in its general form, it states: where f(Nt, Pt) describes the probability of infection (typically, Poisson distribution), λ is the per-capita growth rate of hosts in the absence of parasitoids, and c is the conversion efficiency, as in the Lotka-Volterra model. Competition and mutualism In studies of the populations of two species, the Lotka-Volterra system of equations has been extensively used to describe dynamics of behavior between two species, N1 and N2. Examples include relations between D. discoiderum and E. coli, as well as theoretical analysis of the behavior of the system. The r coefficients give a “base” growth rate to each species, while K coefficients correspond to the carrying capacity. What can really change the dynamics of a system, however are the α terms. These describe the nature of the relationship between the two species. When α12 is negative, it means that N2 has a negative effect on N1, by competing with it, preying on it, or any number of other possibilities. When α12 is positive, however, it means that N2 has a positive effect on N1, through some kind of mutualistic interaction between the two. When both α12 and α21 are negative, the relationship is described as competitive. In this case, each species detracts from the other, potentially over competition for scarce resources. When both α12 and α21 are positive, the relationship becomes one of mutualism. In this case, each species provides a benefit to the other, such that the presence of one aids the population growth of the other. See Competitive Lotka–Volterra equations for further extensions of this model. Neutral theory Unified neutral theory is a hypothesis proposed by Stephen P. Hubbell in 2001. The hypothesis aims to explain the diversity and relative abundance of species in ecological communities, although like other neutral theories in ecology, Hubbell's hypothesis assumes that the differences between members of an ecological community of trophically similar species are "neutral," or irrelevant to their success. Neutrality means that at a given trophic level in a food web, species are equivalent in birth rates, death rates, dispersal rates and speciation rates, when measured on a per-capita basis. This implies that biodiversity arises at random, as each species follows a random walk. This can be considered a null hypothesis to niche theory. The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.