caa a22 4500 445330201 CHVBK 20180317142734.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00285-010-0328-x doi (NATIONALLICENCE)springer-10.1007/s00285-010-0328-x Classical and resource-based competition: a unifying graphical approach [Elektronische Daten] [Mary Ballyk, Gail Wolkowicz] A graphical technique is given for determining the outcome of two species competition for two resources. This method is unifying in the sense that the graphical criterion leading to the various outcomes of competition are consistent across most of the spectrum of resource types (from those that fulfill the same growth needs to those that fulfill different needs) regardless of the classification method used, and the resulting graphs bear a striking resemblance to the well-known phase portraits for two species Lotka-Volterra competition. Our graphical method complements that of Tilman. Both include zero net growth isoclines. However, instead of using the consumption vectors at potential coexistence equilibria to determine input resource concentrations leading to specific competitive outcomes, we introduce curves bounding the feasible set (the set where the resource concentrations of any equilibrium solution must be located). The washout equilibrium (corresponding to the supply point) occurs at an intersection of curves defining the feasible set boundary. The resource concentrations of all other equilibria are found where zero net growth isoclines either intersect each other inside the feasible set or they intersect the feasible set boundary. A species has positive biomass at such an equilibrium only if its zero net growth isocline is involved in such an intersection. The competitive outcomes are then determined from the position of the single species equilibria, just as in the phase portrait analysis for classical competition (rather than from information at potential coexistence equilibria as in Tilman's method). Springer-Verlag, 2010 Multiple resource limitation nationallicence Perfectly substitutable nationallicence Essential nationallicence Complementary nationallicence Homologous nationallicence Heterologous nationallicence Interactive nationallicence Non-interactive nationallicence Lotka-Volterra competition nationallicence Chemostat nationallicence Graphial analysis nationallicence Ballyk Mary Department of Mathematical Sciences, New Mexico State University, MSC 3MB, P. O. Box 30001, 88003-0001, Las Cruces, NM, USA aut Wolkowicz Gail Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada aut Journal of Mathematical Biology Springer-Verlag 62/1(2011-01-01), 81-109 0303-6812 62:1<81 2011 62 285 https://doi.org/10.1007/s00285-010-0328-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0328-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ballyk Mary Department of Mathematical Sciences, New Mexico State University, MSC 3MB, P. O. Box 30001, 88003-0001, Las Cruces, NM, USA aut NATIONALLICENCE 700 1- Wolkowicz Gail Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 62/1(2011-01-01), 81-109 0303-6812 62:1<81 2011 62 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer