Let’s consider two interacting competing species – zebras (species 1) and gazelles (species 2) both are grazers, need water in the savannah ecosystem a given piece of habitat can support 100 zebras or 200 gazelles, each species alone so – zebra k = 100; gazelle k = 200. competition coefficients: measure interspecific competition relative to intraspecific competition, i. e., how many individuals of species 2 are equivalent to one individual of species 1 in terms of their use of the resource? for example, if one zebra is equal to 2 gazelles - alpha or a12 = .5 [effect of gazelles on zebra] beta or a21 = 2 [effect of zebra on gazelles] however, the animals have other effects on the ecosystem that can alter their competition coefficients – such as… so the realized competition coefficients are alpha or a12 = .3 [effect of gazelles on zebra] beta or a21 = .8 [effect of zebra on gazelles] draw phase plane x and y axes – n1 and n2 draw carrying capacities along the axes calculate k1 / alpha and k2 / beta – these go on the opposite axes and define the end of the isocline for that species. draw isoclines - explain isoclines – when the modified logistic equation solution is zero, no change dn1/dt = r1n1 [1 – (n1+ alphan2)/k1] = 0 n1 = k1 – alphan2 and for the other species, n2 = k2 – betan1 n1 n2 combos above or below isoclines will increase and decrease in the n1 or n2 directions (addition of vectors). now consider lions (sp. 1) and tigers (sp. 2) : k1 = 20, k2 = 30; alpha = 2, beta = 3 what happens when the starting numbers are 8 individuals of each?