Multiple models for outbreak decision support in the face of uncertainty.

Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.

Large benefits to youth-focused HIV treatment-as-prevention efforts in generalized heterosexual populations: An agent-based simulation model.

Predominantly heterosexual HIV-1 epidemics like those in sub-Saharan Africa continue to have high HIV incidence in young people. We used a stochastic, agent-based model for age-disparate networks to test the hypothesis that focusing uptake and retention of ART among youth could enhance the efficiency of treatment as prevention (TasP) campaigns. We used the model to identify strategies that reduce incidence to negligible levels (i.e., < 0.1 cases/100 person-years) 20-25 years after initiation of a targeted TasP campaign. The model was parameterized using behavioral, demographic, and clinical data from published papers and national reports. To keep a focus on the underlying age effects we model a generalized heterosexual population with average risks (i.e., no MSM, no PWIDs, no sex workers) and no entry of HIV+ people from other regions. The model assumes that most people (default 95%, range in variant simulations 60-95%) are "linkable"; i.e., could get linked to effective care given sufficient resources. To simplify the accounting, we assume a rapid jump in the number of people receiving treatment at the start of the TasP campaign, followed by a 2% annual increase that continues until all linkable HIV+ people have been treated. Under historical scenarios of CD4-based targeted ART allocation and current policies of untargeted (random) ART allocation, our model predicts that viral replication would need to be suppressed in 60-85% of infected people at the start of the TasP campaign to drive incidence to negligible levels. Under age-based strategies, by contrast, this percentage dropped by 18-54%, depending on the strength of the epidemic and the age target. For our baseline model, targeting those under age 30 halved the number of people who need to be treated. Age-based targeting also minimized total and time-discounted AIDS deaths over 25 years. Age-based targeting yielded benefits without being highly exclusive; in a model in which 60% of infected people were treated, ~87% and ~58% of those initiating therapy during a campaign targeting those <25 and <30 years, respectively, fell outside the target group. Sensitivity analyses revealed that youth-focused TasP is beneficial due to age-related risk factors (e.g. shorter relationship durations), and an age-specific herd immunity (ASHI) effect that protects uninfected adolescents entering the sexually active population. As testing rates increase in response to UNAIDS 90-90-90 goals, efforts to link all young people to care and treatment could contribute enormously to ending the HIV epidemic.

An HIV epidemic model based on viral load dynamics: value in assessing empirical trends in HIV virulence and community viral load.

Trends in HIV virulence have been monitored since the start of the AIDS pandemic, as studying HIV virulence informs our understanding of HIV epidemiology and pathogenesis. Here, we model changes in HIV virulence as a strictly evolutionary process, using set point viral load (SPVL) as a proxy, to make inferences about empirical SPVL trends from longitudinal HIV cohorts. We develop an agent-based epidemic model based on HIV viral load dynamics. The model contains functions for viral load and transmission, SPVL and disease progression, viral load trajectories in multiple stages of infection, and the heritability of SPVL across transmissions. We find that HIV virulence evolves to an intermediate level that balances infectiousness with longer infected lifespans, resulting in an optimal SPVL∼4.75 log10 viral RNA copies/mL. Adaptive viral evolution may explain observed HIV virulence trends: our model produces SPVL trends with magnitudes that are broadly similar to empirical trends. With regard to variation among studies in empirical SPVL trends, results from our model suggest that variation may be explained by the specific epidemic context, e.g. the mean SPVL of the founding lineage or the age of the epidemic; or improvements in HIV screening and diagnosis that results in sampling biases. We also use our model to examine trends in community viral load, a population-level measure of HIV viral load that is thought to reflect a population's overall transmission potential. We find that community viral load evolves in association with SPVL, in the absence of prevention programs such as antiretroviral therapy, and that the mean community viral load is not necessarily a strong predictor of HIV incidence.

Mycobacterium tuberculosis strains lacking surface lipid phthiocerol dimycocerosate are susceptible to killing by an early innate host response.

