Molecular Ecology (2001) 10, 593 – 602

Molecular Ecology (2001)

10

, 593–602

© 2001 Blackwell Science Ltd

Blackwell Science, Ltd

Sustaining genetic variation in a small population: evidence from the Mauritius kestrel

R ICHARD A. NICHOLS,* MICHAEL W. BRUFORD† and J IM J . GROOMBRIDGE‡*

School of Biological Sciences, Queen Mary University of London, London E1 4NS, UK

†

Cardiff School of Biosciences, Cardiff University, PO Box 915, Cathays Park, Cardiff, CF10 3TL, UK

‡

Institute of Zoology, Regent’s Park, London NW1 4RY, UK

Abstract

We obtained measures of genetic diversity in 10 kestrel species at a suite of 12 microsatelliteloci. We estimated the relative effective size (

N

e

) of the species using a Markov chain MonteCarlo (MCMC) approach, which jointly estimated the locus specific mutation rates as nuisanceparameters. There was surprisingly high genetic diversity found in museum specimens ofthe Mauritius kestrel. Being an endemic species on a small island, it is known to have a longhistory of small population size. Conversely, kestrels with a continental distribution had

N

e

estimates that were only one order of magnitude larger and similar to each other, despitehaving current population sizes that were between one and three orders of magnitudelarger than the Mauritius kestrel. We show how many of the theoretical results describingthe effective size of a subdivided population can be captured in terms of three rates whichdescribe the branching pattern of the gene genealogy, and that they are useful in estimatingthe time to migration-drift and mutation-drift equilibrium. We use this approach to arguethat population subdivision has helped retain genetic diversity in the Mauritius kestrel,and that the continental species’ genetic diversity has yet to reach equilibrium after therange changes following the last ice age. We draw parallels with Hewitt’s observation thatgenetic variation seems to survive species’ range compression and is rather vulnerable torange expansion.

Keywords

: coalescent, conservation genetics, glacial refuge, metapopulation, range expansion

Received 4 June 2000; revision received 25 September 2000; accepted 25 September 2000

Introduction

In this paper we compare the genetic variation in 10 differ-ent kestrel species to evaluate the effects of past and presentpopulation size on genetic diversity. Our study species havepopulation ranges that differ by three orders of magnitude,and we examine the differences in genetic diversity atthe same suite of 12 microsatellite loci in each. We payparticular attention to the Mauritius kestrel (

Falco punctatus

).

The Mauritius kestrel

The Mauritius kestrel is the last surviving endemic raptoron Mauritius, and has been the focus of an intensive

conservation effort since 1973 (Jones 1987). Contemporaryrecords indicate that the kestrel suffered a severe but short-lived population bottleneck. Prior to human settlementin 1750, the Mauritius kestrel may have been widelydistributed over the island wherever suitable forest existed(McKelvey 1977; Jones & Owadally 1985). The populationdecline seems to have paralleled the destruction of thenative forest ( Jones 1987), and by 1950 the species was rareand approaching extinction (Hachisuka 1953; Greenway1967). Further drastic decline, as a result of widespreadorganochlorine pesticide use, reduced the population toone known breeding pair in 1974 (Safford & Jones 1997).Since then, the managed population rapidly recovered to222–286 individuals in 1994 (Jones

et al

. 1995), and hascontinued to increase, with a population believed to be inexcess of 400 birds in 1997 (Safford & Jones 1997).

Figure 1 shows the historical decline of distribution andpopulation size for the Mauritius kestrel, and the capture

Correspondence: Dr Richard A. Nichols. Fax: 020 8983 0973;E-mail: [email protected]

MEC1204.fm Page 593 Tuesday, March 13, 2001 10:35 AM

594

R . A . N I C H O L S , M . W. B R U F O R D and J . J . G R O O M B R I D G E

© 2001 Blackwell Science Ltd,

Molecular Ecology

, 10, 593–602

locations of the museum specimens used to estimateancestral variation. The museum specimens, dated between1829 and 1940, predate the reduction of the kestrel popula-tion to extremely low numbers. These samples, therefore,allow a direct estimate of ancestral genetic variation. Theancestral population was itself restricted in area, as theisland is only 25 km in radius. Furthermore, it appears tohave been effectively isolated from neighbouring islands.A molecular phylogeny based on cytochrome

b

indicatesthat the Mauritius kestrel diverged from the Seychelleskestrel

Falco araea

two million years ago (Groombridge 2000).

