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Molecular Ecology (2007)

doi: 10.1111/j.1365-294X.2007.03283.x

Blackwell Publishing Ltd

Recent demographic bottlenecks are not accompanied by a genetic signature in banner-tailed kangaroo rats (Dipodomys spectabilis)

J O S E P H D . B U S C H ,* P E T E R M . W A S E R and J . A N D R E W D e W O O D Y * *Department of Forestry and Natural Resources and Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA

Abstract

Single-sample methods of bottleneck detection are now routine analyses in studies of wild populations and conservation genetics. Three common approaches to bottleneck detection are the heterozygosity excess, mode-shift, and M-ratio tests. Empirical groundtruthing of these methods is difficult, but their performances are critical for the accurate reconstruction of population demography. We use two banner-tailed kangaroo rat (Dipodomys spectabilis) populations from southeastern Arizona (USA) that are known to have experienced recent demographic reductions to search for genetic bottleneck signals with eight microsatellite loci. Over eight total sample-years, neither population showed a genetic bottleneck signature. M-ratios in both populations were large, stable, and never fell below a critical significance value (Mc). The mode shift test did not detect any distortion of allele frequencies, and tests of heterozygosity excess were not significant in postbottleneck samples when we used standard microsatellite mutation models. The genetic effects of bottlenecks like those experienced by our study populations should be strongly influenced by rates of mutation and migration. We used genetic parentage data to estimate a relatively high mutation rate in D. spectabilis (0.0081 mutants/generation/locus), but mutation alone is unlikely to explain the temporal distribution of rare alleles that we observed. Migration (gene flow) is a more likely explanation, despite prior mark­recapture analysis that estimated very low rates of interpopulation dispersal. We interpret our kangaroo rat data in light of the broader literature and conclude that in natural populations connected by dispersal, demographic bottlenecks may prove difficult to detect using molecular genetic data.

Keywords: demographic bottleneck, Dipodomys spectabilis, microsatellite, M-ratio, mutation rate, single-sample methods Received 24 September 2006; revision accepted 8 January 2007

Introduction

The study of population bottlenecks is a critical issue in conservation, including the analysis of real and simulated populations (Luikart & Cornuet 1998; Spencer et al. 2000; Williamson-Natesan 2005). When analysed in the appropriate theoretical framework, molecular genetic methods provide a powerful tool for inferring the demographic history of a population. For instance, DNA sequence data may be used to infer ancient population expansions (Slatkin & Hudson

Correspondence: Joseph D. Busch, Fax: 765-494-9461; E-mail: [email protected] © 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

1991; Rogers & Harpending 1992; Kuhner et al. 1995), while multilocus genotypes from microsatellite and allozyme markers are useful for inferring more recent reductions in census population size (Waples 1989; Cornuet & Luikart 1996; Beaumont 1999) or in effective population size (reviewed in Wang 2005). Marker-based methods take advantage of the fact that rare alleles are lost quickly during a bottleneck (Maruyama & Fuerst 1984) and the frequencies of remaining alleles change from their prebottleneck proportions (Luikart & Cornuet 1998). One advantage of modern methods is the ability to infer demographic history from a single temporal sample, rather than depending on two or more samples that span multiple generations (Waples

2 J . D . B U S C H , P . M . W A S E R and J . A . D e W O O D Y 1989). This property of single-sample methods has made bottleneck analysis feasible for virtually any study that seeks to understand historical demography (Cornuet & Luikart 1996; Luikart & Cornuet 1998; Garza & Williamson 2001). The ability of molecular markers to detect bottlenecks depends on the specific assumptions underlying each approach and how well the assumptions apply to real populations. For example, contemporary methods are especially sensitive to the mutation model employed. Three models have been widely applied to microsatellite markers: the infinite allele model (IAM, Kimura & Crow 1964), the stepwise mutation model (SMM, Ohta & Kimura 1973), and the two-phase model (TPM, Di Rienzo et al. 1994). Empirical data suggest that the TPM is the most appropriate model for microsatellite loci (reviewed in Ellegren 2000, 2004). Although critical TPM parameters such as mutation rate (µ), the probability of changes greater than one step (pg), and the size of non-one-step changes (g) can be adjusted to match the evolution of microsatellite markers, past demographic reductions may still go undetected because life-history traits (e.g. generation time, mating system, postbottleneck growth rate) play an important role in shaping effective population size (Ne) and have the potential to reduce the extent and duration of a genetic bottleneck (Lippe et al. 2006). Immigration, even at low levels, can have a strong effect in erasing bottleneck signatures within a few generations of reduction (Keller et al. 2001). Three commonly used single-sample methods are the heterozygosity excess, mode-shift, and M-ratio tests (Cornuet & Luikart 1996; Luikart & Cornuet 1998; Garza & Williamson 2001, respectively). While the first two methods have been evaluated with many natural and simulated populations (Luikart & Cornuet 1998; Spencer et al. 2000), the M-ratio approach has been used less extensively. A recent evaluation by Williamson-Natesan (2005) uses simulations to show that the M-ratio is powerful in detecting past reductions when the prebottleneck is large ( = 4Neµ) and the bottleneck is multigenerational. As with other methods, the M-ratio takes advantage of the fact that a `sampling error' occurs during a bottleneck and rare alleles are quickly lost. This tends to reduce the number of observed allelic states (k) faster than the size range of those alleles (r), resulting in a decreased M-ratio (M = k/r). The reduction can last for hundreds of generations if Ne or µ remains low, allowing the detection of ancient bottlenecks that may be difficult to observe with the heterozygosity excess or mode shift approaches (Zenger et al. 2003; Abdelkrim et al. 2005; Spear et al. 2006). The M-ratio test can also detect (in theory) very recent bottlenecks; as with the heterozygosity excess and mode shift tests, the power to detect a bottleneck should be strongest in the recovery period immediately following the population crash before rare alleles return via migration and/or mutation.

Fig. 1 Demographic trends of Dipodomys spectabilis from the Rucker and Portal populations. Only adults known to be present in the August census are included in this graph (see Materials and methods).

