Locus-Specific Genetic Differentiation at Rw Among Warfarin-Resistant Rat (Rattus norvegicus) Populations

Corresponding author: Michael H. Kohn, The University of Chicago, 1101 E. 57th St., Chicago, IL 60637., mkohn{at}uchicago.edu (E-mail)

Communicating editor: G. CHURCHILL

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Populations may diverge at fitness-related genes as a result of adaptation to local conditions. The ability to detect this divergence by marker-based genomic scans depends on the relative magnitudes of selection, recombination, and migration. We survey rat (Rattus norvegicus) populations to assess the effect that local selection with anticoagulant rodenticides has had on microsatellite marker variation and differentiation at the warfarin resistance gene (Rw) relative to the effect on the genomic background. Initially, using a small sample of 16 rats, we demonstrate tight linkage of microsatellite D1Rat219 to Rw by association mapping of genotypes expressing an anticoagulant-rodenticide-insensitive vitamin K 2,3-epoxide reductase (VKOR). Then, using allele frequencies at D1Rat219, we show that predicted and observed resistance levels in 27 populations correspond, suggesting intense and recent selection for resistance. A contrast of F_ST values between D1Rat219 and the genomic background revealed that rodenticide selection has overwhelmed drift-mediated population structure only at Rw. A case-controlled design distinguished these locus-specific effects of selection at Rw from background levels of differentiation more effectively than a population-controlled approach. Our results support the notion that an analysis of locus-specific population genetic structure may assist the discovery and mapping of novel candidate loci that are the object of selection or may provide supporting evidence for previously identified loci.

THE genetic structure of natural populations can potentially be utilized to test the fitness relevance of previously identified candidate genes underlying adaptation or to identify novel genes under selection (LEWONTIN and KRAKAUER 1975 ; TAYLOR et al. 1995 ). Specifically, alleles should be distributed among populations according to their selective values and levels of drift and migration (e.g., WRIGHT 1951 ; SLATKIN 1993A ). Following periods of local selection, allele frequencies of fitness-related genes should be dominated by selection. Therefore, population pairs experiencing divergent selection at fitness-related genes are expected to exhibit high levels of differentiation (e.g., LEWONTIN and KRAKAUER 1975 ; ROBERTSON 1975 ; MCDONALD 1994 ) as measured by F_ST (WRIGHT 1951 ) or one of its analogs. Similarly, allele frequencies at loci linked to the genes under selection will be altered as a function of selection intensity and recombination rates (see BARTON 2000 and references therein), a scenario that has been extended to subdivided populations (e.g., STEPHAN 1994 ; CHARLESWORTH et al. 1997 ; SLATKIN and WIEHE 1998 ). Low migration rates are expected to reduce the opportunity for recombination between divergent haplotypes (e.g., SLATKIN and WIEHE 1998 ). Therefore, as predicted by theory that specifically dealt with microsatellite evolution (SLATKIN 1995 ; SLATKIN and WIEHE 1998 ; WIEHE 1998 ), sometimes it may be possible to detect the effects of natural selection on fitness-related genes by studying linked microsatellites (e.g., PATERSON 1998 ; KOHN et al. 2000 ; HARR et al. 2002 ).

A problem with this approach is that stochastic processes may cause populations to diverge in their allele frequencies as well, thereby leading to potentially large variances of F_ST-based estimates of population differentiation (e.g., NEI and CHAKRAVARTI 1977 ; WANG et al. 2001 ). Therefore, inferences concerning selection that are based on F_ST may have high uncertainty (e.g., TSAKAS and KRIMBAS 1976 ). Patterns of variation averaged over many unlinked loci should reflect such stochastic genome-wide historical demographic effects, including founder events, dispersal, and inbreeding (e.g., PRITCHARD et al. 2000 ). To evaluate the degree to which divergence at candidate genes and the regions flanking them is caused by stochastic processes and sampling effects, genetic variation at neutral unlinked loci needs to be surveyed as well (SCHLOTTERER et al. 1997 ; PRITCHARD and ROSENBERG 1999 ).

We examine populations of the brown rat (Rattus norvegicus) that vary dramatically in resistance levels to anticoagulant rodenticide poisons (Fig 1). Anticoagulant rodenticides remain one of the main tools available to control rodent populations worldwide yet their effectiveness is jeopardized by the evolution of resistance (JACKSON 1986 ; HADLER and BUCKLE 1992 ). Warfarin has been the most widely used rodenticide in the past but has now been largely replaced by alternative anticoagulants such as coumatetralyl or second-generation, more potent anticoagulants such as bromadiolone and difenacoum (GREAVES 1986 ; HADLER and BUCKLE 1992 ). Fieldwork has documented intense selection in anticoagulant-exposed rat populations (GREAVES and RENNISON 1973 ; BISHOP et al. 1977 ; PARTRIDGE 1979 ). Progress has been made toward the elucidation of the biochemical mechanism of resistance (e.g., HILDEBRANDT and SUTTIE 1982 ; THIJSSEN 1995 ). Further, the physiological response characteristic of resistant rats (see below) now can be measured, thereby allowing for the more routine detection of resistant rats in the field (MARTIN et al. 1979 ; GILL et al. 1994 ; PELZ and ENDEPOLS 1999 ). The approximate genomic location of the warfarin resistance locus Rw has been derived from linkage mapping with phenotypic markers during laboratory crosses (GREAVES and AYRES 1969 , GREAVES and AYRES 1982 ; WALLACE and MACSWINEY 1976 ) and in a congenic resistant strain of rats with microsatellite markers (KOHN and PELZ 1999 , KOHN and PELZ 2000 ). A screen for localized patterns of linkage disequilibrium on rat chromosome 1 allowed the assignment of Rw to an 2.2-cM interval that contains the microsatellite marker D1Rat219 (KOHN et al. 2000 ).

View larger version (42K): In this window In a new window Download PPT slide   Figure 1. Distribution of resistance to warfarin, RW (A), bromadiolone, RB (B), coumatetralyl, RC (C), and difenacoum, RD (D) in the Münsterland area (inset, ML) of Germany (summary of data published in PELZ 2001 ). Distribution map based on 1168 rats trapped live and tested for resistance with the BCR method between 1990 and 1999 (cf. PELZ et al. 1995 ; PELZ 2001 ). Of the 46 localities depicted, those 25 localities for which tissue samples for genetic typing were available show a population identification number. Samples from farms belonging to the same township were pooled to generate this figure (yielding average resistance frequencies for the locality) and each population identification number is shown. LE, SD, MB, and LH denote populations outside the resistance area tested with the BCR method; only samples from MB and LH were available for the genetic study. Populations numbered 1, 7, 8, 9, 22, 27, and 31 had N < 3 and were excluded from genetic data analyses. Population resistance frequencies given in Table 1 were used for all analyses. Farm names cannot be provided by prior agreement, but details on sampling locations will be provided by request to M. H. Kohn or H.-J. Pelz.

The anticoagulant resistance phenotype is manifest as prolonged prothrombin times [or percentage of clotting activities (PCA)] after a diagnostic dose of anticoagulant has been administered. PCA is estimated with a blood clotting response (BCR) test the values of which are then used to separate resistant from nonresistant phenotypes (MARTIN et al. 1979 ; GILL et al. 1994 ). Biochemical analyses show that the resistance mechanism involves an enzyme complex that has vitamin K 2,3-epoxide reductase (VKOR) activity (e.g., THIJSSEN and JANSSEN 1994 ; CAIN et al. 1998 ; GUENTHNER et al. 1998 ). For small sample sizes, resistance phenotypes and genotypes of rats now can be determined with an in vitro VKOR activity assay (THIJSSEN and PELZ 2001 ). Resistance to various anticoagulants may be due to either different alleles at Rw or additional loci closely linked to it (e.g., GREAVES and AYRES 1982 ). Strain-specific modifier loci, some of which are sex linked, likely affect the resistance phenotype (MACNICOLL 1986 , MACNICOLL 1995 ; KERINS and MACNICOLL 1999 ; SUGANO et al. 2001 ).

Here we utilize new mapping resources, and resistance phenotyping and genotyping technology, to design a study that examines the joint effect of selection, migration, and drift on marker variation and differentiation in resistant rat populations. First, we present further evidence for the tight linkage between Rw and microsatellite D1Rat219 by association mapping, using wild-caught rats for which resistance genotypes are now available (THIJSSEN and PELZ 2001 ). We also examine the involvement of the Rw locus in resistance to other anticoagulant rodenticides and describe aspects of its quantitative genetics. Second, we examine the association between D1Rat219 and resistance phenotype frequencies in a large sample of rats. Third, we contrast variation and differentiation at D1Rat219 with presumably neutral loci. And fourth, we compare these results obtained using the population-controlled approach to those obtained using a case-controlled design.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Notation:
Capital letters denote the phenotypes that are resistant to warfarin, bromadiolone, coumatetralyl, and difenacoum (RW, RB, RC, and RD, respectively). Resistance loci and alleles are denoted in italic as Rw, Rb, and so on, the distinction between the locus and allele symbols being evident from the context. Susceptible phenotypes and alleles are denoted by a plus symbol (+); thus, a heterozygous warfarin-resistant rat would be designated as RW for its phenotype and +/Rw for its genotype. A warfarin susceptible rat would be designated as RW+ for its phenotype and +/+ for its genotype.

Sample populations:
Study farms and townships are located in the Münsterland area of northwestern Germany where warfarin has been used since the early 1950s (PELZ et al. 1995 ; PELZ 2001 ). In 1990, rodent control problems were reported and a survey using the BCR method revealed a resistance area, ML, of >8000 km² (Fig 1A, top right inset). The focus of the survey was on rat-infested townships and farms (PELZ et al. 1995 ). Resistance may dramatically differ between adjacent farms as is depicted in Fig 1A (e.g., populations 9 and 28, 3 and surrounding farms). Resistance frequencies are given in Table 1. Other anticoagulants now have largely replaced warfarin in our study area. Resistance to these agents also has evolved (Fig 1; cf. PELZ et al. 1995 ; PELZ 2001 ). This progression toward the use of alternative anticoagulants in response to the evolution of resistance in Germany parallels that observed in the United Kingdom and in many other localities around the world (GREAVES 1986 ; HADLER and BUCKLE 1992 ). In our study area warfarin resistance has expanded in range and prevalence over the past decade, and resistance to bromadiolone, coumatetralyl, and difenacoum has established itself at localities where it was previously undetectable (PELZ 2001 ).

Fig 1 depicts the 27 localities from which 727 rats were collected (cf. Table 1). Samples were obtained on several occasions between 1995 and 1999 and thus are unlikely to represent family groups. Of these, 677 rats were tested for warfarin resistance with the BCR method (cf. OEPP/EPPO 1995 ) as applied previously (PELZ et al. 1995 ; KOHN and PELZ 1999 ; PELZ 2001 ), 482 for bromadiolone resistance, 364 for coumatetralyl resistance, and 369 for difenacoum resistance. Initially, difficulties were encountered with tests for coumatetralyl resistance that we were able to address during later stages of the project (PELZ and ENDEPOLS 1999 ). Our analyses with respect to the RC phenotype thus should be considered as preliminary.

Warfarin resistance generally occurs in conjunction with resistance to the other anticoagulants in our study area (Table 1). With the exception of RD, the frequency of resistance to one anticoagulant was significantly correlated with the frequency of resistance to another anticoagulant (not shown). Such cross-resistance appears to be a general feature of resistant rodent populations (MACNICOLL 1986 , MACNICOLL 1995 ; HADLER and BUCKLE 1992 ; PELZ et al. 1995 ; THIJSSEN 1995 ). Resistance groups RW, RC, RB, and possibly RD therefore should not be considered as independent samples during further analyses. Conversely, warfarin-susceptible rats almost always were susceptible to the other anticoagulants. Only 3 of 101 (3%) RW+ rats were RB (1), RC (2), or RD (0). For our analyses we considered only one group (RW+) of susceptible rats.

Microsatellite typing and analysis:
DNA from 727 rats was extracted and the microsatellite loci D1Rat219, D2Rat31, D10Rat6, D13Rat18, D14Rat15, and D17Rat38 were assayed following standard procedures (KOHN and PELZ 1999 ). The latter five loci are located on rat chromosomes 2, 10, 13, 14, and 17 and were typed as an indicator of background levels of variation. D1Rat219 was chosen to represent Rw on rat chromosome 1 (see RESULTS; cf. KOHN et al. 2000 ). For map position data of loci, see The Rat Genome Database at the Medical College of Wisconsin, Milwaukee, Wisconsin (http://rgd.mcw.edu/; April 2002).

