The Niche and Limiting Similarity

Abstract

Chapter 2 shows in a general way that there is a limit to the similarity of coexisting species with respect to the sharing of limiting resources. If we consider qualitatively different categories of resources, a simple graphical model described by MacArthur and Levins (1964) shows that the number of coexisting species can at most equal the number of limiting resources. Consider a (R₁, R₂) plane where R₁ and R₂ represent the quantities of two different kinds of renewable resources. Further, assume that there are two species, x₁ and x₂, which both utilize both kinds of resources but with different efficiencies. We might assume that

$$\begin{gathered} d{x_1}/dt = {x_1}({i_{11}}{R_1} + {i_{12}}{R_2} - {J_1}), \hfill \\ d{x_2}/dt = {x_2}({i_{21}}{R_1} + {i_{22}}{R_2} - {J_2}), \hfill \\ \end{gathered} $$

((3.1))

where i _jk is the efficiency with which species j utilizes resource k and J _j is the threshold value for the combined availability of the two resources which allow species j to grow. In the (R₁, R₂) plane we can draw the lines dx _j /dt = 0 according to Eq.(3.1). These lines represent the resource combinations which can just sustain stable populations of x₁ and x ₂ (Fig. 36). [Note: This diagram is different from the (x₁, x₂) planes used for analysis of competition models in the previous chapter. In Figure 36 the populations show positive growth when the resource combination corresponds to a point outside the dx _j /dt = 0 lines.]