We used demographic and genetic data sets from two southeastern Arizona populations (Rucker and Portal) of the banner-tailed kangaroo rat (Dipodomys spectabilis) to empirically evaluate the performance of single-sample bottleneck methods. Conventional mark­recapture techniques (ear tagging) have been ongoing for 25 years ( Jones 1984; Jones 1986; Jones et al. 1988; Waser & Jones 1991; Waser & Ayers 2003; Skvarla et al. 2004) and provide an extensive demographic background that is rare in bottleneck studies. There have been major demographic bottlenecks at both sites, although the duration and intensity of each differs (Fig. 1). At our Rucker site, the reduction was most intense during 2002­2003, when the population numbers were 20% of those during stable years (1993­1998). Assuming a mean generation time of 1.7 years (Swanson 2001), this bottleneck was restricted to one to two generations. The Portal bottleneck was much more severe -- only one adult and six juveniles were trapped in the postreproductive season (August) of 1994. This was the trough of a 10-year, 6-generation decline that spanned two orders of magnitude. Portal numbers have never recovered to prebottleneck levels, while the population at Rucker has rapidly increased since the 2002­2003 reduction. In light of these differences, we predict that Portal will display a more obvious bottleneck signature than Rucker. We focus on the M-ratio, and, explore its sensitivity under species-specific parameters of the TPM. To facilitate this investigation, we estimate the microsatellite mutation rate and mode of evolution from a recent parentage study (Waser et al. 2006). The M-ratio analysis is compared to the results from the mode-shift and heterozygosity excess approaches, which rely on different aspects of genetic markers and are powerful in opposing scenarios, that is, when the prebottleneck is smaller, the bottleneck is less severe, and the population has spent less time in recovery.

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

EMPIRICAL EVALUATION OF BOTTLENECK METHODS 3 Our samples include a time series of 7 years from Rucker that allows us to compare pre- and postbottleneck years. These replicate samples are clearly not independent, but because a relatively small proportion of adults survive to breed across multiple years, our approach is still informative for appraising single-sample methods in stable vs. reduced years. Our study is particularly useful for evaluating bottleneck techniques with real populations because (i) we know the recent demographic history in great detail, and (ii) genetic samples were taken during or immediately after the demographic reductions, when the genetic signatures should be strongest. adult numbers from the August census tend to be 40% smaller than those from March because of mortality during the summer, and thus portray the demographic lows more accurately. Single-sample bottleneck detection methods assume that a population is closed to migration. This assumption is rarely tested and may often be violated in natural populations. In D. spectabilis, a predilection for extremely short dispersal distances has been apparent since the very first trapping efforts (Jones 1984). Since then, a consistent outcome of mark­recapture and parentage studies is that > 80% of dispersing individuals remain within 100 m of their birthplace (Jones 1987; Jones et al. 1988; Waser et al. 2006). Mark­recapture transects covering about 10% of the area surrounding the Portal site found only two animals of 337 left the site in 5 years of trapping (Jones 1987). Taken together, extensive field data suggest that dispersal between populations should be quite low. While mark­recapture data has been collected since 1980, genetic sampling did not begin until 1990. In total, we used genetic samples from the Rucker population in four prebottleneck years (1995­1998), one moderately reduced year (1999), and two recovery years (2004­2005; Table 1). Since we do not have tissue samples from Portal during the early 1980s, when the population was much larger, we restrict our sample to a postbottleneck year with the largest sample size possible (Portal 1998; Fig. 1). We used the entire August census (adults & juveniles) for the M-ratio in order to increase our chances of detecting rare alleles. Only adults were used for the mode-shift and heterozygosity excess analyses in order to minimize Hardy­Weinberg deviations that can arise from sampling overlapping generations.

Materials and methods Field sites, demography, and natural history

The Portal (31°56N, 109°5W) and Rucker (31°37N, 109°15W) sites are located in southeastern Arizona, USA, separated by approximately 35 km. These two populations have different spatial arrangements, with mounds being distributed continuously at the Portal site but clustered into demes at Rucker (separated by 150 ­300 m). Four of the Rucker demes (R1E, R1W, R2, and SSW) were chosen for this study because demographic and genetic sampling has been the most complete at these sites. Adult Dipodomys spectabilis are solitary, with mounds of both sexes interspersed (balanced sex ratio), and the mating system is polygynandrous (Waser et al. 2006). Females usually reach reproductive maturity after 1 year and give birth to 1­3 young/litter; multiple litters per breeding season are common ( Jones 1984). While population growth can be rapid, the mean fecundity is one daughter/female/ year (Waser & Jones 1991). Mortality in the first year is the same for both sexes and depends on whether individuals disperse or are philopatric (62% and 34% mortality, respectively; Jones 1986). After year 1, annual mortality is approximately 60% and independent of age or reproductive effort; only a few animals live beyond their fourth year (Waser & Jones 1991). The mean generation time is 1.7 years (Swanson 2001). Long-term mark­recapture studies (1980-present) have been conducted to study demography and dispersal in D. spectabilis (references noted above). Active D. spectabilis mounds are directly targeted with three long Sherman traps per mound for three nights (Jones 1984), which results in a median capture probability of 0.98 for adults and 0.93 for juveniles (Skvarla et al. 2004). Repeated trapping occasions are used to predict mound ownership with high accuracy, as verified by a telemetry study ( Jones 1986). As a means of temporally delineating the demographic data from Rucker and Portal only animals trapped in August (or known to be alive during that month from subsequent trapping sessions) were used in Fig. 1. The

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

Molecular methods

A 1 × 4 mm sliver of ear tissue was collected from each animal upon first capture and stored in lysis buffer (100 mm Tris-HCl pH 8.4, 50 mm EDTA, 100 mm NaCl, 2% SDS) at ambient temperature in the field. DNA was later extracted using standard phenol­chloroform methods (Sambrook & Russell 2001) or ammonium acetate purification (Puregene kit, Gentra Systems). We genotyped individuals using a panel of eight microsatellite loci specific for D. spectabilis, which consisted of DS01, DS03, and DS28 (Davis et al. 2000) and DS98, DS107, DS109, DS163, and DS281 (Waser et al. 2006). Polymerase chain reaction (PCR) conditions have been described previously (Winters & Waser 2003; Waser et al. 2006). We resolved allele sizes by electrophoresing PCRs on 4.75% polyacrylamide using the ABI 377 platform. genescan 3.1 and genotyper 2.1 software (Applied Biosystems) were used to determine genotypes. Individuals were included in a yearly sample if they amplified at five or more loci.

