Power laws for heavy-tailed distributions: modeling allele and haplotype diversity for the national marrow donor program.

Measures of allele and haplotype diversity, which are fundamental properties in population genetics, often follow heavy tailed distributions. These measures are of particular interest in the field of hematopoietic stem cell transplant (HSCT). Donor/Recipient suitability for HSCT is determined by Human Leukocyte Antigen (HLA) similarity. Match predictions rely upon a precise description of HLA diversity, yet classical estimates are inaccurate given the heavy-tailed nature of the distribution. This directly affects HSCT matching and diversity measures in broader fields such as species richness. We, therefore, have developed a power-law based estimator to measure allele and haplotype diversity that accommodates heavy tails using the concepts of regular variation and occupancy distributions. Application of our estimator to 6.59 million donors in the Be The Match Registry revealed that haplotypes follow a heavy tail distribution across all ethnicities: for example, 44.65% of the European American haplotypes are represented by only 1 individual. Indeed, our discovery rate of all U.S. European American haplotypes is estimated at 23.45% based upon sampling 3.97% of the population, leaving a large number of unobserved haplotypes. Population coverage, however, is much higher at 99.4% given that 90% of European Americans carry one of the 4.5% most frequent haplotypes. Alleles were found to be less diverse suggesting the current registry represents most alleles in the population. Thus, for HSCT registries, haplotype discovery will remain high with continued recruitment to a very deep level of sampling, but population coverage will not. Finally, we compared the convergence of our power-law versus classical diversity estimators such as Capture recapture, Chao, ACE and Jackknife methods. When fit to the haplotype data, our estimator displayed favorable properties in terms of convergence (with respect to sampling depth) and accuracy (with respect to diversity estimates). This suggests that power-law based estimators offer a valid alternative to classical diversity estimators and may have broad applicability in the field of population genetics.

Impact of the shedding level on transmission of persistent infections in Mycobacterium avium subspecies paratuberculosis (MAP).

Super-shedders are infectious individuals that contribute a disproportionate amount of infectious pathogen load to the environment. A super-shedder host may produce up to 10,000 times more pathogens than other infectious hosts. Super-shedders have been reported for multiple human and animal diseases. If their contribution to infection dynamics was linear to the pathogen load, they would dominate infection dynamics. We here focus on quantifying the effect of super-shedders on the spread of infection in natural environments to test if such an effect actually occurs in Mycobacterium avium subspecies paratuberculosis (MAP). We study a case where the infection dynamics and the bacterial load shed by each host at every point in time are known. Using a maximum likelihood approach, we estimate the parameters of a model with multiple transmission routes, including direct contact, indirect contact and a background infection risk. We use longitudinal data from persistent infections (MAP), where infectious individuals have a wide distribution of infectious loads, ranging upward of three orders of magnitude. We show based on these parameters that the effect of super-shedders for MAP is limited and that the effect of the individual bacterial load is limited and the relationship between bacterial load and the infectiousness is highly concave. A 1000-fold increase in the bacterial contribution is equivalent to up to a 2-3 fold increase in infectiousness.