomerase (MPI),
malate dehydrogenase
(MDH),
phosphoglucose
isomerase (PGI) phosphoglucomutase
(PGM) and triosephosphate
isomerase (TPI) and 2 dipeptidases
(leucylglycine
peptidase, PEP-C; phenylalaninylproline
peptidase, PEP-D). Individuals of the smaller species (e.g. Chvdonts
.sphaericu.s) whose body lengths were less than 0.5 mm, only stained reliably for
enzymes with high activity, and were examined for variation at fewer loci than were
taxa with a larger body size. Animals of all species were electrophoresed
within
several days of collection using Titan III cellulose acetate gels (Easteal and Boussy,
1987). Gels were run at 200 volts for 10 I5 minutes in a Tris Glycine buffer (pH
8.5). Details of electrophoretic
procedures are available (Hebert and Beaton, 1989).
Gene frequencies at all polymorphic
loci were determined by direct count. The
extent of gene frequency differentiation
(FS,) among populations
at each locus
within each taxon was determined
using the methods of Nei ( 1977). Genetic
divergence (G,,) was determined using unbiased estimates of H,, the average gene
diversity
within populations
and H,, the average gene diversity
in the total
collective of populations
(Nei and Chesser, 1983) for each species. Because the
sample sizes and number of populations were large, corrections for sampling biases
were minor (Nei and Chesser, 1983; Nei 1986) and our empirical G,, is essentially
the same as Wright’s
(1943) theoretical Fs-,. and Weir and Cockerham’s
(1984)
estimate, 0 (Nei, 1986). The significance of the differences (FsT) among populations
at each locus was assessed by the X2 statistic (Workman
and Niswander,
1970).
Results
Among the 10 species analyzed at Churchill and II at Igloolik, only three species
were present at both sites, Eurycercus glacialis was invariant at both localities in 17
enzyme systems examined (PGI, PGM, AO, GOT, AMY, MPI, MDH, ME, FUM,
PEP-C and D, G3PDH,
6PGDH and ACON) representing
18 loci. Brunchinecta
pulu&su was invariant at Igloolik, but polymorphic
at Churchill in 2 (AMY and
PGI, Table 1) of the 9 enzymes which could be resolved (monomorphic
systems
included APK, GOT, MDH,
ME, FUM, PEP-D and C). The third species, M.
urctica, showed variation (Hebert and Payne, 1985) at both sites, with three loci
Non-equilibrium
29
divergence
Table I. The significance
of gene frequency
differences
at polymorphic
loci examined
in populations
of
I5 pond invertebrate
species from
Igloolik
and Churchill.
n = harmonic
mean
of sample sizes;
.F = number of populations
studied; FST = locus specific gene differentiation;
* = Fs,, significantly
different from 0, P X2 < ,001; G,, = unbiased
gene differentiation.
Site/species
n
s
Locus
FSI
G ST
42.6
15
I2
IO
46.0
8
50.2
51.6
9
IO
52.X
II
41.8
31
,022’
,186’
,030;
.071*
.064*
.048*
,094’
.129*
.223*
.03g*
.120’
.065*
,034’
.076*
.021*
.032*
.053*
,034’
,075
5 I .9
47.4
GOT
PEP
PGM
PC1
MPI
PGM
AMY
MDH
PEP
TPI
PGI
PC1
PGM
PC1
PGM
MPI
PEP
PGM
Churchill
B. pcrludom
43.3
36
c. gluucus
118.8
21
25.0
23
42.8
9
51.4
18
50.0
30
H. .seprentrionalis
3x.5
IO
M. trrcticu
45.6
32
AMY
PC1
FUM
GOT
MPI
PGI
AMY
A0
PGI
MPI
PEP-C
GOT
PGI
PGM
PGI
PGM
AMY
PGI
PGM
MPI
PGM
.370*
.350*
.210*
,183’
.124*
.141*
.l76*
.298*
.064*
,122’
.043*
.068*
.14X*
,062’
,145’
.096*
.104*
.083*
.107*
.189*
,113’
Igloolik
A sr~~~mwoni
H. arcricus
il reproduce
by cyclic
parthenogenesis
,067
,053
,149
,132
,045
,020
,033
,360
.I71
,254
,106
,058
,115
,093
,122
30
Boileau,
Hebert
and Schwartz
polymorphic
at Igloolik (MPI, PEP-D and PGM) and two loci (MPI and PGM) at
Churchill. Polymorphisms
were identified in all other species except L. arcticus at
Igloolik (Beaton and Hebert, 1988), and C. reticulara (AMY, AO, GOT, PGI and
PGM) at Churchill. Specific details of loci studied and levels of polymorphism
for
the other taxa are reported elsewhere (Boileau and Hebert, 1988; Have1 et al.,
1989).