4 J . D . B U S C H , P . M . W A S E R and J . A . D e W O O D Y

Table 1 Sample sizes and preliminary analyses from each year, including mean number of alleles (A), observed heterozygosity (HO), 2 test of Hardy­Weinberg proportions (HW), and fixation indices (FST and FIS). Significant P values are shown in bold italics font. Rucker 1995 n Adults 44 Juveniles 104 Genetic diversity A 7 HO 0.71 HW§ ns Population structure FST 0.0170 P value 0.0075 FIS - 0.0340 P value 0.2606 1996 1997 1998 1999 2004 2005 mean Portal 1998

51 79 7.25 0.71 ns

53 207 7.12 0.73 ns

66 61 6.87 0.65 DS03 (0.004) DS281 (0.005) 0.0053 0.1205 - 0.003 0.9151

38 115 6.62 0.66 ns

33 47 6.5 0.63 DS98 (0.001)

39 137 7.37 0.66 DS107 (0.051) DS163 (0.025) 0.0153 0.0789 0.0154 0.3544

46.3 107.1 6.96 0.68 --

26 48 6.87 0.70 DS163 (0.022)

0.0230 0.0002 - 0.0418 0.1100

0.0100 0.0186 - 0.0508 0.0356

0.0099 0.0490 0.0016 0.9209

- 0.0049 0.6362 0.0692 0.0360

0.0108 -- - 0.0062

-- -- 0.0013 0.4980

August animals only. Sample size of adult genotypes is slightly lower than the census size (Fig. 1) because of quality control measures (see Materials and methods); mean from all Rucker years; §ns: none of the eight loci significant at = 0.10.

Preliminary analyses

To compare general measures of genetic diversity between Rucker and Portal, we took measurements of observed heterozygosity (HO) from adults and the mean number of alleles (A) from adults and juveniles combined. One requirement of the heterozygosity excess approach is that molecular markers be in Hardy­Weinberg equilibrium. We used genalex (Peakall & Smouse 2006) to check for Hardy­Weinberg equilibrium in each individual locus using a 2 goodness-of-fit test on adults from each year. An important assumption of single-sample methods is that no genetic substructure exists within a population. We checked for cryptic differentiation among Rucker demes by estimating pairwise FST in all years using Weir & Cockerham's (1984) estimator in spagedi (Hardy & Vekemans 2002). In addition, we checked for any deviation of FIS from zero in Rucker and Portal. Only adults were used in estimating F-indices.

M-ratio

M-ratios were calculated from microsatellite genotypes using the software m_p_val (Garza & Williamson 2001). The significance of an observed M value is determined by comparing it to a distribution of M values calculated from theoretical populations in mutation­ drift equilibrium; the critical value of M (Mc) is set at the lower 5% tail of this distribution. The program critical_m (Garza & Williamson 2001) generates Mc thresholds, allowing users to modify three TPM parameters (, pg, g ) that approximate the

mutation process in real populations. Increasing , pg, or g will introduce a greater number of gaps in the allele distribution and decrease the Mc cut-off. Lower Mc values are more conservative, because a bottleneck has to be of greater severity in order to drop below this level. Likewise, a larger Mc value (from a smaller , for instance) is more relaxed because the M-ratio has to drop less in order to be significant. Since Ne and µ are typically unknown, most studies base their significance criteria on a wide range of biologically plausible values (e.g. Guinand & Scribner 2003; Abdelkrim et al. 2005). We chose to use both general and speciesspecific estimates of . First, we used two generic Ne values (5, 500) and a common estimate of microsatellite mutation rate suggested by Garza & Williamson (2001): 5.0 × 10 - 4 mutants/generation/locus (Weber & Wong 1993). This estimate might be low for rodents, given their accelerated rate of molecular evolution (Martin & Palumbi 1993; Li et al. 1996; Triant & DeWoody 2006). Therefore, we also considered a faster mutation rate (5.0 × 10-3) to widen our generic window. Substituting these values into = 4Neµ gives a broad range of 0.01­10. We used default values for the remaining two parameters needed for the TPM (pg = 0.1 and g = 3.5 steps; Table 2). We then fine-tuned a narrower range of species-specific Mc cutoffs by generating values from our empirical estimates of µ and Ne (see methods below). In addition, we used inferred mutations to estimate parameters pg and g specific for D. spectabilis (Table 2). As a final post hoc comparison (non-species-specific), we generated an extremely high Mc cut-off by adjusting the TPM to the point of producing nearly all single-step mutations (pg = 0.01 and g = 2).

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

EMPIRICAL EVALUATION OF BOTTLENECK METHODS 5

Table 2 Parameters for the TPM used to generate Mc cutoffs. In the range of parameters we used, increasing , pg, or g serves to decrease the mean M-ratio (and corresponding Mc) in equilibrium populations. Parameters Generic Specific 99% SMM Stringency of Mc relaxed () conservative () relaxed (IAM ) conservative (SMM ) relaxed Ne 5 500 68 142 68 µ 0.0005 0.005 0.0081 0.0081 0.0081

0.01 10 2.2 4.6 2.2

2N 150 150 150 150 150

pg 0.1 0.1 0.41 0.41 0.01

g 3.5 3.5 2.5 2.5 2.0

Mc 0.83 0.77 0.73 0.72 0.91

µ = mutants/generation/locus; = 4Neµ.

