Reed Harder

Human and Helicobacter pylori coevolution shapes the risk of gastric disease

Significance Theory predicts that chronic pathogens with vertical or familial transmission should become less virulent over time because of coevolution. Although transmitted in this way, Helicobacter pylori is the major causative agent of gastric cancer. In two distinct Colombian populations with similar levels of H. pylori infection but different incidences of gastric cancer, we examined human and pathogen ancestry in matched samples to assess whether their genomic variation affects the severity of premalignant lesions. Interaction between human Amerindian ancestry and H. pylori African ancestry accounted for the geographic disparity in clinical presentation. We conclude that coevolutionary relationships are important determinants of gastric disease risk and that the historical colonization of the Americas continues to influence health in modern American populations. Helicobacter pylori is the principal cause of gastric cancer, the second leading cause of cancer mortality worldwide. However, H. pylori prevalence generally does not predict cancer incidence. To determine whether coevolution between host and pathogen influences disease risk, we examined the association between the severity of gastric lesions and patterns of genomic variation in matched human and H. pylori samples. Patients were recruited from two geographically distinct Colombian populations with significantly different incidences of gastric cancer, but virtually identical prevalence of H. pylori infection. All H. pylori isolates contained the genetic signatures of multiple ancestries, with an ancestral African cluster predominating in a low-risk, coastal population and a European cluster in a high-risk, mountain population. The human ancestry of the biopsied individuals also varied with geography, with mostly African ancestry in the coastal region (58%), and mostly Amerindian ancestry in the mountain region (67%). The interaction between the host and pathogen ancestries completely accounted for the difference in the severity of gastric lesions in the two regions of Colombia. In particular, African H. pylori ancestry was relatively benign in humans of African ancestry but was deleterious in individuals with substantial Amerindian ancestry. Thus, coevolution likely modulated disease risk, and the disruption of coevolved human and H. pylori genomes can explain the high incidence of gastric disease in the mountain population.

Evolutionary triangulation: informing genetic association studies with evolutionary evidence

Genetic studies of human diseases have identified many variants associated with pathogenesis and severity. However, most studies have used only statistical association to assess putative relationships to disease, and ignored other factors for evaluation. For example, evolution is a factor that has shaped disease risk, changing allele frequencies as human populations migrated into and inhabited new environments. Since many common variants differ among populations in frequency, as does disease prevalence, we hypothesized that patterns of disease and population structure, taken together, will inform association studies. Thus, the population distributions of allelic risk variants should reflect the distributions of their associated diseases. Evolutionary Triangulation (ET) exploits this evolutionary differentiation by comparing population structure among three populations with variable patterns of disease prevalence. By selecting populations based on patterns where two have similar rates of disease that differ substantially from a third, we performed a proof of principle analysis for this method. We examined three disease phenotypes, lactase persistence, melanoma, and Type 2 diabetes mellitus. We show that for lactase persistence, a phenotype with a simple genetic architecture, ET identifies the key gene, lactase. For melanoma, ET identifies several genes associated with this disease and/or phenotypes related to it, such as skin color genes. ET was less obviously successful for Type 2 diabetes mellitus, perhaps because of the small effect sizes in known risk loci and recent environmental changes that have altered disease risk. Alternatively, ET may have revealed new genes involved in conferring disease risk for diabetes that did not meet nominal GWAS significance thresholds. We also compared ET to another method used to filter for phenotype associated genes, population branch statistic (PBS), and show that ET performs better in identifying genes known to associate with diseases appropriately distributed among populations. Our results indicate that ET can filter association results to improve our ability to discover disease loci.

Genetics of Plasminogen Activator Inhibitor-1 (PAI-1) in a Ghanaian Population

Plasminogen activator inhibitor 1 (PAI-1), a major modulator of the fibrinolytic system, is an important factor in cardiovascular disease (CVD) susceptibility and severity. PAI-1 is highly heritable, but the few genes associated with it explain only a small portion of its variation. Studies of PAI-1 typically employ linear regression to estimate the effects of genetic variants on PAI-1 levels, but PAI-1 is not normally distributed, even after transformation. Therefore, alternative statistical methods may provide greater power to identify important genetic variants. Additionally, most genetic studies of PAI-1 have been performed on populations of European descent, limiting the generalizability of their results. We analyzed >30,000 variants for association with PAI-1 in a Ghanaian population, using median regression, a non-parametric alternative to linear regression. Three variants associated with median PAI-1, the most significant of which was in the gene arylsulfatase B (ARSB) (p = 1.09 x 10−7). We also analyzed the upper quartile of PAI-1, the most clinically relevant part of the distribution, and found 19 SNPs significantly associated in this quartile. Of note an association was found in period circadian clock 3 (PER3). Our results reveal novel associations with median and elevated PAI-1 in an understudied population. The lack of overlap between the two analyses indicates that the genetic effects on PAI-1 are not uniform across its distribution. They also provide evidence of the generalizability of the circadian pathway’s effect on PAI-1, as a recent meta-analysis performed in Caucasian populations identified another circadian clock gene (ARNTL).