Eight taxa with at least one polymorpic
locus were studied at Igloolik in 8-31
populations
and the same number of taxa were studied at Churchill in IO-36
populations (Table I). Genotypic frequencies at polymorphic
loci were generally in
good agreement with binomial expectations. There were only 28 (5.4%) significant
(P < 0.5) deviations of 519 cases tested. This result provided an indirect confirmation of the genetic basis of the observed electrophoretic
patterns.
Gene frequencies were significantly different among conspecific populations at all
loci and all species (Table 1). Estimates of G,, ranged from 0.020 to 0.360. Taxa at
Igloolik showed less gene frequency differentiation
than those at Churchill and the
only species studied at both sites was also much more differentiated at the former
site (G,, = 0.033 vs. GS,. = 0.122). The angularly transformed FsT estimates from 21
loci at Churchill were also significantly greater on average (t = 8.79, P < 0.05) than
the 16 from Igloolik.
Relation
between genetic d$erentiation
and dispersal
The effective number of dispersers exchanged per generation in Wright’s
island
model (mN) is the product of N, the effective sizes of each population in an infinite
array of equal sized populations and m, the proportion
of N dispersing. Using this
model, quantitative estimates were made for each species from the genetic divergences, G,, , in Wright’s (1943) relation,
1 - Gs,
mN = ~
4Gs~ ’
Populations
from each site generally shared the same allelic array so the
quantitative
estimation method of Slatkin (1985) was not applicable to many
species and did not facilitate comparisons.
The estimates of mN ranged from less
than I in two cases, to 12.2 individuals per generation (Table 2). Estimates from the
2 actively dispersing collembolans overlapped with the highest estimates from the
remaining passively dispersed taxa.
Species vagility was evaluated qualitatively
using information
available or inferred in the literature from studies on closely related species (references in Table 2).
Relative vagilities were scored using probable dispersal capabilities. The highest was
given (Table 2) to the two collembolans (I. ciliatus; P. aquaticus) that can disperse
actively, a capacity that we considered more important
than all enhancements
to passive dispersal combined. Passive dispersal of adults and/or resting stages
of other species was assumed to be enhanced by: A) morphological
accessories,
which permit water or wind flotation; B) gastrointestinal
resistance, which allows
Non-equilibrium
31
divergence
Table 2. Characteristics
of dispersal capacities
in 15 invertebrate
taxa at two study sites in northern
Canada.
Passive egg cnhanccmcnt
categories include; A 7 morphological
accessories,
B = gastrointestinal
resistance. C = multi-year
persistence,
D = egg clutches,
E = pigmentation.
mN calculated
from Car in
Table I.
Taxon
Active
Dispersal
Passive
Adults
Passive
A
Egg Enhancements
B
C
Vagility
Score
mN
D
E
-
-
7
7
12.3
5.3
x
X
5
1.2
X
X
4
4
0.7
3.5
X
4
4.6”
Collemhola
P. uquatica
I. di0tu.c
Ostracoda
c. ,~tUu(.N.s
Cladocera
s. l~eIuIu.F
C. .sphuericu.v
Turhcllaria
M. ur(‘/l(‘cl
Copepoda
H. ei,wni
If. rrrcticu.5
H. ric/oriurn.sis
L. IJrrelli
E. rompositrr
H. .~eptrntrinna/i~t
C. cuttudcrkr
Anostraca
B. ptrlutfostr
A. skfunssoni
likely
likely
-
none
likely
none
none
nvne
none
none
none
none
none
none
none
none
none
none
none
x
x
x
x
x
x
none
x
x
x
none
none
none
none
x
x
x
x
x
x
x
x
x
x
x
x
X
x
x
x
x
x
x
x
x
x
x
x
none
none
x
x
likely
none
none
“ Mean of 2 estimates
from
lgloolik
(7.3) and Churchill
References
for passive dispersal characteristics.
I. Ostracoda,
Cladocera
and Anostraca-Loandes.
1930:
Proctor
et a/.. 1967; Mellors,
1975.
2. Turhellaria-Pennak.
1978.
3. Copepoda-Cole.
1953; Fryer and Smyly.
1954; Hehert.
