Measuring Recruitment in an Invasive Species to Determine Eradication Potential

Management and Conservation Article

Measuring Recruitment in an InvasiveSpecies to DetermineEradication Potential

OLIVER BERRY,1 Invasive Animals Co-operative Research Centre, School of Animal Biology (M092), The University of Western Australia, Crawley, WA6009, Australia

ROGER KIRKWOOD, Research Department, Phillip Island Nature Parks, P.O. Box 97, Cowes, VIC 3922, Australia

ABSTRACT Optimal management of invasive pests can benefit from quantitative measures of rates of recruitment, and particularly,

relative contributions of immigration and reproduction. However, these vital rates are difficult to estimate by trapping or observation. Recent

studies have demonstrated that analyses with DNA markers may provide detailed information on the origin of immigrants into pest

populations, but these studies have not provided comparable data on reproductive rates. We integrated genetic and demographic information

from a unique longitudinal data set to comprehensively quantify recruitment during the past 15 years into an island population of red foxes

(Vulpes vulpes) and to reveal relative contributions of immigration and reproduction. This population established 100 years ago and persists

despite several decades of management aimed at population suppression. Primary source of recruits on the island was in situ reproduction

(.95%/annum), although the number of foxes reproducing was small relative to the total number present. Immigration occurred at rates up to

3.6%/annum and was primarily by dispersing males, but is unlikely to be demographically important. We also show that although fox control

effectively reduced fox density, there was evidence that control did not reduce the net number of recruits, most likely because the population

exhibited a density-dependent release from reproductive suppression. Our results imply that fox control on Phillip Island should primarily focus

on reducing on-island abundance and reproduction, but eradication will not be sustained unless immigration ceases.

KEY WORDS eradication, immigration, invasive species, microsatellite, recruitment, reproductive rate, Vulpes vulpes.

Biological invasions can lead to profound ecological changeand large economic costs (Simberloff 2003, McLeod 2004).Island ecosystems are particularly susceptible to invasivespecies and are often a focus for control of pests because oftheir high biodiversity value and because their insular naturecan present unique opportunities for sustained removal ofpests (Atkinson 1989, Courchamp et al. 2003). Recenteradication programs for species such as rats, rabbits, andcats on islands have achieved some remarkable successes(Towns and Broome 2003, Clout and Russell 2007).

Control of invasive pests itself is costly and efforts areongoing to improve efficiencies of these operations(Courchamp et al. 2003). Fundamental to efficient controlof invasive species is an understanding of the biologicalprocesses that underpin persistence and spread of thosespecies (Byers et al. 2002). For invasive species on islands, akey requirement of eradication programs is an understand-ing of the ability of pests to recolonize via immigration orfor the population to repopulate via reproduction fromresidual individuals (Russell et al. 2005, Clout and Russell2007). Regrettably, quantitative measures of recruitmentand other vital rates are difficult to estimate for elusiveinvasive species (Saunders et al. 1995).

Recent DNA-based approaches to identifying immigrantsand their origins have brought major advances in invasivepest management on islands (Robertson and Gemmell 2004,Abdelkrim et al. 2005). However, DNA methodologies alsooffer opportunities to simultaneously estimate reproductiverates for insular populations of invasive species throughidentification of groups of kin using parentage analysis

(Marshall et al. 1998) or by kin-partitioning algorithms(Konovalov et al. 2004). A further potential application ofDNA analyses is to use changes in genetic effectivepopulation size, which can be readily estimated, to indexchanges in population density, which is not readilyestimated (Hauser et al. 2002, Hutchinson et al. 2003).These analyses have rarely been exploited for invasive pests.

The red fox (Vulpes vulpes) is native to Europe, Asia,North America, and North Africa and is a major invasivepest in Australia (Saunders et al. 1995). It is secretive, highlymobile, and ecologically adaptable, making it both difficultto control and difficult to monitor. Since its deliberateintroduction to Australia in the 1870s, the fox has beeninstrumental in numerous faunal declines and extinctionsand is estimated to cost $228 million (Australian currency)annually in both biodiversity and agricultural losses (Rolls1969, Saunders et al. 1995, McLeod 2004).

Considerable effort and resources are expended on foxcontrol in Australia each year. However, sustained eradica-tion of foxes has only been achieved in some specialsituations where recruitment from surrounding areas couldbe eliminated by extensive fencing (Morris et al. 2004,Moseby and Read 2005). Foxes also inhabit offshore islandsin Australia. Phillip Island, an approximately 100-km2

island 500 m from the mainland in Victoria, southeasternAustralia, was colonized by foxes in around 1907 (Gliddon1977). Introduced foxes prey on livestock and native faunaand have had a major impact on breeding colonies of littlepenguins (Eudyptula minor), which have been reduced from10 colonies to 1, largely due to fox predation (Dann 1992).The remaining penguin colony is a major tourist destina-tion, receiving 500,000 visitors annually and generating an

The Journal of Wildlife Management wild-74-08-20.3d 21/9/10 16:13:44 1661 Cust # 2009-482R

1 E-mail: [email protected]

Journal of Wildlife Management 74(8):1661–1670; 2010; DOI: 10.2193/2009-482

Berry and Kirkwood N Measuring Recruitment in an Invasive Species 1661

estimated $96 million (Australian currency) annually indirect and indirect revenue to the Victorian economy(KPMG Management Consulting Pty Ltd 1996).