The innate immune response plays an important but unknown role in host defense against Mycobacterium tuberculosis. To define the function of innate immunity during tuberculosis, we evaluated M. tuberculosis replication dynamics during murine infection. Our data show that the early pulmonary innate immune response limits M. tuberculosis replication in a MyD88-dependent manner. Strikingly, we found that little M. tuberculosis cell death occurs during the first 2 weeks of infection. In contrast, M. tuberculosis cells deficient in the surface lipid phthiocerol dimycocerosate (PDIM) exhibited significant death rates, and consequently, total bacterial numbers were reduced. Host restriction of PDIM-deficient M. tuberculosis was not alleviated by the absence of interferon gamma (IFN-γ), inducible nitric oxide synthase (iNOS), or the phagocyte oxidase subunit p47. Taken together, these data indicate that PDIM protects M. tuberculosis from an early innate host response that is independent of IFN-γ, reactive nitrogen intermediates, and reactive oxygen species. By employing a pathogen replication tracking tool to evaluate M. tuberculosis replication and death during infection, we identify both host and pathogen factors affecting the outcome of infection.

Construction of regulatory networks using expression time-series data of a genotyped population.

The inference of regulatory and biochemical networks from large-scale genomics data is a basic problem in molecular biology. The goal is to generate testable hypotheses of gene-to-gene influences and subsequently to design bench experiments to confirm these network predictions. Coexpression of genes in large-scale gene-expression data implies coregulation and potential gene-gene interactions, but provide little information about the direction of influences. Here, we use both time-series data and genetics data to infer directionality of edges in regulatory networks: time-series data contain information about the chronological order of regulatory events and genetics data allow us to map DNA variations to variations at the RNA level. We generate microarray data measuring time-dependent gene-expression levels in 95 genotyped yeast segregants subjected to a drug perturbation. We develop a Bayesian model averaging regression algorithm that incorporates external information from diverse data types to infer regulatory networks from the time-series and genetics data. Our algorithm is capable of generating feedback loops. We show that our inferred network recovers existing and novel regulatory relationships. Following network construction, we generate independent microarray data on selected deletion mutants to prospectively test network predictions. We demonstrate the potential of our network to discover de novo transcription-factor binding sites. Applying our construction method to previously published data demonstrates that our method is competitive with leading network construction algorithms in the literature.

Evolution of HIV virulence in response to disease-modifying vaccines: A modeling study.

Pathogens face a tradeoff with respect to virulence; while more virulent strains often have higher per-contact transmission rates, they are also more likely to kill their hosts earlier. Because virulence is a heritable trait, there is concern that a disease-modifying vaccine, which reduces the disease severity of an infected vaccinee without changing the underlying pathogen genotype, may result in the evolution of higher pathogen virulence. We explored the potential for such virulence evolution with a disease-modifying HIV-1 vaccine in an agent-based stochastic epidemic model of HIV in United States men who have sex with men (MSM). In the model, vaccinated agents received no protection against infection, but experienced lower viral loads and slower disease progression. We compared the genotypic set point viral load (SPVL), a measure of HIV virulence, in populations given vaccines that varied in the degree of SPVL reduction they induce. Sensitivity analyses were conducted under varying vaccine coverage scenarios. With continual vaccination rollout under ideal circumstances of 90 % coverage over thirty years, the genotypic SPVL of vaccinated individuals evolved to become greater than the genotypic SPVL of unvaccinated individuals. This virulence evolution in turn diminished the public health benefit of the vaccine, and in some scenarios resulted in an accelerated epidemic. These findings demonstrate the complexity of viral evolution and have important implications for the design and development of HIV vaccines.

HIV Therapy Simulator: a graphical user interface for comparing the effectiveness of novel therapy regimens.

UNLABELLED: Computer simulation models can be useful in exploring the efficacy of HIV therapy regimens in preventing the evolution of drug-resistant viruses. Current modeling programs, however, were designed by researchers with expertise in computational biology, limiting their accessibility to those who might lack such a background. We have developed a user-friendly graphical program, HIV Therapy Simulator (HIVSIM), that is accessible to non-technical users. The program allows clinicians and researchers to explore the effectiveness of various therapeutic strategies, such as structured treatment interruptions, booster therapies and induction-maintenance therapies. We anticipate that HIVSIM will be useful for evaluating novel drug-based treatment concepts in clinical research, and as an educational tool. AVAILABILITY: HIV Therapy Simulator is freely available for Mac OS and Windows at http://sites.google.com/site/hivsimulator/. CONTACT: jmittler@uw.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Why does age at HIV infection correlate with set point viral load? An evolutionary hypothesis.

