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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

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. Source

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

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. Source

News Article
Site: http://phys.org/biology-news/

As the American media continues to buzz over who is more or less likely to secure the Republican and Democratic nominations for U.S. President, researchers in the journal Trends in Ecology & Evolution review some interesting perspectives on the nature of leadership. The experts from a wide range of disciplines examined patterns of leadership in a set of small-scale mammalian societies, including humans and other social mammals such as elephants and meerkats. "While previous work has typically started with the premise that leadership is somehow intrinsically different or more complex in humans than in other mammals, we started without a perceived notion about whether this should be the case," said Jennifer Smith of Mills College in Oakland, California. "By approaching this problem with an open mind and by developing comparable measures to compare vastly different societies, we revealed more similarities than previously appreciated between leadership in humans and non-humans." Chimpanzees travel together, capuchins cooperate in fights, and spotted hyenas cooperate in hunting, but the common ways that leaders promote those collective actions has remained mysterious, Smith and her colleagues say. It wasn't clear just how much human leaders living in small-scale societies have in common with those in other mammalian societies either. To consider this issue, a group of biologists, anthropologists, mathematicians, and psychologists gathered at the National Institute for Mathematical and Biological Synthesis. These experts reviewed the evidence for leadership in four domains—movement, food acquisition, within-group conflict mediation, and between-group interactions—to categorize patterns of leadership in five dimensions: distribution across individuals, emergence (achieved versus inherited), power, relative payoff to leadership, and generality across domains. Despite what those ongoing presidential primaries might lead one to think, the analysis by the scientific experts finds that leadership is generally achieved as individuals gain experience, in both humans and non-humans. There are notable exceptions to this rule: leadership is inherited rather than gained through experience among spotted hyenas and the Nootka, a Native Canadian tribe on the northwest coast of North America. In comparison to other mammal species, human leaders aren't so powerful after all. Leadership amongst other mammalian species tends to be more concentrated, with leaders that wield more power over the group. Smith says the similarities probably reflect shared cognitive mechanisms governing dominance and subordination, alliance formation, and decision-making—humans are mammals after all. The differences may be explained in part by humans' tendency to take on more specialized roles within society. "Even in the least complex human societies, the scale of collective action is greater and presumably more critical for survival and reproduction than in most other mammalian societies," Smith said. The researchers now plan to further quantify the various dimensions identified in the new work. There's still plenty more to learn. "As ambitious as our task was, we have only just scraped the surface in characterizing leadership across mammalian societies and some of the most exciting aspects of the project are still yet to come as biologists and anthropologists implement our novel scheme for additional taxa and societies," Smith said. Explore further: Spotted hyenas can increase survival rates by hunting alone More information: Trends in Ecology & Evolution, Smith et al.: "Leadership in Mammalian Societies: Emergence, Distribution, Power, and Payoff" dx.doi.org/10.1016/j.tree.2015.09.013

News Article
Site: http://phys.org/biology-news/

An adult Gelada monkey plays with a juvenile. A new special issue of Adaptive Behavior examines the evolution and origin of play via mathematical and computational approaches. Credit: Elisabetta Palagi Research on the evolution and function of play at the National Institute for Mathematical and Biological Synthesis (NIMBioS) has culminated in a special issue of the journal Adaptive Behavior. The papers represent the first systematic use of computational and mathematical models to investigate the theoretical and empirical origins of play. In a series of meetings from 2011 to 2013, the NIMBioS Working Group on Play, Evolution and Sociality brought together mathematicians, anthropologists, zoologists, neuroscientists, ecologists, psychologists and other top experts to examine play as a window into cognitive evolution and the rules of sociality. Until the Working Group was established, the field lacked a mathematical and computational approaches for understanding how play evolves. Using mathematical tools, the group aimed to uncover factors predicting the dynamics, occurrence and trajectory of play in the animal kingdom, as well as explore the ecological, psychological and life history factors that facilitate and maintain play. The six papers in the special issue include: Explore further: UT professor defines play, discovers even turtles need recess More information: The full special issue can be found at adb.sagepub.com/content/23/6.toc

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

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