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Topological bifurcations in the transition from two single vortices to a pair and a single vortex in the periodic wake behind an oscillating cylinder
- Anne R. Nielsen, Puneet S. Matharu, Morten Brøns
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- Journal:
- Journal of Fluid Mechanics / Volume 940 / 10 June 2022
- Published online by Cambridge University Press:
- 08 April 2022, A22
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We explore the two-dimensional flow past a cylinder undergoing forced transversal oscillations with the aim of elucidating the evolution of the topology of the wake under variation of the forcing amplitude at a Reynolds number of 100. In particular, we study the change from two single vortices (2S mode) to a pair and a single vortex ($\text {P}+ \text {S}$ mode) being shed per period. Matharu et al. (J. Fluid Mech., vol. 918, 2021, p. A21) showed that a dynamical symmetry-breaking pitchfork bifurcation plays a key role in this transition. We show that in addition to this bifurcation, a number of topological bifurcations in the vorticity field occur, both on the symmetric 2S branch and on the asymmetric $\text {P}+ \text {S}$ branch. The topological bifurcations are cusp bifurcations where an extremum of vorticity is created or destroyed. To describe the effect of the topological bifurcations we introduce an extended symbolic classification of the wake modes to account for the spatial variations of the vortex patterns that occur in the transition process. We identify four amplitude values that define critical stages in the transition, and provide a complete qualitative picture of the transition from 2S to $\text {P}+ \text {S}$ mode. We confirm the robustness of the observed transition process by simulations at Reynolds number 80.
Topological bifurcations of vortex pair interactions
- Anne R. Nielsen, Morten Andersen, Jesper S. Hansen, Morten Brøns
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- Journal:
- Journal of Fluid Mechanics / Volume 917 / 25 June 2021
- Published online by Cambridge University Press:
- 23 April 2021, A11
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We investigate vortex pair interactions at low Reynolds numbers. We base our analysis on the Q-criterion, where a vortex is defined as a region where the local rotation dominates the strain, and we make use of a topological approach to describe the qualitative changes of the vortex structure. In order to give a complete description of vortex pair interactions we further develop a general bifurcation theory for $Q$-vortices and prove that a threshold for vortex merging may occur when we allow two parameters to vary. To limit the number of free parameters, we study the interactions with two point vortices as the initial condition and show that the threshold is a codimension two bifurcation that appears as a cusp singularity on a bifurcation curve. We apply the general theory to the analytically tractable core growth model and conclude that a pair of co-rotating vortices merge only if their strength ratio, $\alpha =\varGamma _1/\varGamma _2$ is less than $4.58$. Below this threshold value, we observe two different regimes in which the merging processes can be described with different sequences of bifurcations. By comparison with Navier–Stokes simulations at different Reynolds numbers, we conclude that the merging threshold varies only slightly for Reynolds numbers up to $100$. Furthermore, we observe an excellent agreement between the core growth model and the numerical simulations for Reynolds numbers below 10. We therefore conclude that, instead of solving the Navier–Stokes equation numerically we can, for sufficiently small Reynolds numbers, apply the core growth model as a simple, analytically tractable model with a low dimension.
Bifurcation theory for vortices with application to boundary layer eruption
- Anne R. Nielsen, Matthias Heil, Morten Andersen, Morten Brøns
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- Journal:
- Journal of Fluid Mechanics / Volume 865 / 25 April 2019
- Published online by Cambridge University Press:
- 27 February 2019, pp. 831-849
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We develop a bifurcation theory describing the conditions under which vortices are created or destroyed in a two-dimensional incompressible flow. We define vortices using the $Q$-criterion and analyse the vortex structure by considering the evolution of the zero contours of $Q$. The theory identifies topological changes of the vortex structure and classifies these as four possible types of bifurcations, two occurring away from boundaries, and two occurring near no-slip walls. Our theory provides a description of all possible codimension-one bifurcations where time is treated as the bifurcation parameter. To illustrate our results, we consider the early stages of boundary layer eruption at moderate Reynolds numbers in the range from $Re=750$ to $Re=2250$. By analysing numerical simulations of the phenomenon, we show how to describe the eruption process as sequences of the four possible bifurcations of codimension one. Our simulations show that there is a single codimension-two point within our parameter range. This codimension-two point arises at $Re=1817$ via the coalescence of two codimension-one bifurcations which are associated with the creation and subsequent destruction of one of the vortices that erupt from the boundary layer. We present a theoretical description of this process and explain how the occurrence of this phenomenon separates the parameter space into two regions with distinct evolution of the topology of the vortices.