BACKGROUND: Set-point viral load (SPVL) correlates with the age at which people acquire HIV. Although immunosenescence may seem like a parsimonious explanation for this, it does not easily explain the observation that the relationship between age and SPVL attenuates when accounting for source partner SPVL. Here we propose an alternative explanation that encompasses this latter finding: that decreasing risk of acquisition with older age generates a selection bottleneck that selects for more virulent strains with age. METHODS: We adapted a previously published model of HIV transmission and evolution (EvoNetHIV), parameterized here for men who have sex with men (MSM). We conducted a series of simulation experiments that vary seven behavioral or clinical parameters that affect exposure risk as people age. We conducted regressions to determine the mean increase in SPVL per 10-year increase in seroconversion age, with and without source SPVL in the model. RESULTS: All runs generated significant relationships between seroconversion age and SPVL when not including source SPVL. All saw attenuated relationships, most to near 0, with source SPVL included. Four of our behavioral measures (relational duration, age-related homophily, coital frequency, and mean age at relationship formation) had clear effects on this relationship, all in the hypothesized direction. Combining multiple forms of behavioral heterogeneity yielded an increase of 0.056 log10 copies/mL SPVL per 10-year increase in seroconversion age, nearly as large as that seen in two empirical studies of age-SPVL correlations in MSM. CONCLUSION: The higher virulence of HIV among those infected later in life may be partly explained by a combination of selective bottlenecks and behavioral heterogeneity by age. Variation in the strength of this effect across populations may be in part due to different behavioral, epidemiological and clinical conditions, and not require assumptions about differences in patterns of immunosenescence among populations.

Test-and-treat coverage and HIV virulence evolution among men who have sex with men.

HIV set point viral load (SPVL), the viral load established shortly after initial infection, is a proxy for HIV virulence: higher SPVLs lead to higher risk of transmission and faster disease progression. Three models of test-and-treat scenarios, mainly in heterosexual populations, found that increasing treatment coverage selected for more virulent viruses. We modeled virulence evolution in a population of men who have sex with men (MSM) with increasing test-and-treat coverage. We extended a stochastic, dynamic network model (EvoNetHIV). We varied relationship patterns (MSM vs. heterosexual), HIV transmission models (increasing vs. plateauing probability of transmission at very high viral loads), and treatment roll-out (with explicit testing or fixed intervals between infection and treatment). In scenarios most similar to previous models (longer relational durations and the plateauing transmission function), we replicated trends previously found: increasing treatment coverage led to increased virulence (0.12 log10 increase in mean population SPVL between 20% and 100% treatment coverage). In scenarios reflecting MSM behavioral data using the increasing transmission function, increasing treatment coverage selected for viruses with lower virulence (0.16 log10 decrease in mean population SPVL between 20% and 100% treatment coverage). These findings emphasize the impact of sexual network conditions and transmission function details on predicted epidemiological and evolutionary outcomes. Varying these features creates very different evolutionary environments, which in turn lead to opposite effects in mean population SPVL evolution. Our results suggest that, under some realistic conditions, effective test-and-treat strategies may not face the previously reported tradeoff in which increasing coverage leads to evolution of greater virulence. This suggests instead that a virtuous cycle of increasing treatment coverage and diminishing virulence is possible.

Risk compensation after HIV-1 vaccination may accelerate viral adaptation and reduce cost-effectiveness: a modeling study.