Mutation rate and effective population size

Recent genetic studies (Winters & Waser 2003; Waser & DeWoody 2006; Waser et al. 2006) have used cervus (Marshall et al. 1998) to establish parentage in 214 D. spectabilis families. We estimated the mutation rate in microsatellite markers using candidate families where both parents have been assigned to an offspring with > 95% confidence, yet a single mismatched allele existed in the offspring. We double-checked all candidate mutations, discarding any that were ambiguous. The remaining discrepancies were deemed de novo mutations, and used to calculate an estimated mutation rate (^) using equation 7.13a in Hedrick (2005): ^= x 2 NJ (eqn 1)

1 (1 - H ) - 1 E Ne = 8µ

2

(eqn 3)

Equation 2 assumes the IAM while equation 3 is based on the SMM. Since these models represent the two extremes of mutation processes, the true Ne should lie in between these estimates. In both equations, we use an unbiased estimator for HE (Nei 1987). We used the mean Ne from Rucker 1995 ­ 1998 and our empirically determined µ to parameterize prebottleneck = 4Neµ for generating species-specific values of Mc (Table 2). We chose to use these values for both Rucker and Portal, since prebottleneck samples were not available to parameterize Portal.

Other bottleneck methods

We complemented the M-ratio results with tests of modeshift and heterozygosity excess (Cornuet & Luikart 1996; Luikart & Cornuet 1998). bottleneck version 1.2.02 (Piry et al. 1999) was used to generate the distribution of observed alleles from each year in order to look for a distortion away from the typical l-shaped distribution. Heterozygosity excess was tested under all three mutation models (IAM, TPM, and SMM) to compare the sensitivity of each. The user can adjust two parameters of the TPM in bottleneck: pg and the variance of mutations larger than one step (Piry et al. 1999). As in the M-ratio simulations described above, we set both generic (pg = 0.1, variance = 12) and speciesspecific (pg = 0.41, variance = 4) parameters for bottleneck simulations. The Wilcoxon signed-rank test was used to evaluate any deviation from 50:50 heterozygosity deficiency/ excess (Cornuet & Luikart 1996).

where x is the number of observed mutations in N surveyed families over J loci. In all triads (offspringmother-father), one or more loci were missing data from at least one family member. Therefore, we adjusted J to be the mean number of loci successfully typed in each triad. The character of observed mutations (single vs. multistep) provides valuable insight regarding the mutational process in D. spectabilis. The number of steps for a mutation was estimated by (i) deducing which parent was most likely to have contributed the mutant allele, and (ii) assuming the mutant allele's ancestor is the parental allele closest in size (sensu DeWoody et al. 1998). In other words, we assume microsatellites evolve parsimoniously in a way that minimizes g (Beck et al. 2003; Ellegren 2004). A long-term estimator of Ne is required to estimate . Two estimates of global Ne that are based on expected heterozygosity (HE) and µ are rearrangements of equation 3.15 from Hartl & Clark (1989) and equation 7 from Ohta & Kimura (1973), respectively: Ne = and

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

Results Preliminary analyses

HE 4µ(1 - H E )

(eqn 2)

Deviations of individual microsatellite loci from Hardy­ Weinberg expectations were seen intermittently during the 7 years of this study (Table 1). DS163 was the only marker

6 J . D . B U S C H , P . M . W A S E R and J . A . D e W O O D Y that deviated significantly at both Rucker (2005) and Portal (1998). However, as no single locus was out of Hardy­ Weinberg equilibrium in more than 1 year, these loci are appropriate for the heterozygosity excess test. We observed moderate levels of heterozygosity (mean HO = 0.63­0.73) and allelic diversity (A = 6.5 ­7.37) at these loci in both populations (Table 1). Contrary to our predictions, the greater severity of the Portal bottleneck did not lead to any reduction in HO and A compared to Rucker; in fact, the two populations were nearly identical for both measures. Genetic differentiation between Rucker demes R1E, R1W, R2, and SSW was very low overall, but statistically significant in 4 years (Table 1). Demes in the Rucker population that are immediate neighbours have been observed to exchange 0.45 migrants/year (Skvarla et al. 2004) and such movements provide enough gene flow to prevent the formation of strong substructure (mean FST = 0.0108). FIS values are also low and only significant in 2 years, one prebottleneck (1997) and one postbottleneck (2004). With a mean FIS of -0.0015 and genotype frequencies that match Hardy­Weinberg expectations, these analyses collectively suggest that Rucker acts as a single genetic population, and we treat it as such here. The empirical ^ was used with HE values from the Rucker 1995­1998 populations to estimate a prebottleneck Ne, which is required for simulating equilibrium populations in critical_m. The IAM formula (equation 2) generates a mean Ne estimate of 68, while the SMM-based estimate (equation 3) is 142. This range is generally consistent with 12 years of census data from Rucker, given that the number of adults varied from 17 to 82 (Fig. 1) and these four demes make up approximately 1/3 of the total population at Rucker. Substituting empirical estimates of ^ and Ne into = 4Neµ generates a species-specific window of 2.2­4.6. Using these values and specific parameters for pg (0.41) and g (2.5), we find Mc values that cover a much smaller range than the generic parameters and are more conservative (Table 2). Furthermore, changing the Ne (while keeping µ constant) has a small effect on widening the Mc range.

Bottleneck analyses

In the prebottleneck years (1995­1998), M-values at Rucker are consistently high (Fig. 3). Compared against both generic and specific Mc values, M-ratios in these years were always greater than the relaxed and conservative thresholds. This is congruent with expectations based on mark­recapture data from the stable years (Fig. 1). However, the 1999 Rucker population did not experience a drop in the M-ratio, despite a 50% reduction in the number of adults. Likewise, the postbottleneck M-ratios from Rucker 2004­2005 and Portal 1998 also showed no sign of any demographic bottleneck. A bottleneck signature is only inferred when the TPM parameters are pushed towards a pure SMM, by setting pg to 0.01 and g to two steps (Table 2, Fig. 3). At this Mc threshold, all samples indicate a past genetic bottleneck, including those taken in years of stable demography. Using

Estimation of µ and other TPM parameters

An analysis of the observed mismatches between parents and offspring reveals 22 candidate mutations in the 214 families with two known parents. Substituting these values into equation 1 with J = 6.35 loci (the mean number of genotyped loci in offspring-parent triads) produces a ^ of 0.0081 mutations/locus/generation. Assuming that the parental allele closest in size to the mutant is the progenitor, we find evidence to support the TPM (Fig. 2). The majority of mutations were single-step (pg = 41%).

Fig. 2 Number of inferred steps in mutations from families with one mismatched allele.

Fig. 3 M-ratio values for each year. Ranges of Mc values are given for mutation­drift populations simulated under generic and species-specific parameters (shaded areas). Only a single Mc cutoff was generated for the 99% SMM (dashed line). © 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

EMPIRICAL EVALUATION OF BOTTLENECK METHODS 7

Table 3 Results of the mode-shift and heterozygosity excess bottleneck detection methods. Ratios represent the number of microsatellite loci exhibiting heterozygosity deficiency vs. excess. Rucker 1995 none 1996 none 1997 none 1998 none 1999 none 2004 none 2005 none Portal 1998 none

Mode-shift HE excess SMM Generic Specific TPM (pg = 0.1) TPM (pg = 0.41) IAM

4:4 0.3203 1:7 0.137 1:7 0.977 1:7 0.039

2:6 0.0977 1:7 0.0039 1:7 0.0097 1:7 0.0039

3:5 0.2305 1:7 0.0039 1:7 0.0273 1:7 0.0039

4:4 0.5781 0:8 0.0020 1:7 0.0059 0:8 0.0020

3:5 0.3711 1:7 0.0059 1:7 0.0273 1:7 0.0039

4:4 0.6289 3:5 0.3721 2:6 0. 1914 1:7 0.0059

5:3 0.9629 4:4 0.6797 4:4 0.4219 1:7 0.0059

4:4 0.5273 3:5 0.4727 3:5 0.1250 0:8 0.0020

an SMM for the equilibrium population will increase type I errors (i.e. inferring bottlenecks during a period of demographic stability) if the kangaroo rat microsatellites are actually evolving under a TPM (Williamson-Natesan 2005). The mode-shift test did not detect any evidence of the observed bottleneck (Table 3), despite the expectation that many rare alleles should have been removed. In the case of chronic bottlenecks that last multiple generations, allelic variation can diminish to an average of just two to three alleles/locus (Garza & Williamson 2001). The mean number of alleles in these two populations ranged from 6.5 to 7.37 alleles per locus (Table 1), indicating that allelic variability has not been greatly compromised. Across all loci in the 1999 samples from Rucker, five alleles were lost as compared to the 1998 sample, but this was not enough to cause a mode shift because four alleles were gained in 1999 (Table 4). Alleles were rapidly restored to the Rucker population in the year between 2004 and 2005 (seven gained, one lost). Such patterns (allelic recruitment and turnover) stabilize the allele frequencies and prevent any mode-shift signal. Therefore, the distribution of alleles is L-shaped in both pre- and postbottleneck years. Inferences from the heterozygosity excess tests were heavily influenced by the mutational model. Under the SMM, none of the years show a significant heterozygosity excess, while the exact opposite is true using the IAM (Table 3). The latter model is more robust in detecting subtle genetic bottlenecks, but is also known to occasionally identify heterozygosity excess in nonbottlenecked populations (Luikart & Cornuet 1998). The SMM is less robust when the heterozygosity excess is small, but is thought to be a more appropriate model for use with microsatellites (Luikart & Cornuet 1998). The TPMs gave nearly identical results under generic (pg = 0.1, variance = 12) and specific (pg = 0.1, variance = 4) parameters. Both TPMs register het© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

erozygosity excess at Rucker during the stable years (1995 ­ 1998) and the year of 50% decline (1999), which is similar to the IAM results. The one exception to this is Rucker 1995, which did not show an excess under the species-specific TPM. However, no heterozygosity excess was found in postbottleneck years at Rucker (2004­2005) or Portal (1998).

Discussion

Single-sample bottleneck detection methods provide a potentially powerful approach for inferring past demographic trends in situations where historical demography is of great interest but unavailable. Because of this, such approaches have become standard analyses in the study of natural populations and conservation genetics. The known (recent) demographic history of our banner-tailed kangaroo rat populations provides a rare opportunity to evaluate these methods in a wild population and across both stable and bottlenecked years. We evaluated three approaches that were each unable to detect any consistent genetic signal of a bottleneck, even though samples were taken during or immediately after the population crash and analysed under species-specific parameters for microsatellite evolution. We discuss these results within the theoretical framework of each method, and point out several biological properties of rodent populations that may obfuscate genetic signatures of demographic bottlenecks.

Bottleneck approaches

The M-ratio approach did not support the possibility of a genetic bottleneck at Rucker or Portal. The mean M values were quite stable across all years and well above 0.68, which Garza & Williamson (2001) suggest as an upper limit for postbottleneck M based on data from a wide variety of reduced populations. A recent simulation by