The microbial community of the gut differs between piglets fed sow milk, milk replacer or bovine colostrum
- Ann-Sofie R. Poulsen, Nadieh de Jonge, Sugiharto Sugiharto, Jeppe L. Nielsen, Charlotte Lauridsen, Nuria Canibe
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- Journal:
- British Journal of Nutrition / Volume 117 / Issue 7 / 14 April 2017
- Published online by Cambridge University Press:
- 02 May 2017, pp. 964-978
- Print publication:
- 14 April 2017
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The aim of this study was to characterise the gut microbiota composition of piglets fed bovine colostrum (BC), milk replacer (MR) or sow milk (SM) in the post-weaning period. Piglets (n 36), 23-d old, were randomly allocated to the three diets. Faecal samples were collected at 23, 25, 27 and 30 d of age. Digesta from the stomach, ileum, caecum and mid-colon was collected at 30 d of age. Bacterial DNA from all samples was subjected to amplicon sequencing of the 16S rRNA gene. Bacterial enumerations by culture and SCFA analysis were conducted as well. BC-piglets had the highest abundance of Lactococcus in the stomach (P<0·0001) and ileal (P<0·0001) digesta, whereas SM-piglets had the highest abundance of Lactobacillus in the stomach digesta (P<0·0001). MR-piglets had a high abundance of Enterobacteriaceae in the ileal digesta (P<0·0001) and a higher number of haemolytic bacteria in ileal (P=0·0002) and mid-colon (P=0·001) digesta than SM-piglets. BC-piglets showed the highest colonic concentration of iso-butyric and iso-valeric acid (P=0·02). Sequencing and culture showed that MR-piglets were colonised by a higher number of Enterobacteriaceae, whereas the gut microbiota of BC-piglets was characterised by a change in lactic acid bacteria genera when compared with SM-piglets. We conclude that especially the ileal microbiota of BC-piglets had a closer resemblance to that of SM-piglets in regard to the abundance of potential enteric pathogens than did MR-piglets. The results indicate that BC may be a useful substitute for regular milk replacers, and as a feeding supplement in the immediate post-weaning period.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- Book:
- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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Contributors
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- By Agoston T. Agoston, Syed Z. Ali, Mahul B. Amin, Daniel A. Arber, Pedram Argani, Sylvia L. Asa, Rebecca N. Baergen, Zubair W. Baloch, Andrew M. Bellizzi, Kurt Benirschke, Allen Burke, Kenneth B. Calder, Karen L. Chang, Rebecca D. Chernock, Wang Cheung, Thomas V. Colby, Byron P. Croker, Ronald A. DeLellis, Edward F. DiCarlo, Ralph C. Eagle, Hormoz Ehya, Brett M. Elicker, Tarik M. Elsheikh, Robert E. Fechner, Linda D. Ferrell, Melina B. Flanagan, Douglas B. Flieder, Christopher S. Foster, Lillian Gaber, Karuna Garg, Kim R. Geisinger, Ryan M. Gill, Eric F. Glassy, David J. Glembocki, Zachary D. Goodman, Robert O. Greer, David J. Grignon, Gerardo E. Guiter, Kymberly A. Gyure, Ian S. Hagemann, Michael R. Henry, Jason L. Hornick, Ralph H. Hruban, Phyllis C. Huettner, Peter A. Humphrey, Olga B. Ioffe, Edward C. Klatt, Michael J. Klein, Ernest E. Lack, James N. Lampros, Lester J. Layfield, Robin D. LeGallo, Kevin O. Leslie, James S. Lewis, Virginia A. LiVolsi, Alberto M. Marchevsky, Anne Marie McNicol, Mitra Mehrad, Elizabeth Montgomery, Cesar A. Moran, Christopher A. Moskaluk, George J. Netto, G. Petur Nielsen, Robert D. Odze, Arthur S. Patchefsky, James W. Patterson, Elizabeth N. Pavlisko, John D. Pfeifer, Celeste N. Powers, Richard A. Prayson, Anja C. Roden, Victor L. Roggli, Andrew E. Rosenberg, Sherif Said, Margie A. Scott, Raja R. Seethala, Carlie S. Sigel, Jan F. Silverman, Bruce R. Smoller, Edward B. Stelow, Nora C. J. Sun, Mark W. Teague, Satish K. Tickoo, Thomas M. Ulbright, Paul E. Wakely, Jun Wang, Lawrence M. Weiss, Mark R. Wick, Howard H. Wu, Rhonda K. Yantiss, Charles Zaloudek, Yaxia Zhang, Xiaohui Sheila Zhao
- Edited by Mark R. Wick, University of Virginia, Virginia A. LiVolsi, University of Pennsylvania School of Medicine, John D. Pfeifer, Washington University School of Medicine, St Louis, Edward B. Stelow, University of Virginia, Paul E. Wakely, Jr
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- Silverberg's Principles and Practice of Surgical Pathology and Cytopathology
- Published online:
- 13 March 2015
- Print publication:
- 26 March 2015, pp vii-x
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Modeling suggests frequency estimates are not informative for predicting the long-term effect of horizontal gene transfer in bacteria
- Ann-Kathrin Pettersen, Thomas Bøhn, Raul Primicerio, Paul R. Shorten, Tanya K. Soboleva, Kaare M. Nielsen
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- Journal:
- Environmental Biosafety Research / Volume 4 / Issue 4 / October 2005
- Published online by Cambridge University Press:
- 22 June 2006, pp. 223-233
- Print publication:
- October 2005
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Horizontal gene transfer (HGT) is an important mechanism by which bacteria recombine and acquire novel genes and functions. Risk scenarios where novel plant transgenes transfer horizontally into bacteria have been addressed in numerical theoretical assessments and experimental studies. A key outcome of these studies has been that the frequencies of such inter-domain transfer are very low, if occurring at all, suggesting that such transfers would not occur at a level that is biologically significant. The relationship between transfer frequencies and the subsequent selection or genetic drift of transgene carrying bacteria often remains unresolved in these studies and assessments. Here we present a stochastic model to better understand the initial establishment and population dynamics of rare bacterial transformants carrying horizontally acquired (trans)genes. The following key parameters are considered: initial transformant numbers, strength of selection, bacterial population size and bacterial generations (time). We find that the initial number of transformants is important for the subsequent persistence of transformants only in the range of 1 to ~50 independent HGT events. Our simulations show that transformant populations under a wide range of HGT rates and selection coefficients undergo stochastic developments where they persist at low frequencies for up to several years (at frequencies that are below detection using available field sampling methodology), after which they eventually may go to fixation. Stochastic variability may thus play a crucial but disregarded role in the design of field monitoring strategies e.g. in biosafety assessments. We also estimate the time required for transformants to reach 0.0002% prevalence in a bacterial population, a threshold that allows experimental detection of transgene carrying bacteria through sampling of the larger bacterial populations.