Pathogen populations can evolve in response to selective pressure from vaccine-induced immune responses. For HIV, models predict that viral adaptation, either via strain replacement or selection on de novo mutation, may rapidly reduce the effectiveness of an HIV vaccine. We hypothesized that behavioral risk compensation after vaccination may accelerate the transmission of vaccine resistant strains, increasing the rate of viral adaptation and leading to a more rapid decline in vaccine effectiveness. To test our hypothesis, we modeled: (a) the impact of risk compensation on rates of HIV adaptation via strain replacement in response to a partially effective vaccine; and (b) the combined impact of risk compensation and viral adaptation on vaccine-mediated epidemic control. We used an agent-based epidemic model that was calibrated to HIV-1 trends in South Africa, and includes demographics, sexual network structure and behavior, and within-host disease dynamics. Our model predicts that risk compensation can increase the rate of HIV viral adaptation in response to a vaccine. In combination, risk compensation and viral adaptation can, under certain scenarios, reverse initial declines in prevalence due to vaccination, and result in HIV prevalence at 15 years equal to or greater than prevalence without a vaccine.

Models to predict the public health impact of vaccine resistance: A systematic review.

Pathogen evolution is a potential threat to the long-term benefits provided by public health vaccination campaigns. Mathematical modeling can be a powerful tool to examine the forces responsible for the development of vaccine resistance and to predict its public health implications. We conducted a systematic review of existing literature to understand the construction and application of vaccine resistance models. We identified 26 studies that modeled the public health impact of vaccine resistance for 12 different pathogens. Most models predicted that vaccines would reduce overall disease burden in spite of evolution of vaccine resistance. Relatively few pathogens and populations for which vaccine resistance may be problematic were covered in the reviewed studies, with low- and middle-income countries particularly under-represented. We discuss the key components of model design, as well as patterns of model predictions.

Sexual role and HIV-1 set point viral load among men who have sex with men.

BACKGROUND: HIV-1 set point viral load (SPVL) is a highly variable trait that influences disease progression and transmission risk. Men who are exclusively insertive (EI) during anal intercourse require more sexual contacts to become infected than exclusively receptive (ER) men. Thus, we hypothesize that EIs are more likely to acquire their viruses from highly infectious partners (i.e., with high SPVLs) and to have higher SPVLs than infected ERs. METHODS: We used a one-generation Bernoulli model, a dynamic network model, and data from the Multicenter AIDS Cohort Study (MACS) to examine whether and under what circumstances MSM differ in SPVL by sexual role. RESULTS: Both models predicted higher SPVLs in EIs than role versatile (RV) or ER men, but only in scenarios where longer-term relationships predominated. ER and RV men displayed similar SPVLs. EI men remained far less likely than ER men to become infected, however. When the MACS data were limited by some estimates of lower sex partner counts (a proxy for longer relationships), EI men had higher SPVLs; these differences were clinically relevant (>0.3 log10 copies/mL) and statistically significant (p < 0.05). CONCLUSIONS: Mode of acquisition may be an important aspect of SPVL evolution in MSM, with clinical implications.

Selection dramatically reduces effective population size in HIV-1 infection.

BACKGROUND: In HIV-1 evolution, a 100-100,000 fold discrepancy between census size and effective population size (Ne) has been noted. Although it is well known that selection can reduce Ne, high in vivo mutation and recombination rates complicate attempts to quantify the effects of selection on HIV-1 effective size. RESULTS: We use the inbreeding coefficient and the variance in allele frequency at a linked neutral locus to estimate the reduction in Ne due to selection in the presence of mutation and recombination. With biologically realistic mutation rates, the reduction in Ne due to selection is determined by the strength of selection, i.e., the stronger the selection, the greater the reduction. However, the dependence of Ne on selection can break down if recombination rates are very high (e.g., r > or = 0.1). With biologically likely recombination rates, our model suggests that recurrent selective sweeps similar to those observed in vivo can reduce within-host HIV-1 effective population sizes by a factor of 300 or more. CONCLUSION: Although other factors, such as unequal viral reproduction rates and limited migration between tissue compartments contribute to reductions in Ne, our model suggests that recurrent selection plays a significant role in reducing HIV-1 effective population sizes in vivo.

Optimal timing and duration of induction therapy for HIV-1 infection.