Foxes on Phillip Island have been subjected to controlsince the 1930s. Effort and efficacy of control procedureshave fluctuated but have generally increased over time.Despite ongoing control, foxes persist and continue toadversely impact wildlife and livestock. It is unclear whetherthe fox population on Phillip Island represents thedescendents of one founding event, or whether immigrationis ongoing (Lade et al. 1996). Further, if immigration isongoing, it is unclear whether it makes a significantcontribution to population recruitment on the island. Wesought to address these questions.

The natural isolation and high biodiversity and ecotourismvalue of Phillip Island make it an excellent candidate foreradication of foxes (Bomford and O’Brien 1995), andplanning for this process is now underway (McPhee andBloomfield 2004). We made use of combined ecological andgenetic data sets collected over a 15-year period todetermine the relative contribution of reproduction andimmigration to recruitment into the population of foxes onPhillip Island. In addition, to index fox abundance on theisland and measure the success of fox control, we estimatedthe effective population size of foxes and monitored itschange through time and in response to increased controleffort.

STUDY AREA

Phillip Island (38.48uS, 145.27uE) is characterized by mild towarm summers (average max. 23.7u C) and cool winters(average max. 13.7u C). Annual rainfall was 764 mm (Bureauof Meteorology 2009). Land use was divided between holidayand permanent accommodation, pastoral land uses (predom-inantly sheep farming), and nature conservation (approx. 20%by area). Phillip Island was connected to the mainland by apermanently open bridge (Fig. 1).

METHODS

We collected tissue samples from Phillip Island foxes (n 5

480) that were road-killed or culled as part of a controlprogram (involving spot-lighting, soft-jaw and treadle-snaring, battues with dogs, baiting, and den fumigation)between 1994 and 2008, and we stored samples in 100%ethanol. In addition, we collected samples opportunisticallyfrom foxes on the adjacent mainland in 2007 and 2008 (n 5

28). We collected mainland samples from within 20 km ofthe bridge to Phillip Island (the island is 20 km long;Fig. 1). We extracted DNA using the 96-well silica-basedDNA extraction method described by Ivanova et al. (2006).We diluted DNA extracts 1:3 for use in polymerase chainreactions (PCR).

We collected detailed biological information (age, size,gender, stomach contents, and reproductive status) from allfox carcasses collected on Phillip Island between 1994 and2008. We estimated age in completed years from annualgrowth layers in cementum of canine and premolar teeth(Harris 1978, Grue and Jensen 1979, Coman 1988). We

extracted, sectioned, and stained teeth and counted annualgrowth layers following methods of Johnston and Watt(1980). We assumed 1 October was the birth date of allfoxes in each year, because 1 October approximates themidpoint of a 6-week period when cubs are born (based onobservations of ad denning behavior and sizes of cubssighted (R. Kirkwood, Phillip Island Nature Parks,unpublished data).

Assuming the resident fox population to be closed, wederived several estimates of population parameters. Firstly,we calculated the minimum number of foxes present in eachyear. We assumed, for instance, that a fox killed as a 4-year-old in 2000 must have been present in all years from 1996.Then we estimated minimum numbers of litters each year.Fox litters may contain up to 8 cubs but tend to average 4–5cubs at birth with

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1 cub succumbing in the den, leaving 3–4 cubs on emergence (Lloyd 1980). Hence, we estimatedlitter numbers by dividing the number of cubs born in theyear (a min. figure) by 3 or 4.

Next, we estimated maximum harvest rates. To arrestgrowth in red fox populations after a reduction has beenachieved,

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65% of the population has to be killed annually(Hone 1999). Therefore, harvest rates provide a usefulmeasure of efficacy of control. We derived estimates ofmaximum harvest rates from the number of foxes killed in ayear and the number known to be alive in that year.Estimated rates from later years became meaningless andapproached 100% because there was no opportunity toharvest foxes born in the latter years of the study. Age datarevealed that ,10% of foxes were killed after 3 years of age;therefore, estimates of harvest rates should be reasonable up


Figure 1. A map of Phillip Island, Victoria, Australia, where the residentred fox (Vulpes vulpes) population was sampled for genetic analysis between1994 and 2008. Arrow in lower panel indicates the position of the 500-mbridge between mainland and island. Grayed area indicates the location ofmost penguin breeding sites.