8 J . D . B U S C H , P . M . W A S E R and J . A . D e W O O D Y

Table 4 Observed allele frequencies and individual M-ratios from eight microsatellite loci. Samples include all adults and juveniles genotyped for each year. Rucker Locus DS01 Allele 204 206 208 210 212 214 216 218 220 222 168 170 172 174 176 178 180 182 184 186 178 180 182 184 186 188 190 192 194 196 200 204 208 212 216 220 224 228 232 236 122 124 126 128 130 132 134 136 138 140 1995 0.055 -- 0.048 0.031 0.352 0.228 0.159 0.121 0.007 -- 0.889 -- 0.139 0.119 0.341 0.225 0.079 0.033 0.040 -- 0.023 0.889 0.300 0.154 -- 0.279 0.107 0.100 0.054 -- 0.007 0.778 0.014 0.740 -- 0.207 0.014 -- -- 0.024 -- -- -- 0.625 0.005 -- -- 0.021 -- -- -- 0.195 0.111 0.153 1996 0.051 0.007 0.040 0.033 0.357 0.199 0.173 0.136 0.004 -- 1 -- 0.149 0.170 0.290 0.236 0.069 0.043 0.022 -- 0.022 0.889 0.273 0.121 0.008 0.293 0.133 0.105 0.059 -- 0.008 0.889 0.005 0.753 -- 0.226 0.011 -- -- 0.005 -- -- -- 0.625 0.010 -- -- 0.036 -- -- -- 0.196 0.149 0.119 1997 0.050 0.019 0.040 0.023 0.313 0.169 0.235 0.140 0.010 -- 1 -- 0.176 0.098 0.314 0.239 0.069 0.050 0.025 -- 0.029 0.889 0.208 0.148 0.004 0.313 0.154 0.117 0.050 -- 0.006 0.889 0.007 0.738 -- 0.219 0.021 -- -- 0.014 -- -- -- 0.625 0.007 -- -- 0.051 -- -- -- 0.211 0.145 0.057 1998 0.027 0.012 0.062 0.016 0.283 0.209 0.267 0.112 0.012 -- 1 -- 0.136 0.070 0.360 0.240 0.081 0.062 0.031 -- 0.019 0.889 0.265 0.120 0.004 0.333 0.137 0.085 0.047 -- 0.009 0.889 -- 0.767 -- 0.198 0.025 -- -- 0.010 -- -- -- 0.571 -- -- -- 0.032 -- -- 0.009 0.207 0.090 0.095 1999 0.039 ­ 0.088 0.013 0.308 0.195 0.224 0.123 0.010 -- 0.889 0.007 0.129 0.079 0.301 0.268 0.109 0.040 0.036 -- 0.030 0.857 0.280 0.126 -- 0.346 0.129 0.073 0.045 -- -- 0.857 0.004 0.739 -- 0.216 0.026 -- -- 0.011 0.004 -- -- 0.667 -- -- -- 0.047 -- -- -- 0.194 0.093 0.124 2004 0.013 0.013 0.066 0.007 0.316 0.316 0.151 0.105 0.013 -- 1 -- 0.066 0.092 0.349 0.243 0.099 0.086 0.026 -- 0.039 0.889 0.227 0.093 -- 0.260 0.287 0.120 -- -- 0.013 0.667 0.034 0.740 -- 0.137 0.075 -- -- 0.014 -- -- -- 0.625 -- -- -- -- -- -- -- 0.182 0.074 0.054 2005 0.017 0.020 0.060 0.003 0.298 0.298 0.156 0.136 0.009 0.003 1 -- 0.068 0.085 0.404 0.226 0.059 0.110 0.006 -- 0.042 0.778 0.223 0.097 -- 0.257 0.309 0.106 -- -- 0.009 0.667 0.034 0.676 -- 0.196 0.068 -- -- 0.020 0.003 0.003 -- 0.7 -- -- 0.003 0.020 -- -- 0.006 0.169 0.076 0.059 Portal 1998 0.022 0.007 0.022 0.059 0.338 0.272 0.096 0.096 0.088 -- 1 -- 0.130 0.174 0.370 0.072 0.145 0.058 -- -- 0.051 0.778 0.200 0.157 -- 0.121 0.457 0.057 0.007 -- -- 0.857 0.007 0.659 -- 0.196 0.072 -- -- 0.051 -- -- 0.014 0.545 -- -- 0.036 0.036 -- -- 0.007 0.150 0.143 0.100

M-ratio DS03

M-ratio DS46

M-ratio DS98

M-ratio DS107

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

EMPIRICAL EVALUATION OF BOTTLENECK METHODS 9

Table 4 Continued Rucker Locus Allele 142 144 146 148 150 152 154 M-ratio DS109 130 134 138 208 210 212 214 216 218 220 222 224 226 228 260 264 268 272 1995 0.021 0.053 0.105 0.163 0.163 0.011 -- 0.687 0.005 0.491 0.505 1 0.116 0.116 0.106 0.030 0.263 0.182 0.030 -- 0.101 0.051 0.005 0.909 0.015 0.365 0.575 0.045 1 1996 0.010 0.041 0.108 0.134 0.186 0.010 -- 0.687 0.005 0.555 0.440 1 0.126 0.095 0.068 0.026 0.279 0.195 0.047 -- 0.079 0.074 0.011 0.909 0.014 0.296 0.634 0.056 1 1997 0.020 0.073 0.099 0.139 0.181 0.018 -- 0.687 0.013 0.567 0.420 1 0.134 0.103 0.098 0.008 0.240 0.214 0.036 -- 0.103 0.057 0.008 0.909 -- 0.371 0.589 0.041 1 1998 0.018 0.063 0.144 0.149 0.162 0.032 -- 0.846 0.014 0.586 0.401 1 0.111 0.083 0.078 0.028 0.283 0.250 0.033 -- 0.078 0.056 -- 0.889 -- 0.276 0.676 0.048 1 1999 0.008 0.074 0.093 0.147 0.221 -- -- 0.75 0.030 0.534 0.436 1 0.148 0.127 0.074 0.037 0.254 0.193 0.025 -- 0.086 0.057 -- 0.889 0.004 0.340 0.611 0.045 1 2004 0.088 0.176 0.088 0.095 0.203 0.027 0.014 1 0.040 0.687 0.273 1 0.055 0.185 0.021 -- 0.308 0.110 0.116 -- 0.116 0.089 -- 0.8 0.021 0.250 0.721 0.007 1 2005 0.105 0.150 0.116 0.045 0.232 0.020 -- 0.857 0.051 0.653 0.295 1 0.074 0.162 0.026 -- 0.306 0.106 0.112 0.003 0.132 0.079 -- 0.9 0.020 0.315 0.626 0.040 1 Portal 1998 0.100 0.093 0.071 0.121 0.100 0.043 -- 0.857 0.014 0.743 0.243 1 0.037 0.037 0.185 0.093 0.093 0.185 0.093 -- 0.222 0.056 -- 0.9 -- 0.391 0.523 0.086 1

M-ratio DS163

M-ratio DS281

M-ratio

Williamson-Natesan (2005) tested bottleneck conditions similar to ours ( = 2­10, generations in bottleneck = 1­7) and found the M-ratio has less power to detect bottlenecks when the prebottleneck is small, the bottleneck is of limited duration, and the population is sampled shortly after the bottleneck. These are exactly the conditions under which we empirically tested M in the Rucker samples. However, the Portal site was sampled three to four generations after the bottom of a severe, multigenerational bottleneck that should have left a significant genetic signature. Table 4 shows one aspect of the allele frequency distributions that would prevent the M-ratio from finding any signal: five of the eight loci (DS01, DS03, DS109, DS163, and DS281) have bell-shaped distributions that contain few gaps. Bell-shaped allele frequency distributions drastically impair the power of the M-ratio approach, because losing rare alleles from the ends of the size range does not cause M to drop (Garza & Williamson 2001). The only Mc threshold larger than the observed M values was generated from a set of theoretical populations pushed far towards the

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

SMM (pg = 0.01, g = 2.0). Under this model, all years from Rucker would infer a bottleneck, which is at odds with the known recent demography. It is clear these loci do not evolve according to a strict SMM, as 41% of the 22 inferred mutations were necessarily greater than a single step. Our species-specific estimates of , pg, and g provide a more conservative Mc window than the generic and SMM parameters. This keeps type I errors to a minimum, but also requires bottlenecks to be more severe before detection occurs. The mode shift results were similar to those of the Mratio. None of the samples demonstrated a shift away from the rare allele category. A nearly equal turnover of rare alleles was observed in the Rucker 1999 sample (5 lost, 4 gained), which is consistent with the moderate nature of that bottleneck and bears a close resemblance to the pattern of the four stable years preceding it (4 lost, 3 gained). Allelic gain marked the Rucker 2004­2005 samples (1 lost, 7 gained), which was probably a reflection of the rapid population expansion that occurred. One outcome of prompt replacement is the maintenance of a constant proportion of rare alleles, which prevents any mode-shift signal.

10 J . D . B U S C H , P . M . W A S E R and J . A . D e W O O D Y Likewise, the heterozygosity excess tests did not provide convincing evidence of a genetic bottleneck in the postreduction samples. None of the loci showed an excess under the conservative SMM, which is generally a more appropriate model for microsatellite evolution than the IAM (Ellegren 2000). The latter model was diametrically opposed to the SMM in detecting a heterozygosity excess in all years of this study. This outcome is consistent with the years of demographic reductions, but unexpected for the prebottleneck years at Rucker. While a scenario of historic demographic retraction at Rucker is possible, Luikart & Cornuet (1998) discovered that the IAM occasionally detects heterozygosity excess in nonbottlenecked populations and is more susceptible to type I error than the SMM. These authors also suggest this pattern can be a symptom of samples that are taken from populations not in mutation­drift equilibrium, which might well be the case at Rucker and Portal. A departure from equilibrium would also be consistent with the outcome of both TPMs, which were sensitive enough to detect a subtle genetic change that may have accompanied the demographic bottlenecks. Under the generic and species-specific TPM parameters, a heterozygosity excess was observed in all samples from Rucker 1995­1999 (except Rucker 1995 under the speciesspecific TPM). However, this excess was not found in any of the postbottleneck samples (Rucker 2004 ­2005 and Portal 1998). An examination of Fig. 1 offers one possible explanation: population expansion quickly followed both reductions. In postbottleneck years, the populations enter a recovery phase where the number of individuals is rapidly increasing. Population expansion actually creates heterozygote deficiency because allelic loss is greatly diminished and new mutations increase the number of alleles, which raises the expected heterozygosity in the theoretical population faster than in the real one (Cornuet & Luikart 1996). A heterozygote deficiency would balance the inclination towards excess found in prebottleneck years. However, an elevated mutation rate >> 8.1 × 10-3 would be required to explain the lack of signal in our study populations. Another source for new alleles that arise year by year must be immigration. Although the focus of the D. spectabilis studies that generated these genetic data was their low rate of dispersal, even a single immigrant from outside can introduce a new allele. Moreover, recent parentage analyses have documented occasional cases of cryptic precapture dispersal in juveniles (Waser et al. 2006). Another intriguing possibility is that Dipodomys spectabilis dispersal rates, though generally very low, may vary with density (Waser & Elliott 1991). When populations are small, the arrival of just a few immigrants can erase a bottleneck signature in two to three generations, as seen in song sparrows (Melospiza melodia, Keller et al. 2001). Therefore, long-distance dispersal in years of low density could set the pace for a rapid genetic recovery. Waser et al. (2006) found that 27% of dispersers travelled > 100 m during low-density years, as compared to only 3.7% moving > 100 m in medium-density years. In addition, recolonization of extinct Rucker demes has taken place in four separate instances during 1986­1999 (Swanson 2001). This is intuitive, as dispersers may easily establish territories in demes where all /most mounds are vacant. It also demonstrates the capacity for longer movements, because the minimum distance between neighbouring demes at Rucker is 150­300 m. The arrival of new alleles via immigration has the same effect on bottleneck methods as increased mutation: is increased (through an increase in Ne, rather than µ). Both increased mutation and migration cause missing allele states to be filled more rapidly than they would otherwise, which increases the M-ratio and reduces the window for bottleneck detection (Garza & Williamson 2001). Migration can similarly impair the heterozygosity excess test in two ways. First, infrequent genetic exchange with a differentiated population will increase the total number of observed alleles in a bottlenecked population without an appreciable increase in expected heterozygosity (Cornuet & Luikart 1996). Second, when the migration rate is sufficiently large (> 0.01 migrants/generation) migrants fail to deliver unique alleles but still cause heterozygosity excess under a steppingstone model (Pope et al. 2000). This might explain the excess we observed in stable years at Rucker under both TPMs. Finally, the mode-shift method will also be less useful when migration occurs between differentiated populations, because any new allele that a migrant carries into a population will likely be rare and act to resist the distortion of allele frequencies that normally accompanies a demographic reduction. Besides mutation and migration, other species-specific attributes can also influence bottleneck detection. For instance, long generation times in some vertebrates have been

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

Biological properties of real populations

None of the bottleneck detection methods utilized herein inferred any demographic reductions, presumably because each approach makes assumptions that are violated by unforeseen attributes of kangaroo rats. These might include a (relatively) high mutation rate, undetected immigration, and a demography marked by stochastic fluctuations. These processes do not act in isolation, but rather interact with one another in a way that confounds bottleneck analyses. Rodents are known to have higher rates of nucleotide substitution than other mammals (see References above), and this could presumably extend to microsatellites as well. Our empirically derived mutation rate (0.0081 mutants/ locus/generation) is probably a conservative underestimate because we could not detect homoplasious changes.