Interpreting the genetic data

Hewitt (1999) has pointed out that genetic differentiationbetween populations of many European species seemsto arise because different regions have been populatedfrom different glacial refugia. Instead of arguing that thepopulations went through population bottlenecks, as theybecame restricted to small refugia, he turns the usualargument on its head. He points out that bottlenecks couldoccur as ranges expand and small numbers of migrantsarrive in virgin territory. One major strand of evidence for

Fig. 1 Distribution and population decline of the Mauritius kestrel.


H O W S M A L L W E R E PA S T P O P U L AT I O N S ?

595


Molecular Ecology

, 10, 593–602

this interpretation is that areas in southern Europe, that arepostulated as refuges, typically harbour more geneticvariation than more northern latitudes.

We will search for similar patterns in the kestrel data.Persistent island populations might sustain genetic vari-ation in a similar manner to glacial refuges. On the otherhand, large continental kestrel populations may have lostgenetic variation during range expansions. As in the case ofpopulations in northern Europe, there may have beeninsufficient time for genetic diversity to be replenished bymutation.

The paper is in three parts. First, we conduct a preliminarydata exploration, which summarizes the genetic variationin the kestrel species by estimating heterozygosities. Thisanalysis exposes evidence that there are significant dif-ferences in effective size between the populations and inmutation rate between the loci. These results invalidatethe calculation of averages to combine information acrossloci or populations. In the second part we, therefore, makeuse of a Markov chain Monte Carlo (MCMC) analysis thatcan allow for different mutation rates and summarize thedifference between species as difference in effectivepopulation size.

The third part of the paper deals with the interpretationof differences in effective size. The relationship betweenpopulation size, subdivision and dynamics and effectivesize is not straightforward. For example, Wakeley (1999)argued that human genetic data suggests a reduction ineffective population size. This seems at odds with theincrease in size suggested by the palaeontological andarchaeological record. He pointed out, however, thatmodels of subdivided populations show that an increasein migration rate between human populations could leadto the reduced effective size. Whitlock & Barton (1997)developed more sophisticated models that also incorporatedfluctuating population size and came to the oppositeconclusion, that subdivided populations will often havereduced effective size. Here we point out that the results ofthese and other models can be captured by three rates thatdetermine branching patterns of the gene genealogy. Thisapproach allows a ready application of ecological insight toevaluate which of the theoretical approaches might bemost applicable to the kestrel species, and to assess the rateof approach to equilibrium.

Materials and methods

Extant samples and DNA extraction

Blood sampling was carried out over 3–4 breeding seasonsbetween 1994 and 1998 from each of the three populationsshown in Fig. 1, with the majority of the samples beingobtained from wild offspring bled at the nest. Although 350birds have been sampled, these include several offspring

for many of the nests. In order to obtain independentsamples, we restricted the analysis to adults from one year:1996. In cases where we had not bled either member ofa breeding pair, we included one of their chicks, therebysampling half the adult’s genes. These criteria reduced thesample to 75 individuals.

Between four and 10 fresh blood samples from theSeychelles kestrel, Greater kestrel

Falco rupicoloides

, Lesserkestrel

F. naumanni,

South African rock kestrel

F. tinnunculusrupicolus

and Canary Islands kestrel

F. tinnunculus canariensis

were collected from the brachial wing vein, and storedin a standard Tris:EDTA:SDS storage buffer (10 m

m

Tris, 100 m

m

EDTA, 2% w/v SDS; pH 8.0). Two separatesources of material were sampled for the European kestrel

F. tinnunculus tinnunculus

: (i) muscle preserved in alcoholfrom captive stock in Mauritius (supplied by C.G. Jones,Mauritius Wildlife Foundation); and (ii) previously extractedDNA from a UK source (supplied by J. Wetton, ForensicScience Service, UK). Primary feather samples were obtainedfor the Madagascar kestrel

F. newtoni

and the Kenyankestrel

F. tinnunculus rufescens.

Total DNA was extracted from blood samples using pro-teinase K digestion, phenol–chloroform purification, NaClextraction and ethanol precipitation. Methods followedAusubel

et al

. (1989), but were modified for avian bloodfollowing Miller

et al

. (1988). Total DNA was stored in500

µ

L 10 m

m

Tris-HCl: 1 m

m

EDTA (TE) buffer (pH 8.0) at

−

20

°

C

.

Methods for feather DNA extraction were similar, buttotal extraction volumes were reduced from 5.0 mL to 500

µ

L.

Museum samples and museum DNA extraction

A total of 26 Mauritius kestrel museum specimens ofdifferent tissue types were used in this study, includingtissue from the underside of the footpad (proximal phalanx),dermal skin samples, muscle preserved in alcohol andfeather tips, depending on the collection from which theywere obtained. The museum specimen tissue types, iden-tification details and catalogue numbers are recorded atwww.qmw.ac.uk/~ugbt112, and those samples with locationinformation are included in Fig. 1.

To optimize DNA extraction techniques for the varioustissue types, trials were carried out using material from theEuropean kestrel of similar antiquity (100–170 years), inorder to compare DNA yield and microsatellite amplifica-tion from the same tissues. Samples were extracted usingthe commercially available GFX Genomic DNA PurificationKit (Pharmacia Biotech, UK). DNA was eluted into 200

µ

Lof TE buffer which had been preheated to 80

°

C, and storedat

−

20

°

C. The most reliable tissue type both for DNA yieldand polymerase chain reaction (PCR) amplification wasfootpad skin, as has been found in another study on thegenotyping of avian museum specimens from differenttissue sources (Mundy

et al

. 1997).


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R . A . N I C H O L S , M . W. B R U F O R D and J . J . G R O O M B R I D G E


Molecular Ecology

, 10, 593–602

Microsatellite amplification of extant DNA

The DNA samples were screened using a set of 10 poly-morphic dinucleotide microsatellite markers cloned fromthe Peregrine Falcon (M. Nesje, GenBank accession nosAF118420–118434: Locus

5

,

13

,

31

,

46–1

,

79–1

,

82–2

,

86–2

,

89

,

92–1

,

107

), and a further two loci, a hexanucleotide andtetranucleotide, from the European kestrel ( J. Wetton,unpublished; Locus

Fu1

,

Fu2

).PCR amplification of the extant DNA was carried out

following end-labelling of the forward primer with[

γ

32

P]-dATP according to Ellegren (1991). PCR (10

µ

L)was performed in 96-well microtitre plates using thefollowing reaction mix; 0.75 Units

Taq

polymerase (Gibco,UK), 100

µ

m

of each dNTP, 3.0 m

m

NH

4

buffer (Gibco,UK), 1.5 m

m

MgCl

2

, 0.5 pmol of each primer and approx-imately 50 ng of DNA per reaction in a Hybaid thermalcycler (Hybaid, UK). Cycling parameters were as follows:94

°

C for 3 min, then 30 cycles of 94

°

C for 45 s, 50

°

C for45 s and 72

°

C for 45 s, finishing with 72

°

C for 10 min.Products were mixed with 95% deionized formamideand xylene cyanol/bromophenol-blue dye mixture,preheated to 94

°

C and loaded onto 6% denaturingpolyacrylamide gels to resolve the PCR fragments. Thesizes of alleles were initially determined by electro-phoresis alongside the product of a DNA sequencing reac-tion, and from then on by internal comparison of knownsize PCR products. Gels were dried at 80

°

C and the prod-ucts visualized by autoradiography for between 12 and48 h.

Microsatellite amplification of museum DNA

PCR amplification of museum DNA extractions wascarried out using the same method, but with the followingadjustments; all reagents and tubes were exposed toultraviolet light for 25 min prior to assembly, to degradeany contaminating DNA. Annealing temperatures for allreactions were lowered to 48

°

C (36 cycles) in order toincrease the likelihood of PCR amplification from DNA. Toconfirm PCR amplification and control for allelic drop-out,each PCR was repeated at three different DNA dilutions(1:1, 1:5 and 1:10), and run in consecutive lanes separatedby a blank lane. PCR products of extraction blanks werealso included for each set of reactions, with similar dilutiontreatments. A negative PCR control was also includedfor each set of reactions. PCR products were visualizedby autoradiography using exposures of 2–10 days. PCRamplification of all museum DNA extractions wasrepeated at least twice. Correct identification of alleles, asopposed to spurious PCR product, was confirmed by thepresence of ‘slippage’ products typical of microsatelliteamplification by

Taq

polymerase (Litt & Luty 1989; Luty

et al

. 1990).

Estimates of heterozygosity

An initial data exploration was conducted by estimatingheterozygosities. Likelihood curves were obtained for eachcombination of locus and species using a simple recursivefunction of

F,

the complement of heterozygosity (eqn 1below). The same function has been used to estimate theparameter

F

ST

in a subdivided population (Balding & Nichols1997). For a variety of models of mutation, the probabilitythat the (

n

+ 1)

th

gene drawn from the population is anallele of type

a

depends on

F

and the number of

a

allelespreviously seen in the sample,

x

a

.

(1)

where

p

a

is the probability that a mutation event generatesan

a

allele. Balding & Nichols (1995) pointed out thatsetting

p

a

= 0 gives the Ewens’ sampling formula, suitablefor the infinite alleles model of mutation (Ewens 1979);whereas

p

a

= 1/k

gives the probabilities for the multinomialDirichlet distribution, appropriate for the k-alleles model(Wright 1969). The probability for each sample, given

F,

canbe obtained by arranging the genes in arbitrary order andcalculating the product of eqn 1 for each gene in the sequence.

This probability can be obtained for values of

F

between0 and 1, giving a likelihood curve for each locus in eachpopulation. A preliminary evaluation of differences inheterozygosity between species or between loci can beobtained by combining the likelihood curves. Curves foreach species were obtained by multiplying the likelihoodsfor every locus for each value of

F

. This procedure wouldbe appropriate for unlinked loci with the same mutationrate. The result is shown in Fig. 2(a) (for the infinite allelesmodel). The curves are standardized to have the same area,so that the heights can be treated as probability densitiesgiven a uniform prior. As expected there is a general trendfor the species thought to have larger population size tohave higher heterozygosities.

In order to evaluate differences in mutation rate betweenloci, the curves for the continental species were combinedfor each locus. Differences in mutation rate can be detectedas curves with minimal overlap. Any differences could beobscured if the effective size of the different species weresubstantially different, as this would reduce the precisionof the locus-specific estimates. This is why we restricted thecomparison to the continental species, which appear tohave similar effective population size (

N

e

) as indicated bytheir coincident curves in Fig. 2(a) (similar heterozygosityat the same loci implies similar

N

e

).

Estimating relative population size

The preliminary analysis provided evidence of significantdeviations in heterozygosity between loci and between

P a xa n,( )xaF 1 F–( ) pa+

nF 1 F–( )+-----------------------------------=


H O W S M A L L W E R E PA S T P O P U L AT I O N S ? 597

© 2001 Blackwell Science Ltd, Molecular Ecology, 10, 593–602

species (see below). In addition, there were missing datafor some combinations of loci and species that may havebiased the estimates. We, therefore, make use of a methodthat can deal with these problems. It was used (but notdescribed) by Groombridge et al. (2000), to identify therestored Mauritius and the Seychelles populations asoutliers having heterozygosities substantially lower thanwould be predicted from the size of the species’ range. Themethod deals with differences between loci and species byobtaining joint estimates of the size, Ne, for each species(plus the restored population) and the mutation rate, µ, foreach locus. It is not possible to estimate the absolute Nevalues accurately without knowing the mutation ratesaccurately, because the likelihood calculated using eqn 1depends on the product Neµ. For example, in the case of theinfinite alleles model of mutation, the product enters eqn 1 as

. Nevertheless, it is possible to obtain accurate

estimates of the relative Ne, because the same loci weretyped across species.

The analysis, therefore, estimated a parameter that spe-cified the relative population size of species i, ∆Ni. Thisparameter is defined in terms of a deviation from an aver-age across species, , such that the effective size of eachspecies is given by log(Nei) = + ∆Ni. Similarly the relativemutation rate for each locus j, ∆µj, was estimated, wherethe locus specific mutation rate is given by log(µj) = +∆µj. The parameters , and the deviations ∆Ni for eachpopulation and ∆µj for each locus were estimated using theMetropolis algorithm (Metropolis et al. 1953; Gelman et al.1995). This is an MCMC method that starts from an arbi-trary combination of parameter values and steps throughparameter space. The stepping rule is designed so thatparameter values are chosen with a probability propor-tional to their likelihood. The ∆Ni and ∆µj were allowed tovary by ±5 loge units from their respective means. At each

iteration, all the parameter values were perturbed to newvalues drawn from a uniform distribution centred on theold values. The width of each distribution was one tenth ofthe parameter’s range. The likelihood, Lnew, was calculatedaccording to eqn 1 for the new parameter combination. Thetotal likelihood was obtained as the product of the valuesfor each locus and each population. The species repres-ented by only single individuals (Kenya and Madagascar)were excluded.

If Lnew was greater than the likelihood for the previouscombination, Lold, then the algorithm stepped to the newvalues. If it was smaller, then the step to the new valueswas accepted with probability Lnew/Lold, otherwise the oldvalues were retained.

After a burn-in period of 25 000 iterations, the distribu-tion of parameter values for the next 250 000 iterations wasrecorded. The relative densities of the parameter ∆Ni areshown for each species in Fig. 3. They are equivalent tothe posterior distributions, assuming a uniform prior onthe ∆Ni.

Results and Discussion

Genetic diversity

Table 1 summarizes the results as sample size, mean allelicdiversity and observed heterozygosity (H) for each popu-lation. The total number of alleles per locus and the sizeranges are given in Table 2. We detected seven polymorphicloci from the ancestral samples of the Mauritius kestrel butonly three in the restored population. Comparable data forthe continental species (Table 1), shows polymorphism fora higher proportion of loci.

There is an effect of sample size, most noticeable in theestimates of mean allele number from those species rep-resented by a single individual. Figure 2(a) deals with this

Fig. 2 (a) Heterozygosity estimates for eachpopulation. Dark-shaded curves are themainland kestrel populations; from left toright, Madagascan, Kenyan, Greater, CanaryIslands, European, South African, Lesserkestrel. The white curve is for the Seychellespopulation. (b) Heterozygosity estimatesfor each locus (mainland populations only).

F 11 4Ne µ+-----------------------=

NN

µN µ


598 R . A . N I C H O L S , M . W. B R U F O R D and J . J . G R O O M B R I D G E


bias by estimating the underlying genetic diversity in thespecies rather than that of the samples. The mode (peak) ofeach curve is a maximum likelihood estimate. The esti-mates from Mauritius and the Seychelles are clearly lowerthan the continental species. The differences are significantusing Edwards’ (1972) support limits test (the estimates fortwo species are considered different if there is no single hetero-zygosity value at which the heights of both curves are withintwo loge likelihood units of their peaks). The continentalspecies provide broadly similar estimates with overlappinglikelihood curves despite their very different populationsizes. This result was unexpected, as larger populations areexpected to carry greater heterozygosity at equilibrium.

The locus-specific curves, in Fig. 2(b), indicate that twoloci have significantly higher heterozygosities than most ofthe others, suggesting higher mutation rates. This resultdemonstrates a violation of one of the assumptions that

went into the construction of the species curves in Fig. 2(a):that the mutation rates are equal. This finding was themain reason for using the MCMC method to assess thevalidity of the initial conclusions.

The estimates of ∆Ne obtained from the MCMC methodare shown in Fig. 3 for the k-alleles model (the results forthe infinite-alleles model are essentially indistinguishable).As reported by Groombridge et al. (2000), the genetic datashow a markedly lower effective size in the restored popula-tion, consistent with the historical record of a severe bottle-neck, and evidence of a similar event on the Seychelles.More important, from the point of view of this paper, is therelative size of the ancestral Mauritius and continentalpopulations.

The continental species have Ne estimates only 10 timeslarger than the ancestral Mauritius kestrel (note the scale ofFig. 3 is in natural logarithms). Theoretical descriptions of

Fig. 3 Markov chain Monte Carlo estimatesof ∆Ne: the deviation in Log(Ne) from thepopulation average. The curves for eachspecies are in the same sequence as in Fig. 2except that those based on the small samplesfrom Madagascar and Kenya have beenexcluded. The results shown here werecalculated using the likelihood function forthe k-alleles model.

Table 1 Summary of genetic diversity in each sample

Mauritius Ancestral Seychelles Madagascar SA Rock European Kenyan Canary Is. Greater Lesser

Sample number n = 75 n = 26 n = 4 n = 1 n = 10 n = 10 n = 1 n = 8 n = 10 n = 8Loci polymorphic 3 7 3 4 11 12 6 12 9 11Mean no. alleles 1.41 3.10 1.25 1.33 5.00 5.50 1.50 4.41 4.50 5.41Observed heterozygosity 0.099 0.231 0.062 0.333 0.525 0.608 0.500 0.583 0.400 0.614No. unique alleles — 3 2 0 8 7 1 2 12 17

Table 2 Allelic diversity and size range of each microsatellite locus

Locus 5 13 31 46–1 79–1 82–2 86–2 89 92–1 107 Fu1 Fu2

Alleles 9 7 9 13 7 6 8 7 17 27 10 31Size* 94–118 91–111 124–144 115–137 132–142 126–138 132–146 119–131 100–138 187–291 96–140 168–360

*allele size as total PCR amplified fragment.




populations at equilibrium suggest that Ne is proportionalto the total species population size (see eqn 3 below) atequilibrium. This relationship is not seen with current areaof the species range given in Table 3, which are up to threeorders of magnitude larger. These areas only give a roughguide to the expected Ne at equilibrium as the species’ bio-logy and distributions differ in several ways. For example,the nesting pattern varies from regular spacing in theGreater Kestrel (Falco rupicoloides) to colonial nesting in theLesser Kestrel (F. naumanni). Nevertheless, the EuropeanKestrel’s range is nearly two orders of magnitude largerthan the Greater Kestrel’s and, additionally, estimates of itsdensity are 10 times higher (2 vs. 0.2 per km2; Kemp 1978;Village 1990). It does not seem possible to explain the sim-ilarity of the Ne estimates in terms of the current populationsize and distribution.

The calculations of ∆Ne involved some assumptions. Forexample, there was an implicit uniform prior probabilityfor each species’ ∆Nj, that the loci have the same mutationrate in each species, the mutation model and that theinformation from different loci and species is independent(conditional on the values of the population sizes andmutation rates). The most questionable of these is themutation model, as the mutation process for microsatel-lites is not exactly known. The broad picture of a 10-folddifference seems robust, however. For example, anothercalculation is to substitute the maximum likelihoodestimates for heterozygosity from Fig. 2 into the stand-ard expressions for the mutation parameter θ (θ = 4Neµ).(1 − H) = (1 + θ)–1 for the infinite alleles model or (1 + 2θ)–0.5

for the ladder model (a stepwise mutation model, Kimura1983). Under the assumption of equal mutation rates, theratio of θ values between species will be the ratio of Nevalues. The ratio between median continental values andancestral Mauritius is approximately 14 for the laddermodel and eight for the infinite-alleles model, correspond-ing closely with our estimate of 10.

There are two aspects of the results that call for explana-tion: the small difference in Ne estimates between Mauritiusand the continental species and the even smaller differ-ences between the continental species. Is the amount of

genetic variation observed in the ancestral Mauritiussamples unusually high? If we substitute a mutation ratefor dinucleotide repeats of 2 × 10–4 (Cavalli-Sforza 1998)into the expression for heterozygosity we obtain an Neof around 430. In many wild species the population sizeis around 10 times the Ne (Frankham 1995), so this wouldcorrespond to a population of over 4000. In the mostpopulated areas today, the density is around one pairper square kilometre, so this would require the whole1865 km2 of the island to be populated at peak density;which seems unlikely, especially over extended periods.The mutation rate was estimated for human dinucleotideloci and so this absolute population size estimate mustbe treated with caution. Rates are known to vary betweenspecies and even alleles at the same locus (Jin et al. 1996).When it comes to the continental species, however, thereare clear discrepancies between Ne estimates and currentpopulation size.

Such discrepancies can arise if the population is sub-divided, or prone to extinction of local demes, or has notreached equilibrium between genetic drift and mutation.In the following section we show how many of the existingtheoretical results describing these effects can be capturedin terms of three rates which describe the branching of thegene genealogy. We find that this approach helps us applyour knowledge of the species ecology to interpret thegenetic patterns we have observed in the kestrel data.

Characterizing gene genealogies in subdivided populations

Figure 4 illustrates the island model of population sub-division. We can characterize the effects of subdivision byconsidering the events that occur as we trace the genealogyof a pair of genes back through time. The pattern is specifiedby three rates: the rate at which lineages from the samedeme coalesce (a), or are separated by a migration event (b)and the rate at which lineages from different demes arrivein the same deme (c).

Table 3 Geographic range of each population (km2)*

Lesser Kestrel 25 000 000Greater Kestrel 500 000European Kestrel 42 000 000Kenyan Kestrel 8 000 000South African Rock Kestrel 4 000 000Canary Islands Kestrel 91 000Madagascar Kestrel 600 000Mauritius Kestrel 1 865Seychelles Kestrel 288

*Data from Village (1990).

Fig. 4 The three rates that characterize the genealogical structureof a finite island model. The population is composed of D demesand N diploid individuals. Each individual migrates withprobability m per generation. For simplicity the expressions forrates have excluded multiple events in one generation.




Because genes from the same deme have a higher prob-ability of sharing a common ancestor than those fromdifferent demes, there will be genetic differentiation betweenthe demes. The magnitude of the differentiation is deter-mined by the relative probability, Φ, that two genes fromthe same deme can trace their ancestry directly back to acommon ancestor in that deme. This probability is deter-mined by the relative size of a and b. Simply substituting inthe expressions from Fig. 4 gives an expression for Φ interms of deme size and migration rate:

. (2)

The parameter Φ can be thought of as the value estim-ated by the familiar statistic FST. Wright (1969) showsthat, at migration-drift equilibrium, FST estimates theright-hand term if the mutation rate is low and the numberof islands high.

For the purposes of explaining the kestrel data, we areinterested in explaining the effective size of the differentspecies. This can be thought of as the idealized panmicticpopulation that would retain the same amount of geneticdiversity. We can use the parameter Φ to quantify theeffect of subdivision on the effective size, Ne. In the canon-ical panmictic population, the loss of genetic diversity is

characterized by the coalescence rate, , for of a pair of

genes. In the subdivided population coalescence betweengenes within demes is rapid, and so the longer-term effectsare dominated by the coalescence rate for two lineages indifferent demes. The coalescence rate is approximatelygiven by the rate at which they trace back to the same deme,multiplied by the probability that they then coalesce: cΦ.We can, therefore, obtain an expression for Ne by sub-stituting the values of a, b and c given in Fig. 4 into

(3)

This expression was obtained by Wakeley (1999), by adifferent route. We find it helpful to formulate it in terms a,b and c because we can use our ecological knowledge ofkestrels to evaluate these rates in less idealized situations,and also reason about the approach to equilibrium whenpopulation structure is disrupted (below). The arrangementin eqn 3 emphasizes that Ne increases with populationsubdivision (i.e. reduced m), and is equivalent to a resultfound by Wright: Ne = ND/(1-FST). Could the unexpectedlyhigh genetic diversity of the ancestral kestrel population beexplained by population subdivision?

Whitlock & Barton (1997) are doubtful about the effective-ness of subdivision in promoting diversity. They examinedmore general models of metapopulation structure; extendingthe simple island model to quantify the effects of variation

in deme size, deme extinction and recolonization. Theyconclude Ne will commonly decrease with populationstructure rather than increase as implied by eqn 3. Theirresults can be understood by looking at the implications ofmore realistic population structure on the rate cΦ.

Extinction and recolonization can be introduced usingan approach proposed by Slatkin (1977). Briefly, a propor-tion, e, of demes go extinct each generation leaving D′extant demes. The empty demes are recolonized by kdiploid founders and instantaneously grow up to full size.The founders can be specified to be from the same or differ-ent source demes, or some combination. Migration anddrift occur as before. The rates a, b and c can be recalculatedfor this model. For example, in the case where foundersare drawn at random from all extant demes

The expression for a is composed of two parts, the normalcoalescent rate if the deme did not experience an extinctionlast generation, or the higher rate (1/2k) if it did and therebyexperienced a bottleneck of size k. Similarly the rate atwhich one of a pair of lineages traces back to a differentdeme is the normal expression for migration (2m) plus therate at which they trace back to different demes throughan extinction event. Finally, at rate c lineages in differentdemes can trace back to the same deme either throughmigration or extinction events.

Substituting these expressions into eqn 2 and eqn 3 givesclose approximations to the curves produced by Pannell &Charlesworth (1999) who investigated the effect of extinc-tion on Fst and Ne in this model (one difference seems to bedue to our assumption of diploid recolonization). Increas-ing the extinction rate can either increase or decrease Fst(depending on k) and yet decrease Ne substantially in thiscase because of the increase in c. Although Ne is readilyreduced below the value for an idealized panmictic popu-lation, this is not to say that population subdivision reducesNe. The opposite is arguably the case: Ne is a decreasingfunction of migration so, if the population dynamics areunaltered, increased isolation increases Ne.

Whitlock & Barton (1997) found a similar reduction of Nein a model where demes vary in their contribution to futuregenerations. In that case c is inflated by a term proportionalto the variance. The rate is higher because there is a greaterchance that migrants and colonists trace back to the samedeme as they are more likely to both be descendants of oneof the demes with higher productivity. It remains the casethat reduced migration increases Ne. The converse is,however, found in some cases where migration changes

φ aa b+---------- 1

1 4Nm+--------------------= =

12Ne---------

12Ne--------- cφ;=

⇒ Ne ND 1 14Nm------------+

.=

a 1 e–2N---------- e

2k----- ,+≈

b 2m (1 2m– )e 2k 2–2k 1–--------------

D′ 1–D′

-------------- ,+≈

c 1 (1 e– )(1 m)–[ ] 2–D′

----------------------------------------------.≈




the population dynamics. They give a combination ofparameters for population growth rate and carrying capa-city for which increased migration increases the census sizeof the population, because more demes are extant, anddecreases the variance (in the contribution of each deme)by causing their sizes to fluctuate in synchrony. Both effectscontribute to increasing Ne with increased m. In theory,then, population subdivision could either increase ordecrease effective population size. In practice, the outcomewill depend on a species population dynamics.

Interpretation of kestrel data

These theoretical results help interpret the unexpectedlyhigh ancestral genetic diversity in the Mauritius kestrelpopulation. We have ecological data that suggests popu-lation subdivision. The Mauritius kestrel shows poor dispersal,even across suitable habitat ( Jones et al. 1995). Long-termringing studies have not detected mixing between thethree current populations on Mauritius (Fig. 1). The theorysuggests that subdivision is unlikely to have increased Neabove the census size, but it could have helped sustainmore genetic diversity than in a comparable undividedpopulation. On the contrary, reduced diversity would beexpected if subdivision affected the population dynamicsby reducing the total number of kestrels or increasing thevariability in success of demes. These effects appear unlikelyin the case of the kestrel’s ecology: in the re-establishedpopulations (which are limited in size and isolated)population density appears strongly regulated by theavailability of nest-sites and territories.

The difference between the island and continental spe-cies may reflect the time it takes for the pattern of geneticdiversity to reach equilibrium. In the case of differentiationamong demes, the equilibrium is between coalescence andmovement between demes. These occur at rates a and bso the expected time for one or other to occur is (a + b)–1

generations. In an island model this will be of the order ofdeme size, and Slatkin & Barton (1989) show that FSTreaches equilibrium over this time for a variety of popula-tion structures. Similarly heterozygosity is determined bythe balance between mutation, occurring at rate ≈2µ, andcoalescence between lineages in different demes, at rate≈cΦ. Equilibrium is therefore attained in roughly (cΦ + 2µ)–1

generations, which will be of the order of 2Ne.For the island species we have estimated this to be a few

hundred generations, a period over which the populationstructure may have been relatively constant. The continentalspecies have much larger populations that are unlikely tohave reached equilibrium since the perturbations intro-duced by the climatic fluctuations associated with the iceages. The species range will have changed dramatically,with retreats into refugia and subsequent expansions. Theexample of the Mauritius species suggests that small refugial

populations are capable of sustaining considerable vari-ation. Dramatic loss of variation can, however, occur duringrange expansion (Nichols & Hewitt 1994; Ibrahim et al.1996; Hewitt 1999), especially if the expansion involves longdistance migrants into virgin territory. In that case, a fewfar-dispersing individuals can establish a population thatwill expand to cover a large area in the virgin territory. Asmall number of founders or slow growth rate can leadto genetic impoverishment: Nichols & Beaumont (1996)found that a population with k founders growing at rate runder a rain of M migrants per generation has inbreed-ing coefficient ≈(1 + r)/(1 + kr + 4M). If subsequent rangeexpansion is from such impoverished populations, geneticvariation will be rapidly lost. Genetic diversity will re-establish at a rate limited by mutation. The similar geneticdiversities for the continental kestrel populations with verydifferent current sizes can be explained by a comparablepostglacial history from which they have yet to recover.

The trends that are found in these kestrel species appearto be part of a broader tendency. Hewitt (1999) reviewedDNA sequence evidence from a range of European plantand animal species that had glacial refugia in southernpeninsulas. He suggests that genetic variation can persistover several ice ages in the refugia. Rather than beingvulnerable to range compression, genetic diversity seemsto be lost during expansion into northern latitudes. Thepersistence of diversity in refugia may be due, in part,to the ability of populations to track suitable habitat bymoving up and down in mountainous regions as theclimate fluctuates. The mountainous topography will alsolead to population subdivision, which can play a part insustaining diversity. This proposal might be verified bymolecular phylogenetic surveys within refugial regions,which could provide evidence of ancient but local geo-graphical differentiation.

Acknowledgements

Primers were kindly provided by David Parkin, John Wetton(University of Nottingham) and Marit Nesje (Norwegian Schoolof Veterinary Science, Norway). Access to museum samples waskindly provided by the British Museum of Natural History(Robert Prys-Jones), Cambridge University Museum of Zoology(Adrian Friday and Mike Brookes), Museum Nationale D’HistoireNaturelle, Paris, Museum D’Histoire Naturelle, Geneva, Switzer-land, Mauritius Institute, Mauritius, and Naturhistorisches MuseumWien (Vienna), Austria. Anthony van Zyl, Welcome Glen, SouthAfrica collected most of the mainland kestrel population samples.Funding: Durrell Wildlife Conservation Trust, Jersey; Institute ofZoology, London; Mauritius Wildlife Foundation (Dr Carl Jones);and The Peregrine Fund, USA.

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Molecular Ecology (2001) 10, 593 – 602