( 1.X) used
Proctor,
I .4
2.1
4.1
1.9
1.6
2.4
4.5
3
3
in overall
1964; Proctor
0.4
3.1
comparison
only.
and Malone,
1965;
1985.
propagules to survive ingestion by vectors; C) multi-year persistence in dormancy,
which improves transfer probability; D) formation of clutches, which permits many
eggs to move in one dispersal event and E) pigmentation in adults, which affords
visibility to predators and improves transfer probability.
The passively dispersed
species score was the total number of enhancement characters.
The ranked qualitative vagilities and quantitative
estimates of dispersal were
compared
using Kendall’s
Coefficient
of rank correlation
(Sokal and Rohlf,
1981). Ranked scores of vagility and rnN were not significantly correlated when
all taxa were considered (r, = 0.402, P > 0.05). However,
because there was an
obvious difference in mean Fs,- between the two sites, separate ranked comparisons
were conducted
for each site. Neither of these comparisons
was significant
(r,Igloolik
= 0.134, P > 0.05: r,Churchill
= 0.356. P > 0.05).
32
Boileau,
Hehert
and Schwartz
While it is possible that dispersal agents operate more effectively on some
dispersal enhancement characters than we allow, there was also no obvious linkage
between local dispersal as inferred from genetic divergence and species distributions. For example, both Branchinecta paludosa and Simocephalus L7etulu.s have a
broad distribution
over the Canadian arctic, yet their Churchill populations showed
the greatest divergences suggesting low gene exchange. This lack of correlation with
our expected dispersal capacities and the broad overlap in FsT between actively and
passively dispersing species suggested that there was no simple relationship between
the current gene exchange and the substantial gene frequency divergence observed.
However,
historical perturbations
of current exchange patterns could have confounded the gene frequency distributions
(Slatkin, 1985b). Therefore, we explored
the level of genetic divergence possible due to one historical event, colonization, and
some of the conditions of gene exchange as divergence approaches equilibrium.
If the average number of colonists (K) was small and the number of populations
founded was large, genetic divergence at generation zero may have been substantial
because,
(Wade and McCauley, 1988). The populations we examined must have colonized
these habitats within the last 3000 years. Assuming that the populations expanded
rapidly without genetic drift to identical large sizes, reproduced in discrete generations and dispersers arose at random from the complete island model array of
populations the F& decays constantly by ( 1 - m)’ shown by Wright’s ( 195 I) well
known recurrent relation:
where F,,(g) is the value of FsT in the gth generation. Thus, the half-life of F,, or
the number of generations required to decay any given divergence by half (t) is
inversely related to m, the proportion
of each population that dispersed, by
In 2
f=2m
(Crow and Aoki. 1984), which is approximately
0.347/nz for large populations.
We simulated this model by 100 computer replicates of 25 populations
established from a single infinite sized source population which had 2 alleles in equal
frequency (note there is no dependence on allele number or frequencies in the above
relations).
Populations
were established
from K = 1, 5 and 10 colonists
and
assumed to expand immediately to 3 population sizes (N), 104, IO’ and I06. We
simulated three mN = K exchange rates (there is likely a link between the number
of colonists and subsequent dispersal) to illustrate the length of time required to
erode gene frequency differences. We also used the extreme limitation of K = 1
colonist because cyclic parthenogenetic
taxa can found populations
from one
individual and although impossible for bisexual species, they would decay similarly
after starting from some different initial condition.
Non-equilibrium
33
divergence
Gene frequency differences due to colonization in our simulations (Fig. 1) were
congruent with those expected from the theory [FST(0) = (s - 1)/(2Ks)] and corrected for the finite number of populations colonized (s). It was possible to compare
the theoretical half-life of gene frequency divergence with our simulations (Table 3).
The theoretical half-life of FST was mimicked by our simulations and increased by
an order of magnitude when either the number of dispersers was decreased or the
population size was similarly increased (Table 3).
A significant decline in Fs., was noted (Fig. I) within a few hundred generations
when population sizes were small ( 104). However, when population sizes were larger
(IO’, IO’) divergence showed little decay over a 2000 generation interval even under
considerable dispersal pressure (mN = IO) and founder effects persisted for thousands of generations even in the face of substantial
numbers of exchanged dispersers. Under the conditions of this model gene frequency divergence, established
Fig. I. Decay of gene frequency
difierences
(F,., ) over 2000 generations
from computer
simulations.
The
simulations
examine
the effect of variation
in population
sizes (N = 104, 10’. IO”) for each of three
founder
(K) and dispersal (m/v’) amounts.
K =mN
= 1 0. 5 0 and 10 - + in each simulation.
Table 3. Estimates
of the half-life of decay of genetic differentiation
among populations
at various levels
of gene exchange
(m) and population
sizes (N) using data from computer
simulated
decay curves.
Estimates
for each curve were calculated
by determining
the decay constant as the average proportion
decayed for each 100 year interval
in the simulations.
The half-life was equal to (In 2)/(decay
constant).
The values in parentheses
are those expected from theory (see text).
N = IO4
mN=l
mN=5
3467.5
(3466)
693.5
(694)
mN=lO
349.3
(346)
N=
10’
34.653.8
(34,657)
6931.1
(6932)
3467.5
(3466)
N=lOh
346.504.2
(346,574)
69,242.0
(69,314)
34,615.O
(34,657)
34
because the founder numbers were
populations and gene flow estimates
Boileau.
Hebert
and Schwartz
low, could persist until the present in large
based on the divergence would be inaccurate.
Discussion
The present study confirms that significant variation in gene frequencies among
local populations
of sexually reproducing
pond invertebrates
is a general phenomenon. The extent of genetic divergence is considerable in light of population
proximity.
Values of GST averaged approximately
0.1 (range 0.02 0.36) among
populations less than a kilometer apart. Assuming this variance in gene frequencies
is at equilibrium, the number of dispersers exchanged among populations averaged
3.3 and ranged from 1 to 12 individuals.
The estimates of dispersal from the variance in gene frequencies were not
correlated with the apparent dispersal abilities of taxa, either overall or at single
sites. It is possible that the failure to show such associations simply reflect
inadequacies in the criteria employed in ranking dispersal abilities (Fryer, 1985;
JetTries, 1989). However, broad geographic distributions of taxa with low dispersal
abilities based on gene frequency divergence provides supportive evidence.
Natural selection could also be responsible for sustaining high variance, but
previous allozyme studies have never provided such pervasive evidence of selection.
Moreover, correlations between gene frequencies at specific loci and variation in
physico-chemical parameters such as pH, conductivity, alkalinity and organic acid
content (Boileau, 1989) are generally insignificant. As well, gene frequency distributions in species studied at numerous loci do not differ from the distribution
expected (Fuerst et al., 1977) by neutrality.
The ponds at each site represent an approximation of the pattern considered by
Slatkin’s ( 1977) Model II, recently extended by Wade and McCauley (1988) where
populations exchange dispersers and become established from within a collection of
populations. Equilibrium gene frequency differentiation values as high as those we
observed can be accounted for using Wade and McCauley’s (1988) model. However, population extinction probabilities required in their model (0.01 to 0.05) to
account for the level of divergence we observed are unlikely. Most of the taxa we
studied produce resting eggs. which can remain dormant in pond sediments for
several years or possibly decades (Hairston and DeStasio, 1988) therefore, many
generations of total prereproductive mortality are required before populations
become extinct. Indeed, deliberate prereproductive extermination experiments conducted over a 3 year period (P. Hebert, unpublished data) failed to extirpate
copepod populations. Moreover, surveys of species composition in the Churchill
area over a 10 year period have indicated that speciesassemblagesin single ponds
are stable. Both lines of evidence suggest that extinction rates are extremely low.
Our simulation studies provide an alternate interpretation for the gene frequency
divergence among pond-dwelling organisms. Specifically, if their populations are
founded from few individuals and subsequently undergo rapid growth before
exchanging migrants, gene frequency differences that arise during founding can
Non-equilibrium
35
divergence
persist for thousands of generations (Fig. 1). For example, an array of populations
averaging 10’ individuals requires 3500 years for Gsr to decay from 0.3 to 0.15 if
each population received 100 migrants per generation. By contrast, analyses that
presumed G,,, was at equilibrium at any point during this interval would conclude
that fewer than 2 dispersers were exchanged per generation.
The population sizes employed in our simulations are modest for many invertebrate taxa including those prevalent in freshwater. There is also evidence that large
population sizes can be achieved rapidly. The species included in our study typically
produce more than 20 eggs per brood (Table 4) and females often produce IO- 15
broods during a lifetime (Hebert,
1985). Assuming only 2 clutches per female, a
1 : I sex ratio and complete survivorship
of offspring, no more than 5 generations
are required to reach a population size of IO”. Experimental introductions
of one
copepod species HLjterocope sepptentrionalis have confirmed that such growth trajectories occur (M. Boileau and P. Hebert, personal observations).
The Churchill and Igloolik habitats have a maximum age of 3000 years and as
most of the organisms that inhabit these habitats are univoltine, there have been at
most, only a few thousand generations since their establishment.