Bending the law: geometric tools for quantifying influence in the multinetwork of legal opinions

Legal reasoning requires identification through search of authoritative legal texts (such as statutes, constitutions, or prior judicial opinions) that apply to a given legal question. In this paper, using a network representation of US Supreme Court opinions that integrates citation connectivity and topical similarity, we model the activity of law search as an organizing principle in the evolution of the corpus of legal texts. The network model and (parametrized) probabilistic search behavior generates a Pagerank-style ranking of the texts that in turn gives rise to a natural geometry of the opinion corpus. This enables us to then measure the ways in which new judicial opinions affect the topography of the network and its future evolution. While we deploy it here on the US Supreme Court opinion corpus, there are obvious extensions to large evolving bodies of legal text (or text corpora in general). The model is a proxy for the way in which new opinions influence the search behavior of litigants and judges and thus affect the law. This type of “legal search effect” is a new legal consequence of research practice that has not been previously identified in jurisprudential thought and has never before been subject to empirical analysis. We quantitatively estimate the extent of this effect and find significant relationships between search-related network structures and propensity of future citation. This finding indicates that “search influence” is a pathway through which judicial opinions can affect future legal development.

Two-Stage Game Theoretic Modelling of Airline Frequency and Fare Competition

Airlines make capacity and fare decisions in a competitive environment. Capacity decisions, encompassing decisions about frequency of service and seats-per-flight, affect both the operating costs and revenues of airlines. These decisions have significant implications for the performance of the air transportation system as a whole. Capacity and fare decisions of different airlines are interdependent, both serving as tools in an airlines competitive arsenal. This interdependency motivates a game theoretic approach to modeling the decision process. Capacity (especially frequency) decisions are typically made months in advance of flight departure, with only an approximate knowledge of what fares will be, while fare decisions are made weeks to minutes ahead of flight departure. Several studies have stressed the need to develop two-stage game theoretic models to account for the sequential nature of these decisions, but there are very few analytical, computational, or empirical results available for such models. In this article (working paper available at link in [1]), we develop a two-stage frequency and fare competition model, demonstrate its tractability across a wide range of assumptions, and validate its predictions against observed airline behavior. We take the payoff function of an airline operating in a set of markets to be the sum of the differences between revenues and costs in those markets, with costs as a linear function of flight frequency. To compute revenue, we explore two commonly used multinomial logit models of market share. Frequency decisions are made in the first stage of the game, while fare decisions are made in the second stage. We begin our analysis with a simplified version of this game: two airlines competing in a single market, with no connecting passengers, infinite seating capacity, and the absence of a nofly alternative. Under these assumptions, for either market share model, we are able to prove that (1) the second-stage fare game always has unique pure strategy Nash equilibrium (PSNE), (2) first-stage payoffs for each airline are concave with respect to that airlines frequency strategy across plausible utility parameter ranges, and (3) first-stage payoffs for each airline are submodular functions in the overall frequency strategy space. As the game is two-player, (3) means that by changing the sign of one players strategy space, we can trivially convert the game into a supermodular game. These results demonstrate that subgame-perfect PSNE is a credible and tractable solution concept for our model. In particular, the existence and uniqueness results indicate the suitability of PSNE as a solution concept for the second-stage game. Concave payoffs ensure that individual first-stage payoff maximization problems are efficiently solvable, and supermodularity ensures that several iterative learning dynamics converge to equilibrium [2]. We then relax each of the assumptions made in this simplified model by computationally solving the second stage fare game, generating equilibrium fare decisions and profits for every set of frequency decisions for integer daily frequency values ranging from 1 to 20, for various numbers of players, seats per flight, and values of utility parameters (including the nofly option). Then, we fit quadratic approximations to these profits as functions of the frequencies of all players. We find an excellent fit (R2 > 0.9) in all cases. Additionally, the signs of all estimated coefficients are consistent with submodularity and concavity properties demonstrated earlier. We show that for an N-player game with such concave and submodular quadratic payoff functions, the myopic best response heuristic, where each player optimizes its payoff against fixed opponent strategies iteratively, converges to a PSNE. To test the tractability and predictive validity of our model in practice, we apply it to a 4-airline, 11-airport network in the Western U.S, using publicly available airline operations data. We use the quadratic functions of airline frequency fitted above and additionally enforce the aircraft availability constraints, and solve for equilibrium iteratively using the myopic best response heuristic. To calibrate the 11 free quadratic payoff coefficients of this model, we use a stochastic gradient approximation algorithm to minimize the absolute errors between observed and predicted frequency strategies. In practice, the game convergences to equilibrium quickly, and the calibrated models frequency predictions approximate observed behavior both in-sample and out-ofsample, suggesting that refinements of the model could be pursued for use in scenario analysis, forecasting, planning, and policy making.