Each of the presented analyses used a subset of the total sample. First, 16 rats from population 24 were used for association mapping of Rw (Table 2). Their resistance phenotypes and genotypes were previously determined using the in vitro assay of VKOR activity (THIJSSEN and PELZ 2001 ). Resources were insufficient to apply the VKOR assay to a more extensive sample. In addition to the five unlinked microsatellite loci D2Rat31, D10Rat6, D13Rat18, D14Rat15, and D17Rat3, these 16 rats were typed for four loci that mapped within the 2.2-cM interval on chromosome 1 containing Rw (Table 2; D1Rat67, D1Rat364, D1Rat219, and D1Rat288; KOHN et al. 2000 ).

Second, the entire sample of 727 rats from 27 populations was analyzed (Table 1). Rats for which no BCR testing was done but that were obtained from populations with known resistance phenotype frequencies were included in this population-controlled analysis. Unless stated otherwise, we focused on the analysis of population genetic data with respect to RW. Allele frequencies underlying the population-controlled design are given in supplement 1 at http://www.genetics.org/supplemental/.

Third, only rats of known BCR phenotype were analyzed using a case-controlled design. Warfarin-resistant rats formed the case group, RW, to be compared to the control group, RW+, composed of warfarin-susceptible rats. This analysis ignored the population origin. The groups RB, RC, and RD should not be considered as independent from the RW group (see above) and only brief mention of results will be made. Allele frequencies underlying the case-controlled design are given in supplement 2 at http://www.genetics.org/supplemental/.

Analyses and computations were done as implemented in the Genetic Data Analysis (GDA) software (LEWIS and ZAYKIN 2002 ). The software implements analytical and randomization procedures outlined in WEIR 1996 (and references given therein). Descriptive statistics computed included the number of chromosomes sampled (2N), the number of alleles per locus (k), expected and observed heterozygosity (H_e and H_o), and fixation indices estimated with respect to sample configuration (f). The coefficient D_A was computed and ² analysis was used to test for Hardy-Weinberg equilibrium (HWE). In addition, HWE exact tests were done using the shuffling method for 3200 runs followed by Fisher's exact tests. Loci with P < 0.05 were considered in HW disequilibrium. Composite gametic phase disequilibrium D_AB (i.e., not assuming HWE) between the most frequent alleles at the loci was estimated in the same fashion.

For each locus separately and across loci, WRIGHT'S 1951 F-statistic analogs (F_ST), F (F_IT), and f (F_IS) were estimated and analyzed within an ANOVA framework using GDA software following WEIR 1996 . If applicable, to estimate significance of F-statistics, the 95% confidence interval (CI) about each measure was computed using 1000 bootstrap replicates over loci. Similarly, jackknifing over populations was used to compute mean values and a 1 SD interval.

Spearman's correlation coefficients among the variables , geographical distance, and RW were computed. Here, RW was used as a surrogate measure for divergent selection with warfarin and was computed from Table 1 as the difference in warfarin resistance frequency between population pairs (supplement 3 at http://www.genetics.org/supplemental/). Geographic isolation was measured in kilometers as a straight line connecting any two sampling sites (supplement 3 http://www.genetics.org/supplemental/). Significance of correlation coefficients was assessed within the framework of a two-tailed MANTEL'S 1967 test (SLATKIN 1993B ; RAYMOND and ROUSSET 1995 ).

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Choice of the genetic marker for resistance:
Microsatellite genotyping results for 16 rats were compared to warfarin resistance phenotypes determined with the VKOR method (Table 2). At each marker we designated the allele most commonly associated with warfarin resistance as the Rw allele and the remaining ones as + alleles. On the basis of the presence or absence of the assigned Rw allele, and assuming that the resistance allele was dominant (see below), D1Rat219 correctly classified all 16 rats as either resistant or susceptible according to VKOR testing results (Table 2). D1Rat67 correctly classified 15 (94%) rats, whereas D1Rat288 and D1Rat364 each correctly classified 14 (86%) rats. Loci on the other chromosomes classified between 12 (75%) and 14 (86%) rats correctly by chance.

Microsatellite genotypes at D1Rat364, D1Rat219, and D1Rat67 corresponded to warfarin resistance genotypes determined with the VKOR method in 9 (56%), 15 (94%), and 13 (81%) of 16 cases, respectively (Table 2). Genotypes at D1Rat288 and at the five unlinked loci corresponded to the VKOR genotyping results in five or fewer cases. The single case of inconsistency between D1Rat219 with a VKOR genotype was due to the heterozygous resistant rat 4100 whose VKOR activity was between that of heterozygous and homozygous resistant rats and thus was ambiguous (THIJSSEN and PELZ 2001 ). Overall, only 1 of 18 VKOR genotypes determined in the previous study by THIJSSEN and PELZ 2001 was ambiguous.

Larger values of D_AB are expected between markers closely linked to the trait locus than between more distant markers. The highest D_AB coefficient of 0.16 was found between Rw and D1Rat67 and between Rw and D1Rat219. A Fisher's exact test on the permutated contingency tables yielded the strongest support ( = 0.0001) for tight linkage between Rw and D1Rat219 (Table 2). D_AB coefficients and associated statistics for the loci situated on other chromosomes were not significant. Analysis of D_AB assumed the preservation of haplotypes (i.e., no double crossovers) and thus represented a best-case scenario that was partly supported by significant levels of higher-order composite disequilibria coefficients (D_ABC) among D1Rat364, D1Rat219, and D1Rat67 (not shown).

This analysis further implicated the locus group D1Rat364-D1Rat219-D1Rat67 in the expression of a warfarin-insensitive VKOR and suggested that D1Rat219 is the most suitable marker for resistance of those surveyed (cf. KOHN et al. 2000 ). We chose D1Rat219 as the marker to represent Rw for two additional reasons. First, D1Rat219 is the only framework marker, implying the lowest degree of uncertainty concerning its map location. Second, D1Rat219 has been placed in the newest available gene maps of the rat [e.g., STEEN et al. 1999 ; a high-density integrated genetic linkage and radiation hybrid map of the laboratory rat, The Rat Genome Database: ftp://rgd.mcw.edu/pub/publications/1999/steen_genome_research/].