Unless immigration is extremely high, it seems unlikely that the variance in gene frequencies
established during colonization
has had sufficient time to decay. Alternatively,
if
immigration is low, the existing levels of divergence must closely approximate those
established during population founding. Because the variance is directly linked to
the number of founders, one can reach conclusions concerning the efTective number
of colonists. Indeed, when the observed Gs,. values are corrected for the finite
numbers of populations
sampled (Fig. 2), the results suggest that populations
of
most species were established by fewer than 5 individuals. By extending analysis to
an examination of mitochondrial
DNA haplotype diversity, it should be possible to
verify this conclusion.
Wright’s model and Slatkin’s, (1981, 1985) extensions have been employed by an
increasing number of workers to estimate gene flow among populations. Some have
found that gene frequency differences correlated poorly with other dispersal capability criteria (Varvio-Aho,
1983; Singh and Rhomberg, 1987; Liebherr, 1988). The
Table 4. Brood sizes from arctic
generations
required
for populations
ber of populations.
Species
s
B. puludostr
9
A. .stqfan.woni
II. eiseni
H. cmricus
H. r~ctoriaensis
1.. tb7wlli
8
5
I1
42
and subarctic
crustacean
zooplankton.
G
the number
of discrete
to achieve sizes listed. n number of individuals
counted; s num-
n
74
160
87
400
165
630
Mean
18.0
25.8
25.0
32.6
20.8
22.0
G
105
10”
4
3
3
3
4
3
5
4
4
4
5
4
36
Boileau,
Hchert
and Schwartz
present analysis makes it clear that equilibrium models for estimating gene flow
must be employed with caution. Invertebrate taxa exist in large populations that
might require thousands of years to erode gene frequency differences that arise
during colonization. The frequent extinction and recolonization of habitats also
acts to counter the erosion of gene frequency divergence (Wade and McCauley,
1988).
For practical purposes, gene frequency distributions reflect a dynamic interaction
of founder number with dispersal rate, population sizes and age. Information on all
these parameters is necessary in order to understand the genetic structure of
populations yet few (Bryant et al., 1981; Larsen et al., 1984) have included the
impact of age. Our study has shown that becauseof the substantial half-life periods
required to decay differences that the age must not be ignored when interpreting
genetic data from most North American taxa because glaciers only recently receded
permitting organisms to expand their ranges. Indeed, recent molecular studies on
vagile taxa have suggested that gene flow has not overridden historical influences on
population subdivision, measured using the maternally inherited mitochondrial
DNA (Bermingham and Avise, 1984). We suggest that the interpretations of
allozyme frequency data combined with other information are no longer limited to
the estimation of dispersal rates. It should be possible to estimate the number of
Fig. 2. Shifts in the expected
mean of Fy, as a result of variation
population
(--I;
- - - 5;
10) and the number
of populations
observed
G,-,- for I5 taxa studied at two sites in northern
Canada.
in the number
of founders
per
sampled.
Data points are the
Non-equilibrium
divergence
37
colonists as we have done or gene frequencies combined with actual dispersal and
colonization
rates may also be used to estimate the ages of the populations
in
studies requiring corraborative
evidence of age and dispersal. We expect that studies
of this type will demonstrate a more widespread importance of founders in shaping
the genetic structure of aquatic invertebrate populations.
Acknowledgements
Funding
for the allozyme
analysis was provided
by an operating
grant and a summer scholarship
from
the Nalural
Sciences and Engineering
Research Council of Canada to PDNH
and MGB
respectively
as
well as Department
of Indian Affairs and Northern
Development
Northern
Training
Grants
to MGB.
John MacDonald
and George
Qulaut
of the Eastern
Arctic
Scientific
Resource
Center
assisted
tremendously
in facilitating
research at Igloolik.
Arne Fjellberg
kindly identified
the collembolans
and
Brenda J. Hann provided
the data for Simocephalus
t~etufus. Neil Billington,
Magi Beaton, Terrie Finston
and William
Payne assisted with some of the electrophoresis.
We benefitted
from the comments
of R.
Danzmann,
D. J. Innes. R. D. Ward, L. J. Wcider,
R. Waples and 3 anonymous
reviewers
on earlier
versions
of the manuscript.
A NSERC
postdoctoral
fellowship
to MGB
was instrumental
during the
preparation
of the manuscript
and S. A. Levin and one reviewer
helped clarify the analytical
treatment
of the approach
to equilibrium.
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