1662 The Journal of Wildlife Management N 74(8)

to the last 3 years of the study (i.e., up to 2006). Finally,from the age data we derived annual ratios of first-year toolder foxes. Once a fox population drops below carryingcapacity, many mature individuals (rather than just domi-nants) may breed and also litter sizes may increase (Iossa etal. 2009); therefore, the ratio in the population of first-yearto older foxes should also increase. Thus, monitoring ratiosof first-year to older foxes provide a further measure ofefficacy of control.

DNA AnalysisWe amplified a panel of 34 microsatellite DNA markers byPCR from the samples. In total, 10 multiplexed PCRreactions were required, enabling fragment analysis of allmarkers in 2 capillary lanes (Table 1). We conducted 10-mLPCR reactions consisting of 5 mL of Qiagen PCR MultiplexSupermix (Qiagen, Hilden, Germany), 2 mL of DNA,primers (Table 1), and ultrapure water. Forward primersconsisted of 1/10 fluorescently labeled and 9/10 unlabeledoligonucleotides, which facilitated fragment analysis with-

out the usual requirement to dilute PCR products.Polymerase chain reaction conditions were as follows: 95uC for 15 minutes; followed by 35 cycles of 94u C for30 seconds, Tannealing for 90 seconds, and 72u C for60 seconds; and finally 60u C for 30 minutes. For PCRmultiplexes D and H, Tannealing was 56u C; for all othermultiplexes it was 58u C (Table 1). We conducted fragmentanalysis with GENEMARKER 1.60 software (Softgenetics,State College, PA) and we visually rechecked all genotypes.

We used Program FSTAT (Goudet 1995) to test fordepartures from Hardy–Weinberg equilibria at each locus ineach year and overall, and to check for departures fromgametic disequilibrium within year. We also used FSTATto estimate mean expected and observed heterozygosity andaverage numbers of alleles for each year and to calculate Fst

(h; Weir and Cockerham 1984) between years and betweenmainland and island foxes. We also calculated probability of2 unrelated or full-sibling individuals sharing identicalgenotypes according to the PID(HW) and PID(sib) formulas,respectively (Waits et al. 2001).


Table 1. Details of canid microsatellites amplified from red fox samples collected on Phillip Island, Victoria, Australia (1994–2008).

Locus Multiplexa Labelb Lanec Primer conc. (mM)d Nae Size range Hexp

e Referencef

Ren149M14 A 6Fam 1 0.3 4 353–393 0.015 1Wanv374 A Ned 1 0.1 6 101–113 0.596 7Ren186N13 A Pet 1 0.3 3 137–166 0.478 1FH2164 A Pet 1 0.3 17 196–324 0.549 2Bac373-I19 B Vic 1 0.1 3 156–162 0.004 2Ren01G01 B Vic 1 0.4 5 232–245 0.211 4FH3834 B Ned 1 0.3 6 227–283 0.213 2C01.251 C 6Fam 1 0.1 4 128–134 0.224 1FH2452 C 6Fam 1 0.2 4 180–192 0.088 2Ren 94K C 6Fam 1 0.2 5 238–270 0.241 1FH2834 C 6Fam 1 0.2 4 268–273 0.614 2CPH2 C Vic 1 0.3 3 93–97 0.375 3FH3767 C Ned 1 0.25 6 387–395 0.216 2Ren05D05 D Ned 1 0.3 8 258–390 0.464 4CM5.41 D Pet 1 0.2 8 187–237 0.576 5FH3355 D Pet 1 0.1 7 351–415 0.027 2FH3310 L1 6Fam 1 0.2 5 377–397 0.367 2Fh3969 L1 Vic 1 0.2 5 343–425 0.587 2Ren135K06 E 6Fam 2 0.2 4 152–163 0.281 1FH2168 E 6Fam 2 0.2 5 215–228 0.608 2WanV142 E Vic 2 0.2 5 132–148 0.650 7WanV502 E Ned 2 0.2 3 76–78 0.361 7Ren195B08 F Ned 2 0.1 4 130–149 0.382 1WanV402 F Pet 2 0.1 5 80–93 0.021 7CM8.23 F Pet 2 0.4 5 232–254 0.439 5FH3295 G Vic 2 0.1 9 276–320 0.696 2FH3413 G Vic 2 0.1 9 322–439 0.676 2FH2537 G Ned 2 0.2 9 162–209 0.673 2FH3820 G Pet 2 0.5 7 397–429 0.609 2LadeC213 H 6Fam 2 0.1 3 109–111 0.228 6FH3591 L2 6Fam 2 0.1 10 408–471 0.619 2FH3278 L2 Ned 2 0.1 8 300–360 0.546 2Ren47D L2 Ned 2 0.1 7 315–359 0.433 4Ren229C09 L2 Pet 2 0.1 5 320–330 0.270 1

a Multiplex refers to loci that we co-amplified in polymerase chain reactions.b Label refers to the fluorescent label we attached to the forward primer.c Lane refers to loci that we combined for fragment analysis.d Primer conc. refers to the final concentration of that primer in the PCR multiplex.e Na and Hexp refer to the no. of alleles and expected heterozygosity of loci for Phillip Island foxes.f References are as follows: 1 5 Breen et al. (2001), 2 5 Guyon et al. (2003), 3 5 Fredholm and Winterø (1995), 4 5 Jouquand et al. (2000), 5 5

Kukekova et al. (2004), 6 5 Ostrander et al. (1993), 7 5 Wandeler and Funk (2006).


Identification of ImmigrantsWe used 2 assignment approaches to identify immigrantindividuals. The first was a model-based clustering approachas implemented by Program STRUCTURE 2.1 (Pritchardet al. 2000), which paired the mainland sample (2007, 2008)with each of the years sampled on the island (1994–2008).This analysis assumed allele frequencies did not changesignificantly on the mainland, which is reasonable based onthe large population size of foxes on mainland Australia (seeresults of Ne estimation, and Lade et al. [1996]). ProgramSTRUCTURE settings were as follows: number of clusters(K) 5 2, burn-in 5 10,000 Markov chain Monte Carlo(MCMC) replicates, run length 5 50,000 MCMCreplicates, USEPOPINFO turned off (0), Admixture modelassumed, and allele frequencies uncorrelated. We ranconsecutive analyses with GENSBACK set to zero andthen to one generation, both with a migration prior of 0.01.We set all other model parameters to default values.

The second method to identify immigrants was thelikelihood approach implemented in Program GENE-CLASS 2 (Piry et al. 2004). Here, we used bothlikelihood-ratio tests as well as exclusion to identifyindividuals with genotypes highly atypical of their cohort.We used Rannala and Mountain’s (1997) method toestimate genotype likelihoods and the approach by Paetkauet al. (2004) to simulate genotypes for exclusion testing. Weincluded 10,000 simulated individuals to calculate exclusionprobabilities, with immigrants identified as those excludedfrom their cohort at P , 0.01 but not excluded from themainland. We also used GENECLASS to calculate the log-likelihood ratio between each individual’s cohort and themainland, and we compared this value (22log ratio) to thechi-square distribution with one degree of freedom.

Estimation of Number of Litters Born Each YearWe used the Descending Ratio (DR) method in ProgramKINGROUP (Konovalov et al. 2004) to partition individ-uals into kin groups that had the highest overall likelihood.We applied DR analysis separately to each cohort offoxes born between 1988 and 2008 (see Table S1, availableat ,http://dx.doi.org/10.2193/2009-842.s1.). In KIN-GROUP, we set the primary hypothesis to a groupconsisting of full siblings only and the null hypothesis tounrelated. These groups of kin approximated the number oflitters present in each year sample. Exclusion of half siblingsfrom the null hypothesis removes the ambiguity of assigningpaternal and maternal half siblings to litters, which wouldintroduce an upward and downward bias in the estimate ofthe number of litters, respectively. Determining relativestrengths of these biases is problematic without data onrelative frequencies of polygyny and polyandry in thispopulation, though we note that the most common matingstrategy in red foxes at low densities such as are observed onPhillip Island is monogamous pairs with low rates of extra-pair copulation (Zabel and Taggart 1989, Saunders et al.1995, Iossa et al. 2009).

Because the number of litters identified should depend onthe sample size for each cohort, and sample size varied

between 2 and 49 (x 5 21.9), we approximated the numberof litters born each year with a nonlinear regression ofsample size against the number of litters identified. Wemodeled the relationship with 4 asymptotic accumulationcurves, which we considered to be likely candidates to fit thedata: the hyperbolic, where y 5 (ax)/(b + x); the exponential,where y 5 {1 2 exp[2(bx)]}a; Metcherlich, where y 5 a +bexp2cx; and a curve described by Valiere (2002), where y 5

a 2 a[1 2 (1/a)]x. In all cases, a 5 the asymptote (no. oflitters), and b and c are slope constants. We derived 95%confidence limits for each estimate through bootstrapanalysis in SPSS version 16.0 (SPSS Inc., Chicago, IL).We also calculated Akaike’s Information Criterion scores(AICc) and weights for each model (Burnham and Anderson1998). We estimated mean annual number of fox litters bornon the island by model averaging.

Estimation of Effective Population SizeWe used both single-sample methods, based on gameticdisequilibrium (linkage) and temporal allele frequencychange (temporal), to estimate the effective population size(Ne) of foxes on Phillip Island. The variable Ne represents anidealized population size where all individuals have an equalprobability of reproducing. For linkage methods, we usedthe maximum-likelihood approach implemented in ProgramLDNE (Waples and Do 2008), wherein we assumed amonogamous breeding system and based the analysis onlyon alleles of frequency

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0.05. We also used the approxi-mate Bayesian computation method (Tallmon et al. 2004)implemented in Program ONeSAMP (Tallmon et al. 2008),wherein we specified that minimum and maximum Ne was 2and 300, respectively. We calculated these estimates for eachyear between 1994 and 2008. In addition, for years whenimmigrants were known to be present (2003 and 2007; seeResults), we also report Ne estimates with these individualsremoved.

