Probabilistic Analysis of Facility Location on Random Shortest Path Metrics

The facility location problem is an NP-hard optimization problem. Therefore, approximation algorithms are often used to solve large instances. Such algorithms often perform much better than worst-case analysis suggests. Therefore, probabilistic analysis is a widely used tool to analyze such algorithms. Most research on probabilistic analysis of NP-hard optimization problems involving metric spaces, such as the facility location problem, has been focused on Euclidean instances, and also instances with independent (random) edge lengths, which are non-metric, have been researched. We would like to extend this knowledge to other, more general, metrics. We investigate the facility location problem using random shortest path metrics. We analyze some probabilistic properties for a simple greedy heuristic which gives a solution to the facility location problem: opening the $\kappa$ cheapest facilities (with $\kappa$ only depending on the facility opening costs). If the facility opening costs are such that $\kappa$ is not too large, then we show that this heuristic is asymptotically optimal. On the other hand, for large values of $\kappa$, the analysis becomes more difficult, and we provide a closed-form expression as upper bound for the expected approximation ratio. In the special case where all facility opening costs are equal this closed-form expression reduces to $O(\sqrt[4]{\ln(n)})$ or $O(1)$ or even $1+o(1)$ if the opening costs are sufficiently small.Comment: A preliminary version accepted to CiE 201

Experimental investigation of alternative transmission functions: quantitative evidence for the importance of non-linear transmission dynamics in host-parasite systems

1. Understanding pathogen transmission is crucial for predicting and managing disease. Nonetheless, experimental comparisons of alternative functional forms of transmission remain rare, and those experiments that are conducted are often not designed to test the full range of possible forms. 2. To differentiate among 10 candidate transmission functions, we used a novel experimental design in which we independently varied four factors—duration of exposure, numbers of parasites, numbers of hosts and parasite density—in laboratory infection experiments. 3. We used interactions between amphibian hosts and trematode parasites as a model system and all candidate models incorporated parasite depletion. An additional manipulation involving anaesthesia addressed the effects of host behaviour on transmission form. 4. Across all experiments, nonlinear transmission forms involving either a power law or a negative binomial function were the best‐fitting models and consistently outperformed the linear density‐dependent and density‐independent functions. By testing previously published data for two other host–macroparasite systems, we also found support for the same nonlinear transmission forms. 5. Although manipulations of parasite density are common in transmission studies, the comprehensive set of variables tested in our experiments revealed that variation in density alone was least likely to differentiate among competing transmission functions. Across host–pathogen systems, nonlinear functions may often more accurately represent transmission dynamics and thus provide more realistic predictions for infection

Whether ideal free or not, predatory mites distribute so as to maximize reproduction

Ideal free distribution (IFD) models predict that animals distribute themselves such that no individual can increase its fitness by moving to another patch. Many empirical tests assume that the interference among animals is independent of density and do not quantify the effects of density on fitness traits. Using two species of predatory mites, we measured oviposition as a function of conspecific density. Subsequently, we used these functions to calculate expected distributions on two connected patches. We performed an experimental test of the distributions of mites on two such connected patches, among which one had a food accessibility rate that was twice as high as on the other. For one of the two species, Iphiseius degenerans, the distribution matched the expected distribution. The distribution also coincided with the ratio of food accessibility. The other species, Neoseiulus cucumeris, distributed itself differently than expected. However, the oviposition rates of both species did not differ significantly from the expected oviposition rates based on experiments on single patches. This suggests that the oviposition rate of N. cucumeris was not negatively affected by the observed distribution, despite the fact that N. cucumeris did not match the predicted distributions. Thus, the distribution of one mite species, I. degenerans, was in agreement with IFD theory, whereas for the other mite species, N. cucumeris, unknown factors may have influenced the distribution of the mites. We conclude that density-dependent fitness traits provide essential information for explaining animal distributions

Competition and habitat quality influence age and sex distribution in wintering rusty blackbirds.