Quantitative genetics:
We analyzed D1Rat219 genotypes and VKOR activities of the 16 rats from Table 2 within a coarse quantitative genetic framework (FALCONER and MACKAY 1996 ). Genotypic values derived from the VKOR activity assay of the 254/254 and +/+ rats were set as a and -a, respectively, and that of the +/254 genotype was set as d (Fig 2). The point of zero was set midway between the genotypic values of the two homozygotes. The value of d depends on the degree of dominance (d/a), zero being the expectation for codominant alleles. We found that genotypes at D1Rat219 had significant effects on VKOR activities in the presence of warfarin (ANOVA; P < 0.001, F_Ratio = 132.1, R² = 0.94, d.f. 15; Fig 2, top). Genotypes that lacked the 254-bp allele (+/+) had genotypic values of -43.7 ± 2.1 (SD) whereas genotypes containing one and two copies of the 254-bp allele had genotypic values of -2.8 ± 17.8 and 43.7 ± 5.3, respectively. The effect of two essentially codominant alleles was indicated by a d/a of -0.06. The genotypic values of 254/254 genotypes were significantly higher than the genotypic values of +/254 and +/+ genotypes (Tukey-Kramer comparison of means, all P < 0.01), and the +/254 genotypes had a higher value than the +/+ genotypes (Tukey-Kramer comparison of means, P < 0.01). The mean VKOR activity of 254/254 genotypes was 87% of the expected full (100%) activity, suggesting incomplete penetrance with respect to warfarin.

View larger version (37K): In this window In a new window Download PPT slide   Figure 2. Association between in vitro VKOR activity and D1Rat219 genotypes deduced from 18 rats (cf. Table 2) in the presence of 2 µM warfarin (top), bromadiolone (middle), and difenacoum (bottom). Absolute percentage of VKOR activities are shown on the left axis, and corresponding genotypic values are on the right axis. Assigned genotypic values -a, d, and a as defined in FALCONER and MACKAY 1996 , and the point of zero (dashed line) is midway between -a and a. The degree of dominance is defined as d/a. The dotted line demarcates 50% VKOR activity. Susceptibility alleles were pooled as + (see text). Two additional susceptible rats (IDs 4038 and 4060 in THIJSSEN and PELZ 2001 ) from populations 12 and 28, respectively, with the D1Rat219 genotypes 250/250 and 248/250 were included in this analysis.

Similarly, genotypes at D1Rat219 had significant effects on VKOR activities in the presence of bromadiolone (ANOVA; P < 0.01, F_ratio = 22.7, r² = 0.75, d.f. 15; Fig 2, middle) and difenacoum (ANOVA; P < 0.003, F_ratio = 8.7, r² = 0.54, d.f. 15; Fig 2, bottom). The effects of recessive alleles with respect to bromadiolone and difenacoum were indicated by a degree of dominance of -0.4 for both anticoagulants. Low penetrance of Rw with respect to bromadiolone and difenacoum exposure, respectively, was suggested by a VKOR activity of the 254/254 genotype that was 50 and 15% of the expected full activity. Finally, in the presence of bromadiolone and difenacoum, the 254/254 genotypic values were significantly higher than the genotypic values of the +/254 and +/+ genotypes (for both, Tukey-Kramer comparison of means was P < 0.01). With respect to difenacoum, however, the +/254 genotypic value was not significantly higher than the +/+ genotypic value (Tukey-Kramer comparison of means, not significant (n.s.) at = 0.01).

These data suggest that D1Rat219 is closely linked to one or several tightly linked loci (Rw) that mediate warfarin insensitivity of the VKOR. The incomplete dominance and penetrance inferred from D1Rat219 either were caused by its incomplete association with Rw or reflect real properties of Rw. The RB and RD phenotypes either are due to separate resistance loci Rb and Rd that are less closely linked to D1Rat219 than Rw is or are determined by the Rw locus, which differs in its penetrance and dominance with respect to the three anticoagulants examined. Conceivably, the expression of resistance to bromadiolone and difenacoum then requires the action of modifier loci whose relative contribution to resistance depends on assumptions made concerning the required VKOR activity for proper blood coagulation homeostasis. For instance, if we assume that 50% VKOR activity is needed for coagulation homeostasis (model 1, Fig 2), then Rw/Rw rats would be considered predominantly RW and RB, +/Rw rats likely would be considered RW and RB+, and none would be considered RD. However, lower VKOR activity thresholds needed to maintain coagulation homeostasis have been suggested (THIJSSEN and JANSSEN 1994 ; THIJSSEN and PELZ 2001 ). When only genotypes that express a VKOR with <10% activity are considered as susceptible (model 2, Fig 2), then both +/Rw and Rw/Rw rats would be considered RW and RB, whereas only Rw/Rw rats would be considered RD and +/Rw rats RD+.

Association between D1Rat219 and population resistance frequency:
We considered the Rw allele (254-bp allele) and + alleles (all others) with frequencies p and q, respectively, which were measured in the entire sample of 727 rats (cf. supplement 1 at http://www.genetics.org/supplemental/). We assumed that Rw was dominant (i.e., both model 1 and model 2 in Fig 2) and fully penetrant with respect to warfarin. At HWE we then expected a total of 49% +/Rw rats and 18% Rw/Rw rats in our sample, corresponding to a predicted RW phenotype frequency of 67%, which differed by only 4% from the observed RW phenotype frequency of 63% (Table 1). A BCR classification error may explain as much as 2% of this discrepancy (cf. MARTIN et al. 1979 ; KOHN and PELZ 1999 ).

Similarly, assuming dominance and full penetrance of Rw with respect to bromadiolone (model 2 in Fig 2) and using HWE frequencies at D1Rat219, we estimated that 67% of rats were RB, only 1% less than the observed RB sample frequency of 68% (Table 1). In contrast, observed frequencies of RC (47%) and RD (1%) could not be predicted using allele frequencies at D1Rat219. The discrepancy with respect to RC likely was related to our initial difficulties in adopting the BCR method for RC resistance testing (PELZ and ENDEPOLS 1999 ). Our ability to predict RD frequencies may have been diminished by small sample size and by the presumably recessive nature and low penetrance of Rw with respect to difenacoum (Fig 2, bottom; cf. GREAVES and CULLEN-AYRES 1988 ).

The sample mean of enzymatic activity of the VKOR (genotypic value M) can be predicted on the basis of the underlying HWE genotype frequencies at the trait locus as M = a (p - q) + 2dpq (FALCONER and MACKAY 1996 ). First we applied this approach to the case-controlled sample. Allele frequencies were obtained from supplement 2 and a, -a, and d were derived from Fig 2. Predicted M, given as percentage of VKOR activity in the presence of the respective anticoagulant, was 57, 24, and 13% for the case groups RW, RB, and RD, respectively (Fig 3A). These percentages exceeded a 10% cutoff value for VKOR activity (model 2) and hence may be considered RW, RB, and RD. Only the RW group exceeded 50% of VKOR activity expected under a single dominant genetic model (cf. Fig 2, model 1). Control group RW+ had a predicted VKOR activity of <5% and would be classified as susceptible under both models (cf. Fig 2). Thus, allele frequencies at D1Rat219 measured for the case and control groups enabled predictions to be made concerning VKOR activities (M-values) and resistance status.

View larger version (20K): In this window In a new window Download PPT slide   Figure 3. Percentage of VKOR activities (M-value) in a case-controlled (A) and population-controlled design (B) predicted on the basis of allele frequencies at D1Rat219. In A, we considered the phenotypes warfarin resistance RW, bromadiolone resistance RB, and difenacoum resistance RD. In B, only the RW phenotype and its frequency in populations were considered (see text).

Similarly, we predicted the M-value for each population listed in Table 1 on the basis of D1Rat219 allele frequencies (supplement 1 at http://www.genetics.org/supplemental/). We found a significant association between predicted M-values and RW frequencies (ANOVA, F_Ratio = 50.3, R² = 0.79, d.f. 26, P < 0.0001; Fig 3B) and between predicted M-values and RB frequencies (ANOVA, F_Ratio = 18.5, R² = 0.58, d.f. 25, P < 0.0001; not shown), but not between predicted M-values and RD frequencies (P = 0.27, not shown). To conduct a corresponding analysis for RC, VKOR activities measured with respect to warfarin were used (Fig 2, top). Like warfarin, coumatetralyl is a first-generation, nonacute-acting anticoagulant. The M-value that was obtained was associated with RC frequencies (ANOVA, F_Ratio = 13.8, R² = 0.57, d.f. 19, P = 0.003, not shown). Overall, this coarse regression-based approach (cf. MANTEL 1967 ) allowed for a prediction to be made regarding the mean VKOR activity of populations (M-value) underlying resistance to warfarin, bromadiolone, and coumatetralyl, but not difenacoum.

Population-controlled analysis of variation and differentiation:
We compared variation and differentiation at D1Rat219 and the five neutral loci across 27 rat populations. An average of 2.9 (2.5–3.2) alleles per population occurred at D1Rat219 and 4.3 (3.8–4.7) alleles per locus and population at the neutral loci (Table 3). The mean H_e at D1Rat219 was 0.43, whereas H_e at the neutral loci was 0.60. The 95% confidence intervals of the estimates overlapped. Similarly, the confidence intervals about the mean H_o values of D1Rat219 (0.43) and the neutral loci (0.54) overlapped.

Four populations (23, 24, 28, and 29) deviated from HWE at D1Rat219. Only one of the four deviations (28) was in the direction of heterozygote excess. Sixteen populations displayed deviations from HWE at neutral loci (populations given in parentheses): D2Rat31 (6, 10, 14, 18, 25, 26, LH), D10Rat6 (11, 12, 17, 20, 24, 28, 29), D13Rat18 (6, 12, 26, 28), D14Rat15 (LH), and D17Rat38 (11, 12, 17–20, 23–25). Of the 28 observed deviations from HWE at the five neutral loci, all were in the direction of heterozygote deficiency. Population substructure within farms and townships presumably has caused Wahlund's effect (cf. SELANDER and YANG 1969 ).

Descriptive population genetics statistics from Table 3 yielded no significant relationships between them and resistance frequencies given in Table 1 (ANOVA; P > 0.05). This was valid for the presumably neutral loci as well as for D1Rat219. However, the mean of f at D1Rat219 calculated over all populations (0.01) was one order of magnitude lower than the mean of f at the neutral loci (0.10; Table 3), but since the 95% CIs overlapped, this observation remained statistically inconclusive.

Analysis of population structure at the neutral loci revealed high F-statistics that were significantly different from zero (P < 0.05) at each hierarchical level f, F, and (Table 4A). F (0.226) was most pronounced, followed by (0.133) and f (0.107). Computed standard deviations for each individual neutral locus suggested that with the exception of some f values, F-statistics were significantly different from zero throughout (Table 4A). In contrast, f (-0.024) at D1Rat219 was not significantly different from zero, whereas F (0.214) and (0.232) were significantly different from zero. Hence, overall, D1Rat219 differed from the genomic background by more pronounced levels of outbreeding (f) and population subdivision (). The locus-specific patterns of genetic subdivision measured as at D1Rat219 were in agreement with expectations for loci that are the object of selection. Following POGSON et al. 1995 , we compared values of D1Rat219 with the genomic background using the expression ²_(n-1) = (n-1) [_(D1Rat219)/_{(genomic background)}], where n is the number of populations examined and is computed over the five neutral loci (cf. Table 4A). Using this approach, we found that the difference between D1Rat219 and the genomic background was significant (²₍₂₆₎ = 45.4; P < 0.01). None of the permutations that placed a neutral locus in the nominator were significant at = 0.05.

View this table: In this window In a new window   Table 4. Analysis of f, F, and at D1Rat219 and five neutral loci computed for the population-controlled (A) and the case-controlled design (B)

We tabulated at D1Rat219 and at the neutral loci to test their interrelationship with geographical distance and divergent selection with warfarin (RW; supplement 3 at http://www.genetics.org/supplemental/). The -value at the five neutral loci was significantly related to distance (Fig 4A; Mantel's test; P = 0.02; a = 0.136, b < 0.001), where a and b represent the interception and slope of the linear regression fitted to the points, respectively. Testing the relationship /(1 - ) vs. ln(distance) (SLATKIN 1993B ) was also significant (P = 0.02). Similarly, at locus D1Rat219 distance was significantly correlated with (Fig 4B; P < 0.0001; a = 0.192, b < 0.001) and with /(1 - ) (P < 0.0001). In sharp contrast, at D1Rat219 was significantly related to RW (Fig 4B; P < 0.0001; a = 0.053, b = 0.510) whereas no such relationship was supported for the neutral loci (Fig 4A; P = 0.10; a = 0.138, b = 0.020). RW had no systematic relationship with geographic distance separating localities (P = 0.11; a = 0.317, b = 0.001; cf. Fig 1). Hence, both the neutral alleles and alleles at D1Rat219 were distributed according to geographic distance (R² 40 and 21%, respectively). However, while differentiation at D1Rat219 clearly was dominated by RW (R² 67%), the effect that RW had on differentiation over the genomic background was negligible (R² < 1%).

