The zero isoclines for species 1 and 2 are presented in Figures 14.la and 14.1b.
ID: 56216 • Letter: T
Question
The zero isoclines for species 1 and 2 are presented in Figures 14.la and 14.1b. respectively. These isoclines (lines) represent the combined values of species 1 and species 2 under which the population growth rate is zero (dN/dt = 0; see graph below). For combined values of N1 and N2 that fall below the isocline (the region from the line to the x-y origin), population growth is positive. For values of N1 and N2 above the isocline, population growth is negative. Arrows are used to represent the direction of population change for any point. For the zero isocline of species 1. the arrows are parallel to thex-axis (N1 axis), showing the direction of population change, increasing if pointing in the direction away from the origin and declining if pointing toward the origin. For species 2. the arrows are parallel to the y-axis (N2 axis). To interpret the dynamics for any combination of alpha , beta . K1, and K2. the isoclines for the two species must be drawn on the same x-y graph. Now when any point is plotted on the graph that represents the combined values of species 1 and 2 (N1. jN2), two arrows must be plotted to represent the direction of change for both populations. In the graph shown here, the green arrow represents the change in species 1. and the yellow arrow shows the corresponding change in species 2 at each of the four points (values of (N1, . N2)) that are plotted. The future (predicted) values of N1 and N2 will therefore lie in the direction of the arrow. Therefore, the next point representing the combined values of N1, and N2, must lie somewhere between the two arrows (in the region defined by the dashed line-see insert) and is represented by the black arrow. In Figures 14.1c-14.If. only the black arrows are shown, and the arrows are sometimes bent (curved) to show in which general direction the combined populations will move through time. What is the outcome of competition for the case presented in the graph? What parameters) in the Lolka-Volterra equations (a. p. K1. K2. r1. and r2) ill influence the actual projected values of N1 and N2 (N1 N2) within the region defined by the two arrows (green and yellow)?Explanation / Answer
1)
The outcome of competition for the case presented in the graph is that eventually species 1 or 2 wins (competitive exclusion). In this condition, species 1 carrying capacity (K1) is upper than the competition coefficient (K2/a21) of species 2. The species 2 carrying capacity (K2) is upper than species 1 competition coefficient (K2/a12). It outcome is really depend on the early richness of the two species.
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