Bird habitat quality is often inferred from species abundance measures during the breeding and non-breeding season and used for conservation management decisions. However, during the non-breeding season age and sex classes often occupy different habitats which suggest a need for more habitat-specific data. Rusty Blackbird (Euphagus carolinus) is a forested wetland specialist wintering in bottomland hardwood forests in the south-eastern U. S. and belongs to the most steeply declining songbirds in the U.S. Little information is available to support priority birds such as the Rusty Blackbird wintering in this threatened habitat. We assessed age and sex distribution and body condition of Rusty Blackbirds among the three major habitats used by this species in the Lower Mississippi Alluvial Valley and also measured food availability. Overall, pecan groves had the highest biomass mainly driven by the amount of nuts. Invertebrate biomass was highest in forests but contributed only a small percentage to overall biomass. Age and sex classes were unevenly distributed among habitats with adult males primarily occupying pecan groves containing the highest nut biomass, females being found in forests which had the lowest nut biomass and young males primarily staying in forest fragments along creeks which had intermediate nut biomass. Males were in better body condition than females and were in slightly better condition in pecan groves. The results suggest that adult males occupy the highest quality habitat and may competitively exclude the other age and sex classes

Variation in the COVID-19 infection-fatality ratio by age, time, and geography during the pre-vaccine era: a systematic analysis

Background The infection-fatality ratio (IFR) is a metric that quantifies the likelihood of an individual dying once infected with a pathogen. Understanding the determinants of IFR variation for COVID-19, the disease caused by the SARS-CoV-2 virus, has direct implications for mitigation efforts with respect to clinical practice, non-pharmaceutical interventions, and the prioritisation of risk groups for targeted vaccine delivery. The IFR is also a crucial parameter in COVID-19 dynamic transmission models, providing a way to convert a population's mortality rate into an estimate of infections.Methods We estimated age-specific and all-age IFR by matching seroprevalence surveys to total COVID-19 mortality rates in a population. The term total COVID-19 mortality refers to an estimate of the total number of deaths directly attributable to COVID-19. After applying exclusion criteria to 5131 seroprevalence surveys, the IFR analyses were informed by 2073 all-age surveys and 718 age-specific surveys (3012 age-specific observations). When seroprevalence was reported by age group, we split total COVID-19 mortality into corresponding age groups using a Bayesian hierarchical model to characterise the non-linear age pattern of reported deaths for a given location. To remove the impact of vaccines on the estimated IFR age pattern, we excluded age-specific observations of seroprevalence and deaths that occurred after vaccines were introduced in a location. We estimated age-specific IFR with a non-linear meta-regression and used the resulting age pattern to standardise all-age IFR observations to the global age distribution. All IFR observations were adjusted for baseline and waning antibody-test sensitivity. We then modelled age-standardised IFR as a function of time, geography, and an ensemble of 100 of the top-performing covariate sets. The covariates included seven clinical predictors (eg, age-standardised obesity prevalence) and two measures of health system performance. Final estimates for 190 countries and territories, as well as subnational locations in 11 countries and territories, were obtained by predicting age-standardised IFR conditional on covariates and reversing the age standardisation.Findings We report IFR estimates for April 15, 2020, to January 1, 2021, the period before the introduction of vaccines and widespread evolution of variants. We found substantial heterogeneity in the IFR by age, location, and time. Age-specific IFR estimates form a J shape, with the lowest IFR occurring at age 7 years (0-0023%, 95% uncertainty interval [UI] 0-0015-0-0039) and increasing exponentially through ages 30 years (0-0573%, 0-0418-0-0870), 60 years (1-0035%, 0-7002-1-5727), and 90 years (20-3292%, 14-6888-28-9754). The countries with the highest IFR on July 15, 2020, were Portugal (2-085%, 0-946-4-395), Monaco (1-778%, 1-265-2-915), Japan (1-750%, 1-302-2-690), Spain (1-710%, 0-991-2-718), and Greece (1-637%, 1-155-2-678). All-age IFR varied by a factor of more than 30 among 190 countries and territories.After age standardisation, the countries with the highest IFR on July 15, 2020, were Peru (0-911%, 0-636-1-538), Portugal (0-850%, 0-386-1-793), Oman (0-762%, 0-381-1-399), Spain (0-751%, 0-435-1-193), and Mexico (0-717%, 0-426-1-404). Subnational locations with high IFRs also included hotspots in the UK and southern and eastern states of the USA. Sub-Saharan African countries and Asian countries generally had the lowest all-age and age-standardised IFRs. Population age structure accounted for 74% of logit-scale variation in IFRs estimated for 39 in-sample countries on July 15, 2020. A post-hoc analysis showed that high rates of transmission in the care home population might account for higher IFRs in some locations. Among all countries and territories, we found that the median IFR decreased from 0-466% (interquartile range 0-223-0-840) to 0-314% (0-143-0-551) between April 15, 2020, and Jan 1, 2021.Interpretation Estimating the IFR for global populations helps to identify relative vulnerabilities to COVID-19. Information about how IFR varies by age, time, and location informs clinical practice and non-pharmaceutical interventions like physical distancing measures, and underpins vaccine risk stratification. IFR and mortality risk form a J shape with respect to age, which previous research, such as that by Glynn and Moss in 2020, has identified to be a common pattern among infectious diseases. Understanding the experience of a population with COVID-19 mortality requires consideration for local factors; IFRs varied by a factor of more than 30 among 190 countries and territories in this analysis. In particular, the presence of elevated age-standardised IFRs in countries with well resourced health-care systems indicates that factors beyond health-care capacity are important. Potential extenuating circumstances include outbreaks among care home residents, variable burdens of severe cases, and the population prevalence of comorbid conditions that increase the severity of COVID-19 disease. During the pre-vaccine period, the estimated 33% decrease in median IFR over 8 months suggests that treatment for COVID-19 has improved over time. Estimating IFR for the pre-vaccine era provides an important baseline for describing the progression of COVID-19 mortality patterns.Funding Bill & Melinda Gates Foundation, J Stanton, T Gillespie, and J and E Nordstrom Copyright (c) 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY-NC-ND 4.0 license