We compared 6 temporal methods to estimate Ne. Thefirst was a likelihood-based method described by Berthier etal. (2002), which requires 2 samples separated in time andassumes discrete generations. We estimated generationlength to be 2.22 years from life tables constructed fromPhillip Island foxes over the past 15 years (R. Kirkwood,unpublished data). We ran the likelihood-based methodwith 3 generations collected between 1996 and 2003 and 5generations collected between 1996 and 2006. Fivegenerations (11 yr) was the largest interval for which wehad sufficient sample sizes (n . 35). We also ran analyseswith known immigrant foxes removed.

We derived the second estimate of Ne from the pseudo-likelihood method described by Wang (2001) and imple-mented in Program MLNE. We assumed the islandpopulation was isolated from the mainland. The thirdmethod was Waples’ moment-based Ne estimator asimplemented in Program NeEstimator (Peel et al. 2004).The fourth and fifth methods were Jorde and Ryman’sunbiased Ne estimator (Jorde and Ryman 2007) and Jordeand Ryman’s (1995) Ne estimator that accounts foroverlapping generations. The final method was a modifica-



tion of methods 5 and 6 as implemented in ProgramTempoFpairs (P. Jorde, University of Oslo, personalcommunication). This final method makes use of thecomplete data set by calculating an average value of Ne forall combinations of year intervals. Because estimates of Ne

that include intervals of ,1 generation will be biaseddownward when generations overlap (1- and 2-yr intervals),we applied corrections for the 1-year interval (Jorde andRyman 1995).

RESULTS

Age data collected since 1994 indicated that the PhillipIsland fox population comprised

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140 individuals duringthe late 1990s and probably ,100 during the early 2000s,when control intensity was higher (Table 2). Assumingadult foxes raised 3–4 cubs/litter to an age where cubsbecame vulnerable to control measures, we estimated annualnumber of litters during the late 1990s to be 14.1 (61.2 SE;4 cubs/litter) or 18.8 (61.6 SE; 3 cubs/litter). Rates ofharvest were ,60% of the minimum population estimate upto the early 2000s, and then rose and were sustained at.70% (Table 2). Ratios of first-year to older foxes weregenerally between 1 and 2 during 1994 to 2004, then .2after 2004 (Table 2).

Foxes on Phillip Island exhibited lower observed andexpected heterozygosities and numbers of alleles than themainland sample in all years (Table S1). Probability ofunrelated and full-sibling individual island foxes sharing

identical genotypes was on average ,0.05 after 6 and 11loci, respectively. No locus in any year exhibited a significantdeparture from Hardy–Weinberg expectations after correc-tion for multiple comparisons.

Foxes on Phillip Island were genetically differentiatedfrom those on the mainland. Mean Fst between mainlandfoxes in 2007–2008 and those on the island in all years whenn

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20 was 0.25 6 0.05 (SE; n 5 12 yr). In addition, therewas strong evidence of genetic drift on island foxes. The Fst

calculated between each yearly cohort of juveniles and thosefrom consecutive years showed a steady increase, so thatafter 14 years Fst between the 1994 and 2008 samples was0.1 (Fig. 2).

We identified 3 individuals as immigrants from themainland, with significant log-likelihood ratios (x2 .

3.814, df 5 1). All immigrants were males; 2 were takenin 2003 (one .1 yr old and one ,1 yr old) and one in 2007(,1 yr old). Each immigrant was excluded from its years’cohort but not from the mainland sample. These sameindividuals were identified by STRUCTURE analysis tohave posterior probabilities .0.99 of being from themainland population. An additional fox (.1-yr-old F from2006) had similar genotype-likelihood values for the islandand for the mainland. Program STRUCTURE analysisassigned this fox a 0.0 probability of being an immigrant but0.8 probability of having an immigrant parent (F1) and 0.2probability of being from Phillip Island. Another individual(a .1-yr-old F from 1995) had a 0.3 probability of having a


Table 2. Estimates of effective population size for foxes on Phillip Island, Victoria, Australia, calculated by gametic phase disequilibrium, and statistics forthe number of foxes inhabiting Phillip Island 1994–2009. Where immigrants were known to be present in the sample, we estimated with and without theirpresence (indicated byIM). We did not include field abundance data based on aging after 2007 in average values, because these numbers will be influenced byfoxes killed in the future.

Yr LDNea LDNe 95% CI ONeSAMPbONeSAMP 95%

credible limits

Estimate ofmin. fox

abundance(foxes killed)

Min. no.of littersc

Max. harvestrate (%)

Ratio of

M1-yr-old toolder foxes

1994 31.9 18.1–83.7 13.25 10.82–16.61 79 16 59 1.251995 9.9 7.8–12.4 13.93 11.51–18.08 105 23 67 1.781996 10.6 8.2–13.3 22.64 18.67–30.08 87 16 47 1.261997 18.5 14.6–23.3 28.53 23.00–27.85 142 31 58 1.931998 9.8 6.6–14.4 9.08 7.79–11.38 126 22 59 1.071999 115 21 56 1.192000 23.6 18.5–30.1 22.92 18.76–29.58 125 24 64 1.432001 16.2 12–21.4 17.15 14.20–21.84 79 11 72 0.732002 15.5 10.9–21.6 17.88 15.38–22.18 78 18 71 2.362003 21.4 17.9–25.7 15.97 13.48–19.93 66 13 67 1.572003IM 22.2 16.3–30.4 21.27 17.77–27.082004 26.8 17.5–42.5 24.33 20.0–31.90 57 11 65 1.482005 30.1 20.5–45.0 23.5 19.8–29.3 88 21 74 2.892006 20.1 14.5–27.7 16.06 13.6–19.8 78 18 79 2.132007 22.4 17.0–28.6 19.62 16.3–25.32007IM 19.8 14.8–26.9 25.07 21.2–31.82008 14.2 9.5–21.9 13.20 11.34–16.6420091994–2008

average 19.23 19.02 94 18.8 64 1.621994–2008

SE 1.91 1.33 7 1.57 2 0.16Mainland infinite infinite

a Linkage Disequilibrium method of Waples (1989).b Approximate Bayesian Computation method of Tallmon et al. (2008).c Min. no. of litters assumes litter size of 3.


migrant parent, but its log-likelihood ratio was notsignificant and we could not exclude it from its year cohort.All other individuals had posterior probabilities .0.99 fromtheir sampled population or year.

Descending Ratio analysis consistently partitioned indi-viduals from each birth cohort into groups of full siblings(i.e., litters). Plotting sample size against the number oflitters in each cohort revealed a trend toward an asymptote(Fig. 3). All nonlinear regression models fit the data welland estimates of the asymptote varied between 14.9 and 21.3with 95% confidence limits ranging between 13.0 and 25.4(Table 3). Therefore, we applied model-averaging based onAICc weight values, which provided an asymptote estimateof 18.1 litters/year.

There was a high level of consistency between estimates ofNe derived by the different analytical methods (Tables 2, 4).Annual estimates based on gametic disequilibria variedbetween 9.1 and 31.9 (x LDNe 5 19.23 6 1.91 SE, x

ONeSAMP 5 19.02 6 1.33, although CIs for the LDNEmethod were larger than the credible limits estimated withONeSAMP). Methods based on temporal change in allelefrequencies were of similar magnitude, especially when weremoved the 3 migrant individuals from the analysis andwhen we calculated the estimate over 5 generations(Table 4).

DISCUSSION

We took a multidisciplinary approach to quantifying thesources of recruitment in one of Australia’s most significant

invasive pests and found that most recruitment into the foxpopulation on Phillip Island resulted from local reproduc-tion, with only a minor component contributed byimmigration from the nearby mainland. Our results indicatethat fox eradication programs should prioritize reducing theon-island source of recruits ahead of immigration and thateradication will not be sustained unless external sources ofrecruits are also excluded. As far as we are aware, ours is thefirst study to use DNA markers to simultaneouslycharacterize all components of recruitment.

Prior to our study it was unclear whether the foxpopulation on Phillip Island represented the descendentsof one founding event in 1907 or recurrent low-levelimmigration from the mainland (Lade et al. 1996). Bothscenarios predict that random genetic drift on the island willproduce strong genetic differentiation between mainlandand island and lower genetic diversity on the island relativeto the mainland. We found evidence of both of thesescenarios in our data, confirming that, at the very least, foximmigration to Phillip Island is restricted and thepopulation is small. However, the single versus recurrentinvasion scenarios have distinct implications for manage-ment of island foxes, with potentially large financialconsequences. Specifically, recurrent immigration wouldmake the task of maintaining a fox-free island sanctuarymore difficult (McPhee and Bloomfield 2004).

Development of individual-based approaches to identifi-cation of immigrants (Paetkau et al. 1995, Pritchard et al.


Figure 2. Genetic drift in the red fox population on Philip Island,Victoria, Australia, between 1994 and 2008 as demonstrated by increase ingenetic subdivision (Fst) between birth cohorts as the time interval betweensamples increases (yr). Each line and symbol combination represents thechange in Fst between samples from an initial year and samples fromsubsequent years.

