 We can also derive an expression for the species turnover rate. MacArthur and Wilson as we saw thought that though the number of species on an island would be constant, their identities would be constantly changing. Suppose we are interested in some fraction say 90% of the equilibrium number of species \(S^*\). Then, we multiply both sides of the above by \(0.9\), and have \(0.9S^* = \lambda_{A}P/(\lambda_{A} + \mu_{A}) \times 0.9\). From the above, it follows that \((1 - e^{-(\lambda_{A} + \mu_{A})^{t}}) = 0.9\). With some algebra and taking the natural logarithms, we arrive at the species turnover rate,