Toward a Comprehensive Approach to the Collection and Analysis of Pica Substances, with Emphasis on Geophagic Materials

Pica, the craving and subsequent consumption of non-food substances such as earth, charcoal, and raw starch, has been an enigma for more than 2000 years. Currently, there are little available data for testing major hypotheses about pica because of methodological limitations and lack of attention to the problem.In this paper we critically review procedures and guidelines for interviews and sample collection that are appropriate for a wide variety of pica substances. In addition, we outline methodologies for the physical, mineralogical, and chemical characterization of these substances, with particular focus on geophagic soils and clays. Many of these methods are standard procedures in anthropological, soil, or nutritional sciences, but have rarely or never been applied to the study of pica.Physical properties of geophagic materials including color, particle size distribution, consistency and dispersion/flocculation (coagulation) should be assessed by appropriate methods. Quantitative mineralogical analyses by X-ray diffraction should be made on bulk material as well as on separated clay fractions, and the various clay minerals should be characterized by a variety of supplementary tests. Concentrations of minerals should be determined using X-ray fluorescence for non-food substances and inductively coupled plasma-atomic emission spectroscopy for food-like substances. pH, salt content, cation exchange capacity, organic carbon content and labile forms of iron oxide should also be determined. Finally, analyses relating to biological interactions are recommended, including determination of the bioavailability of nutrients and other bioactive components from pica substances, as well as their detoxification capacities and parasitological profiles.This is the first review of appropriate methodologies for the study of human pica. The comprehensive and multi-disciplinary approach to the collection and analysis of pica substances detailed here is a necessary preliminary step to understanding the nutritional enigma of non-food consumption

Population genomics of speciation and admixture

The application of population genomics to the understanding of speciation has led to the emerging field of speciation genomics. This has brought new insight into how divergence builds up within the genome during speciation and is also revealing the extent to which species can continue to exchange genetic material despite reproductive barriers. It is also providing powerful new approaches for linking genotype to phenotype in admixed populations. In this chapter, we give an overview of some of the methods that have been used and some of the novel insights gained. We also outline some of the pitfalls of the most commonly used methods and possible problems with interpretation of the results

Experimental evolution of adaptive divergence under varying degrees of gene flow

Adaptive divergence is the key evolutionary process generating biodiversity by means of natural selection. Yet, the conditions under which it can arise in the presence of gene flow remain contentious. To address this question, we subjected 132 sexually reproducing fission yeast populations, sourced from two independent genetic backgrounds, to disruptive ecological selection and manipulated the level of migration between environments. Contrary to theoretical expectations, adaptive divergence was most pronounced when migration was either absent (allopatry) or maximal (sympatry), but was much reduced at intermediate rates (parapatry and local mating). This effect was apparent across central life-history components (survival, asexual growth and mating) but differed in magnitude between ancestral genetic backgrounds. The evolution of some fitness components was constrained by pervasive negative correlations (trade-off between asexual growth and mating), while others changed direction under the influence of migration (for example, survival and mating). In allopatry, adaptive divergence was mainly conferred by standing genetic variation and resulted in ecological specialization. In sympatry, divergence was mainly mediated by novel mutations enriched in a subset of genes and was characterized by the repeated emergence of two strategies: an ecological generalist and an asexual growth specialist. Multiple loci showed consistent evidence for antagonistic pleiotropy across migration treatments providing a conceptual link between adaptation and divergence. This evolve-and-resequence experiment shows that rapid ecological differentiation can arise even under high rates of gene flow. It further highlights that adaptive trajectories are governed by complex interactions of gene flow, ancestral variation and genetic correlations