Figure 3. Relationship between sample size and number of red fox littersidentified by Descending Ratio analysis (points) and also showing the fit ofthe 2-parameter hyperbola model. Litters were identified for foxes born onPhillip Island, Victoria, Australia, between 1988 and 2008.

Table 3. Estimates of the asymptote (a) for the approximate number of red fox litters born/year on Phillip Island, Victoria, Australia (1988–2008).

Model Asymptote (a) Lower 95% CI Upper 95% CI R2 AICca AICc wt

2-parameter hyperbola 21.292 17.135 25.448 0.908 24.17 0.358Metcherlich 16.919 13.332 24.077 0.906 28.17 0.048Negative exponential 15.917 13.285 18.549 0.901 25.75 0.163Valiere 14.946 13.044 16.848 0.895 23.80 0.431

a AICc 5 Akaike’s Information Criterion corrected for small sample size.


2000) enabled us to distinguish these scenarios byquantitatively estimating the immigration rate and identi-fying its temporal character. Whereas most foxes in mostyears were evidently not immigrants from the mainland, weidentified 3 immigrant male foxes and 1 female offspringfrom an immigrant–island fox pairing. Considering thenumber of microsatellite markers we employed and the highaccuracy of assignment tests associated with Fst values weobserved (Manel et al. 2002, Berry et al. 2004), our resultsare robust and we may safely conclude that the Phillip Islandfox population is not completely isolated from the largemainland population.

An ensuing question is whether immigrants make asignificant demographic contribution to recruitment on theisland. Reproductively we found little evidence of acontribution because only a single island–mainland F1 wasidentified. Moreover, as a proportion of the foxes sampledover the 15-year period, the migrants we identifiedcorrespond to an immigration rate of 0.2 individuals/year,or 0.27 if we include the parent of the F1 immigrant.Considering an estimated 18 litters were born on the islandeach year (Table 2), immigrants can contribute a moderateproportion of recruits into the population in some years. Forexample, the 2 foxes detected in 2003 represented 3.6% ofcubs from that year (assuming 56 cubs emerged: 18 litters of3 cubs on the island plus the 2 immigrants). Nevertheless, interms of the impact of this rate of recruitment on the vitalrates of the island fox population, the demographic effects ofimmigration are probably minor (Hastings 1993).

The greater significance of recurrent immigration to theisland is the high likelihood that the population would berefounded once island foxes are eradicated. Considering thelikely high cost of an eradication program (McPhee andBloomfield 2004), guarding against reinvasion must form apart of an ongoing management strategy for Phillip Island.We demonstrated that genetic assessments of the prove-nance of any foxes taken on the island after the eradicationprogram has commenced will provide accurate informationon effectiveness of both the on-island eradication effort andmeasures taken to eliminate immigration.

According to harvest-based estimates, minimum foxabundance on Phillip Island varies between approximately80 and 140 individuals, comprising 15 to 30 breeding pairs

producing 50 to 100 cubs annually (Table 2). Encourag-ingly, this estimate of the breeding population sizedetermined from demographic data is highly comparableto estimates obtained from genetic data (i.e., about 18breeding pairs). Whereas both the genetic and demographicestimates of the number of litters are likely to beconservative, it is clear that the number of foxes reproducingon Phillip Island is small and eradication should beachievable (Bomford and O’Brien 1995, Courchamp et al.2003).

Genetic data also suggest a discrepancy between themoderate number of foxes on the island and the smallnumber reproducing. In part, the difference reflects thenumerical dominance of juvenile animals in the population.However, 18 breeding pairs cannot account for the observedharvest estimates of fox abundance in many years (Table 2),particularly because the harvest method is likely tounderestimate abundance. An explanation for the afore-mentioned discrepancy is that a component of the adultpopulation is nonreproductive and potentially reproductivelysuppressed by dominant individuals. Such reproductivesuppression is in line with studies of foxes in their nativeenvironments (Macdonald 1979, Zabel and Taggart 1989,Iossa et al. 2009). The management implication ofnonreproductive adults in the population is a potential fora density-dependent release from reproductive suppressionwhen fox numbers are reduced by control. Thus, whereascontrol operations reduce overall fox abundance on PhillipIsland they may not result in a corresponding reduction inthe number of foxes breeding. Accordingly, the effortrequired to eliminate the fox population may be greater thanit would be in a non–density-dependent situation (Caughleyet al. 1992, Sinclair 1997).

Monitoring effectiveness of control operations for crypticinvasive species such as the fox is difficult (Saunders et al.1995). Single-sample estimators of Ne (linkage methods)have the potential to index changes in population densitybecause linkage disequilibrium should increase in proportionto the amplitude of a population bottleneck (Hill 1981), andeffective population size has been a useful tool to detectchanges in the density of exploited marine species (Hauseret al. 2002, Hutchinson et al. 2003). During our studyperiod, the effort to control foxes on Phillip Island increased


Table 4. Estimates of effective population size (Ne) based on temporal change in allele frequencies for foxes on Phillip Island, Victoria, Australia, sampled1994–2008. The 1996–2006 time frame represents 5 generations; the 1996–2003 time frame represents 3 generations.

Time frameOverlappinggenerationsa

Unbiased nonoverlappinggenerationsb

Moment temporalestimatec Likelihoodd Pseudo-likelihoode

Estimate 95% CI Estimate 95% CI Estimate 95% CI Estimate 95% CI

1996–2006 25.46 18.0 13.0–30.0 18.5 12.4–26.7 19.6 15.0–26.8 26.84 21.3–34.11996–2003 8.0 6.0–12.0 11.7 7.5–18.0 11.56 8.6–15.6 17.97 13.5–24.01996–2003IMf 13.0 10.0–19.0 18.0 11.9–27.2 43.6 27.4–66.5 48.92 35.43–72.3

a Jorde and Ryman (1995).b Jorde and Ryman (2007).c Waples (1989).d Berthier et al. (2002).e Wang (2001).f IM indicates the 2003 sample included individuals known to be immigrants to Phillip Island.


and harvest estimates of fox abundance decreased by close to33% from 2001 onwards. Our expectation was that Ne

should exhibit a comparable reduction, which we did notobserve. A plausible explanation for this pattern is that achange in the ratio of Ne/Ncensus occurred in response to thereduction in fox abundance. This density-dependentmechanism where a larger proportion of the adultpopulation reproduces or produces larger litters when totaldensity is reduced is widely described in red fox populations(Iossa et al. 2009) and is consistent with the increase in theratio of juvenile foxes to adults killed on the island followingan increase in control (Table 2) and the discrepancy betweenthe small number of reproductive animals and the moderatepopulation size (see above). This density-dependent re-sponse in reproduction also illustrates a potential pitfall ofemploying Ne to index change in population density if thespecies under study is, like the red fox, reproductivelyflexible.

The parameter Ne is widely employed to identify plant andanimal populations at risk of deleterious genetic processessuch as inbreeding depression or populations unlikely tohave the capacity to adapt to novel environmentalcircumstances (Allendorf and Luikart 2007). A variety ofNe estimators with different attributes exist (Schwartz et al.1998, 1999; Crandall et al. 1999) and have been extensivelytested, primarily with computer simulations (Tallmon et al.2004). Our longitudinal sampling of a small and insularpopulation provided a unique opportunity to empiricallycompare estimators of effective population size in apopulation with a well-understood demography. Wedemonstrated close agreement between different estimatorsof effective population size, with almost all methodsproducing values close to 20. The similarity of theseestimates is encouraging and is strong evidence that thebreeding population of foxes on Phillip Island is small. Twoexceptions arose from the temporal likelihood and pseudo-likelihood methods (Wang 2001, Berthier et al. 2002) whenwe included 2 migrants in the data set. Inclusion of themigrants inflated the Ne estimate 2- to 3-fold, likelystemming from those methods’ reliance on informationfrom the entire frequency distribution of alleles, rather thanthe point estimates of moment-based estimators. Thesensitivity of some Ne estimators to migrants highlightsthe importance of choosing appropriate estimators whereknowledge of immigrant status is imperfect. Consideringthe advantages of sampling effort required for the linkage-based methods, and no requirement for estimating gener-ation length, the close agreement we find in the estimatesderived from the different approaches suggests that linkage-based estimates will likely be more practical and no lessaccurate in many cases as a means of monitoring effectivepopulation size directly or indexing changes in density ofspecies.

MANAGEMENT IMPLICATIONS

Sustaining the pest-free status of island sanctuaries andestablishing new ones are time-consuming and expensive(Towns and Broome 2003). The Phillip Island fox

population is largely sustained through reproductive recruit-ment from within the island. Eradication programs shouldfocus resources toward suppressing on-island recruitment,while recognizing that the fox population may maintain itsnet reproductive output despite reductions in overall density.Finally, eradication of foxes on Phillip Island will not besustained unless the ongoing immigration is eliminated.

ACKNOWLEDGMENTS

We are grateful for the thoughtful advice of F. Allendorf, W.R. Black, P. England, P. Jorde, J. Kennington, D. Konavalov,N. Ryman, J. Wang, R. Waples, and N. Mitchell. We are alsograteful to Y. Hitchen and M. Penrose for tireless laboratorywork. The manuscript was greatly improved by the commentsof 2 anonymous reviewers. We also acknowledge the rangersof Phillip Island for their enthusiastic and professionalcollection of genetics samples. This project was supported bya grant from the Bureau of Rural Science’s National FeralAnimal Control Program, from Phillip Island Nature Parks,and the Invasive Animals Cooperative Research CentreUptake Program.

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Measuring Recruitment in an Invasive Species to Determine Eradication Potential