View larger version (27K): In this window In a new window Download PPT slide   Figure 4. Isolation-by-distance and isolation-by-divergent selection (RW) at neutral loci (A) and at D1Rat219 (B). For clarity of presentation, -values were grouped in bins and distances >100 km were omitted. Statistical analysis used unmodified data given in supplement 3 at http://www.genetics.org/supplemental/ (see text).

Case-controlled analysis of variation and differentiation:
Rats were grouped by their warfarin resistance phenotype and analyzed within the framework of a case-controlled design. Descriptive statistics k, H_e and H_o, and f at the five neutral loci did not differ between the RW+ and RW groups (paired t-tests, all n.s. at = 0.05; Table 5). Sample size (2N) of the RW+ group (319.2) was lower than that of the RW group (825.6). However, standard deviations associated with statistics were similar between both groups, suggesting sample size had little effect (Table 5). With one exception (D13Rat18, RW+) neutral loci generally departed significantly from HWE (P < 0.001) and exhibited heterozygote deficiency in both groups (not shown), as was expected for intentionally pooled samples derived from subdivided populations.

D1Rat219 was set apart from the genomic background in both the case and control group in that it differed in the magnitude and equity of H_e and H_o values. Specifically, we observed a high level of inbreeding at D1Rat219 (0.38) in the RW+ group that was similar to that observed over the genomic background (0.23 ± 0.16). In contrast, we found no evidence for inbreeding (-0.08) at D1Rat219 in the RW group even though the genomic background in the RW group displayed levels of inbreeding (0.21 ± 0.10) equal to those of the RW+ group (Table 5). Genotype frequencies at D1Rat219 in the RW category were marginally compatible with HWE expectations (P = 0.058) but HWE at D1Rat219 was rejected in the RW+ group (P < 0.01). Results for the RB and RC groups were similar to those presented for the RW group (not shown), and sample size for RD was too low for analysis.

Genetic subdivision between case and control groups at the five presumably neutral loci was low ( = 0.012) yet significantly different from zero at = 0.05 (Table 4B). Moreover, f and F were pronounced (0.214 and 0.224, respectively) and significant at = 0.05 each (Table 4B). In contrast, resistant and nonresistant rats were highly differentiated with regard to D1Rat219, a locus closely linked to Rw. between case and control groups was 0.311 or 30 times more pronounced than that of the genomic background. Although f was small at D1Rat219 (0.037), F was pronounced (0.337). Statistics at D1Rat219 could not be tested for significance using the bootstrap or jackknife procedures. To obtain a measure for the robustness of these estimates, random assignment of 6150 D1Rat219 genotypes (sampled with replacement) to the RW and RW+ groups was done, yielding a nonsignificant (95% CI: -0.001–0.091) and significant ( = 0.05) f (95% CI: 0.129–0.181) and F (95% CI: 0.154–0.225). We predicted that D1Rat219 should be highly differentiated between the case group RW and the control group RW+. For this to be informative, we further predicted that the genetic differentiation across the genomic background should be negligible. We found that when ²_(n-1) = (n - 1) [_(D1Rat219)/_{(genomic background)}] (POGSON et al. 1995 ) was computed, values at D1Rat219 (0.311) and for the genomic background (0.012) were significantly (²₍₁₎ = 25.9; P < 0.001) different. None of the permutations that placed any of the putatively neutral loci in the nominator was significant at = 0.05.

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

D1Rat219 as a marker for resistance:
Our previous research established an association between warfarin resistance as measured by the BCR method and allele frequencies at D1Rat288, D1Rat364, D1Rat219, and D1Rat67 contained in an 2.2-cM interval of rat chromosome 1 (KOHN et al. 2000 ). In accord with previous linkage mapping data, we hypothesized that this interval corresponds to the warfarin resistance locus Rw (KOHN et al. 2000 ). Here, we determined VKOR activity for a small sample of rats (Table 2, Fig 2). VKOR measurement should be linked to the resistance mechanism more directly than prothrombin time (BCR) measurements previously taken (e.g., HILDEBRANDT and SUTTIE 1982 ; THIJSSEN and JANSSEN 1994 ; CAIN et al. 1998 ; GUENTHNER et al. 1998 ; THIJSSEN and PELZ 2001 ). Correspondingly, our genotyping data (Table 2) now suggest that the interval defined by markers D1Rat364, D1Rat219, and D1Rat67 is tightly linked to a locus Rw that mediates warfarin insensitivity via a pathway that involves an anticoagulant-insensitive VKOR (Fig 2) and that promotes normal prothrombin times despite exposure to anticoagulant poison. Our data support earlier suggestions that as little as 10% VKOR activity (model 2 in Fig 2) may be sufficient to maintain coagulation homeostasis, i.e., to express the resistance phenotype (cf. Fig 3A). Finally, our data are compatible with Rw being a component of the VKOR complex, but we cannot exclude the possibility that the Rw locus represents a gene that acts farther upstream of the VKOR (cf. WALLIN et al. 2001 ).

Our results prompt the working hypothesis that Rw also corresponds to Rb, Rc, and Rd and thus is a major locus or cluster of loci underlying resistance to warfarin, bromadiolone, coumatetralyl, and difenacoum (Fig 2 and Fig 3). At least four previous observations support this hypothesis. First, all of these anticoagulant compounds are derivatives of coumarin. Second, VKOR activities measured in the presence of all four anticoagulants are correlated (THIJSSEN and PELZ 2001 ). Third, with the exception of RD, resistance segregated as a major and dominant locus in laboratory crosses (GREAVES and AYRES 1969 , GREAVES and AYRES 1982 ; WALLACE and MACSWINEY 1976 ; KOHN and PELZ 1999 ). RD mapped to the same genomic interval but was found to be recessive (GREAVES and CULLEN-AYRES 1988 ). Finally, cross-resistance to several different anticoagulants occurs in our rat populations (Fig 1 and Table 1; cf. PELZ et al. 1995 ; PELZ 2001 ; THIJSSEN and PELZ 2001 ) and elsewhere in the world (HADLER and BUCKLE 1992 ).