E M P I R I C A L E V A L U A T I O N O F B O T T L E N E C K M E T H O D S 11 shown to prevent genetic bottlenecks that would ordinarily accompany recent demographic reductions (Kuo & Janzen 2003, 2004; Lippe et al. 2006). At the opposite extreme, species exhibiting short generations and cyclic demography (e.g. many rodents) should purge rare alleles on a regular basis, because the time spent at the peak phase is limited (Maruyama & Fuerst 1985). Theoretically, this prevents the accumulation of mutations expected when a population is at mutation­drift equilibrium and reduces Ne to its harmonic mean (Wright 1938; Nei et al. 1975). However, empirical results from cyclic mammals (arvicoline rodents and lagomorphs) contradict theory, as substantial genetic variation is preserved in many naturally fluctuating populations (Burton et al. 2002; Ehrich & Jorde 2005; Berthier et al. 2006). One plausible explanation is that genetic drift acts to increase genetic structure at a local (deme) scale, which preserves diversity in a global sense until years of population expansion occur and immigration begins to admix genes (Berthier et al. 2006). Fluctuations in D. spectabilis populations are probably stochastic, since their numbers are tied closely to rainfall and the productivity of seed-producing annual plants (Munger et al. 1983; Brown & Zeng 1989). However, even random size fluctuations are expected to decrease Ne in the same way as cyclic ones, albeit at a slower rate (Karlin 1968). The demographic collapse and subsequent resurgence at Rucker and Portal imply that stochastic reductions do not suppress Ne levels in the long term, either because bottlenecks are rare or immigration plays a major role in genetic recovery. A review of the bottleneck literature from other rodents and cyclic lagomorphs shows a similar pattern to ours: most populations naturally experience some level of immigration and thus do not preserve genetic signatures of demographic bottlenecks. No evidence for heterozygosity excess or mode shift was uncovered in three studies specifically testing for bottlenecks in mainland populations of voles and snowshoe hares, despite the regular reductions that occur in these periodically cycling species (Burton et al. 2002; Berthier et al. 2006; Redeker et al. 2006). Likewise, these same two methods failed to document a reduction in Eurasian red squirrels in recently fragmented forest habitats (Trizio et al. 2005). Finally, Ehrich & Jorde (2005) found high levels of mitochondrial and microsatellite variation in 72 populations of lemmings (Lemmus and Dicrostonyx). While bottleneck detection methods were not specifically used in that survey, the results highlight a common outcome of rodent genetic studies: many do not infer bottlenecks even when they are known or strongly suspected. Only when populations are sufficiently isolated do bottleneck detection methods identify genetic signatures, and this degree of isolation is apparently rare in rodents. Out of six studies that used contemporary bottleneck detection methods to infer historic demographic reductions, three involved recent founding events on true islands

© 2007 The Authors Journal compilation © 2007 Blackwell Publishing Ltd

(Abdelkrim et al. 2005; Ogden et al. 2005; Wang et al. 2005), two detected bottlenecks in disjunct/isolated continental populations (Lacey 2001; Neumann et al. 2004), and only one inferred a bottleneck in a mainland population that was in close proximity to other nonbottlenecked populations (Redeker et al. 2006). Collectively, these studies suggest that meaningful bottleneck detection in rodents can only occur under a strict adherence to the requirement for population closure, which is rarely met except in island populations. Mainland populations, whether cyclic or not, rarely retain a bottleneck signature (Lacey 2001; Zenger et al. 2003; Cutrera et al. 2006), probably because of gene flow and/or an elevated rate of mutation stemming from greater effective sizes. Clearly, future work on demographics and genetic diversity needs to incorporate the influence of immigration, especially with regards to bottleneck detection (Keller et al. 2001). Genetic approaches may be the only feasible means of assessing contemporary demography for some species (Spear et al. 2006). In the absence of mark­recapture data, our genetic results would have led us to the erroneous conclusion that neither D. spectabilis population had experienced a decline of any sort. This is a clear demonstration that bottleneck inferences must be tempered with an understanding of the important molecular and life-history traits that could obscure the genetic signature of a demographic bottleneck.

Acknowledgements

We express our gratitude to members of the DeWoody laboratory as well as A. Drauch and E. Latch for valuable comments on early versions of this manuscript, and thank G. Dharmarajan for sharing ideas about cyclic species. We thank B. Swanson for his insight and microsatellite genotyping, as well as C. McCormick, J. Winters, and B. Keane. Assistance in the field was provided by B. Fanson, K. Fanson, H. Sahm, and R. Jackson, and DNA extractions from the 2004­2005 samples were performed by S. Hucko and Z. Bulut. Funding to J.D.B. was provided by the AMNH Theodore Roosevelt Memorial Fund and a Bilsland Strategic Initiatives Fellowship from Purdue University. This manuscript is ARP# 2007-18069 from Purdue University.

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Joseph D. Busch is a graduate student using this species to ask questions about population bottlenecks and MHC evolution. Peter Waser's group has used the banner-tailed kangaroo rat as a model system for the study of mammalian dispersal for more than 25 years. Andrew DeWoody's laboratory group studies molecular ecology and evolution in an array of vertebrate taxa.

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