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- https://bio.libretexts.org/Bookshelves/Ecology/Book%3A_Quantitative_Ecology_-_A_New_Unified_Approach_(Lehman_Loberg_and_Clark)/12%3A_Predator_and_Prey/12.04%3A_Phase_SpaceFor example, as explained in Chapter 10, if the prey population is 1.5 and the predator population is 0.5, the population will be 1.5 units to the right on the horizontal axis and 0.5 units up on the ...For example, as explained in Chapter 10, if the prey population is 1.5 and the predator population is 0.5, the population will be 1.5 units to the right on the horizontal axis and 0.5 units up on the vertical axis, at the location of the blue plus sign in the graph.
- https://bio.libretexts.org/Bookshelves/Ecology/Book%3A_Quantitative_Ecology_-_A_New_Unified_Approach_(Lehman_Loberg_and_Clark)/10%3A_Phase_Space/10.02%3A_Phase_SpaceThe basin at Point C corresponds to the carrying capacity, Point B corresponds to extinction at the origin, and Point A corresponds to the unstable Allee point. A marble could be balanced precariously...The basin at Point C corresponds to the carrying capacity, Point B corresponds to extinction at the origin, and Point A corresponds to the unstable Allee point. A marble could be balanced precariously at that place, with the slightest breath of air sending it to extinction at B or carrying capacity in the basin at C, depending on miniscule variations in the breath. Marbles starting farther from the axes are on the other side of a long ridge and roll to the carrying capacity at C.
- https://bio.libretexts.org/Courses/Gettysburg_College/01%3A_Ecology_for_All/15%3A_Competition/15.05%3A_Quantifying_Competition_Using_the_Lotka-Volterra_ModelNote the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1...Note the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1 on the growth rate of Population 2. If we solve for these intercepts, we wind up with the following two coordinates for Population 1: [0, K 1 /a 12 ] (setting x, or the size of Population 1, to 0) and [K 1 , 0] (setting y, or the population size of Population 2, to 0).
- https://bio.libretexts.org/Bookshelves/Ecology/Book%3A_Quantitative_Ecology_-_A_New_Unified_Approach_(Lehman_Loberg_and_Clark)/10%3A_Phase_Space/10.01%3A_Chapter_IntroductionIn differential equation models, the basic population dynamics among species become visible at a glance in “phase space.” The concepts and applications of phase spaces were originally worked out late ...In differential equation models, the basic population dynamics among species become visible at a glance in “phase space.” The concepts and applications of phase spaces were originally worked out late in the nineteenth century by Henri Poincaré and others for the dynamical systems of physics, but the mathematical foundations also apply to the theories of ecology.
- https://bio.libretexts.org/Workbench/General_Ecology_Ecology/Chapter_15%3A_Competition/15.5%3A_Quantifying_Competition_Using_the_Lotka-Volterra_ModelNote the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1...Note the subscripts on the competition coefficients: α 12 expresses the effect of one member of Population 2 on the growth rate of Population 1; α 21 expresses the effect of one member of Population 1 on the growth rate of Population 2. If we solve for these intercepts, we wind up with the following two coordinates for Population 1: [0, K 1 /a 12 ] (setting x, or the size of Population 1, to 0) and [K 1 , 0] (setting y, or the population size of Population 2, to 0).
- https://bio.libretexts.org/Bookshelves/Ecology/Book%3A_Quantitative_Ecology_-_A_New_Unified_Approach_(Lehman_Loberg_and_Clark)/10%3A_Phase_Space