The tradeoff between the need to suppress drug-resistant viruses and the problem of treatment toxicity has led to the development of various drug-sparing HIV-1 treatment strategies. Here we use a stochastic simulation model for viral dynamics to investigate how the timing and duration of the induction phase of induction-maintenance therapies might be optimized. Our model suggests that under a variety of biologically plausible conditions, 6-10 mo of induction therapy are needed to achieve durable suppression and maximize the probability of eradicating viruses resistant to the maintenance regimen. For induction regimens of more limited duration, a delayed-induction or -intensification period initiated sometime after the start of maintenance therapy appears to be optimal. The optimal delay length depends on the fitness of resistant viruses and the rate at which target-cell populations recover after therapy is initiated. These observations have implications for both the timing and the kinds of drugs selected for induction-maintenance and therapy-intensification strategies.

Relational concurrency, stages of infection, and the evolution of HIV set point viral load.

HIV viral load (VL) predicts both transmission potential and rate of disease progression. For reasons that are still not fully understood, the set point viral load (SPVL) established after acute infection varies across individuals and populations. Previous studies have suggested that population mean SPVL (MSPVL) has evolved near an optimum that reflects a trade-off between transmissibility and host survival. Sexual network structures affect rates of potential exposure during different within-host phases of infection marked by different transmission probabilities, and thus affect the number and timing of transmission events. These structures include relational concurrency, which has been argued to explain key differences in HIV burden across populations. We hypothesize that concurrency will alter the fitness landscape for SPVL in ways that differ from other network features whose impacts accrue at other times during infection. To quantitatively test this hypothesis, we developed a dynamic, stochastic, data-driven network model of HIV transmission, and evolution to assess the impact of key sexual network phenomena on MSPVL evolution. Experiments were repeated in sensitivity runs that made different assumptions about transmissibility during acute infection, SPVL heritability, and the functional form of the relationship between VL and transmissibility. For our main transmission model, scenarios yielded MSPVLs ranging from 4.4 to 4.75 log10 copies/ml, covering much of the observed empirical range. MSPVL evolved to be higher in populations with high concurrency and shorter relational durations, with values varying over a clinically significant range. In linear regression analyses on these and other predictors, main effects were significant (P < 0.05), as were interaction terms, indicating that effects are interdependent. We also noted a strong correlation between two key emergent properties measured at the end of the simulations-MSPVL and HIV prevalence-most clearly for phenomena that affect transmission networks early in infection. Controlling for prevalence, high concurrency yielded higher MSPVL than other network phenomena. Interestingly, we observed lower prevalence in runs in which SPVL heritability was zero, indicating the potential for viral evolution to exacerbate disease burden over time. Future efforts to understand empirical variation in MSPVL should consider local HIV burden and basic sexual behavioral and network structure.

HIV population-level adaptation can rapidly diminish the impact of a partially effective vaccine.

BACKGROUND: Development of an HIV vaccine might be essential to ending the HIV/AIDS pandemic. However, vaccines can result in the emergence and spread of vaccine-resistant strains. Indeed, analyses of breakthrough infections in the HIV phase 3 vaccine trial RV144 identified HIV genotypes with differential rates of transmission in vaccine and placebo recipients. We hypothesized that, for HIV vaccination programs based on partially effective vaccines similar to RV144, HIV adaptation will rapidly diminish the expected vaccine impact. METHODS AND FINDINGS: Using two HIV epidemic models, we simulated large-scale vaccination programs and, critically, included HIV strain diversity with respect to the vaccine response. We show here that rapid population-level viral adaptation can lead to decreased overall vaccine efficacy and substantially fewer infections averted by vaccination, when comparing scenarios with and without viral evolution (with outcomes depending on vaccination coverage, vaccine efficacy against the sensitive allele, and the initial resistant allele frequency). Translating this to the epidemic in South Africa, a scenario with 70% vaccination coverage may result in 250,000 infections (non-averted by vaccination) within 10 years of vaccine rollout that are due solely to HIV adaptation, all else being equal. CONCLUSIONS: These findings suggest that approaches to HIV vaccine development, program implementation, and epidemic modeling may require attention to viral adaptation in response to vaccination.

Cachers, scavengers, and thieves: a novel mechanism for desert rodent coexistence.

A biologically explicit simulation model of resource competition between two species of seed-eating heteromyid rodent indicates that stable coexistence is possible on a homogeneous resource if harvested food is stored and consumers steal each other's caches. Here we explore the coexistence mechanisms involved by analyzing how consumer phenotypes and presence of a noncaching consumer affect the competitive outcome. Without cache exchange, the winning consumer is better at harvesting seeds and produces more offspring per gram of stored food. With cache exchange, coexistence is promoted by interspecific trade-offs between harvest ability, metabolic efficiency, and ability to pilfer defended caches of heterospecifics or scavenge undefended caches of dead conspecifics or heterospecifics. Cache exchange via pilferage can equalize competitor fitnesses but has little stabilizing effect and leads to stable coexistence only in the presence of a noncaching consumer. In contrast, scavenging is both equalizing and stabilizing and promotes coexistence without a third consumer. Because body size affects a heteromyid rodent's metabolic rate, seed harvest rate, caching strategy, and ability to steal caches, interspecific differences in body size should produce the trade-offs necessary for coexistence. The observation that coexisting heteromyids differ in body size therefore indicates that cache exchange may promote diversity in heteromyid communities.

Importance and detection of virus reservoirs and compartments of HIV infection.

Current therapies for treating HIV-1 infection are capable of suppressing virus load in blood to undetectable levels, and result in marked clinical improvement. Despite this suppression, HIV-1 infection persists and virus load quickly rebounds when therapy is interrupted. The origin of the rebounding virus is unknown, but is thought to result from continuing viral replication in anatomic or cellular compartments, and the release of virus from latent infection in reservoirs.

Evolution of HIV virulence in response to widespread scale up of antiretroviral therapy: a modeling study.

There are global increases in the use of HIV antiretroviral therapy (ART), guided by clinical benefits of early ART initiation and the efficacy of treatment as prevention of transmission. Separately, it has been shown theoretically and empirically that HIV virulence can evolve over time; observed virulence levels may reflect an adaptive balance between infected lifespan and per-contact transmission rate. However, the potential effects of widespread ART usage on HIV virulence are unknown. To predict these effects, we used an agent-based stochastic model to simulate evolutionary trends in HIV virulence, using set point viral load as a proxy for virulence. We calibrated our model to prevalence and incidence trends of South Africa. We explored two distinct ART scenarios: (1) ART initiation based on HIV-infected individuals reaching a CD4 count threshold; and (2) ART initiation based on individual time elapsed since HIV infection (a scenario that mimics "universal testing and treatment" (UTT) aspirations). In each case, we considered a range in population uptake of ART. We found that HIV virulence is generally unchanged in scenarios of CD4-based initiation. However, with ART initiation based on time since infection, virulence can increase moderately within several years of ART rollout, under high coverage levels and early treatment initiation (albeit within the context of epidemics that are rapidly decreasing in size). Sensitivity analyses suggested the impact of ART on virulence is relatively insensitive to model calibration. Our modeling study suggests that increasing HIV virulence driven by UTT is likely not a major public health concern, but should be monitored in sentinel surveillance, in a manner similar to transmitted resistance to antiretroviral drugs.

Influence of random genetic drift on human immunodeficiency virus type 1 env evolution during chronic infection.

Human immunodeficiency virus type 1 (HIV-1) has high replication and mutation rates that generate large census populations and high levels of genetic variation. We examined the roles of natural selection, population growth, random genetic drift, and recombination in shaping the variation in 1509 C2-V5 env sequences derived from nine men with chronic HIV-1 infection. These sequences were obtained from clinical visits that reflect the first 6-13.7 years of infection. Pairwise comparisons of nonsynonymous and synonymous distances, Tajima's D test, Fu and Li's D* test, and a test of recurrent mutation revealed evidence for episodes of nonneutral evolution in a total of 22 out of 145 blood samples, representing six of the nine individuals. Using three coalescent-based maximum-likelihood estimators, we found viral effective population sizes in all nine individuals to be approximately 10(3). We also show that a previous estimate of the effective population size of approximately 10(5) based on rare haplotype frequencies decreases to approximately 10(3) upon correcting a biased sampling procedure. We conclude that the genetic variation in these data sets can be explained by a predominance of random genetic drift of neutral mutations with brief episodes of natural selection that were frequently masked by recombination.