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Krivan V.,Academy of Sciences of the Czech Republic | Krivan V.,National Institute for Mathematical and Biological Synthesis
Journal of Theoretical Biology | Year: 2011

This article re-analyses a prey-predator model with a refuge introduced by one of the founders of population ecology Gause and his co-workers to explain discrepancies between their observations and predictions of the Lotka-Volterra prey-predator model. They replaced the linear functional response used by Lotka and Volterra by a saturating functional response with a discontinuity at a critical prey density. At concentrations below this critical density prey were effectively in a refuge while at a higher densities they were available to predators. Thus, their functional response was of the Holling type III. They analyzed this model and predicted existence of a limit cycle in predator-prey dynamics. In this article I show that their model is ill posed, because trajectories are not well defined. Using the Filippov method, I define and analyze solutions of the Gause model. I show that depending on parameter values, there are three possibilities: (1) trajectories converge to a limit cycle, as predicted by Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity. © 2011 Elsevier Ltd.


Fitzpatrick B.M.,University of Tennessee at Knoxville | Fitzpatrick B.M.,National Institute for Mathematical and Biological Synthesis
BMC Evolutionary Biology | Year: 2012

Background: Hybridization, genetic mixture of distinct populations, gives rise to myriad recombinant genotypes. Characterizing the genomic composition of hybrids is critical for studies of hybrid zone dynamics, inheritance of traits, and consequences of hybridization for evolution and conservation. Hybrid genomes are often summarized either by an estimate of the proportion of alleles coming from each ancestral population or classification into discrete categories like F1, F2, backcross, or merely "hybrid" vs. "pure". In most cases, it is not realistic to classify individuals into the restricted set of classes produced in the first two generations of admixture. However, the continuous ancestry index misses an important dimension of the genotype. Joint consideration of ancestry together with interclass heterozygosity (proportion of loci with alleles from both ancestral populations) captures all of the information in the discrete classification without the unrealistic assumption that only two generations of admixture have transpired. Methods. I describe a maximum likelihood method for joint estimation of ancestry and interclass heterozygosity. I present two worked examples illustrating the value of the approach for describing variation among hybrid populations and evaluating the validity of the assumption underlying discrete classification. Results: Naively classifying natural hybrids into the standard six line cross categories can be misleading, and false classification can be a serious problem for datasets with few molecular markers. My analysis underscores previous work showing that many (50 or more) ancestry informative markers are needed to avoid erroneous classification. Conclusion: Although classification of hybrids might often be misleading, valuable inferences can be obtained by focusing directly on distributions of ancestry and heterozygosity. Estimating and visualizing the joint distribution of ancestry and interclass heterozygosity is an effective way to compare the genetic structure of hybrid populations and these estimates can be used in classic quantitative genetic methods for assessing additive, dominant, and epistatic genetic effects on hybrid phenotypes and fitness. The methods are implemented in a freely available package "HIest" for the R statistical software. © 2012 Fitzpatrick; licensee BioMed Central Ltd.


Collecting and re-examining more than 5,600 estimates of ocean microbial cell and virus populations recorded over the past 25 years, researchers have found that viral populations vary dramatically from location to location, and at differing depths in the sea. The study highlights another source of uncertainty governing climate models and other biogeochemical measures. "What was surprising was that there was not a constant relationship, as people had assumed, between the number of microbial cells and the number of viruses," said Joshua Weitz, an associate professor in the School of Biology at the Georgia Institute of Technology and one of the paper's two senior co-authors. "Because viruses are parasites, it was assumed that their number would vary linearly with the number of microbes. We found that the ratio does not remain constant, but decreases systematically as the number of microbes increases." The research, which involved authors from 14 different institutions, was initiated as part of a working group from the National Institute for Mathematical and Biological Synthesis (NIMBioS), which is supported by the National Science Foundation. The research was completed with additional support from the Burroughs Wellcome Fund and the Simons Foundation. The research was co-led by Steven Wilhelm, a professor of microbiology at the University of Tennessee, Knoxville. In the datasets examined by the researchers, the ratio of viruses to microbes varied from approximately 1 to 1 and 150 to 1 in surface waters, and from 5 to 1 and 75 to 1 in the deeper ocean. For years, scientists had utilized a baseline ratio of 10 to 1 - ten times more viruses than microbes—which may not adequately represent conditions in many marine ecosystems. "A marine environment with 100-fold more viruses than microbes may have very different rates of microbial recycling than an environment with far fewer viruses," said Weitz. "Our study really begins to challenge the notion of a uniform ecosystem role for viruses." A key target for viruses are cyanobacteria—marine microorganisms that obtain their energy through photosynthesis in a process that takes carbon out of the atmosphere. What happens to the carbon these tiny organisms remove may be determined by whether they are eaten by larger grazing creatures—or die from viral infections. When these cyanobacteria die from infections, their carbon is likely to remain in the top of the water column, where it can nourish other microorganisms. If they are eaten by larger creatures, their carbon is likely to sink into the deeper ocean as the grazers die or excrete the carbon in in their feces. "Viruses have a role in shunting some of the carbon away from the deep ocean and keeping it in the surface ocean," said Wilhelm. "Quantifying the strength of the viral shunt remains a vital issue." Influenza and measles come to mind when most people think of viruses, but the bulk of world's viruses actually infect microorganisms. Estimates suggest that a single liter of seawater typically contain more than ten billion viruses. To better understand this population, the researchers conducted a meta-analysis of the microbial and virus abundance data that had been collected over multiple decades, including datasets collected by many of the co-authors whose laboratories are based in the United States, Canada and Europe. The data had been obtained using a variety of techniques, including epifluorescence microscopy and flow cytometry. By combining data collected by 11 different research groups, the researchers created a big picture from many smaller ones. The statistical relationships between viruses and microbial cells, analyzed by first-author Charles Wigington from Georgia Tech and second-author Derek Sonderegger from Northern Arizona University, show the range of variation. The available data provides information about the abundance of viral particles, not their diversity. Viruses are selective in the microbes the target, meaning the true rates of infection require a renewed focus on virus-microbe infection networks. "Future research should focus on examining the relationship between ocean microorganisms and viruses at the scale of relevant interactions," said Weitz, "And more ocean surveys are needed to fill in the many blanks for this critical part of the carbon cycle. Indeed, virus infections of microbes could change the flux of carbon and nutrients on a global scale." Explore further: Decade-long study reveals recurring patterns of viruses in the open ocean More information: Re-examination of the relationship between marine virus and microbial cell abundances, DOI: 10.1038/nmicrobiol.2015.24


Find Out How Computer Technology Is Changing The World In some parts of the United States, extracting natural gas from shale rock has a negative effect both below and above ground. Such effects of gas extraction on the environment include degrading freshwater systems, displacing rare species, eroding soil and fragmenting fragile habitats. Unfortunately, it has long been established that minimizing the effects of drilling may come at a greater cost for developers. Now, a new algorithm developed by scientists may help reduce environmental impact. Thanks to the algorithm, a team of scientists led by Austin Milt of the National Institute for Mathematical and Biological Synthesis (NIMBioS) have found that the additional costs for developers are actually even smaller than the savings made to the environment. This suggests that the benefits far outweigh the harm. The new NIMBioS study indicates that on average, a 20 percent increase in development costs could cut surface-level environment impact by more than a third. Milt and his colleagues developed an algorithm to quantify the costs of environmental impacts. The main goal was to find out how the construction of additional shale gas sites would help them achieve this plan. The novel algorithm helped them design the construction of access roads, well pads, and pipelines at 84 sites in Pennsylvania, which was chosen to represent shale energy development in the U.S. because of its 10,000 drilled wells. The new algorithm plans infrastructure the same way most developers do, adhering to strict regulations and practices. The only difference is that the primary goal for each plan is to protect the environment, researchers said. In the end, Milt and his team found that while developers can indeed reduce environmental impact at a small cost, the outcomes were dependent on the characteristics of the shale gas site. Several of the effects were easier to address and therefore less costly to avoid than others. For instance, a large portion of the impacts on the environment could be prevented by steering development away from areas considered as habitats for endangered and rare species. Because the results rely on site conditions, scientists say the right approach to regulate infrastructure development is not a one-size-fits-all approach. Milt says there are other, more flexible alternatives that would minimize impacts on the environment at the same or less cost. Details of the study are published in the journal Conservation Biology. © 2016 Tech Times, All rights reserved. Do not reproduce without permission.


A study from the National Institute for Mathematical and Biological Synthesis develops new methods to detect the onset of critical transitions in infectious disease epidemics, such as malaria. "Billions of dollars are spent annually on various interventions to stop diseases like malaria, and the investments have made a difference. But, government and public health agencies need the will to continue making these investments after the initial reduction of cases has occurred. The question becomes at what point does the continued investment pay off?" said lead author and NIMBioS postdoctoral fellow Suzanne O'Regan. "Quantitative evaluation tools can go a long way in helping governments and philanthropic organizations choose the optimal level of investment in control and elimination activities after the number of cases slows down." The method developed in the study, which was published in the journal Theoretical Ecology, identifies the critical slowing-down period in human cases of the mosquito-borne parasite that causes malaria, suggesting that eradicating the disease could be anticipated even without a full of understanding of the underlying mechanisms that are causing the slow down. The researchers used a mathematical model to study the gradual implementation of four common tactics used to control and eliminate malaria: using bed nets to reduce the number of mosquito bites, spraying indoor insecticides to shorten mosquito lifespans, administering drugs that reduce the human infectious period, and eliminating mosquito habitat. The analysis focuses on malaria, but the findings are relevant to other mosquito-borne infections, such as yellow fever, also endemic in some parts of the world. "Our work suggests that online algorithms for detecting changes in leading indicators may be achievable and could eventually be developed, possibly aiding sustainment of the gains made by elimination programs," O'Regan said. Explore further: Virus evolution differs by species of mosquito carrier

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