Ecological genetics:
The nearly ubiquitous presence of the 254-bp allele at D1Rat219 in resistant rats (Fig 2 and Fig 3) suggests a single and recent origin of resistance, followed by a rapid spread throughout our study area (Fig 1). The origin of the resistance allele could be due to de novo mutations resulting from the introduction of the resistance allele from elsewhere. The Rw allele likely became common and spread rapidly in the early 1990s, given the increasing control problems with anticoagulants and high frequencies of resistance on farms where it was not detected less than a decade ago (PELZ et al. 1995 ; PELZ 2001 ). Assuming dominance, a net selection coefficient of as little as 0.05 would be sufficient to attain the observed average Rw allele frequency (26%) within a decade (cf. HARTL and CLARK 1988 , p. 156). Mortality rates between 60 and 100% (LUND 1985 ) suggest more intense selection (e.g., s > 0.4) may occur in exposed rat populations. Hence, intense selection may have led to high levels of resistance within even shorter time periods (e.g., <2 years) at sites (e.g., 7 and 28) located at the eastern border and that until recently had undetectable resistance levels. Overall, given the widespread use of anticoagulants in the ML area, resistance to warfarin, bromadiolone, and coumatetralyl could have developed and easily spread since their initial discovery about a decade ago. The slow increase in difenacoum resistance frequency is compatible with its recessive genetic underpinnings (GREAVES and CULLEN-AYRES 1988 ; cf. HARTL and CLARK 1988 , p. 156).

Owing to the recent and intense selection that has dominated our study system, we were able to estimate warfarin and bromadiolone resistance frequencies within 4% or less of the BCR-deduced value simply by using allele frequencies at D1Rat219. Moreover, using allele frequencies at D1Rat219, we deduced the in vitro VKOR activity of case and control groups (Fig 3A) and of field populations of varying resistance levels (Fig 3B). However, in some populations the association between the 254-bp allele and Rw was weak (e.g., in populations 21 and 29–32). Moreover, we were unable to determine coumatetralyl and difenacoum resistance frequencies. Therefore, PCR-based diagnosis of resistance in the field merits further development and our approach should be adopted only with caution.

Knowledge of the mode of selection at Rw provides insight into the ecological genetics and management of resistant rodent populations (GREAVES 1986 ; HADLER and BUCKLE 1992 ). Warfarin resistance has been adopted as a textbook example of overdominant selection (HARTL and CLARK 1988 ; FALCONER and MACKAY 1996 ). A high nutritional need for vitamin K constitutes the presumed pleiotropic cost associated with the resistant Rw/Rw genotype. In contrast, due to the dominant nature of warfarin resistance, the +/Rw genotype is protected against poisoning but may not suffer measurable vitamin K deficiency. Hence, a balanced polymorphism may be maintained. However, while most previously described resistant rat strains suffered from vitamin K deficiency, other strains did not (SMITH et al. 1993 ; THIJSSEN 1995 ). Hence, an overdominant selection mode at Rw cannot be simply assumed and merits investigation within a strain-specific context.

Overdominance, as narrowly defined, exists when the heterozygote has a higher fitness than both homozygotes at all times and across niches (e.g., HARTL and CLARK 1988 ). This narrow definition may not hold for our rat populations. First, we previously found that variation at microsatellite loci linked to Rw was drastically reduced (KOHN et al. 2000 ). This observation is difficult to reconcile with theoretical expectations for microsatellites linked to genes under balancing selection (SLATKIN 1995 ; WIEHE 1998 ). Second, balancing selection should reduce F_ST values between populations (LEWONTIN and KRAKAUER 1975 ; KARL and AVISE 1992 ; MCDONALD 1994 ). Here we found, to the contrary, that F_ST at D1Rat219 was more pronounced relative to F_ST values distributed on other chromosomes (Table 4A). Fourth, we found no consistent support for heterozygote excess at D1Rat219 within populations (Table 3). However, tests for HWE are not an especially powerful method to detect selection (HARTL and CLARK 1988 ).

Other observations are compatible with overdominant selection models at Rw. First, expected heterozygosity (0.43) equaled the observed heterozygosity (0.43) at D1Rat219, whereas at the neutral loci we found that the expected heterozygosity (0.60) exceeded the observed heterozygosity (0.54; Table 3). Population substructure ( = 0.133; Table 4A) conceivably has led to heterozygote deficiency and Wahlund's effect over the genomic background (i.e., HARTL and CLARK 1988 ). Selection could have counteracted this pattern for microsatellite loci linked to Rw (SLATKIN 1995 ). Second, within populations we find 13 negative f values at D1Rat219 and only 4 at the genomic background (Table 3), an observation that is compatible with a viability of the +/Rw genotype that exceeds the geometric mean of the Rw/Rw and +/+ genotypes (WEIR 1996 ). In all, evidence for overdominant selection at Rw remains ambiguous in our populations and the mode of selection may depend on the poison used. Alternative models that employ a less narrow definition of overdominance (DEMPSTER 1955 ) that may explain facets of our variation data should be explored. These may include those that assume a heterogeneous selection regime over space and time and low migration rates (cf. LEVENE 1953 ; SLATKIN and WIEHE 1998 ; SCHMIDT and RAND 2001 ).

Locus-specific population structure at D1Rat219:
Levels of genetic differentiation at D1Rat219 should exceed those observed over the genomic background. Whereas the former should be dominated by selection, the latter should be influenced predominantly by drift. We found significant differences in F_ST between neutral loci and those linked to Rw (Table 4A). Specifically, the mean value of for D1Rat219 was 1.7 times that for neutral loci (0.232 vs. 0.133; Table 4A). Individual s between populations reached even higher values at D1Rat219, up to 0.8 for populations separated by a mere 37 kilometers (populations 15 and 26; cf. supplement 3 at http://www.genetics.org/supplemental/).

To quantify the relative influence that selection had on the distribution of resistance alleles over the spatial scale represented by our study (Fig 1), we assessed patterns of differentiation with distance. For the neutral loci, the amount of variation in that was explained by variation in geographical distance was 40% (Fig 4A), whereas the contribution of RW to values of was nonsignificant (R² < 1%; Fig 4A). The average value of for the neutral loci was 0.133, corresponding to 1.6 genetically effective migration events per generation under an island model. In contrast, at the resistance marker D1Rat219, 67% of variation in was explained by variation in our surrogate measure of selection RW (Fig 4B) and only 21% was explained by variation in geographical distance. Hence, net rates of migration and fixation at Rw are determined by the scope and intensity of warfarin application, resulting in substantial population differentiation at D1Rat219, a locus linked to Rw. Accordingly, our results support the previously formulated notion (LEWONTIN and KRAKAUER 1975 ; TAYLOR et al. 1995 ) that a comparison of between a candidate locus and the genomic background is a valid method for detecting fitness-related genes.

In contrast to the warfarin resistance allele, most genetic polymorphisms in nature appear to be weakly selected (ENDLER 1986 ; CONNER 2001 ). Structured populations provide more favorable conditions for polymorphism maintenance (e.g., KARLIN 1982 ; NAGYLAKI 1992 ; SLATKIN and WIEHE 1998 ; NAGYLAKI and LOU 2001 ). However, the ability to detect loci under selection may be limited if pronounced population structure has caused the genomic background to be highly differentiated (e.g., ROUSSET 1999 ). Therefore, to explore a strategy that might reduce the noise caused by within-deme events, we pooled our samples into the resistant and nonresistant categories RW and RW+. When genetic differentiation was analyzed within this case-controlled framework, the signal-to-noise ratio was increased compared to a population-controlled design (Table 4). Specifically, while we found that differentiation over the genomic background between the RW and RW+ groups was low ( = 0.012), the value of at D1Rat219 was 0.311, which was 26 times higher than that for the neutral loci (Table 4B). Overall, differentiation at Rw in the case-controlled design was 15 (26/1.7) times more pronounced than that obtained from the population-controlled analysis (Table 4).

Tabulation of all 61 possible allele-specific values obtained from the case-controlled and population-controlled analyses further showed that a case-controlled analysis has more effectively reduced background levels of F_ST (Fig 5). Specifically, in the case-controlled analysis, only 3 of 61 (4.9%) alleles had values >0.1, including the 254-bp allele ( = 0.404) and the 250-bp allele (0.313) at D1Rat219 and one allele at D2Rat31 (0.101). None of the neutral alleles exceeded a value of 0.2 (i.e., N_m 1). In contrast, in the population-controlled analysis, 29 (47.5%) alleles had values >0.1, and 8 (13.1%) alleles exceeded 0.2. Moreover, values of the 254-bp allele and the 250-bp allele at D1Rat219 were lower than those during the case-controlled analysis ( = 0.243 and 0.246, respectively) and equal to or lower than those of four alleles at the neutral loci D17Rat38, D10Rat6, and D2Rat31. Case-controlled designs may generally assist the mapping of adaptive trait loci, and we suggest that theoretical models analogous to those now used in human disease association studies should be explored (e.g., PRITCHARD and DONNELLY 2001 ).

View larger version (17K): In this window In a new window Download PPT slide   Figure 5. Distribution of allele-specific -values computed for a population-controlled design (open bars) and for a case-controlled design (solid bars). Positions of the 250-bp and 254-bp alleles at D1Rat219 in the distribution are indicated by * and **, respectively.

Extensive genetic hitchhiking also presents difficulties for gene localization. For some of our anticoagulant selected rat populations, intense selection has resulted in genetic hitchhiking over an extended genomic interval (KOHN et al. 2000 ). We computed the F_ST analog for the five populations numbered 11, 21, 23, 24, and LH for which we have typed 26 microsatellite loci spanning a 32-cM genomic interval on rat chromosome 1 (KOHN et al. 2000 ). We found a systematic relationship between and our surrogate measure for divergent selection RW (Fig 6; Mantel's test; P < 0.001; R² = 69%). Thus, genetic hitchhiking has attenuated genetic differences between populations far beyond the Rw locus, impairing our ability to narrow the genomic location of the gene in strongly selected populations. A range of parameter values—notably low migration and recombination compared to selection, epistasis, and the difference in the timing of fixation between adjacent and divergently selected demes—affects the time window for which such isolation-by-linkage disequilibrium may persist (FELSENSTEIN 1981 ; SLATKIN and WIEHE 1998 ). For example, in populations having low and moderate levels of resistance, the genomic interval in linkage disequilibrium was much less than that in highly resistant populations (KOHN et al. 2000 ).

View larger version (15K): In this window In a new window Download PPT slide   Figure 6. Chromosomal effects of selection on Rw. The differences in warfarin resistance frequency (RW) was plotted vs. computed for a 32-cM interval on rat chromosome 1 between population pairs (24, 23, 21, 11, and LH) having warfarin resistance levels between 0 and 93%. No isolation-by-distance relationship was supported (not shown).

The existence of genetic differentiation over large genomic intervals as a result of selection at a nearby locus suggests that populations may diverge in characters that initially were not a direct target of natural selection. This mechanism might account for components of the phenotypic divergence observed between some populations (RICE and HOSTERT 1993 ; but see FELSENSTEIN 1981 ). In fact, such hitchhiking effects led to the initial discovery of linkage between Rw and the coat color mutation. In a free-living mouse population from Cambridge, United Kingdom, there was an extraordinarily high frequency of this coat color variant where warfarin selection on the mouse ortholog of Rw (war) was intense and resistance levels were high (WALLACE and MACSWINEY 1976 ). We have found previously that as much as 32 cM (14%) of rat chromosome 1 surrounding the Rw locus is in linkage disequilibrium (KOHN et al. 2000 ). Presumably, other traits influenced by genes contained in this region may have diverged as a result of intense selection at Rw as well. Inspection of recombination maps and gene annotation data from mouse chromosome 7 (the ortholog to rat chromosome 1) suggested that up to 240 genes and 1360 single nucleotide polymorphic sites (http://www.ensembl.org/Mus_musculus/) potentially might be affected by hitchhiking over this distance.

Conclusions:
Our study of the comparative population genetics of neutral and fitness-related markers in rat populations under varying degrees of selection for anticoagulant resistance has led to several consequential findings. First, a small genome interval defined by our study was implicated in the expression of a warfarin-insensitve vitamin K 2,3-epoxide reductase. Second, quantitative genetic analyses were compatible with a model that invokes Rw as a major locus that mediates resistance to several anticoagulant poisons, but that varies in penetrance and dominance with respect to the poison used. Third, we documented that allele frequencies